Toward Enhanced Inertial Sensing via Dynamically Soft Topological States in Piezoelectric Microacoustic Metamaterials

TL;DR

The paper tackles the trade-off between robustness and sensitivity in MEMS gyroscopes by introducing topological interface states in a piezoelectric microacoustic metamaterial. Using an SSH-inspired dual-structure design built from AlScN on Pt with SiO2 rods, the authors demonstrate two interface states with strong localization, supported by toy models and FEM that yield a higher modal compliance $C_{\mathrm{modal}}$ and larger achievable velocities. Experimentally, they achieve a record-high out-of-plane velocity of $v_{\max}=51.3~\mathrm{m/s}$ at modest power (6.4 mW absorbed), with results closely matching FEM and a fourfold advantage over a trivial device on the same die. This work suggests a viable path toward MEMS gyroscopes that combine high scale factors with resilience to shock and vibration, potentially enabling more robust and accurate inertial sensing in compact platforms.

Abstract

In recent decades, microelectromechanical systems (MEMS)-based gyroscopes have been employed to meet positioning and navigation demands of a plethora of commercially available devices. Most of such gyroscopes rely on electrostatic actuators with nanometer-scale air gaps$\unicode{x2013}$an architecture that enables large particle velocities in a proof mass and, consequently, high Coriolis-force sensitivity to angular velocity$\unicode{x2013}$but is inherently susceptible to damage under shock and vibration. This vulnerability is typically mitigated by purposely reducing gyroscopic sensitivity, thereby compromising readout accuracy. Microacoustic gyroscopes, by contrast, offer greater resilience to shock and vibration but currently exhibit significantly lower sensitivities. This limitation stems from the low dynamic compliance of the modes they employ$\unicode{x2013}$typically Lamb or Rayleigh modes$\unicode{x2013}$which restricts their maximum achievable particle velocity. This work presents a piezoelectric microacoustic device that overcomes this fundamental constraint by harnessing a topological interface state at the boundary between two microscale metamaterial structures. We theoretically and experimentally show that this state exhibits much higher modal compliance than Lamb or Rayleigh modes. This enables record-high particle velocities (>51 m/s) never reached, due to material limits, by any previously demonstrated piezoelectric gyroscope.

Figures (6)

• Figure 1: Conventional MEMS gyroscopic devices and the reported topological device: (a) Schematic illustration of a conventional MEMS capacitive vibratory rate gyroscope (CVRG) having a comb-drive actuator with sub-micron air gaps; (b) Schematic illustration of a conventional surface acoustic wave (SAW) gyroscope consisting of a pair of drive and sense resonators, and a forest of pillars. The scale factor of SAW gyroscopes is proportional to the magnitude of the particle velocity in the pillar, which is heavily limited by the high elastic coefficients of typical SAW gyroscopes' forming layers; (c) Schematic illustration of the proposed topological device formed by combining two periodic structures, each consisting of unit cells UC1 and UC2 with identical dispersion characteristics but different Zak phases; (d) Scanning electron microscopy (SEM) image of the reported topological device.
• Figure 2: Verification of the existence of interface states via a toy model: (a) Unit cells of the uncoupled antisymmetric (uncoupled-A) and uncoupled symmetric (uncoupled-S) structures representing the propagation of uncoupled antisymmetric and symmetric waves; (b) Unit cell dispersion curves of the uncoupled structures; (c) The coupling between antisymmetric and symmetric waves is introduced via an interconnecting spring, $s$, forming a coupled unit cell (UCC) of a periodic coupled structure, denoted as coupled antisymmetric-symmetric (coupled-AS) structure; (d) Unit cell dispersion analysis of UCC showing the opening of a complete band gap; (e) Topological structure formed by combining two chains consisting of two different unit cells; (f) Dispersion curves for the topological structure, revealing two interface states inside the same band gap shown in (d).
• Figure 3: Comparison of topological and trivial modes via modal and dynamic local compliances of the mass-spring toy models: (a) Normalized Modal compliance ($C_{modal}$) of uncoupled, coupled, and topological structures, demonstrating that ISs exhibit much higher $C_{modal}$ than any other modes of uncoupled and coupled structures; (b-g) Dynamic local compliance ($C_{Local}$) of uncoupled-A (b), uncoupled-S (c), coupled-AS (d-e), and topological (f-g) structures, showing that masses of the topological structure located near the interface between PC and PC* have significantly higher compliance values compared to trivial modes.
• Figure 4: Evidence of the existence of the reported device's ISs through FEM simulations: (a) Dispersion curves showing that unit cells of the topological structure possess a band gap within which topological states exist. This band gap disappears when rods are distributed uniformly; (b) Structures used in modal compliance ($C_{modal}$) analysis to compare the particle velocity performance of ISs with that of trivial modes; (c) Resulting $C_{modal}$ values around the band gap showing that ISs have higher $C_{modal}$ than any other trivial mode; (d) Total displacement mode shapes of IS-1 and IS-2, showing strong mode localization.
• Figure 5: Experimental results: (a) Laser Doppler Vibrometer measurement of the topological structure showing the magnitude of the out-of-plane velocity around the interface between PS-1 and PS-2 for a driving power equal to 0.06 W; (b) Recorded S21 and the corresponding out-of-plane velocities during interferometric measurements, each normalized to its maximum value at a given absorbed power. Both responses show a Duffing-type softening nonlinearity for power absorbed levels exceeding 4 mW; (c) Measured and FEM simulated maximum out-of-plane particle velocities at the interface between PS-1 and PS-2 under different absorbed power levels. The measured performance of the reported device is closely matching with the expected values based on FEM simulation, achieving a maximum out-of-plane velocity of 51.3 m/s under an absorbed power of 6.4 mW; (d) Scanning Electron Microscope (SEM) image of the device after being tested under 10 mW absorbed power, showing fracture at the interface between two periodic structures; (e) SEM image of the trivial device used in particle velocity performance comparison between IS-1 and the trivial mode; (f) FEM simulated out-of-plane particle velocity distribution of the trivial device, showing the location of the maximum out-of-plane particle velocity indicated by the marker M; (g) Measured maximum out-of-plane particle velocities of the topological and trivial devices, showing that the topological device exhibits higher out-of-plane particle velocities for any given absorbed power level.