GHz-Frequency Lamb Waves

Updated 26 January 2026

GHz-frequency Lamb waves are guided elastic plate modes in thin films, characterized by multi-GHz resonances and engineered dispersion relations.
They enable precise RF signal processing, quantum acoustics, and integrated photonics through advanced lithography and optimized material choices.
State-of-the-art designs leverage phononic crystals, zero-group velocity phenomena, and scalable fabrication techniques to achieve high performance and uniformity.

Gigahertz-frequency (GHz) Lamb waves are guided elastic plate modes that propagate in thin films with lateral wavelengths and resonance frequencies reaching the multi-GHz scale, enabled by advanced lithography, piezoelectric thin-film engineering, and nanomechanical device architectures. Their unique dispersion, mode profiles, and electromechanical coupling quantify their utility for RF signal processing, quantum acoustics, and integrated photonics.

1. Fundamental Dispersion Relations and Mode Classification

Lamb waves are solutions to the elasticity equations in plates with traction-free or specified boundary conditions, resulting in symmetric ( $S_n$ ) and antisymmetric ( $A_n$ ) modal families. The theoretical relations, valid for free-standing plates of thickness $2h$, are written using plate-normal wavenumbers ( $p, q$ ), bulk longitudinal ( $v_L$ ) and shear ( $v_T$ ) velocities, and lateral wavenumber $k$ :

$\tan (qh)\,\tan(ph) = -\frac{4 k^2 p q}{(q^2-k^2)^2}$

with

$p^2 = \left(\frac{\omega}{v_L}\right)^2 - k^2, \quad q^2 = \left(\frac{\omega}{v_T}\right)^2 - k^2$

When attached to substrates or embedded in multilayer stacks, boundary conditions require transfer-matrix or FEM approaches to yield dispersion curves, often solved numerically via eigenfrequency analysis. For supported lithium niobate (LiNbO $_3$ ), substrate coupling introduces strong mode dispersion as $f \cdot t \to 1$ , necessitating full continuity of stress and displacement at interfaces (Chulukhadze et al., 2024).

2. Device Design: Lateral Scaling, Material Choices, and Electromechanical Coupling

Resonator frequencies are set by the in-plane wavelength ( $\lambda = 2 \pi / k$ ), determined lithographically (e.g., IDT pitch $\Lambda$ ). The fundamental $S_0$ resonance for LiNbO $_3$ thin films on sapphire with $v_\mathrm{ph}\simeq 4200\,\mathrm{m/s}$ and $\lambda \approx 260\,\mathrm{nm}$ achieves $f \approx 16\,\mathrm{GHz}$ . Metallization ratios of 50% (equal finger width and spacing) maximize coupling; metal thickness (e.g., $t_\mathrm{Al}=50\,\mathrm{nm}$ ) is optimized for device yield at minimal IDT features (Chulukhadze et al., 2024).

Material parameters (e.g., $c_{11}, c_{12}, c_{44}$ elastic constants, $e_{ij}$ piezoelectric coefficients) determine bulk wave speeds and piezoelectric overlap. Device stacks can exploit high- $e_{11}$ films for strong electromechanical coupling, as demonstrated for LiNbO $_3$ (128° Y-cut, $e_{11}\approx 1.8\,\mathrm{C/m^2}$ ) (Chulukhadze et al., 2024), GaN (Valle et al., 2019), AlN (Tadesse et al., 2015), and ZnO/GaAs (Hamidullah et al., 2021).

The effective coupling coefficient ( $k^2$ ) is extracted via

$k^2 \simeq \frac{f_p^2 - f_s^2}{f_p^2}$

where $f_s$ and $f_p$ are resonance and anti-resonance frequencies. This metric, and the unloaded quality factor $Q = f_0/\Delta f$ , define the figure of merit (FoM) for filter applications: $\mathrm{FoM} = k^2 Q$ Optimized designs balance film thickness, lateral wavelength, and metallization for high FoM (e.g., $k^2 \approx 6\%$ , $Q \approx 391$ , FoM $=23.3$ at $14.9\,\mathrm{GHz}$ in LiNbO $_3$ (Chulukhadze et al., 2024), $Q_\text{max}>3200$ for SH $_0$ -SED in LN/SiC at 1.45 GHz (Zhang et al., 2021)).

