High-Frequency and Spectrum-Clean Shear-Horizontal Acoustic Wave Resonators with AlN Overlay

By bonding the sub-wavelength-thick lithium niobate (LiNbO3) layer to high-phase-velocity (vp) substrates, such as Si, the shear-horizontal (SH) modes no longer couple with the bulk modes leaking into substrates. As the propagation loss is no longer the major concern for these types of nonleaky SH wave devices, the YX-LiNbO3 with a low rotation angle providing ultra-large coupling coefficient (keff2) can be used. In addition, by overlaying a high-velocity layer such as AlN on top of LiNbO3/Si, the vp of the SH wave can be significantly enhanced at a small cost of keff2. By a careful design of the stack, both the wide-band spurious (Lamb wave) and near-band spurious (Rayleigh wave) are suppressed successfully. This paper focuses on the design of layered substrate not only to optimize its resonance characteristics—series frequency (fs), quality factor (Q), keff2, and temperature coefficient of frequency (TCF)—but also for eliminating the out-of-band spurious responses. The optimized substrate design demonstrates the minimal propagation loss, high fs of 3 GHz, large keff2 of 14.4% and a spurious-free response at 0–6 GHz. These novel nonleaky SH wave devices can potentially enable the low loss and wideband processing functions, which is promising for the 5G/6G radio frequency (RF) communication systems.

Long-Term Evolution (LTE)-Advancement Pro, 5G sub-6 GHz new radio (NR), and emerging 6G standards require low-loss and wide-bandwidth (fractional bandwidth > 5%) filters that push the frequency limits SAW technology using optical lithography up to more than 2.5 GHz range [8][9][10][11][12][13][14]. That shrinking SAW resonators size enables the high frequency, while the quality-factor (Q) significantly deteriorates. With the k eff 2 less than 10% and phase velocity (v p ) less than 4500 m/s, the current commercially popular standard-SAW and Temperature Compensated Surface Acoustic Wave (TCSAW) devices can hardly meet the requirements. Intriguingly, the low-angle-rotated YX-LiNbO 3 provides ultralarge intrinsic k eff 2 (~30%). After LiNbO 3 bonded to Si, the propagation-loss problem is resolved and  Figure 1 depicts the FEM-simulated mode shapes of the SH wave propagating in LiNbO 3 substrate, LiNbO 3 /Si layered substrate, and AlN/LiNbO 3 /Si layered substrate. Perfect-matched-layer (PML) physics is assigned to bottom layers of the 3D unit cell models to simulate the substrate that is too thick, comparing it to wavelengths to generate wave reflections from its bottom. The periodic conditions are applied to both x (perpendicular to IDT fingers) and y (in parallel with IDT fingers) directions so that the basic semi-infinite plane condition is assumed for the wave propagation. The material con-stants are from [14][15][16][17] and are listed in Table 2. In the structures shown, h LiNbO3 /λ = 0.25, h AlN /λ = 0.2 are assumed; 8%λ-thick aluminum (Al) is used as IDT electrodes here and throughout the paper.

Substrate Leakage
Micromachines 2022, 13, x FOR PEER REVIEW 3 of 14 assumed; 8%λ-thick aluminum (Al) is used as IDT electrodes here and throughout the paper.  As shown in Figure 1a, the shear component in YX-LiNbO3 substrate still concentrates at the surface, but strong leakage results from coupling to the slow shear bulk acoustic wave and mechanically propagates down obliquely, as shown in uz and ux. The lowercase coordinate x is the propagation direction proportional to IDT, y is the transversal direction parallel to IDT, and z the direction down into substrate. By bonding the highvelocity Si substrate to the sub-wavelength YX-LiNbO3, the SH wave in LiNbO3/Si ( Figure   Figure 1. Comparison of simulated displacement amplitudes of (a) LiNbO 3 substrate, (b) LiNbO 3 /Si, and (c) AlN/ LiNbO 3 /Si for the SH wave. The insets are the mode shapes at antiresonances simulated with periodic structures using FEM simulation (h LiNbO3 /λ = 0.25, h AlN /λ = 0.2, h IDT,Al /λ = 0.08 are used in the plots). As shown in Figure 1a, the shear component in YX-LiNbO 3 substrate still concentrates at the surface, but strong leakage results from coupling to the slow shear bulk acoustic wave and mechanically propagates down obliquely, as shown in u z and u x . The lower-case coordinate x is the propagation direction proportional to IDT, y is the transversal direction parallel to IDT, and z the direction down into substrate. By bonding the high-velocity Si substrate to the sub-wavelength YX-LiNbO 3 , the SH wave in LiNbO 3 /Si (Figure 1b) no longer couples with the bulk mode and leaks into the substrate since the bulk velocity is higher than the SH mode on surface. After adding an AlN coating layer, the SH mode still concentrates in the LiNbO 3 piezoelectric layer and minimizes the leaky component into the Si substrate (Figure 1c).

Propagation Characteristics of SH Wave in LiNbO 3 /Si
The v p and k eff 2 of the SH waves propagating in the single and layered piezoelectric substrates can be theoretically calculated using numerical analysis-Adler's matrix approach [17] or FEM [18]. The material constants for both the calculation and FEM simulation are also listed in Table 2. The numerically calculated propagation characteristics are checked with FEM simulation and agreed well with the FEM results. In the FEM simulation, the model is a 3D building-block cell with periodic boundary conditions (BCs) on both xand ydirections. All the k eff 2 are derived from series-resonance frequency (f s ) and parallel-resonance frequency (f p ) using the IEEE standard definition of the device electromechanical coupling [19]: Comparing to the intrinsic coupling coefficient (k intr 2 ) derived from the difference from the open-and metallized-surface v p : the device-level k eff 2 yields close values to the k intr 2 and considers the electric field more accurately. The differences of these two definitions of couplings are discussed and compared in detail in Figure 2 of the reference [18] . Despite the similarity for a standard device, the impact of the actual electrode cross-sectional shape and coverage ratio can be considered in the k eff 2 derivation but not k intr 2 , so the k eff 2 evaluation offers better accuracy and potential for the future device optimization. As a result, the device-level coupling coefficient k eff 2 is utilized throughout the analysis of this work.

