Characterization of Rotational Mode Disk Resonator Quality Factors in Liquid

Transcription

1 Characterization of Rotational Mode Disk Resonator Quality Factors in Liquid Amir Rahafrooz and Siavash Pourkamali Department of Electrical and Computer Engineering University of Denver Denver, CO, USA Abstract This work presents several variations of microscale single and multiple coupled thermally actuated rotational mode disk resonators capable of high quality factor (Q) operation in liquid. All surfaces of a rotational mode disk resonator slide in parallel to the liquid interface (rather than stroking against it). This minimizes interactions with the surrounding fluid and therefore viscous damping. Quality factors as high as 304 have been demonstrated for rotational mode disk resonators in liquid, which is more than 3X higher than the highest values previously demonstrated for other types of microscale resonators. Based on the measurement results it is suggested that most of the energy loss into the surrounding liquid is through the sidewalls of the disks. This could be blamed on the sidewall roughness caused by deep reactive ion etching, off-center rotation of the disks due to fabrication induced asymmetries, and slight bending of support beams during resonance. Much higher Q values are expected to be achievable by minimizing such limiting factors. I. INTRODUCTION As highly sensitive mass sensors, micromechanical resonators can potentially open up a wide range of new opportunities in biomedical and chemical sensing applications leading to more compact low cost instruments with real-time sensing capabilities. In addition, due to their small size, micro resonators can be integrated in arrays of hundreds to thousands sensing a variety of analytes simultaneously. Most of the biosensing applications require detection and measurement of certain molecules in a liquid solution (typically aqueous). However, the resonant behavior of microscale resonators drastically deteriorates in liquid lowering their sensitivity and mass resolution. This is mainly due to the larger surface to volume ratio for such small scale devices and consequently large viscous damping to elastic energy ratio in them. Over the past decade efforts have been made to operate micromechanical resonators inside liquid. Magnetically actuated cantilever beams resonating in their out-of-plane flexural modes have been used for mass sensing applications in aqueous environments [1-4]. It is not hard to imagine that such a paddling motion faces a lot of resistance from the surrounding liquid leading to excessive viscous damping. This reduces the quality factor of such devices to values as low as 5[1], 23[2], 2[3] and 10[4] in water. Viscous damping can be reduced by operating cantilever beams in their inplane flexural resonant mode. Quality factors as high as 67 have been demonstrated for such devices in liquid [5]. Higher quality factor of the in-plane resonant modes for such thin structures can be attributed to having a much smaller portion of their surface area stroking against the liquid interface compared to their out of plane modes. In an improved design by Seo, et al [6], a structure comprised of two half-disks resonating in an in-plane quasi rotational mode, demonstrated quality factors as high as 94 in water. Despite having improved quality factors, similar to the in-plane flexural modes of microcantilevers, the straight sides of the half disks in such structures still have a perpendicular motion against the liquid interface. In [7] we demonstrated full disk structures with two tangential support beams thermally actuated in their rotational resonant modes. In such structures all the surfaces slide in parallel to the liquid interface exhibiting Qs as high as ~200 in water. In this work, five different variations of single and multiplecoupled rotational mode disk resonators are studied to further understand the loss mechanism and optimize the performance of such structures. II. DEVICE OPERATION Figure 1 shows the schematic view of a single-disk with straight tangential support beams as well as the electrical connections used to operate such device. The support beams act as both thermal actuators and piezoresistive stress sensors simultaneously [7]. Thermal actuation occurs by passing a current between the two pads on the two sides of the structure. By passing a combination of a DC and an AC current, the ohmic power loss will have a component at the same frequency as the applied AC current: P ac = 2R e I dc i ac, where R e is the electrical resistance between the two pads and I dc and i ac are the applied DC and AC currents respectively. Due to their higher electrical resistance, most of the ohmic loss and therefore heat generation is concentrated in the narrow support beams. The applied AC power produces This work was supported by National Science Foundation under grants MRI-RAPID # and MRI #

