Suspended Lamb-Wave Resonators

• Suspended Lamb-wave resonators are MEMS devices featuring a free-standing thin film that guides elastic waves and suppresses substrate leakage for enhanced in-plane acoustic confinement.
• They employ interdigitated transducers on piezoelectric films and diverse confinement strategies such as Bragg mirrors and phononic crystals to achieve precise modal control and high-Q performance.
• Material selection and advanced fabrication techniques, including DUV lithography and XeF2 release, critically influence electromechanical coupling, operating frequency, and device scalability.

Suspended Lamb-wave resonators are acoustic MEMS and nanophononic devices in which a thin free-standing membrane or plate supports guided elastic waves and the active film is released from the substrate to suppress substrate leakage and support resonant standing-wave or cavity-confined states. In many reported devices, interdigitated transducers patterned on piezoelectric thin films provide electrical actuation and readout, while the suspended geometry is used to preserve in-plane acoustic confinement, reduce leakage, and enable operation from hundreds of megahertz to the millimeter-wave regime (Liffredo et al., 2024, Yang et al., 2018). The platform now spans RF front-end filtering, acousto-optic modulation, piezo-optomechanical transduction, phononic metamaterials, and quantum acoustics (Tadesse et al., 2015, Khurana et al., 2022, Diego et al., 20 Jan 2026).

1. Wave physics and modal taxonomy

Lamb waves are guided acoustic waves in thin plates and are classified by symmetry with respect to the plate mid-plane into symmetric ($S$) and antisymmetric ($A$) modes (Liang et al., 25 Feb 2025). Reported suspended resonators use the fundamental symmetric and antisymmetric branches ($S_0$, $A_0$), higher-order modes such as $A_1$, $S_1$, $A_3$, $A_5$, and $A_7$, and related laterally vibrating or shear-horizontal states such as $SH_0$ in lithium-niobate laterally vibrating resonators (Liffredo et al., 2024, Feng et al., 2023, Yang et al., 2018). In thin suspended films, the accessible mode set depends on film thickness, electrode topology, and the orientation of the electric field relative to the piezoelectric tensor.

A recurring design principle is the frequency scaling $A$0, where $A$1 is the phase velocity of the selected Lamb mode and $A$2 is set lithographically by the transducer period (Tadesse et al., 2015). Higher-order asymmetric modes are used specifically to extend operation into K-band and Ka-band without reducing the lateral period to impractically small values. Suspended Z-cut LiNbO$A$3 resonators based on the $A$4 and $A$5 modes reached 21.4 and 29.9 GHz, respectively, with extracted mechanical $A$6 values of 406 and 474 (Yang et al., 2018). In the AlN combined-overtone resonator, multimodal excitation of the second- and third-order asymmetrical Lamb waves in a suspended thin-film plate was used to address the 6–40 GHz range (Chen et al., 2019).

Mode selection is not purely geometric; it is also electromechanical. In top-only, laterally excited LiNbO$A$7 structures, odd-order asymmetric modes are efficiently excited because the field-overlap symmetry suppresses even-order counterparts, whereas in LN-on-LN laterally vibrating resonators the IDT orientation determines whether $A$8 or $A$9 is preferentially driven (Yang et al., 2018, Feng et al., 2023). Reported work also uses several coupling definitions. In AlScN suspended Lamb resonators, one extraction is

$S_0$0

obtained from mBVD fits (Liffredo et al., 2024). In LN-on-LN resonators, the reported effective coupling is

$S_0$1

while LiNbO$S_0$2 A$S_0$3 resonators with through-holes use

$S_0$4

(Feng et al., 2023, Wu et al., 2024).

2. Confinement mechanisms and cavity topologies

The defining function of suspension is the removal of the direct leakage path into the substrate. In suspended AlN membranes for acousto-optic modulation, removal of the substrate confines acoustic waves within the thin membrane, yielding Lamb-wave modes and reducing leakage relative to unsuspended SAW structures (Tadesse et al., 2015). In suspended LiNbO$S_0$5 quantum-acoustic cavities, the membrane geometry was used so that energy remains in the resonator plane, while acoustic Bragg mirrors provided additional lateral confinement (Diego et al., 20 Jan 2026). In laterally vibrating LN-on-LN devices, the suspended region bounded by anchors formed a Fabry–Perot cavity for $S_0$6 and $S_0$7 standing waves (Feng et al., 2023).