Cut Angle
As the propagation loss is no longer the main concern and dictates the cut-angle selection for the nonleaky SH wave in bonded wafers, the optimal cut angle can be chosen to optimize v p and k eff 2 . Figure 2a, 1b) no longer couples with the bulk mode and leaks into the substrate since the bulk velocity is higher than the SH mode on surface. After adding an AlN coating layer, the SH mode still concentrates in the LiNbO3 piezoelectric layer and minimizes the leaky component into the Si substrate ( Figure 1c).

Propagation Characteristics of SH Wave in LiNbO3/Si
The vp and keff 2 of the SH waves propagating in the single and layered piezoelectric substrates can be theoretically calculated using numerical analysis-Adler's matrix approach [17] or FEM [18]. The material constants for both the calculation and FEM simulation are also listed in Table 2. The numerically calculated propagation characteristics are checked with FEM simulation and agreed well with the FEM results. In the FEM simulation, the model is a 3D building-block cell with periodic boundary conditions (BCs) on both x-and y-directions. All the keff 2 are derived from series-resonance frequency (fs) and parallel-resonance frequency (fp) using the IEEE standard definition of the device electromechanical coupling [19]: (1) Comparing to the intrinsic coupling coefficient (k intr 2 ) derived from the difference from the open-and metallized-surface vp: the device-level keff 2 yields close values to the kintr 2 and considers the electric field more accurately. The differences of these two definitions of couplings are discussed and compared in detail in Figure 2 of the reference [18]. Despite the similarity for a standard device, the impact of the actual electrode cross-sectional shape and coverage ratio can be considered in the keff 2 derivation but not kintr 2 , so the keff 2 evaluation offers better accuracy and potential for the future device optimization. As a result, the device-level coupling coefficient keff 2 is utilized throughout the analysis of this work.

Cut Angle
As the propagation loss is no longer the main concern and dictates the cut-angle selection for the nonleaky SH wave in bonded wafers, the optimal cut angle can be chosen to optimize vp and keff 2 . Figure 2a  The impact of the rotation angle on the propagation characteristics of SH mode in LiNbO 3 /Si layered substrate is similar to on the LiNbO 3 substrate [20], as depicted in Figure 2a. Fortunately, a low rotation angle from YX-LiNbO 3 enables high v p,o , large k eff 2 for the SH main mode, and low k eff 2 for Rayleigh mode simultaneously. Therefore, the design range of θ is 10-40 • for the LiNbO 3 /Si-based nonleaky SH wave devices for the high frequency, wide band, and clean spectrum, respectively.
In Figure 2b, it can also be noted that h LiNbO3 = 0.25λ enables higher v p,o than h LiNbO3 = 0.5λ of LiNbO 3 /Si or LiNbO 3 substrate, and the optimized rotation angle also shifts up a bit for the optimum k eff 2 . These indicate weak dispersion in the layered substrate due to the sub-wavelength-thick piezo thin film.

Dispersion and Spurious Modes
As shown in Figure 3a,b, the dispersive curves of the v p,o 's and k eff 2 s of the SH main mode, Rayleigh spurious mode, and S 0 Lamb mode spurious mode propagating in the LiNbO 3 /Si bonded structure with varied rotation angle of YX-LiNbO 3 are presented. Due to the sub-wavelength thick piezo-layer structure, the SH mode and Rayleigh mode show weak dispersive characteristics in the phase velocities. The S 0 Lamb wave, however, shows even stronger dispersion due to its plate-wave type whose characteristics are usually impacted a lot by the piezoelectric-layer thickness normalized to wavelength. Although varying LiNbO 3 thickness does not move the Rayleigh spurious mode away from the SH main mode in frequency, engineering the LiNbO 3 thickness does effectively keep the Lamb modes distant in frequency from the SH mode. Luckily, when the h LiNbO3 < 0.5λ, the closest Lamb mode S 0 mode would be 20% higher in frequency than the SH main mode, which makes a distance of at least 500 MHz if the SH passband is at 2.5 GHz.
the SH main mode, and low keff for Rayleigh mode simultaneously. Therefore, the design range of θ is 10-40° for the LiNbO3/Si-based nonleaky SH wave devices for the high frequency, wide band, and clean spectrum, respectively.
In Figure 2b, it can also be noted that hLiNbO3 = 0.25λ enables higher vp,o than hLiNbO3 = 0.5λ of LiNbO3/Si or LiNbO3 substrate, and the optimized rotation angle also shifts up a bit for the optimum keff 2 . These indicate weak dispersion in the layered substrate due to the sub-wavelength-thick piezo thin film.

