Tunable Electromechanical Coupling Coefficient of a Laterally Excited Bulk Wave Resonator with Composite Piezoelectric Film

A resonator with an appropriate electromechanical coupling coefficient (Kt2) is crucial for filter applications in radio communication. In this paper, we present an effective method to tune the Kt2 of resonators by introducing different materials into a lithium niobate (LiNbO3) piezoelectric matrix. The effective piezoelectric coefficients e33eff and e15eff of composite materials with four different introduced materials were calculated. The results show that the e15eff of SiO2/LiNbO3 composite piezoelectric material was mostly sensitive to an increase in the width of introduced SiO2 material. Simultaneously, the simulation of a laterally excited bulk wave resonator (XBAR) with SiO2/LiNbO3 composite material was also carried out to verify the change in the Kt2 originating from the variation in e15eff. The achievable n79 filter using the SiO2/LiNbO3 composite material demonstrates the promising prospects of tuning Kt2 by introducing different materials into a LiNbO3 piezoelectric matrix.


Introduction
To balance the needs of wide-area coverage and high data rates, 5G new radio (NR) has been proposed [1,2]. Laterally excited bulk acoustic wave resonators (XBAR) are promising candidates for application in fifth-generation mobile communication due to their high frequency, large electromechanical coupling coefficient (K 2 t ), low cost and complementary metal oxide semiconductor (CMOS) compatibility [3][4][5][6][7]. Victor Plessky realized a XBAR based on Z-cut lithium niobate (LiNbO 3 ) thin plate with a resonance frequency of approximately 4.9 GHz [8]. Ruochen Lu presented first-order antisymmetric (A1) mode resonators in thin 128 • Y-cut LiNbO 3 films with a K 2 t of 46.4% [9]. Bohua Peng designed and fabricated a solid-mounted-type XBAR on ZY-LiNbO 3 , operating at 5 GHz [5]. The K 2 t of XBAR has a significant influence on the bandwidth of filters. However, delicate control of the K 2 t of XBARs is crucial for designing filters; for example, the K 2 t of LiNbO 3 -based XBARs is too large for specific n79 filters (4.4 GHz-5.0 GHz) [10].
The K 2 t of XBAR can be adjusted by structural optimization and tuning the piezoelectric coefficients. Gianluca Piazza found that the K 2 t can be tuned by changing the electrical boundary conditions imposed by the excitation electrodes, obtaining a range varying from 3% to 7% [11]. Jie Zou investigated the influence of the Euler angle and thickness of LiNbO 3 film on the K 2 t of the resonator. It was found that the K 2 t of the A1 mode acoustic wave varied rapidly with changes in the Euler angle [12]. V. Plessky analyzed the influence of pitch and duty factor on frequency and K 2 t [13]. Using piezoelectric composite materials is another feasible method for K 2 t tuning. In our previous work, we adopted a ScAlN/AlN composite piezoelectric film to achieve a Lamé Mode resonator with a high K 2 t of 7.83% [14]. In this paper, we propose an effective method for tuning the K 2 t of XBARs by applying composite film consisting of LiNbO 3 piezoelectric material and other materials. The tuning range was as high as 62%, which is efficient compared with other studies, as shown in Table 1. We used FEM to analyze the effective piezoelectric coefficients e e f f 33 and e e f f 15 of composite piezoelectric films with different volume fractions of different materials embedded in LiNbO 3 piezoelectric material. FEM simulative analysis of XBAR utilizing those composite piezoelectric films was also carried out. Finally, an n79 filter was designed using SiO 2 /LiNbO 3 composite thin film-based XBARs with an adjustable K 2 t . The proposed XBAR with LiNbO 3 -based composite piezoelectric film shows promising prospects for constructing filters with different bandwidths at high frequency.