Several distinct confinement strategies have emerged within the suspended platform. One is the released cavity with Bragg reflectors: a 200 nm-thick suspended LiNbO$S_0$8 layer with a central aluminum IDT and mirror arrays of floating Al fingers supported an antisymmetric $S_0$9 cavity mode near 2 GHz and intrinsic quality factors of approximately 6000 at the single-phonon level (Diego et al., 20 Jan 2026). A second is phononic-crystal defect confinement. Suspended LiNbO$A_0$0 phononic crystals with nanoscale grooves created symmetry-protected bound states in the continuum and quasi-BICs by exploiting the decoupling of symmetric and antisymmetric Lamb-wave modes; controlled mirror-symmetry breaking enabled traveling-wave excitation of high-$A_0$1 localized defect states around 1.1–1.15 GHz (Liang et al., 25 Feb 2025). A third is phononic-bandgap shielding, used in single-crystal diamond plates embedded in a phononic crystal lattice, where the fundamental symmetric compression mode near 1 GHz was isolated strongly enough to yield $A_0$2 near 7 K (Li et al., 2024).

Other suspended architectures target lateral leakage and diffraction explicitly. In lateral-field-excited suspended bulk acoustic wave resonators (XBARs), shaping the ScAlN layer into a spherical lens converted a flat-flat cavity to a flat-curved cavity and suppressed non-zero $A_0$3 leakage channels; the resulting lensed devices showed a roughly $A_0$4 improvement in $A_0$5, with values up to $A_0$6 for the trapped mode (Shokati et al., 9 Jan 2026). In graded meta-MEMS on suspended silicon waveguides, flexural Lamb waves hybridized with arrays of lateral micro-resonators, producing local bandgaps, delay-line behavior, and spatially selective trapping of different frequencies (Maspero et al., 2023). In self-assembled silicon-membrane metamaterials, a monolayer of adhered microspheres created local oscillators whose contact resonance at 200 MHz hybridized with the $A_0$7 branch of the suspended membrane, producing an avoided crossing in the dispersion curve (Khanolkar et al., 2015).

A common misconception is that suspension is the only viable route to Lamb-wave confinement. Unreleased thin-film GaN devices have used mass loading from gold electrodes to create a one-dimensional acoustic Bragg stack and trap guided Lamb-wave resonances above 3 GHz without substrate release (Valle et al., 2019). Conversely, zero-group-velocity resonators on supported SOI/AlN were proposed to confine acoustic energy intrinsically at ZGV points without suspended edges or metal strip gratings (Caliendo et al., 2018). These results delimit suspended Lamb-wave resonators as one major branch of a wider Lamb-wave resonator landscape rather than the only confinement paradigm.

3. Materials platforms and fabrication technologies

Suspended Lamb-wave resonators have been demonstrated in AlScN, AlN, LiNbO$A_0$8, LN-on-LN, GaAs, diamond, silicon membranes, and composite stacks such as SOI/AlN (Liffredo et al., 2024, Tadesse et al., 2015, Feng et al., 2023, Khurana et al., 2022, Li et al., 2024). Material choice determines accessible coupling, loss, thermal behavior, optical compatibility, and integration constraints. LiNbO$A_0$9 offers high electromechanical coupling and has been used for K-band, Ka-band, cryogenic, and high-temperature devices (Wu et al., 2024, Yang et al., 2018, Jiang et al., 13 Oct 2025, Chaudhari et al., 16 Sep 2025). AlN and AlScN support high-velocity plate modes and are compatible with high-frequency operation and integrated photonics (Liffredo et al., 2024, Tadesse et al., 2015). GaAs adds strong elasto-optic interactions in a photonic integrated-circuit platform, while diamond enables ultralow damping and direct coupling to color centers (Khurana et al., 2022, Li et al., 2024).

