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

Abstract

By bonding the sub-wavelength-thick lithium niobate (LiNbO₃) layer to high-phase-velocity (v_p) 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 (k_eff²) can be used. In addition, by overlaying a high-velocity layer such as AlN on top of LiNbO₃/Si, the v_p of the SH wave can be significantly enhanced at a small cost of k_eff². 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 (f_s), quality factor (Q), k_eff², 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 f_s of 3 GHz, large k_eff² 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.

1. Introduction

The propagation-loss mechanisms of shear-horizontal (SH)-type waves on LiNbO₃ and LiTaO₃ have been intensively studied recently [1,2,3,4,5,6]. By bonding the sub-wavelength-thick LiNbO₃ or LiTaO₃ layer to a high-velocity substrate, the SH mode no longer couples with the bulk mode in substrate and the leaky component is effectively eliminated [1,2,3,4,5,6]; thus, the SH wave can abandon its traditional name—“leaky-surface acoustic wave (SAW)” but a favorable “nonleaky” feature instead. There are many choices of high-velocity substrates, such as AlN, Si, quartz, diamond, etc. [1,2,3,4,5], and Si is used as an example in this study for its wide availability and cheap price. In addition, given that the acoustic propagation loss no longer dictates the choice of piezoelectric-substrate cut angle and ultra-large effective coupling coefficient (k_eff²), cuts can be taken advantage of, such as low rotation from YX-LiNbO₃ [3,4,5,6,7].

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_eff² 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-LiNbO₃ provides ultralarge intrinsic k_eff² (~30%). After LiNbO₃ bonded to Si, the propagation-loss problem is resolved and high Q is achieved [4]. The multilayered LiNbO₃ SAW devices with ultralarge k_eff² and high Q meet requirements in low frequency (<2.5 GHz)_. However, the v_p is still relatively low (~4000 m/s), limiting its application in LTE high-band (2.5–3.5 GHz, such as band 7, band41, etc.) filters and 5G NR applications. A high-velocity layer beneath the piezoelectric LiNbO₃ or LiTaO₃ does not effectively increase the phase velocity of the SH mode; rather, by adding a high-velocity layer, such as AlN, overlaid on top of the transducer and LiNbO₃, the phase velocity of the SH mode is visibly increased with only minimal trade-off on the k_eff², which can be much larger than needed for majority of the bands. In this way, a desirable nonleaky SH wave resonator with low propagation loss, high frequency (f), and large-k_eff² can be achieved.

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 narrow-band characteristics—f, Q, k_eff², temperature coefficient of frequency (TCF)—but also for eliminating the out-of-band spurious responses.

By using the numerical calculation and finite-element-method (FEM) approaches, propagation characteristics of the SH modes in LiNbO₃/Si and AlN/LiNbO₃/Si are derived with varied substrate designs and the device performance is optimized as well as the presence of spurious modes avoided. Based on the analyses, new stacks with optimized substrate design are obtained, demonstrating the high frequency of 3 GHz at 1 µm interdigital transducer (IDT) pitch, high k_eff² (14.4%) and a spurious free response at 0–6 GHz. After optimizations, these novel AlN/LiNbO₃/Si nonleaky SH devices, featuring superb performance with high frequency ability and being spurious-free, show great potential for filters in next-generation RF front ends.

Symbols used in this paper are listed in

Table 1. Symbols used in this paper.

Symbol	Definition
Q	Quality Factor
keff2	Electromechanical Coupling Coefficient
λ	Acoustic Wavelength
fs	Series-frequency
ux	x-direction displacement
uy	y-direction displacement
uz	z-direction displacement
hLiNbO3	The thickness of LiNbO3
hAlN	The thickness of AlN
S0 mode	The lowest symmetric mode
vp,o	Open phase velocity
TCF	Temperature coefficients of frequency
TCV	Temperature coefficients of velocity

.

2. Substrate Leakage

Figure 1 depicts the FEM-simulated mode shapes of the SH wave propagating in LiNbO₃ substrate, LiNbO₃/Si layered substrate, and AlN/LiNbO₃/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 constants are from [14,15,16,17] and are listed in

Table 2. LiNbO₃, AlN, Si, and Al material constants used in the simulations [14,15,16].

Parameter	Symbol	LiNbO3 [14]	AlN [15]	Si [16]	Al [16]	Units
Stiffness constants	C11E	198.39	345	170	111	(GPa)
	C12E	54.72	125		59
	C13E	65.13	120		59
	C14E	7.88	–		–
	C33E	227.90	395		111
	C44E	59.65	118		26
	C66E	71.84	110		26
Density	ρ	4628	3260	2329	2700	(kg/m3)
Piezoelectric constants	e15	3.69	−0.48	–	–	(C/m2)
	e22	2.42	–	–	–
	e31	0.30	−0.58	–	–
	e33	1.77	1.55	–	–
Dielectric constants	ε11S	45.6	8.0	11.7	1	(10−11 F/m)
	ε33S	26.3	9.5	11.7	1

. 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.

