Sub-6 GHz acoustic filters using laterally-excited bulk acoustic resonator with scattering vias in double-layer electrodes

Abstract

The suppression of in-band ripple and enhancement of power-handling capability (PHC) represent critical research imperatives for next-generation super-high-frequency (SHF) wideband filters. This study presents a laterally-excited bulk acoustic resonator with scattering vias in double-layer electrodes (SV-BAR) and its filter for sub-6G SHF wideband applications, to simultaneously suppress spurious modes by curved scattering boundaries and enhance PHC by gold-filled double-layer electrodes. Fabricated on a 358 nm Z-cut LiNbO₃-on-insulator (LNOI) substrate using a four-mask ion beam etching process, the SV-BAR achieves a K_t² of 24.1%, a Bode_Q_max of 366 at 5.946 GHz, as well as a remarkable product of merit (PoM, f·Bode_Q_max·K_t²) of 5.24 × 10¹¹Hz. In addition, the compact 2.5-order mirror ladder filter (1.949 mm² footprint) exhibits a center frequency of 5.8585 GHz, a 9.71% fractional bandwidth (569 MHz), 23.97 dB out-of-band rejection, and a temperature coefficient of frequency (TCF) of -64.04 ppm/°C. Notably, it demonstrates exceptional PHC of +30.88 dBm at 6.162 GHz (1-dB compression point), attributed to its mechanical stability, low ohmic loss, and thermal stability (3-dB lower cutoff TCF_l = -84.11 ppm/°C vs. upper cutoff TCF_h = -45.83 ppm/°C). This breakthrough enables ultra-wideband, miniaturized filters in next-generation wireless systems.

Introduction

As the demand for advanced services continues to grow and the number of connected devices increases, wireless communication systems need to scale to meet the quality of service, throughput, latency, connectivity, and security¹. Researchers have started exploring sub-6 GHz and even higher ranges to provide broader bandwidth and increased transmission rates. Wi-Fi 6 or IEEE 802.11ax, the major communication technology for wireless networks (WLANs), features a high operating frequency and a large bandwidth. The 5 GHz band (5.17-5.835 GHz) utilized by Wi-Fi 6 represents one of the most commercially valuable communication spectrums, making it a prime research focus in wireless technology development².

Acoustic wave filters currently dominate the RF front-end market for mobile devices, primarily owing to their superior miniaturization capabilities. Surface acoustic wave (SAW) and bulk acoustic wave (BAW) resonators are the two mainstream options in the current market. The operating frequency of the SAW resonator depends mainly on the electrode pitch (P) of the interdigital transducer (IDT). Higher frequency necessitates narrower electrodes, increasing photolithography costs. Additionally, narrow electrodes induce substantial ohmic losses, significantly limiting power handling capability and mechanical quality factor (Q). By utilizing the heterogeneous piezoelectric substrate and high-velocity longitudinal leaky SAW (LL-SAW) mode, the operating frequency of SAW can be extended to over 6 GHz^3,4. However, the constraints of incorporating small Q, moderate electromechanical coupling coefficient (K_t²), and spurious modes still need to be addressed^5–7. The coupled shear mode SAW (CS-SAW) resonator has been demonstrated to achieve a high frequency over 10 GHz with a large K_t² of 34% and a narrow critical dimension of less than 500 nm^8,9. These structures rely on the e-beam lithography (EBL), but the EBL process remains impractical for mass production. On the other hand, bulk acoustic wave (BAW) devices are typically fabricated based on Aluminum Nitride (AlN), where the operating frequency is determined by the thickness of the piezoelectric layer. While the frequency can be extended beyond 9 GHz simply by reducing this thickness, performance is often limited by the low K_t² of sub-7%¹⁰. The Scandium-doped aluminum nitride (ScAlN) can effectively enhance the K_t² of BAW resonators¹¹. The K_t² progressively increases with higher Sc concentrations (peaking at 43%)^12,13. Nevertheless, higher Sc doping levels simultaneously degrade the Q-factor of resonators.

