Anisotropic propagation of GHz surface and bulk acoustic waves in gallium arsenide studied by random scattering

Abstract

Understanding the complex anisotropic acoustic propagation in crystals is crucial for optimizing the performance of surface and bulk acoustic wave devices. Here, we investigate the anisotropy and coupling of GHz acoustic modes in (001)-cut gallium arsenide through theory and experiment. We first numerically calculate the angle-dependent phase velocities for surface and bulk modes, and we provide a code which can easily be adapted to different material systems. We validate our theoretical model experimentally by exciting surface modes with an interdigital transducer, and achieve omnidirectional acoustic propagation through random scattering of the acoustic waves. We measure the complex acoustic field with a scanning optical interferometer, and extract the angle-dependent velocities of surface and bulk modes using Fourier domain analysis. Our method could be used for the optimization of GHz-range classical and quantum acoustic devices, by studying losses of surface and bulk modes.

Figures (5)

• Figure 1: Crystal structure and surface wave displacement. GaAs crystal structure (a), where the coordinate system $(x_1,x_2,x_3)$ is aligned with the crystallographic directions. Sketch of a SAW propagating in the [100] direction (b), where the surface is defined by the $(x_1,x_3)$ plane. Depth-dependent longitudinal ($u_L$) and transverse ($u_T$) displacements (c) for the same SAW mode.
• Figure 2: BAW displacements and surface mode velocities and polarization. Sketches (a-c) of the mechanical displacement of the three BAW modes, propagating in the [100] direction. Theoretical boundary condition fullfillment (d), $s_{min}$, of the four chosen partial waves from the Stroh formalism, plotted on a logarithmic scale between the [110] and [100] crystal axes. Relative angle-dependent amplitudes (e) of the mechanical polarizations of the SAW and pSAW modes.
• Figure 3: Experimental setup. Schematic (a) of the acoustic scattering sample, where the inset depicts the optical measurement of the acoustic field. Optical microscope image (b) of the acoustic scattering device, with inset showing a scanning electron microscope image of the IDT finger structure.
• Figure 4: Experimental results and comparison to theory. Rms amplitude amplitude (a, logarithmic scale) and phase (b) of the 1.03205 GHz demodulated interferometric signal, measured on the area indicated by the black dashed box in the microscope image (d). Absolute value (c) of the spatial Fourier transform of the complex measurement of the area indicated by the red dashed box in (d). The data is folded to a 45 degree sector and the values $(\bar{\nu}_x,\bar{\nu}_y)$ are shown in red. Comparison (e) between the measured (red dots) and theoretical angle-dependent velocities of the surface (black curves) and bulk (dashed black curves) acoustic modes.
• Figure 5: Flowchart of the numerical procedure used to construct SAW and pSAW modes and to determine their angle-dependent velocities.