A central fabrication milestone is the scalable DUV process for suspended AlScN Lamb-wave resonators. The reported flow starts with 4-inch, double-side polished, high-resistivity silicon wafers, followed by a 10 nm adhesion layer and a 25 nm Pt bottom electrode. All lithography uses a 248 nm KrF PAS 5500-350C DUV stepper with resolution $A_1$0 nm and overlay $A_1$1 nm; the photoresist-BARC stack consists of 400 nm JSR M108Y on 60 nm Brewer DS-K101, and a reflow bake at $A_1$2C for 90 s is used to smooth the resist profile (Liffredo et al., 2024). Experimental results showed reliable patterning down to 250 nm widths with pitches as small as 500 nm and alignment between three critical layers maintained to $A_1$3 nm across the wafer. Al$A_1$4Sc$A_1$5N was deposited at $A_1$6 nm thickness, and a multi-angle pulsed ion beam etch at $A_1$7, $A_1$8, and $A_1$9 achieved nearly vertical $S_1$0 sidewalls before XeF$S_1$1 release (Liffredo et al., 2024).

Release engineering is equally important. LN-on-LN resonators use vapor-HF etching of the buried oxide and asymmetric release windows to avoid central oxide pillars while preserving aluminum IDTs (Feng et al., 2023). Suspended LiNbO$S_1$2 A$S_1$3 resonators with sub-wavelength through-holes introduce etchant access points directly in the suspended film, reducing the ineffective suspension area by 40–60% and standardizing etching distances across differently sized resonators on the same wafer without additional process steps (Wu et al., 2024). High-temperature stoichiometric-LN devices are fabricated on a 1 $S_1$4m amorphous-silicon sacrificial layer with 40 nm Pt top electrodes and a 5 nm Ti adhesion layer, followed by XeF$S_1$5 release (Chaudhari et al., 16 Sep 2025).

Manufacturability and metrology have become part of the resonator problem rather than external process concerns. In the DUV AlScN study, 93 device replications per wafer were used for process-uniformity extraction and the standard deviation of the $S_1$6 mode frequency was kept below 1% for pitches $S_1$7m (Liffredo et al., 2024). In direct real-space measurements on suspended AlN phononic circuits, transmission-mode microwave impedance microscopy resolved individual $S_1$8 and $S_1$9 eigenmodes, enabling extraction of propagation losses of approximately 20 dB/mm and 35 dB/mm, respectively, and a power coupling efficiency of $A_3$0 between the waveguide and parabolic couplers (Lee et al., 2021). This suggests that fabrication scalability and mode-resolved diagnostics are now tightly coupled research themes.

4. Performance envelope and design trade-offs

Representative results span large ranges in frequency, coupling, and quality factor, reflecting major differences in material system, mode order, and confinement mechanism.

Platform	Mode / frequency	Representative performance
Suspended AlScN DUV resonator	$A_3$1, up to 7.5 GHz	$A_3$2 up to 8%; $A_3$3 deviation $A_3$4 (Liffredo et al., 2024)
LN-on-LN laterally vibrating resonator	$A_3$5 at 418 MHz; $A_3$6 at 713–719 MHz	$A_3$7 from 500 to 2600; $A_3$8 up to 13.9%; FOM up to 294 (Feng et al., 2023)
Suspended Z-cut LiNbO$A_3$9 higher-order device	$A_5$0 at 21.4 GHz; $A_5$1 at 29.9 GHz	$A_5$2 of 1.5% and 0.94%; extracted mechanical $A_5$3 of 406 and 474 (Yang et al., 2018)
Suspended LiNbO$A_5$4 quantum cavity	$A_5$5 at $A_5$6 GHz	intrinsic $A_5$7 of approximately 6000 at the single-phonon level (Diego et al., 20 Jan 2026)
Diamond Lamb-wave resonator	compression mode at 0.977 GHz	$A_5$8 near 7 K (Li et al., 2024)

Within individual platforms, the trade-offs are equally explicit. In the scalable AlScN process, $A_5$9 devices reached 6–8% coupling across pitch, while $A_7$0 reached up to 6%; the $A_7$1 mode showed frequency deviation of about 3%, mainly thickness-driven, whereas $A_7$2 remained below 1% for pitches above $A_7$3m (Liffredo et al., 2024). In LN-on-LN resonators, the $A_7$4 mode showed the best reported combination of $A_7$5, $A_7$6, and FOM $A_7$7, while $A_7$8 modes provided $A_7$9–1344 and $SH_0$0–10% (Feng et al., 2023). In the AlN combined-overtone resonator, an 8.8 GHz prototype showed $SH_0$1, $SH_0$2, and $SH_0$3 (Chen et al., 2019).