Recently, the laterally-excited bulk acoustic resonator (XBAR) has become an important direction of research due to its high acoustic velocity, large piezoelectric coefficient (e₁₅ = 4.47 C/m²), and high-quality film, enabling high frequency over 15 GHz¹⁴, large K_t² of 57%¹⁵, and high Q over 1211¹⁶. Since 2008, Kadota et al. have proposed an A₁ resonator based on Z-cut Lithium Niobate (LiNbO₃ or LN) thin film deposited by chemical vapor deposition system (CVD) for the first time with a high velocity of 14,000 m/s¹⁷. In 2019, Plessky et al. developed a high-performance A₁ resonator using Smart-cut LN thin films, achieving a K_t² of ~25% and operating at 4.8 GHz. This breakthrough device was officially designated as XBAR¹⁸.

Although its potential to enable broadband and low-loss filters, XBARs demonstrated so far suffer from lateral spurious modes and low power-handling capability (PHC), which seriously degrade the performance of filters^15,19–22. Researchers have made various efforts to suppress the spurious modes. Liu and Tong et al. adopt the piston mode electrodes to suppress the lateral spurious modes^23,24. Through analysis of the BAW slowness surface, Naumenko demonstrated that the spurious modes are suppressed effectively by optimizing the electrode thickness, duty factor (DF), and LN film thickness^25,26. Yang et al. present an A₁ resonator with embedded electrodes that exploits dispersion matching to suppress the spurious modes²⁷. These methods either exhibit limited effectiveness in suppressing spurious modes or present significant challenges in manufacturing processes. Additionally, there is little research on improving the PHC of XBAR. In our prior work, a double-layer-electrode XBAR with scattering vias (SV-BAR) is proposed to enhance PHC and suppress spurious modes. This design achieved a PHC exceeding +35 dBm while effectively eliminating spurious mode interference²⁸.

In this work, the SV-BAR and its filter are designed and fabricated around 6 GHz, of which S-parameters, temperature coefficient of frequency (TCF), and PHC are evaluated. Compared to the traditional XBAR, the SV-BAR exhibits good electrical, thermal, and mechanical properties, which are demonstrated by the simulation of COMSOL finite element analysis (FEA). The different metallic fill materials (Al, Ti, Cu, W, Au, and Cr) in Mo electrodes on SV-BAR is investigated, with results indicating that Au provides the optimal solution. Then, a 2.5-order mirror Ladder topology filter is designed for Wi-Fi 6 through resonator size studies targeting C₀ and operating frequency. The fabricated SV-BAR features a high performance with a large K_t² of 24.1%, Bode_Q_max of 366 at 5.946 GHz, as well as a large product of merit (PoM, f·Bode_Q_max·K_t²) of 5.24 × 10¹¹Hz. The SV-BAR filter is fabricated using an ion beam etching (IBE) thinning process to tune frequency, which exhibits a center frequency (f₀) of 5.8585 GHz, a 3-dB bandwidth (BW) of 569 MHz (fractional bandwidth, FBW = 9.71%), an out-of-band (OoB) rejection of 23.97 dB, and a small footprint of 1.949 mm². The measured PHC is +30.88 dBm at 6.162 GHz by extracting the 1-dB compression point (P_1dB). Compared to the 3-dB higher cutoff frequency (f_h, TCF_h = -45.83 ppm/°C), the 3-dB lower cutoff frequency (f_l, TCF_l = -84.11 ppm/°C) demonstrates higher temperature sensitivity, which contributes to high PHC. The proposed SV-BAR filter shows significant potential for 6 G wideband applications.

