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PIEZOELECTRIC RESPONSE OPTIMIZATION OF MULTI ROOF TILE-SHAPED MODES IN MEMS RESONATORS BY VARIATION OF THE SUPPORT BOUNDARY CONDITIONS G. Pfusterschmied1, M. Kucera1,2, E. Wistrela1, W. Steindl1,2, V. Ruiz-Díez3, A. Bittner1, J.L. Sánchez-Rojas3 and U. Schmid1 1 Institute of Sensor and Actuator Systems, Vienna University of Technology, AUSTRIA 2 Austrian Center of Competence for Tribology, AC2T research GmbH, AUSTRIA 3 Group of Microsystems, Actuators and Sensors, E.T.S.I. Industriales, Universidad de Castilla-La Mancha Ciudad Real, SPAIN fundamental roof tile-shaped vibration-mode which is preferred for liquid sensing purposes due to the highest Qfactors of a cantilever-based MEMS resonator in liquid media up to now [7]. Additionally, an optimized electrode design is implemented to maximize the conductance peak ΔG, as reported in [8]. The fabrication process of the resonators is based on previous work published recently [9]. This work comprises a complete electrical and optical characterization in combination with finite element method (FEM) simulations, thus paving the way to design guidelines for other types of resonantly excited sensors.
ABSTRACT This paper investigates strain-related conductance peaks ΔG of advanced roof tile-shaped vibration-modes in piezoelectrically actuated resonators by variation of the support boundary conditions, leading to a complete new class of liquid monitoring sensors. These new vibrationmodes feature very high Q-factors in liquid media and enhanced volume-strain values in the device. Combined with an optimized electrode design, the enhanced volumestrain results in very high strain-related conductance peaks ΔG. Furthermore, the impact on the piezoelectric response ΔG/Q is studied, leading to an increased ΔG/Q ratio by ~25% compared to single-side clamped resonators. These features predestinate this new class of vibration-modes for a large variety of challenging resonator-based sensing applications in liquid media exceeding the overall performance of commonly used out-of-plane vibrationmodes.
DEVICE FABRICATION The used micromachined resonators are in-house fabricated on 4-inch SOI-wafers. The resonators have a length of L = 2524 µm, a width of W = 1274 µm and a thickness of T = 20 µm and differ in the support boundary condition (i.e. single-side clamped, double-side clamped and free-free-clamped), as depicted in Fig. 1. Additionally, the electrode design is optimized for the excited mode using design guidelines published recently [8]. This approach results in IN- or ANTI-parallel connected electrode stripes ensuring a collection of all charges without a charge cancellation. More information on this optimized electrode design is given in Refs. [8, 9].
KEYWORDS Piezoelectric, MEMS resonators, liquid sensing.
INTRODUCTION Since many years, the demand of micromachined resonator-based sensors, capable to measure physical properties such as density and viscosity [1-4], is continuously increasing. It is well reported in literature [3, 5, 6] to use in-plane modes for liquid sensing to overcome the obstacle of the high viscous damping caused by the surrounding fluid. This approach has the huge drawback of a relatively low displacement and measurement signal, compared to out of plane modes. This present study on resonantly excited sensors, which provide both, high Qfactors and good piezoelectric response characteristics in liquids is therefore of major interest. State of the art cantilever-type resonators realized in [1] support high Qfactors, but highly strained areas are only located in the tip region. Consequently, the strain-related conductance peak ΔG is mainly generated by this strained region of the cantilevers. In this paper the influence of the support boundary conditions on the conductance peak ΔG and the piezoelectric response ΔG/Q is investigated [1, 7] and in further consequence, the performance of sensors in liquid media. The used excitation mode is based on the
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Figure 1: Visualization of the fundamental (a-c) roof tile-shaped modes (X2-modes) and the 2nd orders (d-e) of the roof tile-shaped mode (X3-modes) for a single-side clamped cantilever (a, d), a double-side clamped plate (b,e) and a free-free clamped plate (c,f), respectively. The colored areas on the cantilever surface represent the local volume strain distribution.