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 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-LiNbO₃, the SH wave in LiNbO₃/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 LiNbO₃ piezoelectric layer and minimizes the leaky component into the Si substrate (Figure 1c).

3. Propagation Characteristics of SH Wave in LiNbO₃/Si

The v_p and k_eff² 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 k_eff² 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]:

$$k_{\mathrm{eff}}^2=\frac{\pi }{2}\frac{f_s}{f_p}{[\tan (\frac{\pi }{2}\frac{f_s}{f_p})]}^{-1}.$$

(1)

Comparing to the intrinsic coupling coefficient (k _intr²) derived from the difference from the open- and metallized-surface v_p:

$$k_{\mathrm{intr}}^2=\frac{v_{p,o}^2-v_{p,m}^2}{v_{p,o}^2}$$

(2)

the device-level k_eff² yields close values to the k_intr² 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_eff² derivation but not k_intr², so the k_eff² evaluation offers better accuracy and potential for the future device optimization. As a result, the device-level coupling coefficient k_eff² is utilized throughout the analysis of this work.

3.1. 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_eff². Figure 2a,b depicts the open-surface phase velocities v_p,o and k_eff² for LiNbO₃/Si across all rotation angles θ from the YX-LiNbO₃ with varied thicknesses of LiNbO₃ for both the SH main mode and the Rayleigh spurious mode.

The impact of the rotation angle on the propagation characteristics of SH mode in LiNbO₃/Si layered substrate is similar to on the LiNbO₃ substrate [20], as depicted in Figure 2a. Fortunately, a low rotation angle from YX-LiNbO₃ enables high v_p,o, large k_eff² for the SH main mode, and low k_eff² 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 h_LiNbO3 = 0.25λ enables higher v_p,o than h_LiNbO3 = 0.5λ of LiNbO₃/Si or LiNbO₃ substrate, and the optimized rotation angle also shifts up a bit for the optimum k_eff². These indicate weak dispersion in the layered substrate due to the sub-wavelength-thick piezo thin film.

3.2. 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 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 h_LiNbO3 < 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 k_eff² is stronger than in v_p,o for the SH mode, as shown in Figure 3b. In other words, the change of k_eff² for SH mode with h_LiNbO3 is more obvious than that of v_p,o. In order to achieve a high k_eff², 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 cut-angle combination smartly. For the S₀ Lamb mode, the case is simpler since its k_eff² will lower at smaller LiNbO₃ thicknesses under different LiNbO₃ cut angle, and the design range of h_LiNbO3 < 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 < h_LiNbO3 < 0.5λ design range, such as 30° YX-LiNbO₃.

3.3. Frequency Response

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 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).

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 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.

In addition, for the LiNbO₃/Si and at this LiNbO₃ cut angle and LiNbO₃ layer thickness designed to lower the Rayleigh k_eff² 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.

4. Propagation Characteristics of SH Wave in AlN/LiNbO₃/Si

4.1. Cut Angle

Figure 5a,b depict the open-surface phase velocities v_p,o for varied normalized thicknesses of AlN overlay layer on top of the IDT transducers sitting on LiNbO₃/Si and the piezo-layer is across all rotation angles from the YX-LiNbO₃ with h_LiNbO3/λ = 0.25 and h_LiNbO3/λ = 0.5, respectively. The c-axis-oriented AlN material constants are from literature [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 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 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_eff² for varied thicknesses of AlN overlay layer on LiNbO₃/Si across all rotation angles from the YX LiNbO₃ with h_LiNbO3/λ = 0.25 and h_LiNbO3/λ = 0.5, respectively. Although the AlN overlay apparently lowers the k_eff², the degraded k_eff² would still be more than enough and much larger than the current technologies. Moreover, the reduction in k_eff² would converge when h_AlN is larger than 0.2λ. For both LiNbO₃ thickness cases, and for cut angles between 0° and 60°, the k_eff² can be as high as above 11%. Comparing two LiNbO₃ thicknesses, the peak k_eff² 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 k_eff² of SH mode is maximized and at the same time the k_eff² 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_eff² for the SH mode, as well as low- k_eff² for Rayleigh mode.

4.2. Trade-Offs between v_p,o and k_eff²

The trade-offs between the v_p,o and k_eff² 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 v_p,o and k_eff² saturate when h_AlN > 0.4λ. For both 15° YX-LiNbO₃ and 30° YX-LiNbO₃, the v_p,o is much higher for the case of h_LiNbO3 = 0.25λ than h_LiNbO3 = 0.5λ, and the k_eff² 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.

