Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Thin Films

Transcription

1 Journal of the Korean Physical Society, Vol. 57, No. 3, September 2010, pp Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Thin Films Gwiy-Sang Chung and Duy-Thach Phan School of Electrical Engineering, University of Ulsan, Ulsan (Received 5 April 2010) This paper describes the simulation of surface acoustic waves (SAW) in piezoelectric thin films by using a finite element method (FEM). SAW resonators were simulated based on piezoelectric thin films of aluminum-nitride (AlN) or zinc-oxide (ZnO) on silicon (Si) substrates. Various parameters of the surface waves in the films, such as the surface velocity and the displacement of the piezoelectric thin film, were evaluated by using FEM software such as ANSYS or COMSOL. Many fundamental or harmonic wave modes are also discussed in this work. For accuracy in the evaluation of modeling with a FEM, the a SAW resonator was also fabricated and measured, based on AlN/Si or ZnO/Si structures resonator was fabricated and measured, and was compared to the simulation results. PACS numbers: Ns, Bs, Pt Keywords: FEM, Surface acoustic wave, Zinc oxide, Aluminum nitride, Piezoelectric material DOI: /jkps I. INTRODUCTION In a typical surface acoustic wave (SAW) device, a mechanical wave is generated and propagates on the surface of the material through the piezoelectric effect, either in a Rayleigh mode or as a shear wave. The velocity of the surface wave depends on the material s parameters, such as, the elasticity, density and quality of the piezoelectric layer. As such, SAW sensors are very sensitive to changes in an ambient environment and have potential for use in passive wireless sensors [1]. Accurate SAW sensor response simulations have become indispensable for designing high- performance sensors. Methods used to analyze inter-digital transducers (IDTs) include the δ function model [2], the equivalent circuit model [3], the P-matrix model that analyzes SAW devices by using mathematical methods [4], and utilization of coupling-of-modes (COM) theory [5]. However, these methods require considerable computational resources, making them inconvenient for use in modeling, especially since there are no commercially available interfaces to implement these methods. In contrast, the finite element method (FEM), which may be implemented via commercial software, such as ANSYS or COMSOL, has proven to have excellent capability for modeling and analyzing SAW sensors. FEM uses simple methods to analyze complicated geometries. Changes in the propagation characteristics of SAW devices, in terms of time delay in voltage, particle displacement due to the ex- gschung@ulsan.ac.kr; Fax: posure of a palladium (Pd) thin film to hydrogen, and insertion loss, are described in Ref. 6. FEM modeling is applied to SAW organic vapor sensors in Ref. 7, and the effects of film properties on the sensitivity of SAW chemical sensors are discussed in Ref. 8. Bulk piezoelectric materials, such as lithium-tantalate (LiTaO 3 ), lithium-niobate (LiNbO 3 ), or quartz, have traditionally been used in SAW sensor production; therefore, almost all of the SAW simulations constructed in previous reports focused on these bulk substrates [6-8]. Recently, there have been increased efforts to identify materials that are better able to propagate SAWs swiftly and effectively, with an eye towards achieving higher frequencies and full compatibility with microelectromechanical systems (MEMS). Hence, new applications for SAW sensors based on a piezoelectric thin film of AlN or ZnO are rapidlyfastly being developed [9,10]. However, research regarding the modeling of SAW sensors on thin films is rare and doesis not corresponding to its development trend. The evaluations of SAW propagation properties, such as wave modes or the resonant frequency of piezoelectric thin films on Si, such as AlN and ZnO, are necessary to improve the design of SAW sensors [11]. Some FEM modeling of surface acoustic waves in piezoelectric thin films has been reported for AlN/diamond layered structures [12] and ZnO/diamond structures [13]. This work presents FEM modeling for a SAW device based on AlN/Si and ZnO/Si by using COMSOL Multiphysics 3.3 fromby COMSOL AB Inc.. The SAW velocity and wave modes are then analyzed and compared to experimental results.

