Direct Visualization of Gigahertz Acoustic Wave Propagation in Suspended Phononic Circuits

We report direct visualization of gigahertz-frequency Lamb-wave propagation in aluminum nitride phononic circuits by transmission-mode microwave impedance microscopy (TMIM). Consistent with finite-element modeling, the acoustic eigenmodes in both a horn-shaped coupler and a subwavelength waveguide are revealed in the TMIM images. Using fast Fourier-transform filtering, we quantitatively analyze the acoustic loss of individual Lamb modes along the waveguide and the power-coupling coefficient between the waveguide and the parabolic couplers. Our work provides insightful information on the propagation, mode conversion, and attenuation of acoustic waves in piezoelectric nanostructures, which is highly desirable for designing and optimizing phononic devices for microwave-signal processing and quantum-information transduction.

Figure 1

(a) Optical image of the $\mathrm{Al}\mathrm{N}$ phononic circuits. Inset on the left shows an AFM image of the split-finger IDT. (b) S₁₁ and (c) S₂₁ spectra of the device measured by a VNA, showing the acoustic resonance at f = 3.44 GHz. (d) Simulation results plotted in deformed grids showing the antisymmetric (A) and (e) symmetric (S) modes of the free-standing membrane at the IDT region.

Figure 2

(a) Calculated dispersion relationship of a free-standing $\mathrm{Al}\mathrm{N}$ phononic waveguide of 1 µm wide. Red and blue curves represent antisymmetric and symmetric modes, respectively. Intersection points between the dashed line at f = 3.44 GHz and three lowest branches of the dispersion curves are labeled as A0, S0, and A1 (see text). (b) 3D simulation results showing the mode shape of A0 and (c) A1 modes with colors indicating the displacement magnitude.

Figure 3

(a) Schematics of the suspended phononic circuit and the TMIM setup. (b) SEM image of the device. Four dashed boxes show the locations where TMIM images are acquired. (c) TMIM image and (d) 2D FFT spectral image in box 1. (e) FFT image after removing the diffusive spots at the center. (f) Inverse FFT image of (e). (g)–(j) Same as (c)–(e) in box 2. (k)–(n) Same as (c)–(e) in box 3. Scale bars are 2 µm for real-space images and 2π × 2 μm⁻¹ for k-space FFT images. False-color scales for panels (c),(g),(k) are the same, so are (d),(e),(h),(i),(l),(m) and (f),(j),(n).

Figure 4

(a) TMIM image and (b) its 2D FFT spectral image in box 4 in Fig. 3. (c) Filtered TMIM and (d) FFT images of the topographic artifact due to tranches on both sides of the waveguide. (e) Filtered TMIM and (f) FFT images associated with the A1 mode. (g) Filtered TMIM and (h) FFT images associated with the A0 mode. Insets of (e),(g) show line cuts through center of the images. Note that (a) is the superposition of (c),(e),(g) in the real space and (b) superposition of (d),(f),(h) in the k-space. Scale bars are 2 µm for real-space images and 2π × 2 µm⁻¹ for k-space FFT images.

Figure 5

TMIM signals of (a) A1 and (b) A0 modes along the 100-µm waveguide. Insets show the filtered TMIM images associated with A1 and A0 modes near the entrance and exit points of the waveguide. Red dashed lines are linear fits to semilogarithmic plots. All scale bars are 2 µm.

Figure 6

Finite-element modeling results of (a)–(c) S0, (d)–(f) A0, and (g)–(i) A1 modes of the suspended $\mathrm{Al}\mathrm{N}$ waveguide (330 nm thick and 1 µm wide). Panels (a),(d),(g) are 3D views. Panels (b),(e),(h) are projections in the x-z plane. Panels (c),(f),(i) are projections in the y-z plane. Periodic boundary conditions are used for the x-z plane and free-moving boundary for the x-y and y-z planes.

Figure 7

(a) AFM, (b) TMIM-1, and (c) TMIM-2 images in a large field of view. Scale bars are 5 µm. (d) TMIM-2 signals along the center of the waveguide in (c).

Figure 8

Simulated displacement fields and electric potential on the suspended $\mathrm{Al}\mathrm{N}$ membrane device under ±1 V excitation or about 10-mV input power at the split-finger IDT. Mechanical oscillation amplitude is in the order of 10 pm. Both out-of-plane and in-plane displacements contribute to the surface potential through different piezoelectric components (d₃₃ and d₃₁) of the c-axis polycrystalline $\mathrm{Al}\mathrm{N}$ membrane. OOP, out of plane; IP, in plane; PML, perfectly matching layer.