STUDY ON CHARACTERISTICS OF SURFACE ACOUSTIC WAVE BASED ON (110)ScAlN/R-SAPPHIRE STRUCTRUE

Jing XU1, Yan WANG1,2,*, Zhi-jie JIA1, Ying-cai XIE1

1School of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210046,

China2Lab of Modern Acoustics, Institute of Acoustics, Nanjing University, Nanjing 210093, China

*Corresponding author, E-mail: ywang@njupt.edu.cn; Tel.: 86-25-85866145

The propagation characteristics of surface acoustic wave (SAW) in IDT/(110)ScAlN/R-sapphire, including the Rayleigh

wave propagating along [001] direction and Love wave propagating along [100] direction, are investigated by 3

dimension-finite element method (3D-FEM). The phase velocity (vp), electromechanical coupling coefficient (k2) and

mass sensitivity (Sm) of first two orders of Rayleigh wave and Love wave are calculated. The simulated results show that

the mode 0 of SAWs has better performances than that of mode 1. The mode 0 of Rayleigh wave shows the maximum k2

of 3.57% as h/λ=1 associated with vp of 3676 m/s and Sm of 23.6 m2/kg ; and the mode 0 of Love wave exhibits the

maximum k2 of 6.39% as h/λ=0.33 associated with vp of 4644 m/s and Sm of 38.3 m2/kg. The results indicate that

(110)ScAlN/R-sapphire structure can be used for the fabrication of SAW devices with high frequency and good

sensitivity.

Keywords: ScAlN; R-sapphire; electromechanical coupling coefficient; mass sensitivity

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1. INTRODUCTION

Surface acoustic wave (SAW) devices are widely used in environmental monitoring, communications, biochemistry and other fields [1-3]. With the rapid development of science and technology, the demands for the performance of SAW devices are increasing, such as the increasing of operating frequency and the broadening of application area. However, how to realize the extension of operating frequency range is one of the biggest issues. From the point of lift-off technique, the electrode width of IDTs, for SAW devices operated at frequency higher than 2.5GHz, will be the limitation [4]. Therefore, improving the phase velocity of SAW devices is another valid method to solve the problem. However, the phase velocity of conventional piezoelectric substrates, such as LiTaO3, LiNbO3 and quartz, are not high enough for SAW devices operated at GHz frequency. So the layered structure with piezoelectric thin film deposited on non-piezoelectric substrate with high acoustic velocity is an effective method. Among the non-piezoelectric substrates, sapphire has been studied experimentally and theoretically [5,6], due to the superior properties of high acoustic velocity, low acoustic attenuation loss and so on.

AlN films have the larger phase velocity, but the piezoelectricity is weaker. Recently, Scandium-doped AlN (ScAlN) films have drawn much attention due to its strong piezoelectricity [7-13], Alihiko et al. reported that ScxAl1-xN thin film has a large piezoelectric coefficient d33 of 24.6 pC/N when the concentration of Sc was 43% [7]. Hashimoto et al. theoretically shown that the Sezawa wave excited by IDT/ScAlN/6H-SiC structure exhibits relatively large k2 (5.26%) associated with phase velocity of 6310 m/s as hScAlN/λ=0.58. In addition, Rayleigh wave excited by IDT/ScAlN/Diamond structure has the maximum k2 of 5.48% at hScAlN/λ=0.71 associated with phase velocity of 6248 m/s [8,9]. ZHANG et al. reported that Rayleigh wave and Sezawa wave propagated in ScAlN/IDT/Diamond structure have the maximum value k2 of 14.35% and 10%, respectively [10].

In this work, the 3 dimension-finite element method (3D-FEM) based on COMSOL 4.3b is employed to study

theoretically the propagation characteristics of SAWs in the structure of IDT/(110)ScAlN/R-sapphire. The properties of first two orders of Rayleigh wave propagating along [001] direction of (110)ScAlN film and Love wave propagating along [100] direction of (110)ScAlN film, including phase velocity vp, electromechanical coupling coefficient k2 and mass sensitivity Sm, are calculated.

