Acoustic Wave Propagation in a Hexagonal Surface Acoustic Wave Biosensor Based on LiTaO3: a Finite Element Study
Subramanian K.R.S. Sankaranarayanan1, Stefan Cular2, and Venkat Bhethanabotla2. (1) School of Engineering and Applied Sciences, Harvard University, 9 & 15 Oxford Street, Cambridge, MA 02138, (2) Department of Chemical Engineering, University of South Florida, 4202 East Fowler Ave., ENB 118, Tampa, FL 33620
The main advantage of numerical methods such as Finite Elements in modeling surface acoustic wave (SAW) devices lies in their ability to model devices involving complicated transducer geometries. We present a 3-D finite element model of a novel hexagonal SAW biosensor based on LiTaO3 substrate1. This SAW biosensor shown in Fig. 1 involves the use of one delay path for biological species detection whereas the other delay paths are used to simultaneously remove the non-specifically bound proteins using the acoustic streaming phenomenon, thus eliminating biofouling issues associated with other biosensors2. Prior to this biosensor fabrication on any piezoelectric substrate, it is important to establish the type of waves that are generated along the various delay paths. The choice of a delay path for sensing and simultaneous cleaning application depends on the propagation characteristics of the wave generated along the crystal cut and orientation corresponding to that delay path. The frequency response as well as wave propagation characteristics along the delay path corresponding to crystal orientation with on axis propagation along 36° YX LiTaO3 substrate is analyzed using a FE model. Similar analysis is extended to the off-axis propagation directions corresponding to Euler rotations by 60° and -60° along the x-z plane. Our findings indicate that the on-axis direction with a significant surface horizontal (SH) component should be employed for biological species detection whereas the off axis directions having mixed modes with a dominant Rayleigh wave component are most suitable for simultaneous cleaning or removal application. The 3-D FE model describes three two-port delay line structures along each of the Euler direction and consists of three finger pairs in each port. The inter-digital transducer (IDT) fingers are defined on the surface of a lithium tantalate substrate and the fingers are considered as mass-less electrodes to ignore the second-order effects arising from electrode mass, thereby simplifying computation. The periodicity of the finger pairs is 40 microns and the aperture width is 200 microns. The transmitting and receiving IDT's are spaced 130 microns or 3.25λ apart. The substrate for 36° YX LiTaO3 was defined as 1600 microns in propagation length, 300 microns wide and 200 microns deep. For simulating the other two propagation directions in the hexagonal biosensor, the geometry of substrate is kept the same, whereas the crystal coordinates are rotated. To achieve this, the material properties i.e. stiffness, piezoelectric and permittivity matrices are rotated by 60° and -60° along the x-z plane to model off axis directions, respectively. The simulated models have a total of approx. 250000 nodes and are solved for four degrees of freedom (three displacements and voltage). The model was created to have the highest densities throughout the surface and middle of the substrate. Two kinds of analysis are carried out along each of the three delay lines: (1) An impulse input of 10 V over 1 ns is applied to study the frequency response of the device and (2) AC analysis with a 5 V peak-peak input and 100 MHz frequency to study the wave propagation characteristics. Our simulation results indicate that the on axis shear horizontal component of displacement at the output IDT is an order of magnitude higher than the surface normal and longitudinal components indicative of shear horizontal wave motion (Fig. 2). Thus a shear horizontal (SH) surface acoustic wave propagates along the on-axis direction (36° YX LiTaO3) which is most suitable for biosensing application. For the off axis direction, the surface normal and longitudinal components of displacement at the output IDT are an order of magnitude higher than the shear horizontal component indicative of wave motion which is more or less ellipsoidal. This type of wave motion corresponds closely to that of the Rayleigh mode. The displacement profiles of the other off-axis component showed lesser amplitude variations amongst the three directions indicative of mixed wave modes which are a combination of more than one wave type such as pure Rayleigh or shear horizontal modes. The wave propagation along the on-axis direction i.e. 36° YX LiTaO3 substrate is shown in Fig. 3. At approximately 120 ns, the wave has reached the end of the substrate. We also observe wave reflections along the edges at longer simulation times. By applying an impulse function as an input, the frequency response of the hexagonal SAW biosensor device was also calculated. The calculated frequency response for an input impulse (1 ns) of 10 V for the on-axis and off-axis direction is shown in Fig. 4. The calculated device frequency along the three directions indicated that least attenuation occurred along the on-axis direction whereas higher propagation losses were observed for the off-axis directions. A 3-D FE model of the acoustic wave propagation can thus be useful in understanding acoustic wave propagation in piezoelectric substrates. Efforts are underway to simulate Hexagonal SAWs based on other substrates such as langasite which could help identify better biosensor element for liquid phase applications.