Local resonances and transverse wave propagation in a monocrystalline silicon wafer

Abstract

In anisotropic media, the power flux of guided elastic waves is not necessarily collinear with the wave vector [1]. This leads to extraordinary behavior of local resonances in infinite plates, the so-called zero-group-velocity (ZGV) resonances. These exist only along a finite set of directions [2]. In other directions we find transverse-group-velocity (TGV) waves, whose power flux is orthogonal to the wave vector [2]. In Fig. 1 (top), we show a laser-ultrasonic measurement of the TGV wave obtained on a monocrystalline silicon wafer of cubic anisotropy. Furthermore, due to the non-vanishing power flux of TGV waves, time acts as a filter in the wavenumber domain. After some time, only eight wave vectors remain close to the source: the ZGV resonances located on the <100> axes (ZGV1) and the <110> axes (ZGV2) of the crystal. This intuitively explains the complex resonance pattern that emerges naturally on the surface of the wafer after an impulsive point source excitation. The ZGV1 and ZGV2 modes occur at distinct frequencies and wavenumbers, which leads to beating of the overall pattern when the two interfere. Although this wave field exhibits a vanishing power flux, the phase fronts move spatially. The two ZGV resonance patterns obtained by temporal Fourier transform of the experimentally acquired field are depicted in Fig. 1 (bottom). They form checkerboard patterns, in contrast to the concentric nodal lines seen in isotropic plates.

Daniel A. Kiefer

Researcher at Institut Langevin

Research in guided elastodynamic waves, fluid-structure interaction, simulation and signal processing for ultrasonic sensors and nondestructive testing.