2. THEORETICAL ANALYSIS

For COMSOL Multiphysics simulation software, the motion equation and the electric field equation (quasi-static approximation) are given by Eq. (1) and Eq. (2), which shows the relation between the stress (T), strain (S), electric filed (E), and electric displacement (D) of piezoelectric materials [14].

(1)

(2)

The phase velocity of SAWs can be obtained by using Eq. (3) [15]:

, (3)

where λ and f are the wavelength of SAW and frequency, respectively.

The electromechanical coupling coefficient k2

describes the degree of mutual coupling between the mechanical energy and electromagnetic energy [6]. The formula is shown as follows:

， (4)

where vf and vm are the velocities of SAWs corresponding to the free surface and metallized surface, respectively.

For SAW devices, the mass sensitivity Sm can be calculated using Eq. (5) [16]:

， (5)

2

where f0 is the oscillation frequency of the SAW device without mass loading, Δm/A is the mass per unit area applied to the top surface of SAW device, and Δf is the frequency shift caused by the mass loading. In our calculations, a layer of PMMA is added to the top surface of SAW devices as the surface perturbation.

3. MODELING AND SIMULATION

The (110)ScAlN/R-sapphire structure is modeled by COMSOL as shown in Fig. 1, where h and hs are the thickness of ScAlN film and R-sapphire substrate, respectively. The IDTs on the top of the (110)ScAlN film are designed with the same electrode length and the wavelength (λ) of 16 µm. In the calculations, the effects of IDTs on SAW properties are ignored, because the thickness of IDTs is much smaller than that of wavelength.

Figure 1. Schematic of (110)ScAlN/R-sapphire structure

The boundary conditions of (110)ScAlN/R-sapphire structure are as follows: Γ1, Γ2 and Γ3 are free, continuous and fixed for mechanical boundary

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conditions, respectively; meanwhile, all of the boundaries are with zero charge for electrical boundary conditions. Besides, the other four side faces are periodic boundaries for mechanical and electrical boundary conditions.And the material parameters of ScAlN (r=40%) and sapphire are listed in Table 1.

Table 1. Material parameters used in simulations [6,9,16]

Parameter Symbol ScAlN Sapphire PMMA

Elastic constant

(1010N/m2)

C11 16.9 49.4 --

C12 6.12 15.8 --

C13 5.88 11.4 --

C14 -- -2.3 --

C33 21.1 49.6 --

C44 5.15 14.5

Piezoelectric constants

(C/m2)

e15 -1.31 -- --

e31 -1.58 -- --

e33 4.42 -- --

Relative dielectric

constants

ε11/ε0 30.5 9.34 --

ε33/ε0 30.3 11.54 --

Density (kg/m3) 3760 3986 1190

Young’s modulus

(GPa)E -- -- 3

Poisson’s ratio µ -- -- 0.4

In the calculation, the Free Triangular mesh and Swept of COMSOL software are used. And it is necessary to ensure that the two side faces of x direction and y direction are symmetr ic while extremely fine mesh

4. RESULTS AND DISCUSSION

4.1. Impedance responses of SAW resonators

Figure 2 show the impedance responses of SAWs excited by IDT/(110)ScAlN/R-sapphire structure, by which the mode of SAWs can be identified easily. Figure 2(a) is the impedance response of Rayleigh wave with h/λ (the ratio of ScAlN film thickness to wavelength) of 0.75, it can be seen that the frequency of mode 0 and mode 1 are f0=245 MHz and f1=363 MHz, respectively. Figure 2(b) shows the impedance response of Love wave with h/λ=0.63, the operating frequency of mode 0 and mode 1 are f0=258 MHz and f1=334 MHz, respectively.

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Figure 2. Impedance responses of IDT/(110)ScAlN

/R-sapphire structure: (a) Rayleigh wave; (b)

Love wave

In order to accurately distinguish the propagation properties of SAWs in this structure, the displacements of the first two orders of Rayleigh wave and Love wave are shown in Fig. 3.

