2008海峽兩岸大學校長論壇暨科學技術研討會
台灣 義守大學
2008 年 5 月 26-27 日
Propagation Characteristics of Surface Acoustic Waves in AlN/128°Y-X LiNbO3 Structures Ruyen Ro, Ruyue Lee, Sean Wu1, Zhi-Xun Lin2, and Maw-Shung Lee2 Department of Electrical Engineering, I-Shou University Dashu Township, Kaohsiung County, Taiwan 840, R.O.C. Email:
[email protected] 1 Department of Electronics Engineering and Computer Science, Tung-Fang Institute of Technology Hunei Shiang, Kaohsiung County, Taiwan 829, R.O.C. Email:
[email protected] 2 Department of Electronics Engineering, National Kaohsiung University of Applied Science Kaohsiung, Taiwan 807, R.O.C. Abstract In this study, propagation characteristics of surface acoustic waves (SAWs) in a layered piezoelectric structure consisting of an AlN thin film sputtered on 128°Y-X LiNbO3 are investigated. The phase velocity and coupling coefficient of the layered structure with interdigital transducers (IDTs) and/or metal thin films deposited at various interfaces will be calculated numerically. The effects of the polarity of 128°Y-X LiNbO3 on SAW characteristics are illustrated. By substituting the constituting relations into the Christoffel equations along with enforcing the appropriate boundary conditions on the interfaces, SAW characteristics of layered piezoelectric structures are determined by employing a matrix approach. Phase velocity and coupling coefficient of SAWs are presented versus h/λ, where h is the thickness of the AlN film and λ is the wavelength. Simulation results are compared with experimental data, which are calculated from S-parameter measurements of transversal SAW filters. A well matched comparison is demonstrated. Results obtained can be applied for the design of SAW devices using AlN/128°Y-X LiNbO3 structures.
I. INTRODUCTION 128°Y-X LiNbO3 substrate has been used extensively in the development of surface acoustic wave (SAW) devices, based on its excellent material properties such as a large piezoelectric coupling constant (5.36 %) and a high SAW velocity (3994 m/s). However, it has poor temperature stability (Temperature Coefficient of Delay, TCD = 75 ppm/℃). The use of thin films to improve the temperature stability, phase velocity, or coupling coefficient of the substrate has been proposed and implemented by many researchers. Hickernell has addressed the role of thin-films played in SAW technology [1]. The zero temperature coefficient of frequency (TCF) structure using SiO2/Y-Z LiTaO3 has been reported by Parker and Wichansky [2]. The use of SiO2 thin film sputtered on LiNbO3 to achieve a high temperature stable SAW device with super high coupling has been reported by Yamanouchi and Ishii [3]. Kadota has
widely investigated the effects of ZnO thin films sputtered on different substrates such as glass and quartz [4]. Nakamura and Hanaoka have studied the propagation characteristics of SAWs in ZnO/128°Y-X LiNbO3 structures [5]. The mode coupling phenomenon between the Rayleigh and Love waves has been discussed and also the effects of the polarities between two piezoelectric media on characteristics of SAWs have been investigated. Characteristics of sputtering ZnO films on langasite and its SAW properties were reported by Wu et al. [6]. AlN and ZnO are the primary materials of piezoelectric films, and they have the same crystal structure, the hexagonal wurtzite structure. AlN thin films have some excellent characteristics, such as a high SAW velocity (nearly twice that of quartz and LiNbO3), piezoelectricity, high-temperature stability, and stable chemical properties. Therefore, depositing AlN films on 128°Y LiNbO3 may provide a new piezoelectric material for SAW devices. Characteristics of sputtering AlN films on 128°Y LiNbO3 were examined [7] and their SAW properties were measured [8, 9]. Highly c-axis-oriented AlN films were achieved via the investigation of X-ray diffraction (XRD) [7]. Experimental results of transversal SAW filters revealed that 128°Y LiNbO3 with an AlN film can increase the SAW velocity but at the expense of the decrease of coupling coefficient [9]. As h/λ increases, the absolute value of TCF decreases, which implies that the temperature stability of the substrate has been improved via an AlN film [9]. In order for using the proposed structure, AlN/128°Y-X LiNbO3, to design SAW devices with the optimum performance, SAW characteristics have to be determined in the h/λ range of interest, which may be realized by employing a numerical approach. To the authors’ best knowledge, the corresponding numerical data have never been presented in the public domain. To attain this goal, propagation characteristics of SAWs in AlN/128°Y-X LiNbO3 are investigated in this study. Following the approach proposed by Campbell and Jones [10, 11], a matrix method is presented to determine SAW characteristics of layered piezoelectric structures with IDTs and/or metal thin films deposited at different
台灣 義守大學
2008海峽兩岸大學校長論壇暨科學技術研討會
interfaces. Detailed derivations are discussed in Section II. Simulation results obtained versus h/λ are illustrated in Section III. The effects of the polarity of 128°Y LiNbO3 on phase velocity and coupling coefficient will be elucidated. Simulated data are compared with measurement results, which are obtained from S-parameter measurements of transversal SAW filters [9]. A good agreement is presented. The last section is the conclusions.
