Finite-element simulation of photoinduced strain dynamics in silicon thin plates

Abstract

In this paper, we investigate the femtosecond-optical-pulse-induced strain dynamics in relatively thin (100 nm) and thick (10 000 nm) silicon plates based on finite-element simulations. In the thin sample, almost spatially homogeneous excitation by the optical pulse predominantly generates a standing wave of the lowest-order acoustic resonance mode along the out-of-plane direction. At the same time, laterally propagating plate waves are emitted at the sample edge through the open edge deformation. Fourier transformation analysis reveals that the plate waves in the thin sample are mainly composed of two symmetric Lamb waves, reflecting the spatially uniform photoexcitation. In the thick sample, on the other hand, only the near surface region is photo-excited and thus a strain pulse that propagates along the out-of-plane direction is generated, accompanying the laterally propagating pulse-like strain dynamics through the edge deformation. These lateral strain pulses consist of multiple Lamb waves, including asymmetric and higher-order symmetric modes. Our simulations quantitatively demonstrate the out-of-plane and in-plane photoinduced strain dynamics in realistic silicon plates, ranging from the plate wave form to pulse trains, depending on material parameters such as sample thickness, optical penetration depth, and sound velocity.

Ultrafast Nanoimaging of Spin-Mediated Shear Waves in an Acoustic Cavity

“…39−41 Because of the homogeneous laser excitation, the even harmonics in a defect-free sample, which exhibit symmetric displacement profiles (Figures 1d and 1f) relative to the sample central layer, are forbidden. 39,41 However, different from these reports where only odd harmonics were observed, we observed both even and odd harmonics, suggesting that asymmetric stress is present in the sample. 42 The asymmetric stress may originate in the defective layers, which we will discuss later.…”

“…We found that only odd harmonics are excited in the defect-free, homogeneously excited sample, in agreement with the previously study. 41 However, when a defect layer is present, as long as its location breaks the mirror symmetry with respect to the middle atomic layer, even harmonics would appear. Such defect that presents either inside the sample or at the surface (e.g., oxidized surface layers or stacking fault) can result in even harmonics detected sensitively by the ultrafast nanoscale imaging measurements.…”

Characterizing an Optically Induced Sub-micrometer Gigahertz Acoustic Wave in a Silicon Thin Plate

“…Recent studies further utilize the acoustic properties in nanostructures such as ultrathin plates, nanowires, semiconductor superlattice, semiconductor interface, and phononic crystal . For example, when an ultrathin semiconductor plate is irradiated by pulsed light with penetration depth much larger than the sample thickness, the sample is photoexcited almost uniformly along the out-of-plane direction [Figure (a)].…”

“…3,4 As reported in the pioneering works in the 1980's, 5,6 photoexcitation of metals and semiconductors with ultrashort laser pulses can generate GHz-THz acoustic waves on picosecond time-scale at the materials' surface through sudden lattice heating (thermoelastic effect) and/or deformation potential induced by photocarriers. 4,5,7,8 Recent studies further utilize the acoustic properties in nanostructures such as ultrathin plates, 10 nanowires, 11 semiconductor superlattice, 9 semiconductor interface, 12 and phononic crystal. 13 For example, when an ultrathin semiconductor plate is irradiated by pulsed light with penetration depth much larger than the sample thickness, the sample is photoexcited almost uniformly along the out-of-plane direction [Figure 1(a)].…”

“…We confirmed that all values in Figure 2(b) are zero at t < 0 before applying the high-pass filter. First, we theoretically investigated the nanoplate waves in an ultrathin silicon plate based on the finite-element method presented in the literature 10 (see Section 2 in the Supporting Information for details), as shown in Figures 2(a−c). We prepared a three-dimensional thin plate of [331] oriented single crystalline silicon with a thickness d = 230 nm to compare with the experimental results.…”