Cryogenic studies show that loss mechanisms remain mode dependent. In higher-order antisymmetric LiNbO$SH_0$4 resonators, the $SH_0$5 mode quality factor increased steadily on cooling and reached four times the room-temperature value at millikelvin temperatures, while $SH_0$6 showed non-monotonic temperature dependence and a sharp $SH_0$7 jump below the superconducting transition of aluminum electrodes, indicating that ohmic and electrical losses were significant for that mode family (Jiang et al., 13 Oct 2025). In suspended LiNbO$SH_0$8 quantum cavities, $SH_0$9 decreased at the lowest excitation and saturated at higher phonon number, behavior described as consistent with two-level-system loss models (Diego et al., 20 Jan 2026). These results show that “higher frequency” and “higher order” do not map onto a single loss trend.

Spurious response is another critical trade-off. The cryogenic LiNbO$A$00 study reported that $A$01 spurious modes were effectively suppressed with a recessed electrode design using 70 nm Al, whereas $A$02 devices were intrinsically free from spurious modes in the studied designs (Jiang et al., 13 Oct 2025). The through-hole LiNbO$A$03 A$A$04 resonators likewise reported no extra spurious modes while maintaining operating frequency, coupling, and quality factor (Wu et al., 2024). A plausible implication is that suspension engineering increasingly must be co-designed with spurious-mode engineering rather than treated as a separate post-release concern.

5. System-level functions and application domains

The most established application domain is RF filtering. Suspended Lamb-wave resonators are explicitly targeted at telecommunication front ends in the sub-6 GHz, K-band, Ka-band, and broader mmWave regimes (Liffredo et al., 2024, Wu et al., 2024, Yang et al., 2018, Chen et al., 2019). The DUV-fabricated AlScN platform reached resonance frequencies up to 7.5 GHz with electromechanical couplings up to 8%, and its full-wafer uniformity was presented as suitable for quick scale-up toward RF filter chains (Liffredo et al., 2024). K-band LiNbO$A$05 A$A$06 resonators above 21 GHz used sub-wavelength through-holes to standardize etch time across differently sized devices on one wafer, a direct filter-bank integration problem (Wu et al., 2024). For 5G mmWave filtering, the suspended AlN combined-overtone resonator was modeled to deliver contiguous filters with bandwidths between 355 and 592 MHz and aggregated bandwidth above 2 GHz (Chen et al., 2019).

Suspended Lamb-wave structures have also become a central electromechanical interface for photonics. In a suspended GaAs photonic integrated-circuit platform, Lamb-wave resonators hybridized with mechanical breathing modes of a rib waveguide to form mechanical supermodes; this enabled signal transduction up to 7 GHz and an approximately $A$07 increase in transduction efficiency for the hybridized mode at $A$08 GHz (Khurana et al., 2022). In suspended AlN membranes, traveling Lamb waves driven by IDTs with periods down to 300 nm modulated a photonic crystal nanocavity up to 19.20 GHz, with reported acousto-optic modulation efficiencies of 16.39 MHz/mW$A$09 for the $A$10 mode at 1.35 GHz and 19.20 MHz/mW$A$11 for the $A$12 mode at 5.28 GHz for a 2.0 $A$13m period device (Tadesse et al., 2015).