II. METHOD OF ANALYSIS The schematic of a layered piezoelectric structure, as depicted in Fig. 1, consists of an AlN film of thickness h and a 128°Y cut LiNbO3 substrate. Note that the AlN film may be deposited on the positive surface or negative surface of the substrate. The angle between the positive surface normal and the Y-axis (crystallographic coordinate) is 128 degree, while for the negative surface is −52 degree. Highly c-axis-oriented AlN films were achieved on the substrate by rf magnetron sputtering, and are assumed to be independent of the substrate polarity [7]. Following the similar approach as developed by Campbell and Jones [10-12], a matrix method is employed here to calculate the SAW velocity in a layered piezoelectric structure.
128o Y
− 52o Y
Fig. 1. Schematic of a layered piezoelectric structure consisting of an AlN film of thickness h and a 128ºY or −52ºY cut LiNbO3 substrate. Rayleigh or leaky SAWs are assumed to be propagating along the x-axis.
The acoustic and electric fields in media 1 and 2 can be expressed as
(
4
)
u (j1) = ∑ C m a (jm ) exp ikb (m ) z exp[ik (Px − vt )] , m =1
j = 1, 2, 3 ,
φ
(1)
4
(1)
(
= ∑ C m a4 exp ikb m =1 8
(m )
(
(m )
u j = ∑ Χ mα j exp ikβ (2 )
(m )
)
z exp[ik (Px − vt )] , (2)
(m )
)
z exp[ik (Px − vt )] , (3)
m =1 8
φ (2 ) = ∑ Χ mα 4(m ) exp(ikβ (m ) z )exp[ik (Px − vt )] , (4) m =1
where u is the acoustic displacement, φ the electric potential, v the phase velocity, k the wave number in the x-direction, P = 1 + iγ, γ is the attenuation coefficient, b and β the wave number ratios, and a and α the associated partial field amplitudes. Substituting eqs. (1) and (2) into stiffened Christoffel equations yields an eight-order algebraic equation in the wave number ratio b. Thus for
2008 年 5 月 26-27 日
each pair of values of (v, γ), there are eight real or complex values of b. For a semi-infinite piezoelectric crystal, medium 1 in this case, four complex roots with negative imaginary parts are selected for a Rayleigh wave; meanwhile, in the case for a leaky SAW, one complex root, instead, has a positive imaginary part [13]. In the medium 2, eight roots of β are all selected. The boundary conditions require that the acoustic displacements and stresses be continuous at z = 0 and the stress-free surface is assumed at z = h. In addition, the electric potential and the normal component of electric displacement must be continuous at the interface for an electrically free surface. For a metallized (metal thin film) surface, the electric potential is vanished. Substituting eqs. (1)-(4) into boundary conditions, the phase velocity v and attenuation coefficient γ can be obtained numerically. The electromechanical coupling coefficient K2 can be calculated from
K2 = 2
v f − vm vf
,
(5)
where vf and vm are phase velocities obtained when the electrical boundary conditions at the interface at which the IDT is placed are assumed to be electrically free and shorted, respectively. The phase velocities and coupling coefficients are calculated for the following four cases according to the positions of the IDT electrodes and/or metal thin films. (a) IDT/AlN/128°Y- or −52°Y-X LiNbO3 (b) IDT/AlN/metal thin film/128°Y- or −52°Y-X LiNbO3 (c) AlN/IDT/128°Y- or −52°Y-X LiNbO3 (d) Metal thin film/AlN/IDT/128°Y- or −52°Y-X LiNbO3. The matrix approach employed to compute the SAW propagation characteristics is detailed below. In the case (a), the IDT electrodes are placed on the z = h surface. At z = 0, by enforcing the boundary conditions, one can obtain M 1u 8×4 Cm 4×1 = M 2l 8×8 X m 8×1 , (6)
[
] [ ]
[
] [ ]
while at z = h after simple manipulation yields
[M ] [X ] 2 uf 4×8
m 8×1
=0
(7a)
for an electrically free surface and for an electrically shorted surface we obtain M 2um 4×8 X m 8×1 = 0 . (7b)
[
] [ ]
Substituting eq. (6) into eq. (7a) or eq. (7b) yields M ta 4×4 C m 4×1 = 0 .