2 Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Gwiy-Sang Chung and Duy-Thach Phan II. MODEL DESCRIPTION AND EXPERIMENTS SAW propagation is governed by differential equations that must be solved along with design problems, including the geometric complexity of the device, the material properties, and the boundary conditions. FEM provides numerical solutions defined by associated differential equations. The FEM method used to analyze piezoelectric material in COMSOL is explained in Ref. 14. The relationships between stress, strain, electric field, and electric displacement field, in the a stress -charge of a piezoelectric crystal, are given by the piezoelectric constructive as: T ij = C E ijkl S kl e T ijk E k, (1) D i = e ikl S kl + ε S ij E j, (2) where, T ij represents the stress vector, C ijkl is the elasticity matrix (N/m 2 ), e ijk is the piezoelectric matrix (C/m 2 ), ɛ ij is the permittivity matrix (F/m), E k is the electric field vector (V/m), S kl is the strain vector, and D i is the electrical displacement (C/m 2 ). The degrees of freedom (dependent variables) are the global displacements u 1, u 2, and u 3 in the global x 1, x 2, and x 3 directions. The electrical potential V can be obtained by solving the Newton and Maxwell equations related to Eqs. (1) and (2), such that: ijk kl C E ijkl e jkl 2 u l + jk 2 u l jk e kij ε s jk 2 V = ρ 2 u i t 2, (3) 2 V = 0, (4) for i, j, k, l = 1, 2, and 3. Surface acoustic waves propagate on the surface of an elastic medium with most of the energy concentrated near the surface. The interdigital transducers (IDT), which is a metallic electrode fabricated over the piezoelectric substrate, converts electrical energy to mechanical energy and vice versa. The IDT has a comb-like structure, where the distance between the fingers in the IDT determines the frequency of the waves propagating over the substrate. The distance p between successive electrodes, as shown in Fig. 1, determines the elastic wavelength λ and is related by λ = 2p. The associated frequency, f, of waves propagating with a velocity v, is given by f = v/λ. IDTs are periodic in nature, alternatively consisting of positive and negative potentials. Thus, one period of the electrode is sufficient to model the SAW resonator as a whole, as shown in Fig. 1. The SAW resonator may have hundreds of electrodes, and each electrode s length can be far larger than its width. Edge effects can, therefore, be ignored, and the model geometry can be reduced to athe periodic cell [7]. Fig. 1. Geometry employed for a as periodic cell in the simulation. The modeled geometry modeled as a periodic cell in the simulation is shown in Fig. 1. We used the multiphysics finite element package COM- SOL 3.3, in the two-dimensional (2D) piezo plane strain mode (smppn), to simulate surface acoustic wave propagation in piezoelectric thin films. This application mode assumes that the out-of-plane strain is zero (x 2 X 2 direction). The surface wave is generated by the piezoelectric thin film;, and therefore, the thickness of the silicon does not affect the wave characteristics. In this report, a a modeled the piezoelectric thin film with a 1- µm thickness on a 2λ (8-µm) thick silicon substrate and a bottom boundary that remained in a fixed position is modeled. A stress -free boundary condition is assigned to the top surface of the piezoelectric layer. A polarization voltage value of 1 V iwas assigned to the aluminum electrode, which has a thickness of 100 nm. The periodic boundary conditions, wherein the left Γ L and the right Γ R boundaries are applied, are shown in Fig. 1. The detailed boundary conditions of the simulation are listed in Table 1. Using the material constants reported in Refs. [15] and [16] and summarized in Table 2 tofor describeing the piezoelectric thin film, we determinedand the Young s modulus, the Poisson ratio and the density of the silicon for the simulation were determined to be 131 Gpa, 0.27 and 2330 kg/m 3, respectively. The width of the IDT finger is 1 µm, and the periodicity (λ) is fixed at 4 µm. The piezoelectric thin film thickness (h) is fixed at 1 µm. To assess the accuracy of the simulation by using the FEM, we fabricated a two-port SAW resonators on AlN/Si and ZnO/Si substrates, with λ = 40 µm. The fabrication process and the geometry of the SAW device

3 -448- Journal of the Korean Physical Society, Vol. 57, No. 3, September 2010 Table 1. Boundary conditions of the simulation. Mechanical boundary condition Electrical boundary condition Γ 1 Free Zero charge/symmetry Γ 2 Free continuity Γ 3 Fixed Ground Γ R1, Γ R2 Γ L1, Γ L2 Periodical boundary condition Table 2. Set of material constants used in the FEM model. Material AlN ZnO Density (kg/m 3 ) P Elastic cnstants (GPa) Piezoelectric constants (C/m 2 ) Relative permittivity C C C C C C e e e ε ε wereas similar to thoseat described in Ref. 17. Highquality polycrystalline layers were deposited as 1-µm thick (002)-oriented AIN or ZnO piezoelectric thin films onto (100)-Si wafers by using a sputtering system. TA thin aluminum layers with a thicknesses of 100 nm wereas deposited on the AlN/Si andor ZnO/Si samples by using the thermal evaporator method. Then, IDTs and reflectors were made using UV lithography and Al wet etching. The transmission characteristics of the two-port SAW resonators were