Quantum-acoustic use cases are now a separate branch rather than a distant extension. Suspended LiNbO$A$14 Lamb-wave cavities with Bragg mirrors were modeled for inductive coupling to flip-chip superconducting transmon qubits, with $A$15 MHz and up to 10 MHz for larger-aperture designs (Diego et al., 20 Jan 2026). Suspended LiNbO$A$16 quasi-BIC phononic-crystal resonators support multiplexing of multiple high-$A$17 resonances along a single transmission line, each at a distinct frequency and spatial position, which is relevant to integrated signal processing and quantum acoustics (Liang et al., 25 Feb 2025). In diamond, the Lamb-wave resonator platform couples GHz compression modes to silicon-vacancy centers via strain and sideband spectroscopy, establishing a spin-mechanical cavity-QED architecture with $A$18 near 7 K (Li et al., 2024). Diamond Lamb-wave resonator arrays have also been analyzed as mechanical Wannier–Stark ladders, where the localization length is set by the ratio of coupling rate to frequency spacing and thereby tunes the effective range of phonon-mediated spin–spin coupling (Andrango et al., 2024).

Suspended Lamb-wave devices are also used for sensing, wave manipulation, and metamaterials. Graded meta-MEMS based on suspended silicon waveguides and lateral resonator arrays demonstrated frequency-selective trapping, amplification, filtering, and delay-line behavior with resonator $A$19 (Maspero et al., 2023). Self-assembled microsphere-on-membrane structures revealed contact resonance, spheroidal resonance, and hybridization with flexural Lamb waves, providing a route to microscale contact-mechanics sensing and locally resonant acoustic metamaterials (Khanolkar et al., 2015). High-temperature suspended thin-film LiNbO$A$20 resonators remained operable after annealing to 750 $A$21C, indicating use in harsh-environment sensing and actuation even though most devices became inoperable after 800 $A$22C (Chaudhari et al., 16 Sep 2025).

6. Loss mechanisms, misconceptions, and current research directions

A persistent misconception is that suspension by itself guarantees high $A$23. The literature identifies multiple limiting channels: anchor loss, electrode damping, lateral diffraction, substrate leakage if release is incomplete, surface damage from processing, metal ohmic loss, and cryogenic two-level-system loss (Lee et al., 2021, Jiang et al., 13 Oct 2025, Diego et al., 20 Jan 2026). The lensed XBAR work isolates diffraction as a major mechanism by showing that non-zero $A$24 components disappear in the lensed geometry and $A$25 increases by roughly $A$26 (Shokati et al., 9 Jan 2026). The direct-visualization study on suspended AlN phononic circuits showed that undesired mode conversion from a membrane anti-symmetric mode into the $A$27 waveguide mode could dominate over the intended $A$28 channel, emphasizing that coupler design can determine the effective loss budget (Lee et al., 2021).

Thermal robustness is another active boundary condition. In suspended stoichiometric-LN $A$29-mode resonators with Pt/Ti electrodes, little visible change was reported up to 400 $A$30C, cracks became visible after 500 $A$31C, severe cracking and anchor failure developed between 700 and 750 $A$32C, and most devices were inoperable after 800 $A$33C (Chaudhari et al., 16 Sep 2025). XRD revealed the emergence of LiNb$A$34O$A$35 after 600 $A$36C, while the quality factor could either decrease because of accumulated damage or increase in partially broken devices because of reduced anchor loss (Chaudhari et al., 16 Sep 2025). These results complicate any simple assumption that suspended architectures are intrinsically fragile or intrinsically robust; the outcome depends on electrode choice, adhesion layer, crystal stoichiometry, anchor layout, and thermal-expansion mismatch.

Current work increasingly combines suspension with higher-order mode engineering, defect-state physics, and scalable processing rather than treating the resonator as an isolated membrane. DUV photolithography with $A$37 nm overlay and 250 nm IDT linewidths addresses wafer-level reproducibility (Liffredo et al., 2024). Through-hole suspension addresses release-time standardization for multi-resonator filters (Wu et al., 2024). Quasi-BIC cavities address the excitability problem of strict symmetry-protected BICs by controlled mirror-symmetry breaking (Liang et al., 25 Feb 2025). Mechanical supermodes in GaAs address the impedance mismatch between efficient phonon injection and strong optomechanical coupling (Khurana et al., 2022). A plausible implication is that the field is converging on suspended Lamb-wave resonators as configurable electromechanical subsystems—combining release engineering, mode-shape engineering, and integration strategy—rather than as a single device archetype defined only by a suspended membrane.