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surface patterning represents the volume strain and thus, the piezoelectrically generated surface charge distribution. According to Fig. 2, the comparison of top views of the illustrated roof tile-shaped modes show the largest strained areas for plates with optimized support boundary conditions (see Figs. 1c, f). The corresponding devices designed for the 02- and 03-mode, packaged and wire-bonded are depicted in Fig. 3.
EXPERIMENTAL DETAILS Advanced roof tile-shaped mode This new class of vibration-modes can be described as a transversal out-of-plane vibration-mode with a free-free boundary conditions in superposition with a longitudinal out-of-plane vibration-mode with varying boundary conditions. Considering Leissa’s nomenclature [10] by counting the number of nodal lines in x- and y-direction, the advanced roof tile-shaped modes are named in the following 1X-mode (see Figs. 1a, d), 2X-mode (see Figs. 1b, e) and 0X-mode (see Figs. 1c, f). Fig. 2 depicts the impact of the support boundary conditions on the mode-shape, resulting in a different strain distribution across the resonator surface. In case of the free-free boundary condition (see Figs 2c, f) the support of the plates correlates with the nodal lines of the vibration mode, what enables a quasi-free oscillation, compared to those being single-side (see Figs 2a, d) and double-side clamped (see Figs 2b, e). This leads to strained areas across the complete device surface resulting in a very high piezoelectric response ΔG/Q.
Figure 3: Confocal micrograph of the in-house fabricated silicon die (6 x 6 mm²), containing two released plates (dimensions: 2524 x 1274 µm²) anchored by 6 (front) and 4 (back) supports. The two resonators use a superior electrode patterning considering the volume strain of the modal shape presented in Figs. 1c and 1f.
Fig. 4 compares the electrical (a) and the optical (b) measurements of resonating plates with different support boundary conditions in air, showing a good match in the resonance frequency.
Figure 2: Top view of the presented roof tile-shaped modes from Fig. 1, showing (a) the 12-mode, (b) the 22-mode, (c) the 02-mode, (d) the 13-mode, (e) the 23-mode and (f) the 03-mode. The colored areas on the cantilever surface represent the local volume strain distribution. Red indicates positive (+) and blue indicates negative (-) strained areas, respectively. Figure 4: Electrical (a) and optical (b) characterization of the X2and X3-mode in air. The deflection spectrum is measured with a Polytec Laser Doppler Vibrometer MSV-400, whereas the electrical characterization is performed with an Agilent 4294A precision impedance analyzer.
Device Characterization Fig. 1 illustrates the results of finite element method (FEM) analyses of the 1st and 2nd roof tile-shaped mode for a single-side clamped cantilever in Figs. 1a, d, a clampedclamped plate in Figs. 1 b, e and a plate with free-free support boundary condition in Figs. 1 c, f. The colored
The highest deflections are obtained for the 12/13-mode followed by the 02/03-mode and the 22/23-mode. The
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(0.316 µS). This latter finding agrees well to results shown in Figs. 1, 2 and 4, which show strained areas along the entire plate surface resulting in the highest ΔG/Q compared to single-side and double-side clamped devices. The piezoelectric response ΔG/Q depicts a constant behavior over a wide region from ~0.3 to ~0.8 cm3/(g·cP). This finding, however, is not applicable for high viscous liquids like N100 or D500 ((ρµ)-0.5 < 0.1 cm3/(g·cP)) due to the low conductance peak ΔG and hence, the poor fitting when determining the Q-factor. The outstanding performance, shown with the 03-mode, predestinates this new class of 0X vibration modes for a large variety of challenging resonator-based sensing applications in liquid media exceeding the overall performance of commonly used out-of-plane vibration modes.
deflected areas for the 12/13-mode are located only in the tip area. The support-related region, however, experiences only minimal deflection and less strain, leading to a negligible contribution to the piezoelectric response ΔG/Q. The 22/23-mode show, due to the double-side clamped support boundary condition, a similar behavior, which results in a piezoelectric response concentrated in the midarea of the resonator (see Figs. 2c, e). The free-fee boundary condition of the 02/03-mode correlates with the nodal lines of the vibration mode, which leads to strained areas across the entire plate surface resulting in an elevated piezoelectric response. In combination with Table 1 the support boundary conditions show a significant impact on the conductance peak, which leads for free-free supports to elevated ΔG/Q values up to ~0.774 µS. Table 1: List of Q-factors, conductance peak heights ΔG and the piezoelectric response ΔG/Q for devices exited in the 2nd order mode with clamped-free, clamped-clamped and free-free support boundary conditions in isopropanol.