Analysis and design

Resonator analysis

The SV-BAR consists of Mo IDTs with scattering vias and 358 nm Z-cut LN thin films, where the Au is deposited on the Mo electrodes to reduce the ohmic loss and enhance the mechanical reliability and thermal conductivity of thin films, as shown in Fig. 1a. In Fig. 1b, the Au electrode is recessed by 1 μm relative to the Mo electrode (W_A = 4 μm, W_M = 6 μm) to mitigate the effect of lithography overlay error. In Fig. 1c, the high velocity thickness shear vibration of A₁ mode is excited by IDTs under the inverse piezoelectric effect of LN thin films. And the lateral high-order of A₁ mode (A_1-X) is generated within the IDTs due to the acoustic impedance mismatch at the interface between the IDT and the gap region. Here, the thicknesses of Mo (T_M), Au (T_A), and scattering vias (T_V) are 300 nm, 500 nm, and 300 nm. Spurious modes propagating within IDTs are suppressed by integrating 3 μm-diameter (D) scattering vias along their propagation direction. These vias employ curved scattering boundaries to disrupt and dissipate the unwanted wave energy, eliminating the spurious modes²⁰. As shown in Fig. 1d–f, the performance of SV-BAR in the ohmic loss bulk density, steady-state temperature, thermal stress, thermal deformation, and other aspects is significantly better than that of traditional XBAR, leading to a higher PHC²⁸.

Fig. 1. Structure and performance comparison of the SV-BAR device.

a Main view, b top view, and c cross-section view of the SV-BAR structure. Comparison of simulated performance between the SV-BAR and a traditional XBAR design: d ohmic loss bulk density distribution, e steady-state temperature profile, and f thermal stress and deformation

For SV-BAR, the key is that the acoustic impedance (Z) of the material in scattering vias needs to differ from the Mo IDTs to form an acoustic scattering-curved interface. Table 1 lists the parameters of typically used metals (Al, Ti, Cu, W, Au, and Cr) for SV-BARs, which are ordered by acoustic reflection coefficient (R) between metal-filled materials and Mo. The Z and R are derived using the equation as follows²⁹:

$$Z=\sqrt{\rho E}$$ 1

$$R=\frac{Z_2-Z_1}{Z_2+Z_1}$$ 2

Where the ρ and E are the density and Young’s modulus, respectively. The Z₁ is the acoustic impedance of first medium, and the Z₂ is the acoustic impedance of second medium.

Table 1.

Material parameters of typically used metals

Metal	Density [kg/m3]	Young’s modulus 1e9 [N/m2]	Acoustic impedance 1e7 [Pa·s/m]	Reflection coefficient	Thermal expansion coefficient 1e−6 [1/K]	Thermal conductivity [W/(m·K)]	Electrical conductivity 1e6 [S/m]
Mo	10,200	312	5.64	0.00	4.8	138	17.6
Al	2700	70	1.38	0.61	23.1	237	35.5
Ti	4506	115.7	2.28	0.42	8.6	21.9	2.6
Cu	8960	120	3.28	0.26	16.5	401	58.1
W	19,350	411	8.92	0.23	4.5	174	20
Au	19,300	70	3.68	0.21	14.2	317	45.6
Cr	7150	279	4.47	0.12	4.90	93.7	7.9

As illustrated in Fig. 2a, the acoustic energy at the electrode is primarily confined to the low acoustic velocity regions covered by Al due to the strong mass-loading effect of Al. The scattered energy is strongly confined within the vias and inter-via gaps due to strong interfacial reflection (Mo/Al, R = 0.61) and parallel boundary reflections at the IDT edges. This confinement induces intense resonant coupling of scattered acoustic waves in these regions, thereby exciting spurious modes. In contrast, the configuration with weaker interfacial reflection (Mo/Au, R = 0.21) exhibits limited energy confinement, significantly suppressing via-resonance, and yielding a cleaner spectrum, as shown in Fig. 2b. However, excessively low R (Mo/Cr, R = 0.12) degrades acoustic scattering efficiency, while the energy easily leaks from vias into gaps that enhance gap-localized spurious modes. At the extreme case of zero reflection coefficient (Mo/Mo, R = 0), the lateral spurious modes in the electrode region are further enhanced due to the severely weakened wave scattering effect. Consequently, excessively high or low R both lead to increased spurious modes, which is confirmed by the simulated admittance characteristics of SV-BAR with metal-filled materials listed in Table 1, as shown in Fig. 2c–i. Additionally, among the typically used metals listed in Table 1, Au exhibits superior integrated performance. It demonstrates a high electrical conductivity of 45.6 × 10⁶S/m and a high thermal conductivity of 317 W/(m·K), second only to Cu. Furthermore, its thermal expansion coefficient shows closer compatibility with Mo than Al and Cu, effectively mitigating thermal stress generation in electrodes under high-temperature. Therefore, Au is selected as the filling metal for the scattering vias in the IDT to suppress spurious modes and improve PHC.