2 periodic temperature fluctuations in the thermal actuators (Fig. 1) which in turn causes alternating stress and strain in the support beams, actuating the disk in its rotational resonance mode (periodically rotating back and forth). As the resonator vibrates the resulting periodic stress changes result in fluctuations in the electrical resistance of the resonator due to the piezoresistive effect. This modulates the DC current passing through the resonator leading to an AC output motional current component that can be used to monitor the resonator vibration amplitude. While the disk is vibrating in its rotational mode, the support beams vibrate in their extensional mode (periodically elongate and contract). As a result, all the surfaces of both the disk and its support beams move in parallel to the liquid interface, minimizing the energy loss to the surrounding liquid. Figure 2a shows the COMSOL modal analysis results showing the mode shape for a µm diameter, 20µm thick disk with 4µm wide, 26µm long support beams. III. FABRICATION AND MEASUREMENT RESULTS In this work, five different variations of single and multiple-coupled rotational mode disk resonators were fabricated and characterized (Fig. 2); 1. Single disks with straight tangential support beams, 2. Single disks with rounded support beams, 3. Parallel dual-disks, 4. Series dual-disks, and 5. Interconnected quad-disks. They were fabricated using the standard single mask SOI-MEMS process [8]. The fabrication process includes silicon DRIE to form the structures out of the silicon device layer, and releasing them by etching the underlying buried oxide (BOX) layer in hydrofluoric acid (HF). Resonators were fabricated on low resistivity N-type f Hep = 4.05MHz Q Air = 3,000 Q Hep = 215 Fig. 1. Schematic view of a thermally actuated disk resonator showing the qualitative distribution of AC temperature fluctuation amplitude in the resonator (red being the maximum and blue minimum). The electrical connections required for one-port operation of the resonator are also shown. substrates with different device layer and BOX thicknesses. To optimize resonator electromechanical transduction, the support beams are aligned to the <> crystalline direction where the longitudinal piezoresistive coefficients are maximum [8]. The holes in the middle of the disks are to reduce the undercut time in HF. Due to circular shape of the holes and relatively small vibration amplitude in the center of the disks such holes are expected to have negligible effect on viscous damping of the resonator. The resonators were tested in a one-port configuration as shown in Fig. 1. The liquid tests were performed in heptane to provide better electrical isolation and avoid contamination resulting from electrolysis of water. Figure 3 shows the measured frequency responses for the µm single disk f Hep = 5.46MHz Q Air = 1,700 Q Hep = 304 a) b) c) f Hep = 5.35MHz Q Air = 7,800 Q Hep = 140 f Hep = 7.67MHz Q Air = 5,000 Q Hep = 170 f Hep = 7.58MHz Q Air = 15,000 Q Hep = 150 d) e) f) Fig. 2. a) Finite element modal analysis of the rotational resonant mode of the proposed disk structure. Red and blue show the maximum and minimum vibration amplitudes respectively. SEM view of fabricated devices along with their measured Q in both air and liquid for: b) single disk with straight tangential support beam, c) single disk with rounded support beam, d) parallel dual-disk, e) series dual-disk, f) interconnected quad-disk. The thermal actuators are along <> crystalline direction for optimized transduction.

3 resonator of Fig. 2c with rounded thermal actuators both in air and heptane. As expected, the resonator has relatively low quality factors in air (due to excessive support loss), however, unprecedented quality factor of 304 was measured in heptane. Such high Q values in heptane confirm our hypothesis that elimination of the stroking surfaces from the mode shape can significantly improve resonator Q in liquid. Table I summarizes the measurement results for a variety of resonators of different types with different dimensions in both air and liquid. It also shows the finite element modal analysis for different structures demonstrating the vibration amplitude at different parts of the structure. The modal analysis results show that unlike the other structures the interconnected quaddisks have an off-center rotation which justifies their lower Q in liquid despite their relatively high Q in Air. Fig. 3. Measured frequency response for the µm diameter 20µm thick disk resonator shown in Fig. 2c with rounded support beams in air and heptanes. TABLE I MEASUREMENT RESULTS, AND MODE SHAPES FOR DIFFERENT TYPES OF SINGLE AND MULTIPLE DISK ROTATIONAL MODE RESONATORS. MEASUREMENT RESULTS IN BOTH AIR AND LIQUID (HEPTANES) ARE PRESENTED (W=2µ METER FOR ALL THE SUPPORT BEAMS). Type Single Disk with Straight tangential support beam Single Disk with Rounded support beam Parallel Dual- Disk Series Dual- Disk Interconnected Quad-Disk Finite Element Modal Analysis Showing Resonant Mode Shape Resonator Dimensions (µm) D L th H Freq. Air (MHz) Q. Air Freq. Hep. (MHz) Q. Hep