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 v_p,o and k_eff² are larger in the case of h_LiNbO3 = 0.25λ compared to h_LiNbO3 = 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 k_eff² than 0.25λ-thick LiNbO₃ 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_eff² 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 v_p,o and similar k_eff².

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_eff² 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 K² of the low-angle-rotated YX-LiNbO₃.

4.3. 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_eff² of the Rayleigh spurious mode versus AlN thicknesses for the AlN/LiNbO₃/Si with different rotation angle and h_LiNbO3/λ = 0.25. While the 30° and 35° rotation angles enable near-zero k_eff² of the Rayleigh mode, when AlN overlay becomes thicker, the preferred rotation angle is smaller for the low k_eff² 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 k_eff² 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 k_eff² 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 suppression of the Rayleigh spurious mode, as well as enabling large v_p and high k_eff² for the main SH main mode simultaneously.

4.4. 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 narrow-band characteristics—f, Q, k_eff², 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

$$TC{F}_{s,1st}=\frac{1}{f_s}\frac{\partial f_s}{T}=\frac{1}{v_{p,SC}}\frac{\partial v_{p,SC}}{T}-{\alpha }_x,$$

(3)

$$TC{F}_{p,1st}=\frac{1}{f_p}\frac{\partial f_p}{T}=\frac{1}{v_{p,OC}}\frac{\partial v_{p,OC}}{T}-{\alpha }_x,$$

(4)

where v_p,SC and v_p,OC refer to the phase velocities under short-circuited (SC) and open-circuited (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 LiNbO₃, AlN, Si, and Al listed in

Table 3. Temperature coefficients of material constants of LiNbO₃, AlN, Si, and Al used in the simulations [15,16,21].

Parameter	Symbol	LiNbO3 [21]	AlN [15]	Si [16]	Al [15]	Units
Temperature coefficients of stiffness constants (1st order)	Tc11	−174	−37	−63	−590	(10–6 1/°C)
	Tc12	−252	−1.8		−80
	Tc13	−159	−1.8		−80
	Tc14	−214	–		–
	Tc33	−153	−65		−590
	Tc44	−204	−50		−520
	Tc66	−143	−57		−520
Temperature coefficients of piezoelectric constants	Te15	147	–	–	–	(10–6 1/°C)
	Te22	79
	Te31	221
	Te33	887
Temperature coefficients of permittivity	Tε11	323	–	–	–	(10–6 1/°C)
	Tε33	627
Thermal-expansion coefficients	α11	15.4	5.27	2.6	18	(10–6 1/°C)
	α33	7.5	4.15	2.6	18

. 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 LiNbO₃ and AlN, the effect of thermal expansion is limited by the clamping substrate Si, and its α₁₁ 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/LiNbO₃/Si with the 0.25λ- thick 15° YX-LiNbO₃ 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 LiNbO₃—~−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 Te₁₅ and Te₂₂ of LiNbO₃; at a high temperature, k_eff² would increase slightly.

4.5. 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_eff² of the SH wave versus different propagation directions on the LiNbO₃ substrate, LiNbO₃/Si (h_LiNbO3/λ = 0.25), and AlN/LiNbO₃/Si (h_LiNbO3/λ = 0.25, h_AlN/λ = 0.2). The slowness curve for the LiNbO₃ substrate shows a concave feature, whereas for the LiNbO₃/Si and AlN/ LiNbO₃/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.

In Figure 11b, the k_eff² decreases drastically when the propagation direction deviates from the X-axis. In propagation directions close to X, the k_eff² is slightly reduced from LiNbO₃ substrate to the LiNbO₃/Si nonleaky stack (agreeing with Figure 2b in the X axis case); in propagation directions close to Z, the k_eff² is very slightly improved from LiNbO₃ substrate to the LiNbO₃/Si bonded structure. After adding the AlN overlay on top of the transducer, the k_eff² reduces drastically due to the mechanical loading effect, and in the X direction the k_eff² 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 k_eff². The wave is also better-guided in the transversal direction compared to the traditional leaky-SH resonator based on LiNbO₃ substrate.

4.6. Frequency Response

Combining the previous analysis toward a high-f, large- k_eff², and spurious-free response utilizing the nonleaky SH wave, a stack with optimized substrate values is achieved: 5° YX-LiNbO₃, 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/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 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/ 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 (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).

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 k_eff² 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.

5. 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 k_eff². 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_eff². 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_eff² of 14.4% and a spurious-free response throughout 0–6 GHz, showing a great potential for 5G/6G RF communication systems.