Phononic crystal (PnC) patterning introduces periodic perturbations in the thickness or stiffness, engineering bandgaps and avoided crossings between symmetric and antisymmetric modes. True BICs (bound states in the continuum) occur when defect-induced modes are orthogonal to all radiative channels, yielding $Q \to \infty$ ; mirror-symmetry breaking or material disorder creates quasi-BICs accessible by traveling waves. Total Q is then

$Q_\text{tot} = \omega_0 / (\gamma_\text{intr} + \Gamma_\text{rad})$

with radiative leakage $\Gamma_\text{rad} \simeq |\kappa|^2/\gamma_S$ (Liang et al., 25 Feb 2025). Tunable multiplexed arrays (spacing $\Delta f \sim 5$ MHz) enable multi-frequency readout on a single transmission line.

Similarly, zero-group-velocity (ZGV) points in dispersion curves ( $d\omega/dk=0$ , $\omega/k>0$ ) trap energy without external reflectors, forming inherently localized, high- $Q$ GHz resonances. Measured Q-factors for ZGV modes ( $Q>10^3$ ) and micron-scale field localization have been directly imaged optically (Xie et al., 2019). SOI/AlN composite structures can realize ZGV resonators at 0.3–1.9 GHz with low TCF (e.g., –17 to –34 ppm/°C) and strong confinement (Caliendo et al., 2018).

4. Fabrication Techniques for High-Frequency, High-Uniformity Lamb Wave Devices

Advanced techniques include electron-beam lithography for sub-200 nm IDT fingers (Chulukhadze et al., 2024), vapor-phase etching for membrane release (Diego et al., 20 Jan 2026), DUV photolithography for wafer-scale production of suspended resonators with critical dimensions down to 250 nm and alignment accuracy <100 nm (Liffredo et al., 2024), and blanket argon-ion milling with staged thinning for sub-100 nm film geometries (Xie et al., 5 Aug 2025). Hard-mask etching and lift-off yield vertical sidewalls and minimal process-induced roughness; frequency deviation of the $S_0$ mode can be held below 1% across a 100 mm wafer (Liffredo et al., 2024).

Wafer-level uniformity, precision in pitch and film thickness, and controlled metallization are crucial for scalable multi-frequency filter arrays (e.g., eight ladder filters spanning 1.4–6.0 GHz, FBW up to 13.3% on a 4×2.5 mm $^2$ die (Zhang et al., 2021)).

5. Experimental Performance Metrics and Scaling Limitations

Measured quantities include admittance ( $|Y_{11}|$ ), S-parameters ( $|S_{21}|$ ), and direct imaging via techniques such as transmission-mode microwave impedance microscopy (TMIM) for spatially resolved loss and mode conversion (Lee et al., 2021), as well as ultrafast optical pump-probe for ZGV Lamb waves (Xie et al., 2019). Quality factors in LiNbO $_3$ reach $Q_\text{max}\approx391$ at 14.9 GHz, with k² around 6% (Chulukhadze et al., 2024), while diamond Lamb wave resonators display $Q>10^7$ at 1 GHz and 7 K (Li et al., 2024).

Limiting factors at high frequency ( $f>10$ GHz) include:

Anchor loss: increases with shrinking $\lambda$ ; tethers mitigate but introduce collapse risk (Chulukhadze et al., 2024).
Metal conductivity loss: shadowing in narrow gaps thins Al, raising series resistance and lowering Q (Chulukhadze et al., 2024).
Substrate leakage: evanescent coupling grows for high-order modes; careful membrane release and reflector design are essential (Chulukhadze et al., 2024).
Surface-related losses: for sub-100 nm films, Q drops substantially due to fabrication-induced damage, addressed by chemical-mechanical polishing and atomic-layer deposition remediation (Xie et al., 5 Aug 2025).