4 a) b) c) Fig. 4. Finite element modal analysis showing different effects potentially limiting resonator quality factors in liquid: a,b) bending support beams stroking against the surrounding liquid, c) mismatched support beams causing off-center resonance. In this extreme case, the support beams have widths of 2µm and 3µm and equal lengths. The axial stress in all the support beams of the single disk designs and half of the support beams in dual-disks is directly transferred to their clamping points and consequently into the substrate. Therefore, in air, where Q is mainly limited by support loss, the Q of single disk designs is generally smaller than that of the dual-disks, which is in turn smaller than that of the quad-disks. In liquid however, viscous damping becomes the dominant source of loss and the Q for all designs drops to values in the -300 range. Although the highest Q of 304 in heptane obtained from the single disk structure with rounded supports of Fig. 2c, not much of a difference was observed between the performance of single disks with straight and rounded thermal actuators. Although higher quality factors are expected from the thicker resonators due to their smaller surface to volume ratio, measurement results do not show any significant improvement in quality factor of 20µm thick devices compared to 5µm thick devices. This suggests that most of the viscous damping is associated with the resonator sidewalls rather than their upper and lower surfaces. Resonator sidewall area is proportional to the resonator thickness and consequently the amount of elastic energy stored in the resonator. Therefore, if the sidewalls are the main source of loss no significant dependence of resonator quality factor to its thickness is expected. This could be blamed on the sidewall roughness caused by deep reactive ion etching, slight bending of support beams during resonance and off-center rotation of the disks due to fabrication induced asymmetries. Figure 4a and b demonstrate the bending of the rounded and straight support beams during the rotational vibration of the disks and Fig. 4c shows the effect of a fabrication induced asymmetry on the resonance mode of single disks which causes off-center rotation and therefore stroking against the liquid interface. IV. CONCLUSIONS AND FUTURE WORKS Five different variations of single and multiple coupled disk resonators were fabricated and successfully operated in heptane with relatively high quality factors. The highest Q of 304 in liquid was obtained from a single disk structure with rounded support beams, which is 3X larger than the highest values previously reported for other types of microresonators. In addition, by studying the performance of different disk resonators with different structures and dimensions, the main energy loss mechanisms in liquid were further investigated. No significant improvement in the quality factor values for rotational mode disk resonators was observed by increasing their structural thickness. This suggests that such resonators mainly lose their energy through their sidewalls rather than upper and lower surfaces.. Micromechanical resonators with such high quality factors in liquid can enable direct high precision sensing of different analytes in liquid media paving the way towards label-free real-time biochemical sensors with fully electronic readout. Future work includes further characterization and design optimization of the disk resonators to lower their energy loss in liquid. For instance, the structure of supporting beams can be optimized to reduce their stroking against the liquid. ACKNOWLEDGMENT Authors would like to thank staffs at Georgia Tech nanotechnology research center and also Dr. Ashwin Samarao for their help with silicon deep reactive ion etching. REFERENCES [1] A. Vidic, D. Then, and C. Ziegler, A new cantilever system for gas and liquid sensing, Ultramicroscopy, vol. 97, no. 1, pp , Oct [2] Y. Li, C. Vancura, et al, Very high Q-factor in water achieved by monolithic, resonant cantilever sensor with fully integrated feedback, in Proc. IEEE Sensors Conf., 2003, pp [3] J. Tamayo, A.D.L. Humphris, A.M. Malloy, M.J. Miles, Chemical sensors and biosensors in liquid environment based on microcantilevers with amplied quality factor, Ultramicroscopy, vol. 86, no 1-2, pp , Jan [4] C. Vancura, Y. Li, J. Lichtenberg, K.U. Kirstein and A. Hierlemann, Liquid-phase chemical and biochemical detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems, Analytical Chemistry, vol. 79, no. 4, pp , Feb [5] L.A. Beardslee, K.S. Demirci, Y. Luzinova, J.J. Su, B. Mizaikoff, S. Heinrich, F. Josse, O. Brand, In-plane mode resonant cantilevers as liquid phase chemical sensors with ppb range limits of detection, in Tech. Dig. Solid-State Sens.,Actuator Microsyst. Workshop, Hilton Head Island, SC, Jun. 2010, pp [6] J. H. Seo and O. Brand, High Q-Factor In-Plane-Mode Resonant Microsensor Platform for Gaseous/Liquid Environment, JMEMS 2008, Vol. 17, issue 2, pp

5 [7] A. Rahafrooz, and S. Pourkamali, Rotational mode disk resonators for high-q operation in liquid, proceedings, IEEE Sensors conference, 2010, pp [8] A. Rahafrooz, and S. Pourkamali, High-frequency thermally actuated electromechanical resonators with piezoresistive readout, IEEE Trans. On Electron Device, 2011, Vol. 58, issue 4, pp