Theoretical Calculation of Piezoelectric Coefficient
The theory of linear piezoelectricity couples the interaction between the electric and elastic variables via the following constitutive equations [15]: where ε kl and σ ij are the components of the elastic strain and the components of the stress tensor, respectively; E i and D i are the components of the electric field and the components of the electric displacement, respectively; C ijkl is the components of the fourth-order elastic stiffness tensor obtained in the absence of an applied electric field; e lij is the components of the piezoelectric modulus tensor obtained without an applied strain; and κ ik is the components of the dielectric modulus obtained without an applied strain. It is convenient to treat the elastic and the electric variables in a similar fashion when modeling the piezoelectric behavior. This is accomplished by employing a notation introduced by Barnett and Lothe [16] and a generalized Voigt two-index notation [17]. Therefore, the constitutive equations can be represented as: The calculation of the effective properties of composite films is then realized utilizing the homogenization method, which relates the volume-averaged strain, stress, electric field, and electric displacement to the effective properties of the composite film. The composite films can thus be modeled as homogenized media. Using FEM, volume averages can be calculated as follows [18]: Micromachines 2022, 13, 641 3 of 9 where V is the volume of the representative volume elements (RVE). σ ij , ε ij , D i , and E i are the volume-averaged values of stress, strain, electric displacement, and electric field, respectively. In terms of these average values, the constitutive equations of linear piezoelectricity for composite material can be expressed in matrix form as follows: As shown in Figure 1, the RVE consisted of Z-cut LiNbO 3 and other materials. Other materials were embedded in the thin LiNbO 3 film, and the width of the other materials is expressed as P.  Table 2. In Table 2, u, v, and w are the displacement components along the x-, y-, and z-coordinate axes, respectively, and V0 is the applied electric potential.
As shown in Figure 1, the RVE consisted of Z-cut LiNbO3 and other materials. Other materials were embedded in the thin LiNbO3 film, and the width of the other materials is expressed as P. Here, four different materials commonly used in MEMS were taken under consideration, including SiC, Al2O3, AlN and SiO2. The boundary conditions applied to the six surfaces of the RVE are in the form of prescribed displacements and prescribed electric potentials. For calculation of the piezoelectric coefficients 33 and 15 , the boundary conditions applied to the six surfaces and the postprocessing steps for assessing the piezoelectric coefficients 33 and 15 are listed in Table 2. In Table 2, , v, and are the displacement components along the -, -, and -coordinate axes, respectively, and 0 is the applied electric potential.
The calculated effective piezoelectric coefficients 33 and 15 of LiNbO3 composites using all four kinds of materials are presented as a function of the width of material (P) in Figure 2. The P of the other material ranged from zero to a maximum of 19 µ m. It is shown that the effective piezoelectric coefficients 33 and 15 declined predictably

FEM Simulation of XBAR
FEM simulation of an XBAR with LiNbO3 composite material was also carried out to demonstrate tuning of the 2 . As illustrated in Figure 3a, the XBAR consisted of a suspended 300 nm-thick LiNbO3 composite platelet and a set of 100 nm-thick Mo electrodes on top. The electrical potentials were alternatingly applied to adjacent electrodes, as illustrated by the "+" and "−" signs in Figure 3b, creating a lateral electric field along the X axis. Due to the strong piezoelectric coefficient 15 of LiNbO3, the alternating lateral electric field could excite vertical shear vibration in A1 mode within the platelet [19]. Structural optimization was implemented by adjusting the P of the SiO2 embedded in the thin LiNbO3 film within a range from 0 to 15 µ m, while the thickness of SiO2 (t) remained 150 nm, as shown in Figure 3c.

FEM Simulation of XBAR
FEM simulation of an XBAR with LiNbO 3 composite material was also carried out to demonstrate tuning of the K 2 t . As illustrated in Figure 3a, the XBAR consisted of a suspended 300 nm-thick LiNbO 3 composite platelet and a set of 100 nm-thick Mo electrodes on top. The electrical potentials were alternatingly applied to adjacent electrodes, as illustrated by the "+" and "−" signs in Figure 3b, creating a lateral electric field along the X axis. Due to the strong piezoelectric coefficient e e f f 15 of LiNbO 3 , the alternating lateral electric field could excite vertical shear vibration in A1 mode within the platelet [19]. Structural optimization was implemented by adjusting the P of the SiO 2 embedded in the thin LiNbO 3 film within a range from 0 to 15 µm, while the thickness of SiO 2 (t) remained 150 nm, as shown in Figure 3c.
The series frequency of XBAR with thin LiNbO 3 film (p = 0) is approximately 6.14 GHz and the parallel frequency is 7.25 GHz. As the value of p increased, the parallel frequency of XBAR declined consistently, while the series frequency remained almost the same, as shown in Figure 4. The parallel frequency declined from 7.25 GHz to 6.52 GHz as P increased from 0 to 15 µm. The series frequency of XBAR can be expressed as the following formula [20]: where h is the thickness of the piezoelectric thin film and G is the gap between two adjacent electrodes. In our simulations, the thickness of the piezoelectric thin film and the gap between two adjacent electrodes remained the same; therefore, it is reasonable to assume that the series frequency remained almost constant. The effective electromechanical coupling coefficient (K 2 t ) can be calculated using the following formula [21,22]: ε r ε 0 C 44 (11) Figure 2. Effective piezoelectric coefficients 33 (a) and 15 (b) of four different LiNbO3-based composite materials as function of the width of nonpiezoelectric materials (P).