Dispersion and Spurious Modes
As shown in Figure 3a,b, the dispersive curves of the vp,o's and keff 2′ s of the SH main mode, Rayleigh spurious mode, and S0 Lamb mode spurious mode propagating in the LiNbO3/Si bonded structure with varied rotation angle of YX-LiNbO3 are presented. Due to the sub-wavelength thick piezo-layer structure, the SH mode and Rayleigh mode show weak dispersive characteristics in the phase velocities. The S0 Lamb wave, however, shows even stronger dispersion due to its plate-wave type whose characteristics are usually impacted a lot by the piezoelectric-layer thickness normalized to wavelength. Although varying LiNbO3 thickness does not move the Rayleigh spurious mode away from the SH main mode in frequency, engineering the LiNbO3 thickness does effectively keep the Lamb modes distant in frequency from the SH mode. Luckily, when the hLiNbO3 < 0.5λ, the closest Lamb mode S0 mode would be 20% higher in frequency than the SH main mode, which makes a distance of at least 500 MHz if the SH passband is at 2.5 GHz.
The dispersive characteristics in keff 2 is stronger than in vp,o for the SH mode, as shown in Figure 3b. In other words, the change of keff 2 for SH mode with hLiNbO3 is more obvious than that of vp,o. In order to achieve a high keff 2 , the LiNbO3 cannot be too thin or too thick and the design range is preferred to be > 0.2λ and < 0.5λ. In addition, the Rayleigh and S0 Lamb spurious modes can also be suppressed by choosing the LiNbO3 thickness and cutangle combination smartly. For the S0 Lamb mode, the case is simpler since its keff 2 will lower at smaller LiNbO3 thicknesses under different LiNbO3 cut angle, and the design range of hLiNbO3 < 0.5λ fortunately happens to be able to suppress the S0 Lamb modes. As a contrary, the LiNbO3 thickness and rotation angle have to be optimized together for the Rayleigh mode, and a slightly larger rotation angle is preferred for the 0.2λ < hLiNbO3 < 0.5λ design range, such as 30° YX-LiNbO3. The dispersive characteristics in k eff 2 is stronger than in v p,o for the SH mode, as shown in Figure 3b. In other words, the change of k eff 2 for SH mode with h LiNbO3 is more obvious than that of v p,o. In order to achieve a high k eff 2 , the LiNbO 3 cannot be too thin or too thick and the design range is preferred to be >0.2λ and <0.5λ. In addition, the Rayleigh and S 0 Lamb spurious modes can also be suppressed by choosing the LiNbO 3 thickness and cut-angle combination smartly. For the S 0 Lamb mode, the case is simpler since its k eff 2 will lower at smaller LiNbO 3 thicknesses under different LiNbO 3 cut angle, and the design range of h LiNbO3 < 0.5λ fortunately happens to be able to suppress the S 0 Lamb modes. As a contrary, the LiNbO 3 thickness and rotation angle have to be optimized together for the Rayleigh mode, and a slightly larger rotation angle is preferred for the 0.2λ < h LiNbO3 < 0.5λ design range, such as 30 • YX-LiNbO 3 . Figure 4a,b show the FEM-simulated narrow-band response compared to LiNbO 3 substrate and wide-band response with periodic structure, which is a 1.5-dimension (1.5 D) model based on LiNbO 3 /Si with 30 • YX-LiNbO 3 and h LiNbO3 /λ = 0.25. By the 1.5D model we assume an infinite number of IDT fingers (NF) and infinite aperture lengths, but the stack setup in z direction is fully considered (1D), as well as the IDT duty factor (DF = finger width/pitch) and IDT shape in periodicity (0.5D). Figure 4a,b show the FEM-simulated narrow-band response compared to LiNbO3 substrate and wide-band response with periodic structure, which is a 1.5-dimension (1.5 D) model based on LiNbO3/Si with 30° YX-LiNbO3 and hLiNbO3/λ = 0.25. By the 1.5D model we assume an infinite number of IDT fingers (NF) and infinite aperture lengths, but the stack setup in z direction is fully considered (1D), as well as the IDT duty factor (DF = finger width/pitch) and IDT shape in periodicity (0.5D).

Frequency Response
Comparing the conductance and admittance curves of the SH modes in LiNbO3 substrate and LiNbO3/Si in Figure 4a, it is clearly seen that in LiNbO3 substrate, as the bulk wave velocity is lower than SH wave, the antiresonance is distorted with low-Q, and from the conductance curve it could be observed that the wave cannot be effectively reflected in the stopband as well. On the contrary, for LiNbO3/Si stack, the parallel resonance features a very sharp response and the conductance level is very deep around the fp and throughout the stopband thanks to the minimal bulk radiation, again indicating the ultralow propagation loss and the fact of nonleaky characteristics. In addition, for the LiNbO3/Si and at this LiNbO3 cut angle and LiNbO3 layer thickness designed to lower the Rayleigh keff 2 to near-zero, the narrow-band response ( Figure  4a) is clean from the Rayleigh mode, which presents in the response based on LiNbO3 substrate. On the other hand, since the LiNbO3 is thin enough, the wide-band response of the LiNbO3/Si resonator also shows an extremely clean spectrum from 0 to 6 GHz.  [15] and listed in Table 2. The nonleaky SH wave propagating in the AlN/LiNbO3/Si stack shows a similar trend to that in the LiNbO3/Si layered stack. For both LiNbO3 thickness cases, the phase velocity can be effectively enhanced by the AlN overlay, and the improvement converges when hAlN is larger than 0.2λ. The phase velocities of the SH modes in Figure 5a with hLiNbO3/λ = 0.25 are in general larger than the case in Figure 5b with hLiNbO3/λ = 0.5. As can be observed in Figure 5a, with hLiNbO3/λ = 0.25 and for θ between 20° and 80°, the vp,o can be as high as above 5000 m/s thanks to the AlN coating with hAlN > 0.2λ. Comparing the conductance and admittance curves of the SH modes in LiNbO 3 substrate and LiNbO 3 /Si in Figure 4a, it is clearly seen that in LiNbO 3 substrate, as the bulk wave velocity is lower than SH wave, the antiresonance is distorted with low-Q, and from the conductance curve it could be observed that the wave cannot be effectively reflected in the stopband as well. On the contrary, for LiNbO 3 /Si stack, the parallel resonance features a very sharp response and the conductance level is very deep around the f p and throughout the stopband thanks to the minimal bulk radiation, again indicating the ultra-low propagation loss and the fact of nonleaky characteristics.