[
] [ ]
(8)
and the The SAW phase velocities, vfa and vma, attenuation coefficients, γfa and γma, for the case (a) then can be determined by vanishing the determinant of the matrix Mta, i.e., det Mta = 0, and, in turn, the acoustic and electric fields in media 1 and 2 can be obtained. For the case (b), the IDT electrodes are still placed on the z = h surface, but a metal thin film is assumed to be deposited on the z = 0 plane. At z =0, the electrical boundary conditions for cases (a) and (b) are significantly different from each other and, hence, eq. (6) is now modified to three sets of equations as given by M 1′u 6×4 Cm 4×1 = M 2′ l 6×8 X m 8×1 , (9a)
[
] [ ]
[
] [ ]
台灣 義守大學
2008海峽兩岸大學校長論壇暨科學技術研討會
and
[M 2′lm ]1×8 [X m ]8×1 = 0 .
From eq. (9b), one can obtain C 4 = C 4 (C1 , C 2 , C3 ) ,
(9c) (10a)
and also from eq. (9c) and one equation in eq. (7a) or eq. (7b) we can express Χ1 and Χ8 in terms of the rest Χms as given by Χ1 = Χ1(Χ 2 , Χ 3 , Χ 4 , Χ 5 , Χ 6 , Χ 7 ) (10b)
Χ 8 = Χ 8 (Χ 2 , Χ 3, Χ 4 , Χ 5 , Χ 6 , Χ 7 ) .
(10c)
Substituting eqs. (10a)-(10c) into eq. (9a), and then using the rest equations in eq. (7a) or eq. (7b) yields M tb 3×3 Cm 3×1 = 0 . (11)
[
] [ ]
The SAW phase velocities (vfb and vmb) and attenuation coefficients (γfb and γmb) for the electrically free and shorted surfaces are determined by vanishing the determinant of the corresponding matrix Mtb. For the rest two cases, cases (c) and (d), the corresponding propagation characteristics of SAWs are equal to those in the cases (a) and (b), i.e., vfc = vfa, vmc = vfb, vfd = vma, and vmd = vmb.
III. RESULTS AND DISCUSSION The material constants of AlN and LiNbO3 employed here were obtained from the study reported by Gualtieri et al. [14]. The phase velocities, for the case (a), presented in Fig. 2 are obtained by vanishing the determinant of the matrix Mta, as indicated in eq. (8). The subscripts 1 and 2 in vfa1 and vfa2 indicate the AlN film is deposited on the positive surface and negative surface of the substrate (denoted respectively by 128°Y and −52°Y cut LiNbO3), respectively. Both vf and vm increase with increasing h/λ, where h is the thickness of the AlN film and λ is the wavelength. This is because the Rayleigh wave velocity for AlN, around 5400 m/s, is greater than that for 128°Y-X LiNbO3, 3994 m/s. When h/λ is around 0.013, the phase velocities, vfa1 and vfa2, approach 4079 m/s, which is the shear bulk wave velocity for 128°Y cut LiNbO3. Therefore, a leaky wave solution to the substrate is searched when the SAW phase velocity is greater than 4079 m/s. The associated attenuation coefficients are presented in Fig. 3. The attenuation coefficient is zero for the Rayleigh wave and has a significantly large value for the leaky wave especially in the region when the SAW velocity is slightly higher than the shear velocity. Therefore, our discussion is mostly restricted on the Rayleigh wave region. The value marked with a dot in Fig. 2 represents the measured effective velocity of transversal SAW filters [9]. The measured velocity was obtained using veff = f0*λ0, where f0 is the center frequency estimated in S21 and λ0 is the period of IDT. It is clear that the measured velocity has the same trend as the simulated data, i.e., the velocity increases as h/λ increases. The measured center frequency is shifted downward due to the effect of the slow phase velocity in the metallization region and, hence, the
measured effective velocity should be less than vf. For the IDT with metallization ratio 0.5, the effective velocity can be calculated from vf and vm as given by
veff = 2
v f vm v f + vm
.