Fig. 2. Displacement and admittance characteristics of the SV-BAR with different electrode materials.

Displacement profiles of the SV-BAR with a Mo/Al and b Mo/Au double-layer electrodes. Simulated admittance curves of the device with various metal-filled materials: c Al, d Ti, e Cu, f W, g Au, h Cr, and i Mo

In addition to the metal-filled materials, the DF is also a critical parameter for SV-BAR to suppress spurious modes and improve the PHC. Considering the complexity of fabrication process, XBARs with different DF are fabricated and tested to investigate the impact of DF on the PHC. In Fig. 3a, the PHC of XBAR increases initially with the DF, then decreases, reaching a peak around DF = 0.7. The increase of PHC with DF is attributed to the following mechanisms in Fig. 3b: reduced ohmic losses in the electrodes lead to diminished Joule heating, thereby lowering the operational temperature of the resonator. This temperature reduction mitigates thermal stress and deformation, and the high-DF electrodes enhance the mechanical reliability of the thin film. However, the excessively narrow gap between IDTs significantly intensifies the electric field in the inter-electrode region. Combined with the piezoelectric coupling effect, this enhanced field exacerbates mechanical vibrations and deformations, ultimately causing fracture of the LN thin film at the electrode root (a region prone to stress concentration). Consequently, when DF exceeds a critical threshold (~0.7), the PHC decreases with further increases in DF.

Fig. 3. Impact of duty factor on device performance.

a Measured power handling capability of XBARs under different duty factors. b Quantitative analysis of the effects of duty factor on ohmic loss, temperature variation, thermal deformation, and mechanical stress. c Influence of duty factor on aspect ratio and static capacitance of the SV-BAR. Simulated admittance characteristics and stress distributions of the SV-BAR with varying duty factors: d 0.4, e 0.5, f 0.6, g 0.7, h 0.8, and i 0.9

Although DF = 0.7 maximizes the PHC, the DF is set as 0.5 to achieve an optimal trade-off among spurious modes, PHC, C₀, and admittance ratio (AR). As shown in Fig. 3c, the AR of SV-BARs decreases with increasing DF because the intensified spurious modes disperse energy from the primary resonant mode. In contrast, the C₀ increases with increasing DF because the narrower gap directly elevates C₀³⁰. To further analyze the influence of DF on spurious modes and stress, the admittance characteristics and stress distributions of the resonator under different DF are simulated in Fig. 3d–i. The spurious modes increase with increasing DF because of the enhanced mechanical loading of the electrodes and the vertical component of the electric field. Meanwhile, significant stress concentration is observed in the root areas on both electrode sides. The stress gradually increases with rising DF because the decreased electrode gap width enhances the electric field intensity between IDTs, amplifying stress through the inverse piezoelectric effect.

Proper C₀ for series and parallel resonators are essential for filter design to optimize 50 Ω impedance matching, minimize insertion loss (IL), and suppress in-band ripple. Adjusting C₀ balances the impedance of the resonator, reducing reflections and ensuring efficient signal transfer across the passband. As shown in Fig. 4a–e, the C₀ of the resonator increases linearly with T_LN, aperture (AP), and the number of electrodes (N). It gradually decreases with increasing P and increases with a higher DF. These can be interpreted by:

$$C_0=(N-1)\cdot C_P=(N-1)\cdot \frac{{\epsilon }_r{\epsilon }_0{T}_{LN}AP}{P(1-DF)}$$ 3

where the C_P is the static capacitance of a pair of electrodes, ε_r is the relative dielectric constant of the piezoelectric material, and ε₀ is the permittivity of vacuum of the piezoelectric material.