4.2. vp and k2 of SAWs in IDT/(110)ScAlN/R-sapphire

The effects of the thickness of ScAlN films on the SAWs characteristics are studied, including vp and k2 dispersion curves of first two orders of SAW. Fig ure 4 is the characteristics of Rayleigh wave propagating along [001] direction of (110)ScAlN films. As shown in Fig. 4(a), the phase velocities decrease with the thickness increase of ScAlN films for all modes, and the mode 1 of Rayleigh wave appears at the critical point of h/λ=0.75. The k2

results of Rayleigh wave are shown in Fig. 4(b). For mode 0, there is a minimum k2 of 1.33% with h/λ=0.25, and then, the k2 increases with the increase of h/λ, and the maximum k2 of 3.57% is obtained as h/λ=1. The k2 value of mode 1 is very small and close to zero.

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Figure 3. Displacement distributions in symmetric and

anti-symmetric modes of Rayleigh wave and

Love wave

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Figure 4. Characteristics of Rayleigh waves as a

function of h/λ in (110)ScAlN/R-sapphire

structure: (a) vp; (b) k2

Fig ure 5 shows the properties of first two orders of Love wave propagating along [100] direction of (110)ScAlN films as a function of h/λ. For each mode of Love wave, vp also decreases monotonically with the increasing of h/λ as shown in Fig. 5(a), and mode 1 appears at the point of h/λ=0.63. It can be seen from Fig. 5(b) that, for mode 0 of Love wave, the k2 increase firstly and then decrease with the increase of h/λ, and the maximum value of 6.39% at h/λ=0.33 is obtained. The k2

values of mode 1 are smaller than that of mode 0, but larger than that of Rayleigh wave with the same value of h/λ.

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Figure 5. Characteristics of Love waves as a function

of h/λ in (110)ScAlN/R-sapphire structure:

(a) vp; (b) k2

4.3. Mass sensitivity of SAWs in (110)ScAlN /R-sapphire structure

The mass sensitivities of Rayleigh wave and Love wave in (110)ScAlN/R-sapphire structure are calculated. Figure 6 shows the results of Sm as a function of h/λ for mode 0 of Rayleigh wave and Love wave. It can be seen clearly that, for both SAW, Sm increasing firstly, and then decrease with the increasing of h/λ. The Sm of Rayleigh wave is smaller than that of Love wave when h/λ<0.28, while, with the further increasing of h/λ, the Sm of Rayleigh wave is larger than that of Love wave. The maxima Sm of Rayleigh wave and Love wave are 39.4 m2/kg and 40.4 m2/kg at h/λ=0.25, respectively. Summarized the results of Fig. 4-6, for the mode 0 of Rayleigh wave, the maximum k2 is 3.57% associated with vp of 3676 m/s and Sm of 23.6 m2/kg at h/λ=1; and for the mode 0 of Love wave, the maximum k2 is 6.39% associated with vp of 4644 m/s and Sm of 38.3 m2/kg at h/λ=0.33.

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Figure 6. Mass sensitivity of SAWs as a function of

h/λ in (110)ScAlN/R-sapphire structure

5. CONCLUSION

In this paper, the propagation characteristics of first two orders of SAWs in (110)ScAlN/R-sapphire structure, including phase velocity vp, electromechanical coupling coefficient k2 and mass sensitivity Sm, have been theoretically analyzed by 3D-FEM. The simulated results show that the mode 0 of SAWs excited by (110) ScAlN/R-sapphire structure has better performance than that of mode 1. Mode 0 of Rayleigh wave has the maximum k2 of 3.57% with phase velocity of 3676 m/s and Sm of 23.6 m2/kg at h/λ=1. And mode 0 of Love wave has the maximum k2 of 6.39% associated with phase velocity of 4644 m/s and Sm of 38.3 m2/kg at h/λ=0.33. In conclusion, (110)ScAlN/R-sapphire structure can be used for the fabrication of SAW devices with high frequency and good sensitivity.

ACKNOWLEDGEMENTS

This research was supported by National Natural Science Foundation of China (Grant No.11304160), the Natural Science Foundation of Jiangsu Higher Education Institutions of China (Grant No.13KJB140008) and the Foundation of Nanjing University of Posts and Telecommunications (Grant No. NY213018).

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