Cut Angle
In addition, for the LiNbO 3 /Si and at this LiNbO 3 cut angle and LiNbO 3 layer thickness designed to lower the Rayleigh k eff 2 to near-zero, the narrow-band response ( Figure 4a) is clean from the Rayleigh mode, which presents in the response based on LiNbO 3 substrate. On the other hand, since the LiNbO 3 is thin enough, the wide-band response of the LiNbO 3 /Si resonator also shows an extremely clean spectrum from 0 to 6 GHz.  Table 2. The nonleaky SH wave propagating in the AlN/LiNbO 3 /Si stack shows a similar trend to that in the LiNbO 3 /Si layered stack. For both LiNbO 3 thickness cases, the phase velocity can be effectively enhanced by the AlN overlay, and the improvement converges when h AlN is larger than 0.2λ. The phase velocities of the SH modes in Figure 5a with h LiNbO3 /λ = 0.25 are in general larger than the case in Figure 5b with h LiNbO3 /λ = 0.5. As can be observed in Figure 5a, with h LiNbO3 /λ = 0.25 and for θ between 20 • and 80 • , the v p,o can be as high as above 5000 m/s thanks to the AlN coating with h AlN > 0.2λ. Furthermore, the Rayleigh mode in the case of hLiNbO3/λ = 0.25 are less coupled with the SH mode at a high rotation angle of around 128°, and also less perturbed by θ than the case of hLiNbO3/λ = 0.5. At low θ < 30°; however, the Rayleigh spurious mode is slightly closer to the SH mode in the case of hLiNbO3/λ = 0.25 than in the thicker case, which is in a similar trend with Figure 3a.  Figure 6a and b depict the effective coupling coefficient keff 2 for varied thicknesses of AlN overlay layer on LiNbO3/Si across all rotation angles from the YX LiNbO3 with hLiNbO3/λ = 0.25 and hLiNbO3/λ = 0.5, respectively. Although the AlN overlay apparently lowers the keff 2 , the degraded keff 2 would still be more than enough and much larger than the current technologies. Moreover, the reduction in keff 2 would converge when hAlN is larger than 0.2λ. For both LiNbO3 thickness cases, and for cut angles between 0° and 60°, the keff 2 can be as high as above 11%. Comparing two LiNbO3 thicknesses, the peak keff 2 of the SH mode in AlN/LiNbO3/Si across a wide rotation-angle range are at similar level.

Cut Angle
It is also interesting to note that at θ ~ 10°-30°, the keff 2 of SH mode is maximized and at the same time the keff 2 of Rayleigh mode is minimized, where the Rayleigh spurious mode can be suppressed in the nonleaky SH SAW resonator or filter. With AlN overlays, the optimized cut angle for Rayleigh mode elimination shifts down a bit. The optimal cutangle design range would be of 10°-30° for simultaneously achieving high vp,o and large keff 2 for the SH mode, as well as low-keff 2 for Rayleigh mode.  Furthermore, the Rayleigh mode in the case of h LiNbO3 /λ = 0.25 are less coupled with the SH mode at a high rotation angle of around 128 • , and also less perturbed by θ than the case of h LiNbO3 /λ = 0.5. At low θ < 30 • ; however, the Rayleigh spurious mode is slightly closer to the SH mode in the case of h LiNbO3 /λ = 0.25 than in the thicker case, which is in a similar trend with Figure 3a. Figure 6a and b depict the effective coupling coefficient k eff 2 for varied thicknesses of AlN overlay layer on LiNbO 3 /Si across all rotation angles from the YX LiNbO 3 with h LiNbO3 /λ = 0.25 and h LiNbO3 /λ = 0.5, respectively. Although the AlN overlay apparently lowers the k eff 2 , the degraded k eff 2 would still be more than enough and much larger than the current technologies. Moreover, the reduction in k eff 2 would converge when h AlN is larger than 0.2λ. For both LiNbO 3 thickness cases, and for cut angles between 0 • and 60 • , the k eff 2 can be as high as above 11%. Comparing two LiNbO 3 thicknesses, the peak k eff 2 of the SH mode in AlN/LiNbO 3 /Si across a wide rotation-angle range are at similar level.
Furthermore, the Rayleigh mode in the case of hLiNbO3/λ = 0.25 are less coupled with the SH mode at a high rotation angle of around 128°, and also less perturbed by θ than the case of hLiNbO3/λ = 0.5. At low θ < 30°; however, the Rayleigh spurious mode is slightly closer to the SH mode in the case of hLiNbO3/λ = 0.25 than in the thicker case, which is in a similar trend with Figure 3a.  Figure 6a and b depict the effective coupling coefficient keff 2 for varied thicknesses of AlN overlay layer on LiNbO3/Si across all rotation angles from the YX LiNbO3 with hLiNbO3/λ = 0.25 and hLiNbO3/λ = 0.5, respectively. Although the AlN overlay apparently lowers the keff 2 , the degraded keff 2 would still be more than enough and much larger than the current technologies. Moreover, the reduction in keff 2 would converge when hAlN is larger than 0.2λ. For both LiNbO3 thickness cases, and for cut angles between 0° and 60°, the keff 2 can be as high as above 11%. Comparing two LiNbO3 thicknesses, the peak keff 2 of the SH mode in AlN/LiNbO3/Si across a wide rotation-angle range are at similar level.
It is also interesting to note that at θ ~ 10°-30°, the keff 2 of SH mode is maximized and at the same time the keff 2 of Rayleigh mode is minimized, where the Rayleigh spurious mode can be suppressed in the nonleaky SH SAW resonator or filter. With AlN overlays, the optimized cut angle for Rayleigh mode elimination shifts down a bit. The optimal cutangle design range would be of 10°-30° for simultaneously achieving high vp,o and large keff 2 for the SH mode, as well as low-keff 2 for Rayleigh mode.  It is also interesting to note that at θ~10 • -30 • , the k eff 2 of SH mode is maximized and at the same time the k eff 2 of Rayleigh mode is minimized, where the Rayleigh spurious mode can be suppressed in the nonleaky SH SAW resonator or filter. With AlN overlays, the optimized cut angle for Rayleigh mode elimination shifts down a bit. The optimal cut-angle design range would be of 10 • -30 • for simultaneously achieving high v p,o and large k eff 2 for the SH mode, as well as low-k eff 2 for Rayleigh mode.