Performance in Q, insertion loss, and bandwidth is tabulated in device reports. For instance:

Mode	$f_r$ (GHz)	$k^2$ (%)	$Q_\text{max}$	FoM
$S_0$ (LN)	14.9	6.0	391	23.3
SH $_0$ -SED	1.45	7.9	3680	291
$S_0$ (LN/SiC)	4.40	29.3	1020	299

6. Applications in RF Signal Processing, Quantum Acoustics, and Integrated Photonics

Multi-GHz Lamb wave devices underpin RF-FEM modules for 4G-LTE, 5G, and 6G: compact filters, oscillators, and correlators exploit wavelength scaling and traveling wave nature for small die footprints and multi-band coverage (Chulukhadze et al., 2024, Zhang et al., 2021). Mass-loaded thin-film GaN resonators ( $f>3$ GHz, $Q_\text{mech}\sim2000$ ) serve monolithic front-ends (Valle et al., 2019). Suspended LiNbO $_3$ Lamb wave cavities ( $Q_i\sim6000$ at 2 GHz, single-phonon regime) directly interface with superconducting qubits via mutual inductance, enabling quantum acoustic memory and quantum networking (Diego et al., 20 Jan 2026).

In photonics and optomechanics, GHz Lamb waves efficiently modulate photonic crystal nanocavities (AlN, $f$ up to 19 GHz, $G\sim7$ MHz/mW $^{1/2}$ ) (Tadesse et al., 2015), mediate piezo-optomechanical transduction (integrated GaAs, $g_0/2\pi\sim100-200$ kHz) (Khurana et al., 2022), and realize helical drum modes with tunable optical orbital angular momentum transfer ( $l=\pm1$ ) for acousto-optical chiral systems (Ashurbekov et al., 28 Feb 2025).

Spin-mechanical diamond Lamb resonators ( $Q>10^7$ at GHz, $T\sim7$ K) couple via strain to SiV centers, establishing a platform for phononic cavity QED and coherent quantum control (Li et al., 2024).

7. Future Prospects: Extreme Frequency Scaling and Monolithic Integration

Aggressive thinning of piezoelectric films (e.g., LiNbO $_3$ to $h=67\,\text{nm}$ ) pushes Lamb-wave resonances into the 220 GHz regime, approaching terahertz nanomechanics (Xie et al., 5 Aug 2025). Feasibility of frequency scaling into Ka-band ( $f=25-30$ GHz) is demonstrated with sub-200 nm features and optimized metallization (Chulukhadze et al., 2024). Addressing surface and anchor-related losses via advanced fabrication and passivation will determine ultimate performance in quantum and RF applications.

Monolithic integration of multi-frequency Lamb-wave arrays is achieved on the same film and electrode process, opening scalable RF front-ends with >100 filters, compact transversal filters, and integrated quantum modules (Zhang et al., 2021, Chulukhadze et al., 2024). DUV photolithography and standard MEMS/CMOS flows support high-throughput production with sub-nm control of dimensions for next-generation telecommunication systems (Liffredo et al., 2024).

Key references: (Chulukhadze et al., 2024, Liang et al., 25 Feb 2025, Diego et al., 20 Jan 2026, Valle et al., 2019, Li et al., 2024, Zhang et al., 2021, Xie et al., 5 Aug 2025, Liffredo et al., 2024, Tadesse et al., 2015, Khurana et al., 2022, Lee et al., 2021, Hamidullah et al., 2021, Caliendo et al., 2018, Xie et al., 2019, Ashurbekov et al., 28 Feb 2025).