In-Plane Q Anisotropy of Higher-Order XBARs

Technical Summary: In-Plane Q Anisotropy of Higher-Order XBARs in 128°Y-Cut Lithium Niobate

Problem Statement
128°Y-cut lithium niobate (LN) laterally field-excited higher-order antisymmetric bulk acoustic resonators (XBARs) are critical for high-frequency acoustic devices due to their high electromechanical coupling coefficient ($k^2$) and quality factor ($Q$). While the in-plane orientation of these resonators is routinely optimized to maximize $k^2$ (and thus bandwidth), the in-plane anisotropy of the quality factor ($Q$) remains under-explored. A significant gap exists in understanding whether the propagation direction that maximizes coupling also optimizes $Q$, or if orientation-dependent loss mechanisms degrade performance in specific directions. Previous studies have noted anisotropic $Q$ in other LN cuts (e.g., X-cut S0 and 36°Y-cut SH0), but a systematic investigation of this phenomenon in 128°Y-cut LN XBARs is lacking.

Methodology
The authors experimentally investigated the anisotropic $Q$ of higher-order antisymmetric modes (A3, A5, and A7) in 500-nm-thick 128°Y-cut LN on silicon.

• Device Design: Resonator arrays were fabricated with interdigitated transducers (IDTs) patterned on suspended LN membranes. Devices were arranged at various in-plane propagation angles (from 10° to 170° in 20° increments) relative to the material x-axis. The design included spurious-mode suppression features to isolate the intended antisymmetric modes.
• Fabrication: The process involved photolithography, electron-beam evaporation of 50 nm Pt electrodes, 80 nm Au buslines, ion milling for release windows, and XeF2 isotropic etching to suspend the LN layer.
• Characterization: Wideband admittance responses were measured to extract resonant frequencies ($f_s$, $f_p$), coupling coefficients ($k^2$), and quality factors (Bode $Q$ and $Q_{3dB,fp}$). A multi-branch modified Butterworth–Van Dyke (mBVD) model was employed to accurately extract parameters, separating parasitic effects from the motional branches.
• Simulation: Finite Element Analysis (FEA) was conducted to visualize mode shapes, stress distributions, and displacement fields. Simulations examined the power flow angle (PFA) and the evolution of displacement profiles near anchor regions as a function of propagation angle.

Key Results
The study reveals a strong correlation between the in-plane propagation angle and both $k^2$ and $Q$, with performance peaking near 0°/180° and degrading significantly near 90°.

• Performance Metrics:
  • A3 Mode (~10.4 GHz): Average Bode $Q$ of 735 and $Q_{3dB,fp}$ of 556 at optimal angles, dropping to 66 at 90°.
  • A5 Mode (~17 GHz): Average Bode $Q$ of 204 and $Q_{3dB,fp}$ of 149, dropping to 9 at 90°.
  • A7 Mode (~24 GHz): Average Bode $Q$ of 59 and $Q_{3dB,fp}$ of 37, dropping to 12 at 90°.
• Coupling Coefficient: The extracted $k^2$ values follow the same trend, decreasing from ~4.8% (A3), 2.0% (A5), and 0.9% (A7) at 0°/180° to nearly 0% at 90°.
• Loss Mechanism Analysis:
  • Power Flow Angle (PFA): Simulations showed that while PFA varies with angle (peaking around 50° and 130°), the minimum $Q$ occurs at 90° where PFA is near zero. This indicates that PFA-induced loss is not the primary driver of the observed $Q$ degradation.
  • Transverse Displacement and Anchor Loss: FEA results demonstrated that as the propagation angle approaches 90°, the intended thickness-shear excitation weakens, and unintended transverse displacement components become increasingly pronounced, particularly near the anchor regions. This enhanced transverse motion facilitates acoustic energy leakage through the anchors, directly reducing $Q$.

Significance and Claims
The paper claims to provide the first systematic experimental evidence of orientation-dependent $Q$ degradation in 128°Y-cut LN XBARs. The authors conclude that the degradation of $Q$ near 90° is not solely a function of reduced coupling but is strongly linked to orientation-dependent mode deformation. Specifically, the shift from pure thickness-shear motion to significant transverse displacement near the anchors creates a dominant loss pathway via anchor leakage.

These findings offer critical design guidance for high-frequency acoustic devices. They suggest that optimizing device performance requires a joint consideration of $k^2$ and $Q$, as the propagation direction that maximizes coupling (0°/180°) also minimizes anchor-mediated energy leakage. Conversely, orientations near 90° should be avoided not only for their low coupling but also for their severe $Q$ degradation caused by transverse mode deformation. This work fills a gap in the understanding of anisotropic loss mechanisms in LN XBARs, enabling more robust filter synthesis and resonator design.