Trade-Offs between v p,o and k eff 2
The trade-offs between the v p,o and k eff 2 by varying AlN thickness are compared for the nonleaky SH wave propagating in AlN/LiNbO 3 /Si with two different rotation angles of the piezoelectric LiNbO 3 , as presented in Figure 7a,b. It can be noted that both the v p,o and k eff 2 saturate when h AlN > 0.4λ. For both 15 • YX-LiNbO 3 and 30 • YX-LiNbO 3 , the v p,o is much higher for the case of h LiNbO3 = 0.25λ than h LiNbO3 = 0.5λ, and the k eff 2 is also slightly higher for the thinner case. At θ = 15 • , the saturated v p,o is as high as 5280 m/s when h LiNbO3 = 0.25λ; at θ = 30 • , the saturated v p,o is 5240 m/s when h LiNbO3 = 0.25λ. The preferred AlN thickness design range would be between 0.2λ and 0.4λ right before the convergence in order to avoid additional mass loading on the device coupling.
higher for the thinner case. At θ = 15°, the saturated vp,o is as high as 5280 m/s when hLiNbO3 = 0.25λ; at θ = 30°, the saturated vp,o is 5240 m/s when hLiNbO3 = 0.25λ. The preferred AlN thickness design range would be between 0.2λ and 0.4λ right before the convergence in order to avoid additional mass loading on the device coupling. Figure 8 depicts the displacement field as well as the first principal stress field of the nonleaky SH mode on the AlN/LiNbO3/Si with increasing AlN normalized thicknesses. It is most obvious that the mechanical fields become more penetrated and uniform when AlN becomes thicker. It is also intriguing to note that when the AlN layer is thicker than 0.4λ, the vibration becomes off the surface and concentrated in the highly piezo LiNbO3 layer; the AlN film then starts to be free of the mechanical vibration and transduction, indicating a stable mechanical-loading effect only instead of wave perturbation.
Both the saturated values of vp,o and keff 2 are larger in the case of hLiNbO3 = 0.25λ compared to hLiNbO3 = 0.5λ for either 15° YX-LiNbO3 or 30° YX-LiNbO3. Note at for the 15° YX-LiNbO3 case, 0.5λ-thick LiNbO3 yields larger keff 2 than 0.25λ-thick LiNbO3 when AlN overlay is not applied and hAlN = 0, which can also be observed from Figure 4b. However, even with slight AlN overlay, the keff 2 of 0.25λ-thick LiNbO3 becomes similar or larger. As a result, for both rotation-angle cases, the 0.25λ-thick LiNbO3 enables much higher vp,o and similar keff 2 .   Figure 8 depicts the displacement field as well as the first principal stress field of the nonleaky SH mode on the AlN/LiNbO 3 /Si with increasing AlN normalized thicknesses. It is most obvious that the mechanical fields become more penetrated and uniform when AlN becomes thicker. It is also intriguing to note that when the AlN layer is thicker than 0.4λ, the vibration becomes off the surface and concentrated in the highly piezo LiNbO 3 layer; the AlN film then starts to be free of the mechanical vibration and transduction, indicating a stable mechanical-loading effect only instead of wave perturbation.

Trade-Offs between vp,o and keff 2
The trade-offs between the vp,o and keff 2 by varying AlN thickness are compared for the nonleaky SH wave propagating in AlN/LiNbO3/Si with two different rotation angles of the piezoelectric LiNbO3, as presented in Figure 7a,b. It can be noted that both the vp,o and keff 2 saturate when hAlN > 0.4λ. For both 15° YX-LiNbO3 and 30° YX-LiNbO3, the vp,o is much higher for the case of hLiNbO3 = 0.25λ than hLiNbO3 = 0.5λ, and the keff 2 is also slightly higher for the thinner case. At θ = 15°, the saturated vp,o is as high as 5280 m/s when hLiNbO3 = 0.25λ; at θ = 30°, the saturated vp,o is 5240 m/s when hLiNbO3 = 0.25λ. The preferred AlN thickness design range would be between 0.2λ and 0.4λ right before the convergence in order to avoid additional mass loading on the device coupling. Figure 8 depicts the displacement field as well as the first principal stress field of the nonleaky SH mode on the AlN/LiNbO3/Si with increasing AlN normalized thicknesses. It is most obvious that the mechanical fields become more penetrated and uniform when AlN becomes thicker. It is also intriguing to note that when the AlN layer is thicker than 0.4λ, the vibration becomes off the surface and concentrated in the highly piezo LiNbO3 layer; the AlN film then starts to be free of the mechanical vibration and transduction, indicating a stable mechanical-loading effect only instead of wave perturbation.
Both the saturated values of vp,o and keff 2 are larger in the case of hLiNbO3 = 0.25λ compared to hLiNbO3 = 0.5λ for either 15° YX-LiNbO3 or 30° YX-LiNbO3. Note at for the 15° YX-LiNbO3 case, 0.5λ-thick LiNbO3 yields larger keff 2 than 0.25λ-thick LiNbO3 when AlN overlay is not applied and hAlN = 0, which can also be observed from Figure 4b. However, even with slight AlN overlay, the keff 2 of 0.25λ-thick LiNbO3 becomes similar or larger. As a result, for both rotation-angle cases, the 0.25λ-thick LiNbO3 enables much higher vp,o and similar keff 2 .  the 15 • YX-LiNbO 3 case, 0.5λ-thick LiNbO 3 yields larger k eff 2 than 0.25λ-thick LiNbO 3 when AlN overlay is not applied and h AlN = 0, which can also be observed from Figure 4b. However, even with slight AlN overlay, the k eff 2 of 0.25λ-thick LiNbO 3 becomes similar or larger. As a result, for both rotation-angle cases, the 0.25λ-thick LiNbO 3 enables much higher v p,o and similar k eff 2 . When h LiNbO3 = 0.25λ, the v p,o can be effectively boosted from 4420 m/s to 5280 m/s, showing a near 20% increase when h AlN is up to >0.4λ. Although the k eff 2 is decreased by increasing h AlN , the absolute value is still above 14% even with a large h AlN , which is sufficient for most commercial bandwidths, thanks to the super-large intrinsic material electromechanical coupling K 2 of the low-angle-rotated YX-LiNbO 3 .