Fig. 4. Relationship between C₀ and structural parameters in the resonator.

a T_LN, b P, c AP, d DF, and e N. f Dispersion curve of the A₁ mode in SV-BAR with a P of 12 μm

For the SV-BAR filter design, the resonant frequency (f_s) of the series resonator should approximate the anti-resonant frequency (f_p) of the parallel resonator to achieve a smooth passband at the center frequency³¹. The f_s of the resonator is influenced by both lateral (x-axis) and vertical (z-axis) modes:

$$T_{LN}=\frac{m}{2}{\lambda }_z,P=\frac{n}{2}{\lambda }_x$$ 4

Then, the formula for the f_s of the A₁ resonator is given by³²:

$$f_s^{mn}=\sqrt{{\left(\frac{m{v}_z}{2T_{LN}}\right)}^2+{\left(\frac{n{v}_x}{2P}\right)}^2}\approx \frac{m{v}_z}{2T_{LN}}$$ 5

where T_LN is the thickness of LN thin films, while W denotes the width of the main resonant region along the acoustic wave propagation direction (x-axis). The m and n represent the mode orders in the z-axis and x-axis directions, respectively (m = 1 and n = 1 for the A₁ mode). λ_z and λ_x correspond to the wavelengths in the z-axis and x-axis directions, while v_z and v_x indicate the modal acoustic velocities along their respective axes.

By adjusting the LN thin-film thickness, the required frequency offset is precisely controlled as shown in Fig. 4f. Notably, the frequency varies nonlinearly with T_LN due to the dispersion characteristics of the A₁ mode.

Based on the above analysis, the key design parameters for series and parallel resonators targeting the Wi-Fi 6 filter are summarized in Table 2. The T_LN for series and parallel resonators is set to 323 nm and 358 nm to achieve a frequency offset of 560 MHz. The P of the resonator is set to 12 μm to suppress spurious modes. The apertures of both series and parallel resonators are configured as 120 μm to achieve a sufficiently large C₀ while facilitating the opening of back cavity holes during deep silicon etching. The N for the series and parallel resonators is designed as 48 and 70, respectively, to reduce oscillation energy radiation loss.

Table 2.

Design parameters of the series and parallel resonators

Parameter	TLN (nm)	P (μm)	AP (μm)	DF	N	C0 (pF)
Series resonator	323	12	120	0.5	48	0.251
Parallel resonator	358	12	120	0.5	70	0.402

Filter design

With the optimized SV-BAR, a mirrored ladder topology consisting of 4 basic half-sections symmetrically connected is used for the filter design to reduce inter-stage reflection and IL, as shown in Fig. 5a. The dual series resonators (S2 and S3) are equivalently substituted by a single series resonator (S0), implemented to reduce component count and minimize the footprint of the filter while maintaining overall device performance. The product and ratio of C₀ of parallel and series resonators (C_0p·C_0s and C_0p/C_0s) are important parameters for filter design. The C_0p·C_0s relates to the impedance matching condition between the input and output ports, which must satisfy the Eq. (6)³³.

$$C_{0\mathrm{p}}\cdot C_{0\mathrm{s}}\approx 1/{\left(2\pi f_0{R}_0\right)}^2$$ 6

where the f₀ is the center frequency of the filter, and R₀ is the characteristic impedance of the source and load.

Fig. 5. Design methodology and parameter optimization of the mirrored ladder filter.

a Mirrored ladder topology for filter design. b, c Comparison of insertion loss curves with different C_0p/C_0s ratios. d Design map for determining C_0p and C_0s at a f₀ of 5.5025 GHz

Here, the f₀ and R₀ are 5.5025 GHz and 50 Ω, respectively. Thereby, the calculated C_0p·C_0s yields 0.33. Besides, the C_0p/ C_0s can be adjusted to govern IL and OoB rejection, which are traded off against each other. In Fig. 5b, c, due to the trade-off relation, as the C_0p/C_0s increases from 1.2 to 2, the OoB rejection of the filter is significantly improved, while both in-band IL and ripple progressively increase. At C_0p/C_0s = 2, the in-band IL exceeds 3 dB with a ripple of 2.193 dB. Consequently, the C_0p/C_0s is set to 1.6 to balance IL and OoB rejection. In Fig. 5d, the intersection points between the C_0p·C_0s curve and the C_0p/C_0s straight line provide the optimized C₀ of series-parallel resonators in filters. Nevertheless, an excessive C₀ requires more resonator pairs and a larger aperture, leading to thin film rupture during the resonator release and an oversized filter. Therefore, the implemented series and parallel capacitances are designed as 0.251 pF and 0.402 pF in Table 2 to prevent excessive footprint, both being smaller than the optimal values.