measured with an Agilent 8802A Network Analyzer. III. RESULTS AND DISCUSSION We used an eigen-frequency analysis to determine the eigen-frequencies and the modes of deformation in the modeled structure. Through the use of simulations, we were able to determine the wave types by observing the vibration of the wave in the structure and comparing this to wave definitions. The model was meshed with pre-defined normal parameters in a free mesh. Since the SAW displacements are largest near the substrate surface, the meshing domain is meshed to higher densities near the surface rather than near the bottom. Figure 2 shows the effects of the number of meshing elements on the resonant frequency of the Rayleigh surface wave, which were detected in the AlN/Si structure. The res- Fig. 2. (Color online) Effect of the number of elements on the resonance of a Rayleigh surface wave. onance frequency changed from 1317 MHz with 722 elements, to 1295 MHz with elements. For using a wavelength λ of 4 µm in the simulation, the SAW velocity in the AlN film is approximately 5268 m/s to 5180 m/s, depending on the number of elements. Figure 3 shows the fundamental modes of the Rayleigh waves detected in the piezoelectric AlN and ZnO thin filmss, with equal numbers of elements. The wavelengths are equal to the width of the modeled periodic cell. The electric field vector (red colored arrow) shown in Fig. 3 is similar to the actual electric field present in the device which, and indicates that the finite element calculation provides a more realistic representation of the electric field than other models [2 5]. The contour curve displacement and deformation profile shows that the Rayleigh wave propagatesion over the thin film substrate, with amplitudeamplitude of 3.5 nm in the AlN/Si structure and 4.1 nm in the ZnO/Si structure. The larger wave amplitude of the ZnO film can be explained byas the larger coupling coefficient d 33 (piezoelectric coefficient) of the ZnO film, as compared to the AlN film [10]. However, with the same geometry, the eigen-frequencyy of the AlN/Si structure is 1295 MHz, greater than the 694 MHz of the ZnO/Si structure. The eigen-frequenciesy corresponding to a 4-µm wavelength

4 Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Gwiy-Sang Chung and Duy-Thach Phan Fig. 5. (Color online) The (a) Rayleigh and (b) Sezawa mode waves detected in a SAW detected by using the FEM at hk = 1.6 in a ZnO/Si structure. Fig. 3. (Color online) Influences of the electric field vector distribution, contour curve displacement, and color on the deformation strength of a SAW resonator: (a) AlN/Si; and (b) ZnO/Si. Fig. 4. Frequency response, S 12, of two-port SAW resonators withof AlN/Si and ZnO/Si structures. are, computes to 1295 MHz and 694 MHz, giving a phase velocitiesy of 5180 m/s in the AlN film and 2776 m/s in the ZnO film, respectively. The AlN films have higher acoustic velocity than the ZnO films because of theirits higher Young s modulus value (Table 2). The Rayleigh wave shape in the bulk piezoelectric material [7] shows a penetration depth greater than in the thin film of this report. This is related to the difference between the piezoelectricity in bulk and thin films piezoelectric. Figure 4 shows the experimental frequency response S 12, of a two-port SAW resonators on ZnO/Si(100) and AlN/Si(100) substrates, measured by using a network analyzer. The SAW resonators were fabricated with equal thin film thicknesses (1 µm) and mask geome- triesy. The resulting SAW resonator of AlN/Si, has a resonant frequency of MHz, corresponding to a wave length of 40 µm, and providing a phase velocity of the a Rayleigh wave of 5208 m/s at h/λ = This value is consistent with the results of a previous studyies by our group [17] and another groups [18]. The phase velocities in the AlN/Si structure were detected in a FEM simulation at h/λ = 0.25 were from 5180 m/s (11552 elements meshing) to 5268 m/s (722 elements meshing). Theise values indicates that including larger numbers of elements improves accuracy and that the SAW modeled by the FEM is similar to the experimental results. Although the h/λ ratio is different between the experimental and the simulated results, the Rayleigh wave in the AlN film is fairly consistent. The wave results agreed with the results in Ref. [18]; the phase velocity of the AlN/Si film was approximately 5100 with aan h/λ ratio from to 0.4. The peak S 12 of the SAW two-port resonator in the ZnO/Si structure (Fig. 4) wais 122 MHz with λ = 40 µm. The phase velocity of the Rayleigh wave in the ZnO/Si film was 4880 m/s at hk = 0.16 (k = 2π/λ; wave vector, h: thickness piezoelectric film). These experimental results agree with published data [11]. The phase velocity in the ZnO/Si, obtained by using ain simulation, wasis 2776 m/s at hk = 1.6 and is quite different from the experimental results due to the differences in the hk ratios. The ZnO film thickness has a large affect on surface acoustic wave modes and acoustic streaming [11], sotherefore, the phase velocity in the simulation, with hk = 1.6, is close to 3000 m/s at the same hk ratio as in Ref. 11. For the detected wave mode in the ZnO piezoelectric thin film, the desired number of eigen-frequencies in the analysis mode is expanded. This results in the Sezawa mode being detected at f = 1348 MHz, as shown in Fig. 5.