Rayleigh Spurious
With the ability of high electromechanical coupling, the Rayleigh mode performs as the major spurious mode for most SH main-mode devices. In addition to the phase velocities of the Rayleigh mode always being very close to the SH mode, the Rayleigh spurious mode could generate prominent passband notches and near-band spikes for the SH wave filters, and pose severe risks for the application of the nonleaky SH waves. Therefore, the suppression of the Rayleigh spurious mode is highly desirable. Figure 9 depicts the simulated k eff 2 of the Rayleigh spurious mode versus AlN thicknesses for the AlN/LiNbO 3 /Si with different rotation angle and h LiNbO3 /λ = 0.25. While the 30 • and 35 • rotation angles enable near-zero k eff 2 of the Rayleigh mode, when AlN overlay becomes thicker, the preferred rotation angle is smaller for the low k eff 2 of the Rayleigh mode. Or, in other words, for different rotation angles of the LiNbO 3 layer, the optimized AlN thicknesses for zero-coupling Rayleigh mode are varied: for relatively lower rotation angle, the optimized AlN thickness would be large to diminish the Rayleigh mode. When hLiNbO3 = 0.25λ, the vp,o can be effectively boosted from 4420 m/s to 5280 m/s, showing a near 20% increase when hAlN is up to > 0.4λ. Although the keff 2 is decreased by increasing hAlN, the absolute value is still above 14% even with a large hAlN, which is sufficient for most commercial bandwidths, thanks to the super-large intrinsic material electromechanical coupling K 2 of the low-angle-rotated YX-LiNbO3.

Rayleigh Spurious
With the ability of high electromechanical coupling, the Rayleigh mode performs as the major spurious mode for most SH main-mode devices. In addition to the phase velocities of the Rayleigh mode always being very close to the SH mode, the Rayleigh spurious mode could generate prominent passband notches and near-band spikes for the SH wave filters, and pose severe risks for the application of the nonleaky SH waves. Therefore, the suppression of the Rayleigh spurious mode is highly desirable. Figure 9 depicts the simulated keff 2 of the Rayleigh spurious mode versus AlN thicknesses for the AlN/LiNbO3/Si with different rotation angle and hLiNbO3/λ = 0.25. While the 30° and 35° rotation angles enable near-zero keff 2 of the Rayleigh mode, when AlN overlay becomes thicker, the preferred rotation angle is smaller for the low keff 2 of the Rayleigh mode. Or, in other words, for different rotation angles of the LiNbO3 layer, the optimized AlN thicknesses for zero-coupling Rayleigh mode are varied: for relatively lower rotation angle, the optimized AlN thickness would be large to diminish the Rayleigh mode. As concluded in the previous section, 0.2λ-0.4λ thick AlN overlay is preferred for enabling the large velocity and keff 2 level at the same time. The optimized cut angle for the near-zero coupling of the Rayleigh spurious mode would be between 10° and 15° YX-LiNbO3, as shown in the yellow and green curves as examples inside the design range marked in Figure 9. Again, from the green and blue curves in Figure 6a, it can be found that 15° YX-LiNbO3 with 0.2λ AlN enables larger keff 2 of the main mode than 10° YX-LiNbO3 with 0.3λ AlN. As a result, 15° YX-LiNbO3 with 0.2λ AlN can be chosen for a high As concluded in the previous section, 0.2λ-0.4λ thick AlN overlay is preferred for enabling the large velocity and k eff 2 level at the same time. The optimized cut angle for the near-zero coupling of the Rayleigh spurious mode would be between 10 • and 15 • YX-LiNbO 3 , as shown in the yellow and green curves as examples inside the design range marked in Figure 9. Again, from the green and blue curves in Figure 6a, it can be found that 15 • YX-LiNbO 3 with 0.2λ AlN enables larger k eff 2 of the main mode than 10 • YX-LiNbO 3 with 0.3λ AlN. As a result, 15 • YX-LiNbO 3 with 0.2λ AlN can be chosen for a high suppression of the Rayleigh spurious mode, as well as enabling large v p and high k eff 2 for the main SH main mode simultaneously.