Device fabrication

The detailed fabrication process for SV-BAR filters is demonstrated in Fig. 6a. The SV-BAR filter is fabricated using a 358 nm Z-cut LiNbO₃ on an insulator (LNOI) substrate, and the LN thin films are etched 35 nm by ion beam etching (IBE) with an etch rate of 15.7 nm/min³⁴ to achieve thinning-induced frequency tuning. 300-nm-thick Mo is deposited as IDTs on the top of the wafer. Then, a 500-nm-thick Au layer is defined on Mo electrodes by a lift-off process to fill the scattering vias and form pads. A SiO₂ layer is deposited on both the wafer frontside and backside. The frontside SiO₂ serves as a surface protection layer, while the backside SiO₂ functions as a hard mask for backside cavity etching via the Bosch process. Finally, the device is released by buffered oxide etch (BOE)-based wet etching. All photolithography processes in this work are completed using a SUSS MicroTec MA8. In Fig. 6b, the fabricated SV-BAR filter demonstrates excellent surface topography and achieves a footprint of 1.949 mm² (1.692 mm × 1.152 mm).

Fig. 6. Fabrication process and SEM characterization of the SV-BAR filter.

a Schematic illustration of the fabrication process: (Ⅰ) LNOI substrate preparation; (Ⅱ) formation of thinning-induced frequency tuning by ion beam etching of the LN thin film; (Ⅲ) Mo electrode patterning; (Ⅳ) pad patterning and scattering via filling by lift-off of the Au layer; (Ⅴ) SiO₂ layer deposition and back cavity etching by Bosch process; and (Ⅵ) SiO₂ layer removal b SEM images of the fabricated SV-BAR filter

Results and discussion

The resonators and the filter are measured by a vector network analyzer (VNA, operated with 0-dBm nominal power at 50 Ω) in the air at room temperature. Before device testing, a standard SOLT (short-open-load-through) calibration is performed on the RF test path, ensuring post-calibration S21 parameter variation within ±0.005 dB in the through state. The measured admittance curves of series and parallel resonators are fitted by the modified Butterworth Van-Dyke (MBVD), as shown in Fig. 7a. Both series and parallel resonators exhibit clean spectra, validating the simulation design. The parallel resonator resonates at 5.189 GHz with a high K_t² of 25.3%, a Bode_Q_max of 148, and a C₀ of 0.379 pF. And the series resonator resonates at 5.946 GHz with a high K_t² of 24.1%, a Bode_Q_max of 366, a C₀ of 0.203 pF, and a large PoM of 5.24×10¹¹Hz. The results demonstrate that the series resonator maintains a high Q after IBE thinning, owing to preserved surface roughness following the argon ion bombardment. The measured SV-BAR filter and conventional XBAR filter response under 50 Ω is shown in Fig. 8b. The SV-BAR filter exhibits a cleaner spectrum than conventional XBAR filter, while achieving a f₀ of 5.8585 GHz, an IL_min of 5.394 dB, a 3-dB BW of 569 MHz (FBW = 9.71%), and a large OoB rejection of 31.82 dB at right stop band, 23.97 dB at left stop band.

