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IEEE SENSORS JOURNAL, VOL. 11, NO. 10, OCTOBER 2011
Oscillatory Factor in Film Bulk Acoustic Resonators With Integrated Microfluidic Channels Wencheng Xu, Abbas Abbaspour-Tamijani, Senior Member, IEEE, and Junseok Chae, Member, IEEE Abstract—When a film bulk acoustic resonator (FBAR) is coupled to a liquid layer with thickness comparable to the acoustic factor varies in a damped oscillatory pattern wavelength, the with the liquid thickness. This letter reports an analytical modeling and experimental demonstration of this behavior by integrating microfluidic channels to MEMS-based FBARs. It is found that assumes its maxima and minima when the channel thickness is an odd multiple of quarter-wavelength and a multiple of half-wavelength, respectively. The microfluidics integrated FBARs achieve a improvement of over fully immersed FBARs, showing the potential of use as high-resolution sensors involving liquids. Index Terms—Acoustic resonators, microfluidic channel, piezoelectric transducers, -factor.
I. INTRODUCTION
N
ONLABELING sensors are preferable to fluorescent and radioactive labeling devices for biomolecular sensing applications, due to the elimination of the labeling process that introduces chemical modifications to the target molecules [1]. However, quartz crystal microbalance (QCM), one of the most commonly used nonlabeling sensors, is considerably less sensitive than labeling methods [1]. Film bulk acoustic resonators (FBARs) are structurally similar to QCM, but their physical miniaturization significantly improves their sensitivity and allows for batch fabrication and integration into large-scale sensor arrays. A typical FBAR consists of a piezoelectric thin film (AlN or ZnO) sandwiched between two metal electrodes. The very thin piezoelectric composite results in a high resonance frequency in the microwave range, thus offering a large frequency shift upon an extremely minute mass loading ( ng/cm ) [2], [3]. State-of-the-art FBARs possess a mass sensitivity of Hz cm /ng, which is more than 1000 times higher than that of QCM [4], [5]. FBAR sensors yield high resolutions when operating in a gaseous environment, where the large impedance mismatch between the gas and solid entraps the acoustic energy inside the FBAR body to achieve high , which results in a small minimum detectable frequency shift and, consequently, high mass resolutions. However, longitudinal mode FBARs experience viscous damping in the presence of liquids [6], [7]; this damping phenomenon constitutes a challenge to the sensing application of FBARs in liquids. Compressional waves dissipate into the contacting liquid and cause significant degradation. The previously reported of 15 in water indicates a 95% reduction in mass resolution with respect to that in the air [8]. Shear Manuscript received October 28, 2010; revised February 01, 2011; accepted March 23, 2011. Date of publication April 05, 2011; date of current version August 12, 2011. The associate editor coordinating the review of this paper and approving it for publication was Prof. Bernhard Jakoby. The authors are with the School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail:
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2011.2138129
mode and contour mode FBARs experience less viscous drag from the surrounding liquid, partially mitigating this problem [9], [10]. of 100–190 has been reported in water, but the sensitivities are typically significantly lower than that of a longitudinal mode sensor with similar dimensions [10], [11]. II. MODELING In this letter, we report a high- , high-sensitivity FBAR for use in liquids, achieved by integrating a microfluidic channel onto a longitudinal-mode resonator. The basic idea of this design is that when an FBAR comes into contact with a liquid, a substantial acoustic intensity can be reflected at the liquid/microfluidic enclosure interface if the liquid is confined to a thin layer of which the thickness is comparable to the acoustic wavelength. We designed the FBAR based on a piezoelectric ZnO film sandwiched by an Al bottom electrode and a Au top electrode and implemented a thin layer of liquid onto the FBAR by forming a microfluidic channel of a polydimethylsiloxane (PDMS) groove ceiling with a flat glass lid [Fig. 1(a)]. By precisely controlling the thickness of the channel, we were able to tune the incident acoustic impedance at the FBAR/liquid interface. Changing the thickness alters the mismatch between this incident impedance and the impedance of the FBAR body, resulting in a quasi-periodic change in the reflection coefficient, which results in oscillatory variations of the quality factor as a function of the thickness. This behavior could be physically explained by the constructive or destructive interference between the reflections from FBAR/liquid/glass interfaces. The constructive interference of the two reflection components causes a mirroring effect and high , while destructive interference leads to cancellation of the reflection and high leakage, hence lower . Here, through modeling and experimental verifications, we show that the of the resonator in the proposed topology exhibits the oscillatory behavior as a function of the channel thickness. At certain thicknesses of the channel, where the resulting impedance mismatch at the FBAR/liquid interface is highest, is maximal; at thickness values where the mismatch is lowest, assumes its minima. To explain this behavior theoretically, we used a transmission-line model, in which the six physical layers of the FBAR-microchannel are modeled by transmission-line , phase segments of characteristic impedances velocities , and lengths , where and are the mass density and thickness of the th layer. The attenuations, denoted by the , are defined only in the water, glass, damping coefficients and SiN layers, because: i) the water layer is lossy due to the high bulk viscosity of water; ii) the SiN layer is directly exposed to the compressional deformation; and iii) due to the large thickness ( m), the glass lid acts as a homogeneous half space allowing for the acoustic wave to radiate and dissipate inside or otherwise channeled outside the resonator system. The losses in the ZnO and metal layers are relatively small and are corrected into the attenuation of SiN layer to avoid an infinite of the
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XU et al.: OSCILLATORY
FACTOR IN FILM BULK ACOUSTIC RESONATORS WITH INTEGRATED MICROFLUIDIC CHANNELS
Fig. 1. (a) Schematic of the cross-section view. (b) A photograph of the top view of a fabricated FBAR integrated with a microfluidic channel (the glass ceiling has been removed).