Improvement of TCF
In addition, without a careful design of the substrate, the layered SH potentially has spurious responses in the out-of-band frequencies (Lamb modes) and near-band frequencies. This paper focuses on the design of layered substrate not only to optimize its narrowband characteristics-f, Q, k eff 2 , temperature coefficient of frequency (TCF)-but also for eliminating the out-of-band spurious responses.
The TCF performance measuring the thermal stability of a resonator is set by the temperature dependence of phase velocity and the thermal-expansion coefficient of the wave along the propagation direction. The first-order TCF's for the series resonance (TCF s,1st ) and parallel resonance (TCF p,1st ) are calculated as where v p,SC and v p,OC refer to the phase velocities under short-circuited (SC) and opencircuited (OC) grating BCs, shown in the inset of FIG 10. From the coupling-of-modes (COM) theory, these BCs corresponds to the f s and f p , respectively. Their temperature dependence ∂/∂T is calculated from the temperature coefficients of stiffness constants, temperature coefficients of piezoelectric constants, and temperature coefficients of permittivity of LiNbO 3 , AlN, Si, and Al listed in Table 3. The α x corresponds to the thermal-expansion coefficient of the substrate in the wave-propagation direction x, also listed in Table 3. Since the Si substrate is much thicker than the LiNbO 3 and AlN, the effect of thermal expansion is limited by the clamping substrate Si, and its α 11 of 2.6 ppm/ • C from literature [19] is used herein for the derivation.  Figure 10 shows the calculated TCF s,1st and TCF p,1st by varying the AlN thickness for the nonleaky SH waves propagating in AlN/LiNbO 3 /Si with the 0.25λ-thick 15 • YX-LiNbO 3 optimized from the previous analysis. Although AlN also becomes softer (contributing to TCV) and larger (contributing to α) when temperature rises, its TCF absolute value is much lower than LiNbO 3~− 26 ppm/ • C. Thus, the thicker AlN can reduce the thermal dependence of the phase velocity for the SH wave traveling in the composite structure. The TCF p,1st is always lower than TCF s,1st due to the positive Te 15 and Te 22 of LiNbO 3 ; at a high temperature, k eff 2 would increase slightly. Figure 10 shows the calculated TCFs,1st and TCFp,1st by varying t the nonleaky SH waves propagating in AlN/LiNbO3/Si with the 0 LiNbO3 optimized from the previous analysis. Although AlN also b tributing to TCV) and larger (contributing to α) when temperature ri value is much lower than LiNbO3-~−26 ppm/°C. Thus, the thicker thermal dependence of the phase velocity for the SH wave traveli structure. The TCFp,1st is always lower than TCFs,1st due to the posi LiNbO3; at a high temperature, keff 2 would increase slightly.

Slowness Curve and Propagation Direction
Although the propagation direction can be lithographically con along the X direction (all the previous analysis assumes the X propag polar plots of propagating characteristics versus propagation directi cators for understanding the wave properties as well as fostering th Figure 11a,b show the slowness (S) curve and the keff 2 of the SH w propagation directions on the LiNbO3 substrate, LiNbO3/Si (hL AlN/LiNbO3/Si (hLiNbO3/λ = 0.25, hAlN/λ = 0.2). The slowness curve for t shows a concave feature, whereas for the LiNbO3/Si and AlN/ LiNbO straight near the x-axis, indicating minimal diffraction of the nonleak for a well-guided wave with convex slowness curves, a faster regio lateral ends to guide the wave, and for the concave case there might the fast regions. For the "straight" type [3], the IDT gap region desig and less sensitive to the concave or convex cases. In addition, from F vp's is largely enhanced in all propagation directions after adding the In Figure 11b, the keff 2 decreases drastically when the propagatio from the X-axis. In propagation directions close to X, the keff 2 is sl

Slowness Curve and Propagation Direction
Although the propagation direction can be lithographically controlled in most cases along the X direction (all the previous analysis assumes the X propagation direction), the polar plots of propagating characteristics versus propagation direction can be good indicators for understanding the wave properties as well as fostering the device design [20]. Figure 11a,b show the slowness (S) curve and the k eff 2 of the SH wave versus different propagation directions on the LiNbO 3 substrate, LiNbO 3 /Si (h LiNbO3 /λ = 0.25), and AlN/LiNbO 3 /Si (h LiNbO3 /λ = 0.25, h AlN /λ = 0.2). The slowness curve for the LiNbO 3 substrate shows a concave feature, whereas for the LiNbO 3 /Si and AlN/ LiNbO 3 /Si stacks it is nearly straight near the x-axis, indicating minimal diffraction of the nonleaky SH wave. Usually, for a well-guided wave with convex slowness curves, a faster region is required at the lateral ends to guide the wave, and for the concave case there might be lateral leakage to the fast regions. For the "straight" type [3], the IDT gap region design would be different and less sensitive to the concave or convex cases. In addition, from Figure 11a, the phase v p 's is largely enhanced in all propagation directions after adding the AlN overlay. direction the keff 2 falls to between 10% and 15%, which is still more than enough for the advanced LTE bandwidth specification and most of the 5G NR bands. In summary, the optimized propagation direction for the AlN/LiNbO3/Si resonator is the material X direction of LiNbO3 thanks for the fast wave-travelling velocity and the ultralarge keff 2 . The wave is also better-guided in the transversal direction compared to the traditional leaky-SH resonator based on LiNbO3 substrate.