(12)
The calculated effective velocities (veff1 and veff2) for h/λ = 0, 0.008, 0.031, and 0.045 are (3940, 3940), (4001, 4016), (4134, 4173), and (4197, 4236), respectively. Comparing those data with the corresponding measured velocities 3918, 3953, 4105, and 4152, the maximum difference between measured and calculated effective velocity is less than 2%. The calculated effective velocities (veff1 and veff2) for h/λ = 0, 0.008, 0.031, and 0.045 are (3940, 3940), (4001, 4016), (4134, 4173), and (4197, 4236), respectively. Comparing those data with the corresponding measured velocities 3918, 3953, 4105, and 4152, the maximum difference between measured and calculated effective velocity is less than 2%. 4700 4600
v f2
4500 Velocity (m/s)
(9b)
4400 4300
v f1
4200
v m2
v m1
4100 4000 3900
measured velocity
3800 0.00
0.04
0.08
0.12
0.16
0.20
h /λ
Fig. 2. Calculated phase velocity presented versus h/λ for the case (a) with an IDT/AlN/128ºY or −52ºY cut LiNbO3 structure. The subscripts 1 and 2 indicate the AlN film is deposited on the positive surface and negative surface of the substrate, respectively. The dot value presents the measured effective velocity of transversal SAW filters [9]. 0.010
Attenuation Coefficient
[M 1′um ]1×4 [Cm ]4×1 = 0 ,
2008 年 5 月 26-27 日
0.008
γ m2
γ m1
0.006 0.004 0.002
γ f1( ≈ γ f2)
0.000 0.00
0.04
0.08
0.12
0.16
0.20
h /λ
Fig. 3. Calculated attenuation coefficients for the case (a).
The coupling coefficient presented versus h/λ is shown in Figs. 4(a)-4(d), which corresponds to the cases (a)-(d), as studied in this paper. First, we consider the effects of the polarity of the substrate on K2. Except for the case (b), K21 is different from K22. The subscripts 1 and 2 in K21 and
台灣 義守大學
2008海峽兩岸大學校長論壇暨科學技術研討會
4 N B0
f = f0
,
K 21
0.05 0.04 0.03 0.02
K 22 measured K
0 0.00
2
0.04
0.08
0.12
0.16
0.20
h /λ
Fig. 4(a). Calculated electromechanical coupling coefficients for the case (a). The dot value presents measured coupling coefficient of transversal SAW filters [9]. The effects of the polarity of the substrate are apparent, i.e., 2 2 K 1 is different from K 2. The value of the measured 2 coupling coefficient approximates that of K 2.
(13)
where N is the number of IDT finger pairs, and G0 and B0 are radiation conductance and susceptance, respectively. It is obvious in Fig. 4(a) that the measured K2 not only has the same trend as K22 but its value is approximates that of K22. This implies that the substrate for fabricating SAW devices is −52°Y cut LiNbO3. In Fig. 4(b), K21 (= K22) has a very small value as compared with the rest three cases. This illustrates that the metal thin film deposited on the interface plane between two piezoelectric media decreases the coupling coefficient significantly. For the case (c), K21 and K22 in Fig. 4(c) have almost the same values in the Rayleigh wave region. A peak value of 6.1% is observed at h/λ = 0.01. Comparing Fig. 4(c) with Fig. 4(a), a peak value of 6.1 % can be found in the Rayleigh wave region for the case (c) regardless of the polarity of the substrate. However, for the case (a) a peak is observed only in K21. The coupling coefficient with a metal thin film deposited on the top surface is presented in Fig. 4(d). The value of K2 is smaller than that in Fig. 4(a) or Fig. 4(c) in the Rayleigh wave region. This shows that a metal thin film on the top surface may also decrease the coupling coefficient. According to the simulation and measurement data presented in Figs. 4(a)-4(d), in the Rayleigh wave region the AlN/IDT/128°Y-X LiNbO3 structure can exhibit the best performance with a proper h/λ among all the cases investigated in this study, and, especially, the effects of the polarity of the substrate are almost vanished in the corresponding structure. This information can be employed as a design rule for the fabrication of SAW devices using AlN/128°Y-X LiNbO3 structures.