Fig. 7. Electrical and thermal performance characterization of the SV-BAR filter.

a Measured and MBVD-fitted admittance curves of the series and parallel resonators. b S-parameter comparison between the SV-BAR filter and conventional XBAR filters. Temperature characteristics of the SV-BAR filter: c Measured frequency response of thefabricated SV-BAR filter under temperature variation from 12 °C to 85 °C, d Measured TCF of SV-BAR filters

Fig. 8. PHC and failure analysis of the SV-BAR filter.

a Power simulation results of the SV-BAR filter with an input power of +30 dBm. b Normalized insertion loss variation at f_h versus input power. c Optical micrograph of the filter before power testing. d, e Optical microscope images of the SV-BAR filter after applying an input power of +31.45 dBm

For analyzing the temperature characteristics, the frequency response of the SV-BAR filter is measured at different temperatures ranging from 12°C to 85°C. In Fig. 7c, the passband shifts to the left with the work temperature increases, leading to a negative temperature coefficient of frequency (TCF) because of the negative temperature coefficient of velocity (TCV) of LN demonstrated by the following formula:

$$TCF=\frac{1}{f}\frac{\partial f}{\partial T}=TCV-CTE$$ 7

where the f is resonant frequency, and CTE is thermal expansion coefficient.

Compared to the higher boundary (f_h), the lower boundary (f_l) of the 3-dB bandwidth is more sensitive to temperature. The frequency variations of the f_l and f_h under varying temperatures are shown in Fig. 7d. These experimental points exhibit strong linearity, and a fitted straight line is plotted based on these points. The TCF at f_l (TCF_l) and f_h (TCF_h) are −84.11 and −45.83 ppm/°C, respectively. And the TCF at f₀ (TCF₀) is -64.04 ppm/°C, which can be compensated using SiO₂ thin films featuring a positive TCF³⁵.

It is noteworthy that few studies have addressed the PHC of A₁ filters. Although reference³⁶ specifies that the fabricated A₁ filter features a PHC of +31 dBm, it lacks in-depth analysis and characterization of this property. In Fig. 8a, the power of the SV-BAR filter is simulated with an input power of +30 dBm. The active power on each resonator exhibits significant frequency-dependent variation, with peaks occurring outside the passband of the filter. The peak power of the first series resonator (S1) is the highest, followed by the second (S0). And the peak power dissipation frequency aligns with the voltage maximum rather than the current maximum. Summarily, the first series resonator becomes the most vulnerable at the f_h under high power, constituting the primary limiting factor for the PHC of filters. From the temperature characteristics, applying RF power causes the filter’s temperature to rise due to heating from electrode ohmic losses, dielectric losses, and heat from mechanical vibrations. This causes the passband of the filter to shift to a lower frequency due to the negative temperature coefficient. IL at f_l decreases as the passband shifts, reducing energy dissipation and mitigating heating. Conversely, IL at f_h increases, leading to greater energy dissipation and exacerbated heating. This further raises the device temperature, causing the passband to shift even lower, increasing IL, and forming a vicious cycle. Fortunately, SV-BAR filters are most sensitive to temperature changes at f_l, not f_h. Therefore, the SV-BAR filter is tested under various input powers, and the IL at f_h under these power conditions is extracted to accurately evaluate the PHC described by the 1-dB compression point (P_1dB), as illustrated in Fig. 8b. The SV-BAR filter features a PHC of +30.88 dBm at 6.162 GHz.

As shown in Fig. 8c–e, the filter initially exhibits a well-defined surface morphology. However, with increasing input power, the resonator experiences heating due to dielectric loss, ohmic loss in the electrodes, acoustic propagation loss, and mechanical vibration, which raises its temperature. This temperature rise induces thermal deformation. Simultaneously, the mismatch in the CTE between the electrodes and the LiNbO₃ film, as well as between the substrate and the LiNbO₃ film, generates localized thermal stress at the interfaces. This stress further degrades regions where stress was already concentrated. Furthermore, the elastic coefficient of LiNbO₃ decreases with rising temperature due to its negative temperature coefficient of elasticity (TCE), leading to material softening that amplifies the thermal deformation. The vibration intensity of the resonator increases with the input power, which promotes the initiation and propagation of cracks within the degraded stress-concentration regions, ultimately causing film rupture. Since continued increases in power, this rupture worsens with heat accumulation. Moreover, the exposed Mo electrodes undergo gradual oxidation and darkening, while the concurrent melting of the Au electrodes results in a substantial increase in surface roughness.