5 -450- Journal of the Korean Physical Society, Vol. 57, No. 3, September 2010 they are intended to help guide experimental SAW sensor development. Future research efforts should include investigating the varyingied phase velocity of the wave modes in piezoelectric thin films as a function of hk by using FEM modeling and experimental results. ACKNOWLEDGMENTS Fig. 6. Frequency response, S 12o, of a ZnO/Si SAW resonator atperformed with hk = The Rayleigh wave has the with peaks of the first and second harmonics 1 and harmonic 3. The Sezawa mode wave in SAWs with layered structures has a higher acoustic velocity than the Rayleigh mode. Therefore, two wavelengths of waves in the Sezawa mode were detected in one periodic cell, as shown in Fig. 5(b), instead of the single wavelength for the Rayleigh wave, as shown in Fig. 5(a). The appearance of the Sezawa mode depends on the ratio hk. With hk = 1.6 in the simulation, the Sezawa mode shown in Fig. 5(b) has a phase velocity of 5392 m/s, two times greater than the Rayleigh mode, which has a phase velocity of 2776 m/s. The phase velocity of the Sezawa mode in ZnO/Si at hk = 1.6, was approximately 5000 m/s in [11]. However, with hk = 0.16 in the experiment, athe high- order harmonic of the Rayleigh wave wasis detected, as shown in Fig. 6, rather that the Sezawa mode, because the Sezawa mode is not applicable when hk 1 [11,19]. Figure 6 shows a wide ( MHz) frequency response range of the SAW resonators on the ZnO/Si fabricated structures. An additional peak, corresponding to the third harmonic of the Rayleigh mode, can be observed at 340 MHz. IV. CONCLUSIONS In this paper, we illustrate the use of FEM modeling for estimating the phase velocity, wave mode and harmonic mode in SAWs, based on piezoelectric thin films. We compared the results of simulation studies to experimental results and previously published data [11,18,19]. The estimatesion of these parameters constitutes a valuable tool for determining the optimal film thickness, mode and desired harmonic mode when designing SAW sensors. Because of limitations in the accuracy of the published material constants, andconstants, and the effects of the IDT aperture in the X 2 direction, these estimates are not intended to be precise predictions; rather, This research was supported by the Korea Research Foundation Grant funded by 2010 the Korean Government which was conducted by the Ministry of Education, Science and Technology. REFERENCES [1] A. Pohl, IEEE Trans. Ultrason. Ferrolectr. Freq. Control 47, 317 (2000). [2] K.-Y. Hashimoto and M. Yamaguchi, Proceedings IEEE International Frequency Control Symposium (Salt Lake City, Ultah, 1993), p [3] A. Hachigo and D. C. Malocha, Proceedings IEEE Ultrasonics Symposiump (San Antonio, Texas, 1996), p [4] G. Kovacs, IEEE Ultrason. Symp. 1, 707 (2003). [5] K. Hashimoto, T. Omori and M. Yamaguchi, Proceedings IEEE Ultrasonics. Symposium. (Atlanta, Georgia, 2001), p [6] M. Z. Atashbar, B. J. Bazuin, M. Simpeh and S. Krishnamurthy, Sens. Actuators B , 213 (2005). [7] Y.-G. Zhao, M. Liu, D.-M. Li, J.-J. Li and J.-B. Niu, Sens. Actuators A 154, 30 (2009). [8] X. Wang and G. Xu, Proceedings IEEE International Frequency Control Symposium and Exposition (Vancouver, British Columbia, 2005), p. 442 [9] G. Hu, J. Xu, G. W. Auner, J. Smolinski and H. Ying, Sens. Actuators, B 132, 272 (2008). [10] Y. Q. Fu, J. K. Luo, X. Y. Du, A. J. Flewitt, Y. Li, G. H. Markx, A. J. Walton and W. I. Milne, Sens. Actuators B 143, 606 (2010). [11] X. Y. Du et al., Appl. Phys. Lett. 93, (2008). [12] L. Le Brizoual and O. Elmazria, Diamond and Relat. Mater. 16, 987 (2007). [13] L. Le Brizoual, F. Sarry, F. Moreira and O. Elmazria, Phys. Status. Solidi A. 203, 3179 (2006). [14] COMSOL Multiphysics User s Guide, Version 3.3 (COMSOL AB, 2006). [15] M.-S. Lee, S. Wu, Z.-X. Lin and R. Ro, Jpn. J. Appl. Phys. 46, 6719 (2007). [16] S. Wu, Z.-X. Lin, M.-S. Lee and R. Ro, J. Appl. Phys. 102, (2007). [17] H. S. Hong and G. S. Chung, J. Korean Phys. Soc. 54, 1519 (2009). [18] C. Caliendo, P. Imperatori and E. Cianci, Thin Solid Films 441, 32 (2003). [19] L. Le Brizoual, O. Elmazria, F. Sarry, M. El Hakiki, A. Talbi and P. Alnot, Ultrasonics 45, 100 (2006).