FEM Simulation of XBAR
FEM simulation of an XBAR with LiNbO3 composite material was also carried out to demonstrate tuning of the 2 . As illustrated in Figure 3a, the XBAR consisted of a suspended 300 nm-thick LiNbO3 composite platelet and a set of 100 nm-thick Mo electrodes on top. The electrical potentials were alternatingly applied to adjacent electrodes, as illustrated by the "+" and "−" signs in Figure 3b, creating a lateral electric field along the X axis. Due to the strong piezoelectric coefficient 15 of LiNbO3, the alternating lateral electric field could excite vertical shear vibration in A1 mode within the platelet [19]. Structural optimization was implemented by adjusting the P of the SiO2 embedded in the thin LiNbO3 film within a range from 0 to 15 µ m, while the thickness of SiO2 (t) remained 150 nm, as shown in Figure 3c. The series frequency of XBAR with thin LiNbO3 film (P = 0) is approximately 6.14 GHz and the parallel frequency is 7.25 GHz. As the value of P increased, the parallel frequency of XBAR declined consistently, while the series frequency remained almost the same, as shown in Figure 4. The parallel frequency declined from 7.25 GHz to 6.52 GHz as P increased from 0 to 15 µ m. The series frequency of XBAR can be expressed as the following formula [20]: where h is the thickness of the piezoelectric thin film and G is the gap between two adjacent electrodes. In our simulations, the thickness of the piezoelectric thin film and the gap between two adjacent electrodes remained the same; therefore, it is reasonable to assume that the series frequency remained almost constant. The effective electromechanical coupling coefficient ( 2 ) can be calculated using the following formula [21,22]:  As shown in Figure 5, when P increased to 1 µ m, 2 decreased sharply from 32% to 20.7%, and 2 then declined slowly with the increase in P from 2 to 11 µ m. When P increased beyond 11 µ m, 2 no longer changed. The variation trend of 2 is highly consistent with the change in the calculated effective piezoelectric coefficient 15 , which demonstrates that introducing other materials to a LiNbO3 piezoelectric matrix is an effective method for tuning the 2 of XBARs. As shown in Figure 5, when P increased to 1 µm, K 2 t decreased sharply from 32% to 20.7%, and K 2 t then declined slowly with the increase in P from 2 to 11 µm. When P increased beyond 11 µm, K 2 t no longer changed. The variation trend of K 2 t is highly consistent with the change in the calculated effective piezoelectric coefficient e e f f 15 , which demonstrates that introducing other materials to a LiNbO 3 piezoelectric matrix is an effective method for tuning the K 2 t of XBARs.
As shown in Figure 5, when P increased to 1 µ m, 2 decreased sharply from 32% to 20.7%, and 2 then declined slowly with the increase in P from 2 to 11 µ m. When P increased beyond 11 µ m, 2 no longer changed. The variation trend of 2 is highly consistent with the change in the calculated effective piezoelectric coefficient 15 , which demonstrates that introducing other materials to a LiNbO3 piezoelectric matrix is an effective method for tuning the 2 of XBARs. Here, we provide a possible fabrication process flow for our devices, as shown in Figure 6. The substrate wafer consists of a thin Z-cut LiNbO 3 film and a Si substrate. Firstly, the thin LiNbO 3 film is etched via electron beam lithography; the depth is controlled by the etching time. A 150 nm-thick layer of SiO 2 is deposited on the surface of the LiNbO 3 film and then polished to a smooth plate. Then, molybdenum (Mo) electrodes are deposited on the surface of the thin SiO 2 /LiNbO 3 film and patterned by lithography and reactive ion etching technology. Subsequently, the release holes are realized via electron beam lithography, which enables formation of the cavity by removing the Si substrate with Xef 2 . By exactly controlling the release time, resonators with only a suspended working area are realized. Here, we provide a possible fabrication process flow for our devices, as shown in Figure 6. The substrate wafer consists of a thin Z-cut LiNbO3 film and a Si substrate. Firstly, the thin LiNbO3 film is etched via electron beam lithography; the depth is controlled by the etching time. A 150 nm-thick layer of SiO2 is deposited on the surface of the LiNbO3 film and then polished to a smooth plate. Then, molybdenum (Mo) electrodes are deposited on the surface of the thin SiO2/LiNbO3 film and patterned by lithography and reactive ion etching technology. Subsequently, the release holes are realized via electron beam lithography, which enables formation of the cavity by removing the Si substrate with Xef2. By exactly controlling the release time, resonators with only a suspended working area are realized.