Frequency Response
Combining the previous analysis toward a high-f, large-keff 2 , and spurious-free response utilizing the nonleaky SH wave, a stack with optimized substrate values is achieved: 5° YX-LiNbO3, hLiNbO3/λ = 0.25, and hAlN/λ = 0.2. Figure 12a,b plot the FEM-simulated narrow-band responses of the SH wave in the AlN/LiNbO3/Si layered stack compared to LiNbO3/Si and LiNbO3 substrate, as well as wide-band response with periodic structure (1.5D model). Intriguingly, the AlN/LiNbO3/Si layered structure enables frequency as high as 3 GHz while the IDT pitch is as large as 1 µm, ensuing good power handling. The f can further scale up if smaller λ is employed. The frequency or vp has been increased by 18%, breaking the frequency limits for SAW resonators and filters and applicable to high-frequency bands in LTE-Advancement Pro and 5G NR.
Comparing admittance curves of the SH modes in AlN/ LiNbO3/Si, LiNbO3/Si, and LiNbO3 substrate in Figure 12a, it can be noted that the antiresonances for both AlN/LiNbO3/Si and LiNbO3/Si are very sharp, indicating a very high-quality factor at parallel-resonance (Qp) due to the elimination of bulk leakage (quality factor at series resonance (Qs) is usually dominated by the transducer resistance Rs and Qp dominated by the acoustic propagation loss).
In addition, the AlN/ LiNbO3/Si layered substrate with the optimized parameters shows an extremely clean response in both narrow and wide spectrums. The Rayleigh mode and Lamb modes are suppressed with keff 2 of near-zero. By the analysis and careful design, the novel stack provides high performance, the ability of high frequency, and an extremely clean spectrum from 0 to 6 GHz simultaneously. In Figure 11b, the k eff 2 decreases drastically when the propagation direction deviates from the X-axis. In propagation directions close to X, the k eff 2 is slightly reduced from LiNbO 3 substrate to the LiNbO 3 /Si nonleaky stack (agreeing with Figure 2b in the X axis case); in propagation directions close to Z, the k eff 2 is very slightly improved from LiNbO 3 substrate to the LiNbO 3 /Si bonded structure. After adding the AlN overlay on top of the transducer, the k eff 2 reduces drastically due to the mechanical loading effect, and in the X direction the k eff 2 falls to between 10% and 15%, which is still more than enough for the advanced LTE bandwidth specification and most of the 5G NR bands.
In summary, the optimized propagation direction for the AlN/LiNbO 3 /Si resonator is the material X direction of LiNbO 3 thanks for the fast wave-travelling velocity and the ultralarge k eff 2 . The wave is also better-guided in the transversal direction compared to the traditional leaky-SH resonator based on LiNbO 3 substrate.

Frequency Response
Combining the previous analysis toward a high-f, large-k eff 2 , and spurious-free response utilizing the nonleaky SH wave, a stack with optimized substrate values is achieved: 5 • YX-LiNbO 3 , h LiNbO3 /λ = 0.25, and h AlN /λ = 0.2. Figure 12a,b plot the FEM-simulated narrow-band responses of the SH wave in the AlN/LiNbO 3 /Si layered stack compared to LiNbO 3 /Si and LiNbO 3 substrate, as well as wide-band response with periodic structure (1.5D model). Intriguingly, the AlN/LiNbO 3 /Si layered structure enables frequency as high as 3 GHz while the IDT pitch is as large as 1 µm, ensuing good power handling. The f can further scale up if smaller λ is employed. The frequency or v p has been increased by 18%, breaking the frequency limits for SAW resonators and filters and applicable to high-frequency bands in LTE-Advancement Pro and 5G NR.
Comparing admittance curves of the SH modes in AlN/ LiNbO 3 /Si, LiNbO 3 /Si, and LiNbO 3 substrate in Figure 12a, it can be noted that the antiresonances for both AlN/LiNbO 3 /Si and LiNbO 3 /Si are very sharp, indicating a very high-quality factor at parallel-resonance (Q p ) due to the elimination of bulk leakage (quality factor at series resonance (Q s ) is usually dominated by the transducer resistance R s and Q p dominated by the acoustic propagation loss).

Conclusions
In this study, high-frequency nonleaky SH SAW resonators on AlN/LiNbO3/Si are demonstrated with thermal stability, large coupling and spurious-free. The high-velocity Si substrate was used to reduce the propagation leakage into substrate, and 15-30° rotation angles from YX-LiNbO3 were selected to provide the ultralarge keff 2 . A careful tradeoff analysis is provided on the AlN coating thickness between the enhanced vp (f for given transducer) and the cost of extra keff 2 . Furthermore, the out-of-band and near-band spurious modes in the layered SAW structures were analyzed by using FEM simulations and the requirements for the substrate were derived to avoid the presence of spurious modes. Based on this analysis, a new nonleaky SH resonators with optimized substrate design are obtained, demonstrating the ability with a high frequency of 3 GHz at 1 µm IDT pitch, a high keff 2 of 14.4% and a spurious-free response throughout 0-6 GHz, showing a great potential for 5G/6G RF communication systems.
Funding: This research was supported in part by the Natural Science Foundation of Shanghai under Grant No. 21YF1402500.

Data Availability Statement:
The data that support the finding of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest:
The authors declare no conflicts of interest. In addition, the AlN/ LiNbO 3 /Si layered substrate with the optimized parameters shows an extremely clean response in both narrow and wide spectrums. The Rayleigh mode and Lamb modes are suppressed with k eff 2 of near-zero. By the analysis and careful design, the novel stack provides high performance, the ability of high frequency, and an extremely clean spectrum from 0 to 6 GHz simultaneously.

Conclusions
In this study, high-frequency nonleaky SH SAW resonators on AlN/LiNbO 3 /Si are demonstrated with thermal stability, large coupling and spurious-free. The high-velocity Si substrate was used to reduce the propagation leakage into substrate, and 15-30 • rotation angles from YX-LiNbO 3 were selected to provide the ultralarge k eff 2 . A careful trade-off analysis is provided on the AlN coating thickness between the enhanced v p (f for given transducer) and the cost of extra k eff 2 . Furthermore, the out-of-band and near-band spurious modes in the layered SAW structures were analyzed by using FEM simulations and the requirements for the substrate were derived to avoid the presence of spurious modes. Based on this analysis, a new nonleaky SH resonators with optimized substrate design are obtained, demonstrating the ability with a high frequency of 3 GHz at 1 µm IDT pitch, a high k eff 2 of 14.4% and a spurious-free response throughout 0-6 GHz, showing a great potential for 5G/6G RF communication systems.