Fig. 2. (a) Theoretically predicted versus the ratio of the fluidic channel thickness to the acoustic wavelength. (b) Measured values of in a magnified area of the simulation pattern at a small ratio regime. (c) The Smith chart of the at FBAR/water interface (normalized to ). incident impedance
FBAR itself. Material parameters [12] used in this model are listed in the supporting document. Fig. 2(a) shows the simulated values of versus the thickness of the water layer, normalized to the acoustic wavelength. For ( m at 1.041 GHz), approaches , corresponding to the case of a fully immersed shows an oscillatory patresonator. For tern as the ratio changes. The minimum is observed at zero water thickness, where the thick glass lid is in direct contact with the Au surface of the FBAR. The value of in this case is lower than that in the fully immersed case because the impedance mismatch between Au and the glass lid is less than that between Au and water, and the glass lid is very thick (0.5 mm), which leads to considerably high leakage (loss) as compared with other thin film layers. This situation repeats itself whenever the channel thickness is an integer multiple of a half wavelength in water . As the channel thickness increases, the acoustic attenuation of water reduces the effect of reflection from the water/glass interface, causing a gradual reduction in the difference between the maximum and minimum values of . This damped oscillatory behavior can be understood from the Smith chart of the system [Fig. 2(c)]. The spiral shows the trajectory , at the Au/water interface of the input acoustic impedance, as the channel thickness increases from zero to infinity. peaks when the channel thickness becomes an odd integer multiple of a quarter wavelength , where the impedance transformation through the water layer causes a large mismatch between the intrinsic impedance at Au surface and the input impedance . III. EXPERIMENTS To experimentally verify these observations, we fabricated FBARs with integrated microfluidic channels using standard silicon micromachining technology [Fig. 1(b)] (see supporting
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was thereafter measured: 1) in air, which cordocument). responds to a minimum damping; 2) in contact with a water droplet that mimics an infinite-thickness water layer; and 3) with water confined in the integrated microfluidic channels of different thicknesses. We characterized the devices by measuring using a network anathe one-port reflection coefficient lyzer. of the series resonance was calculated from [2]: , where is the frequency of the series resonance and is the phase of the impedance . For the case of FBARs in air, a resonance frequency of 1.041 GHz and of 480 were measured, indicating a small energy leakage. dropped to approximately 10 when we applied a water droplet on the top surface of the FBAR. The thickness m, substantially larger than of the water volume was m) or the penetration the acoustic wavelength in water ( m), thus, this thickness was practically infinite and depth ( corresponding to the positions shown at the far right in Fig. 2(a). For partial damping conditions for which FBARs were integrated with microfluidic channels, the measured ’s were shown on top of the simulated curve in Fig. 2(b), ranging from 50 to 150, which were within 15% of the predicted values. The discrepancy between the transmission model and measurements is mainly due to the noninfinite ratio of diameter/thickness of the FBAR and the anchor loss through the supporting membrane, which are assumed to have the ratio of infinite and loss-free environment in the model. periodically increased and decreased as the channel thickness varied. Maximum ’s were found at channel thickness of 4.77 m and 5.58 m, close to 13/4 and 15/4 of the wavelength in water. The experimental validation of the transmission line model at partial damping region was also performed with an FBAR with methanol filled channel (supporting document). IV. CONCLUSION Both analysis and experiments demonstrate the oscillatory with the thickness of coupled liquid layer in variations of FBAR sensors. The sensor has integrated microfluidic channels, which have a comparable thickness to the acoustic wavelength in water. Maximum values can be obtained for the channel thickness that is odd integer multiples of the quarter wavelength. REFERENCES [1] T. Burg and S. Manalis, Appl. Phys. Lett., vol. 83, p. 2698, 2003. [2] H. Zhang and E. S. Kim, J. Microelectromech. Syst., vol. 14, p. 699, 2005. [3] H. Campanella, J. Esteve, J. Montserrat, A. Uranga, G. Abadal, N. Barniol, and A. Romano-Rodriguez, Appl. Phys. Lett., vol. 89, p. 033507, 2006. [4] L. Yan, W. Pang, E. S. Kim, and W. Tang, Appl. Phys. Lett., vol. 87, p. 154103, 2005. [5] R. Gabl, H.-D. Feucht, H. Zeininger, G. Eckstein, M. Schreiter, R. Primig, D. Pitzer, and W. Wersing, Biosens. Bioelectron., vol. 19, p. 615, 2004. [6] Y. H. Cho, A. P. Pisano, and R. T. Howe, J. Microelectromech. Syst., vol. 3, p. 81, 1994. [7] W. Xu, X. Zhang, H. Yu, A. Abbaspour-Tamijani, and J. Chae, IEEE Elect. Dev. Lett., vol. 30, no. 6, pp. 647–649, Jun. 2009. [8] H. Zhang, M. S. Marma, E. S. Kim, C. E. McKenna, and M. E. Thompson, J. Micromech. Microeng., vol. 15, p. 1911, 2005. [9] G. Wingqvist, J. Bjurstrom, L. Liljeholm, V. Yantchev, and I. Katardjiev, Sens. Actuators, vol. B123, p. 466, 2007. [10] W. Xu, S. Choi, and J. Chae, Appl. Phys. Lett., vol. 96, p. 053703, 2010. [11] M. Link, M. Schreiter, J. Weber, R. Primig, D. Pitzer, and R. Gabl, IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 2, pp. 492–496, Feb. 2006. [12] N. Akashi, J.-I. Kushibiki, and F. Dunn, Ultrasonics, vol. 38, p. 915, 2000.