Device clamped-free clamped-clamped free-free
Q 66 67 70
ΔG [µS] 41.6 21.2 54.8
ΔG/Q [µS] 0.623 0.316 0.774
Fig. 5 presents the conductance peak as a function of the inverse viscosity-density product in several liquids showing superior performance for the 03-mode and the highest ΔG of ~55 µS in isopropanol followed by the 13-mode (~41 µS) and 23-mode (~ 21.2 µS). The Q-factors are evaluated using a measurement setup reported recently [9]. Figure 6: Piezoelectric response ΔG/Q vs. the inverse viscositydensity product measured in different liquids (isopropanol, and viscosity standards D5, N10 N100, D500).
CONCLUSIONS Micromachined piezoelectric resonators with different support boundary conditions (i.e. single-side clamped, double-side clamped and free-free-clamped) were fabricated, actuated in advanced roof tiled-shape mode of the 2nd and 3rd order. An optimized electrode design was implemented to enable an optimized collection of all piezoelectrically charges without any compensation effect. The performed finite element modelling analyses showed the largest strained areas for resonators with free-free clamped boundary condition. This result implies an increased electrical performance compared to resonators with single side or double-side clamped support boundary conditions, what could be demonstrated by electrical and optical measurements. Finally, the piezoelectric response ΔG/Q was derived in several liquids (D500, N100, N10, D5 and isopropanol), showing the highest ΔG/Q of 0.774 µS for a plate with free-free clamped boundary condition in isopropanol. These results predestinate the advanced roof tiled-shape mode, in combination with a free-free clamped
Figure 5: Electrical characterization of the X2- and X3-modes in different liquids (isopropanol, and viscosity standards D5, N10 N100, D500) represented by the conductance peak ΔG as a function of the inverse viscosity-density product.
Fig. 6 shows the correlation between the piezoelectric response ΔG/Q and the inverse viscosity-density product, resulting in a fluid independent behavior, having the highest ΔG/Q ratio in isopropanol in the 03-mode of 0.774 µS followed by the 13-mode (0.623 µS) and the 23-mode
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boundary condition, for a large variety of challenging resonator-based sensing applications in liquid media exceeding the overall performance of commonly used outof-plane vibration modes. Furthermore, the independence of fluid properties over a wide parameter range predestinates the piezoelectric response ΔG/Q as an appropriate figure of merit for piezoelectric excited MEMS resonators.
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[9]
ACKNOWLEDGEMENTS This work has been supported by the Austrian Research Promotion Agency within the COMET-K2 Project XTribology (Project-No. 824187). The financial support given by the Spanish Ministerio de Economıa y Competitividad: Project Ref. DPI2012-31203, FPU Grant (Ref. AP2010-6059) awarded to Vıctor Ruiz is gratefully acknowledged.
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monitoring purposes," Applied Physics Letters, vol. 104, p. 233501, 2014. G. Pfusterschmied, M. Kucera, V. Ruiz-Diez, A. Bittner, J. L. Sanchez-Rojas, and U. Schmid, "Multi roof tile-shaped vibration modes in mems cantilever sensors for liquid monitoring purposes," in Micro Electro Mechanical Systems (MEMS), 2015 28th IEEE International Conference on, 2015, pp. 718-721. M. Kucera, E. Wistrela, G. Pfusterschmied, V. Ruiz-Díez, T. Manzaneque, J. Hernando-García, et al., "Design-dependent performance of selfactuated and self-sensing piezoelectric-AlN cantilevers in liquid media oscillating in the fundamental in-plane bending mode," Sensors and Actuators B: Chemical, vol. 200, pp. 235-244, 9/ 2014. A. W. Leissa, "The free vibration of rectangular plates," Journal of Sound and Vibration, vol. 31, pp. 257-293, 12/8/ 1973.
CONTACT *G. Pfusterschmied, tel:
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