At +30.88 dBm, the filter reaches the upper limit of its linear operating region. Beyond this, at +31.45 dBm, intense thin-film vibration causes rupture at stress concentration points near the electrode base, and electrode damage leads to complete filter failure. Notably, the S1 of the filter suffers the most severe damage due to bearing the highest energy, followed by S2, which aligns with the simulation results. Consequently, from the perspective of filters, the PHC is limited by the first series resonator at the signal input, which has the highest energy distribution density. From the perspective of resonators, the PHC is constrained by the mechanical reliability of LN thin films and the ohmic loss of the electrodes. Furthermore, Table 3 illustrates the comparison between the proposed SV-BAR filter and the state-of-the-art works. The SV-BAR filter exhibits balanced performance in f₀, 3-dB BW/FBW, OoB rejection, PHC, and footprint area.

Table 3.

Comparison of the proposed SV-BAR filter with the existing state-of-the-art works

Reference	LN Cut	f0 (GHz)	ILmin (dB)	3-dB BW/FBW (MHz, %)	OoB (dB)	PHC (dBm)	Footprint (mm2)	In-band Ripple
Wu et al.37	128°YX	1.83	0.97	432, 23.7%	~17.0	–	0.54	high
Plessky et al.36	Z-cut	4.70	1.35	600, 12.8%	~18.5	+31.0	2.52	low
Fang et al.38	Z-cut	5.06	2.58	860, 17.0%	23.0	–	2.42	high
Zeng et al.39,40	Z-cut	5.77	~7.50	450, 7.8%	~12.0	–	~3.06	high
		6.04	3.84	670, 11.1%	24.4	–	2.39	high
Tong et al.23	Z-cut	6.17	3.90	621, 10.0%	>25.0	–	~1.63	high
Zheng et al.41	128°YX	6.18	2.40	1000, 16.2%	~26.0	–	3.08	high
This work	Z-cut	5.86	5.39	569, 9.7%	24.0	+30.9	1.95	low

The bold values in the table represent the measured performance parameters of the SV-BAR fi lter fabricated in this work. By comparing these data with those of other filters reported in the literature, the technical level, advantages, and limitations of this study are clearly demonstrated

Conclusion

In this paper, the SV-BAR and its filter are designed and fabricated around 6 GHz, of which S-parameters, TCF, and PHC are evaluated. The SV-BAR exhibits excellent electrical performance and mechanical reliability compared to traditional XBAR demonstrated by COMSOL FEA. The metal-filled material and DF are adopted by Au and 0.5 to suppress spurious modes and enhance PHC. Then, a 2.5-order mirror Ladder topology filter is designed for Wi-Fi 6 through resonator size studies targeting C₀ and operating frequency. The fabricated SV-BAR features a high performance with a large K_t² of 24.1%, Bode_Q_max of 366 at 5.946 GHz, and a significant PoM of 5.24 × 10¹¹Hz. The measured SV-BAR filter exhibits a f₀ of 5.8585 GHz, a 3-dB BW of 569 MHz (FBW = 9.71%), OoB rejection of 23.97 dB, and a small footprint of 1.949 mm² (1.692 mm × 1.152 mm). The TCF of the SV-BAR filter is -64.04 ppm/°C. Compared to the 3-dB higher cutoff frequency (f_h, TCF_h = -45.83 ppm/°C), the 3-dB lower cutoff frequency (f_l, TCF_l = -84.11 ppm/°C) demonstrates higher temperature sensitivity, which contributes to high PHC. The measured PHC of the SV-BAR filter is +30.88 dBm at 6.162 GHz, described by P_1dB. Summarily, the SV-BAR filter has great potential to be applied to plenty of 6 G wideband applications.

Author contributions

Z.W. performed design, simulation, experiment, analysis, and the device’s fabrication; W.L. and C.S. discussed the manuscript and analysis; L.J. and W.R. contributed to the design of the MEMS mechanism and simulations; Z.M. contributed to the device’s fabrication; Y.Q. contributed to the analysis and writing; Y.L. and Y.C. contributed to the analysis.

Competing interests

The authors declare no competing interests.