Design of N79 Filters
As discussed in Section 3, the 2 of XBAR can be adjusted by introducing other materials into the LiNbO3 piezoelectric film, which enables the construction of different bandwidth filters for 5G. For example, the 2 of an XBAR based on pure LiNbO3 film is calculated as being approximately 35% and the −3 dB bandwidth of the corresponding filter is 1050 MHz, as shown in Figure 7a,c, which exceeds the bandwidth requirements of the n79 filter. As seen from Figure 5, the 2 of XBARs decreased to approximately 21% when the P of the SiO2 in the SiO2/LiNbO3 composite film was 1 µ m, which is suitable for the bandwidth requirement of the n79 filter. Therefore, we designed a filter based on thin SiO2/LiNbO3 composite film with a P of 1 µ m. The resonant and anti-resonant frequencies of the series resonator were 4.71 GHz and 5.17 GHz, respectively, and those of the parallel

Design of N79 Filters
As discussed in Section 3, the K 2 t of XBAR can be adjusted by introducing other materials into the LiNbO 3 piezoelectric film, which enables the construction of different bandwidth filters for 5G. For example, the K 2 t of an XBAR based on pure LiNbO 3 film is calculated as being approximately 35% and the −3 dB bandwidth of the corresponding filter is 1050 MHz, as shown in Figure 7a,c, which exceeds the bandwidth requirements of the n79 filter. As seen from Figure 5, the K 2 t of XBARs decreased to approximately 21% when the P of the SiO 2 in the SiO 2 /LiNbO 3 composite film was 1 µm, which is suitable for the bandwidth requirement of the n79 filter. Therefore, we designed a filter based on thin SiO 2 /LiNbO 3 composite film with a P of 1 µm. The resonant and anti-resonant frequencies of the series resonator were 4.71 GHz and 5.17 GHz, respectively, and those of the parallel resonator were 4.35 GHz and 4.7 GHz, respectively, as shown in Figure 7b. As shown in Figure 7d, the transmission response of the filter showed a −3 dB bandwidth of 600 MHz, ranging from 4.4 GHz to 5.0 GHz, which satisfies the requirements of the n79 very well.

Conclusions
In summary, an effective method for tuning the 2 of XBARs, by using composite piezoelectric materials combining LiNbO3 piezoelectric material with other materials, is demonstrated in this work. The effective piezoelectric coefficients 33 and 15 of the four kinds of LiNbO3-based composite materials were calculated through FEM simulation. Among the four different composite materials, the effective piezoelectric coefficients 33 and 15 of the SiO2/LiNbO3 composite material had the largest variation. The 15 of SiO2/LiNbO3 composite material declined from 3.65 to 1.31 as P increased from 0 to 19 µ m. The 33 of SiO2/LiNbO3 composite material declined from 1.72 to 0.19 as P increased from 0 to 19 µ m. Simultaneously, we also carried out the simulation of an XBAR using SiO2/LiNbO3 composite material to verify the change in the 2 , owing to the variation in 15 . The 2 decreased from 34% to approximately 11% as P increased from 0 to 17 µ m, which was highly consistent with the change in 15 . Finally, we designed a filter made with SiO2/LiNbO3 composite material, which satisfied the bandwidth requirement of the

Conclusions
In summary, an effective method for tuning the K 2 t of XBARs, by using composite piezoelectric materials combining LiNbO 3 piezoelectric material with other materials, is demonstrated in this work. The effective piezoelectric coefficients e The e e f f 33 of SiO 2 /LiNbO 3 composite material declined from 1.72 to 0.19 as P increased from 0 to 19 µm. Simultaneously, we also carried out the simulation of an XBAR using SiO 2 /LiNbO 3 composite material to verify the change in the K 2 t , owing to the variation in e e f f 15 . The K 2 t decreased from 34% to approximately 11% as P increased from 0 to 17 µm, which was highly consistent with the change in e e f f 15 . Finally, we designed a filter made with SiO 2 /LiNbO 3 composite material, which satisfied the bandwidth requirement of the n79 very well, demonstrating that XBARs with LiNbO 3 -based composite piezoelectric film show fascinating prospects for fabricating different bandwidth filters at high frequencies in the future.