0.06
0.01
0.005 0.004 Coupling Coefficient
π G0
0.07
K
2 2 1≈K 2
0.003 0.002 0.001 0 0.00
0.04
0.08
0.12
0.16
0.20
h /λ
Fig. 4(b). Calculated coupling coefficient in an IDT/AlN/metal thin film/128ºY or −52ºY cut LiNbO3 structure, named case (b) in this study. K21 and K22 have almost the same value in the h/λ range of interest. The coupling coefficient has the smallest value among all the cases studied in this paper.
0.12 K 21
0.1 Coupling Coefficient
K2 =
0.08
Coupling Coefficient
K22 denote the AlN film is deposited on the positive surface and negative surface of the substrate, respectively. This indicates that the polarity of the substrate may affect the SAW propagation characteristics. In the case (b), a metal thin film is deposited on the interface plane between AlN and LiNbO3 and, hence, the electric fields in AlN and LiNbO3 are isolated from each other; this causes the effects of polarity vanished and such that K21 = K22. In Fig. 4(a), K21 is greater than K22 in the whole h/λ ranges of interest. In the Rayleigh wave region, say h/λ less than 0.013, K21 increases from 5.36% to a peak value of 5.58%, at h/λ = 0.007 and then becomes decreasing. In the same region, K22 decreases monotonically. Though a maximum value around 6.76% is shown in K21, it is occurred in the leaky wave region with the attenuation coefficient of a very large value, 2.51×10−3. The dot value in Fig. 4(a) is measured from S11 of transversal SAW filters [9]. The value of K2 is calculated using [6, 9]
2008 年 5 月 26-27 日
0.08
K 22
0.06 0.04 0.02 0 0.00
0.04
0.08
0.12
0.16
0.20
h /λ
Fig. 4(c). Calculated coupling coefficient in an AlN/IDT/128ºY or −52ºY cut LiNbO3 structure, case(c) in this study. In the Rayleigh wave region (h/λ < 0.013), K21 and K22 have almost the same values and both reach a peak value of 6.1% at h/λ = 0.01.
台灣 義守大學
2008海峽兩岸大學校長論壇暨科學技術研討會
[2]
0.12 K
Coupling Coefficient
0.1
2 2
0.08
[3]
0.06
K
2 1
0.04
[4]
0.02 0 0.00
0.04
0.08
0.12
0.16
0.20
h /λ
[5] Fig. 4(d). Calculated coupling coefficient in a metal thin film/AlN/IDT/128ºY or −52ºY cut LiNbO3 structure. In the Rayleigh wave region, the value of K2 is smaller than that in Fig. 4(a) or Fig. 4(c).
[6]
IV. Conclusions In this paper, a matrix method was employed to calculate the SAW phase velocity in a layered piezoelectric structure consisting of an AlN thin film sputtered on 128°Y-X LiNbO3. Propagation characteristics of SAWs in different layered structures such as IDT/AlN/128°Y-X LiNbO3 or metal thin film/AlN/IDT/128°Y-X LiNbO3 with positive and negative polarities of the substrate were investigated and demonstrated versus various h/λ. For the IDT/AlN/128°Y-X LiNbO3 structure, the effects of the polarity were apparent in the coupling coefficient; the calculated phase velocity and coupling coefficient were compared with experimental data. A well matched comparison is shown between the calculated and measured effective velocities. The measured coupling coefficient approximates the calculated data obtained with a negative polarity of the substrate, −52°Y cut LiNbO3. In the Rayleigh wave region, the AlN/IDT/128°Y-X LiNbO3 structure shows that the effects of the polarity of the substrate can be neglected and exhibits a highest coupling coefficient among all the cases studied in this paper. This information can be employed as a design rule for the fabrication of SAW devices using AlN/128°Y-X LiNbO3 structures. Simulation results also indicate that a metal thin film deposited on the interface plane between two piezoelectric media can significantly decrease the coupling coefficient and in the Rayleigh wave region the metal thin film on the top surface will also decrease the coupling coefficient.
ACKNOWLEDGEMENT The authors would like to express their gratitude to the I-Shou University for their financial support of this research under contract no. ISU97-01-14 .
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