Elastic characterization of a supported porous silicon layer by Brillouin scattering

Abstract

Brillouin spectroscopy was used to study surface acoustic waves on a supported layer of (111)-oriented porous silicon having a thickness of 2.7 μm and a porosity of 30%. The Rayleigh surface wave velocities were found to be significantly lower than corresponding velocities for crystalline silicon. A complete set of elastic constants for the porous layer was determined from the measured directional dependence of the surface wave velocity in the (111) plane. The best-fit constants are C11=56.0±0.7 GPa, C12=6.7±0.3 GPa and C44=37.0±0.8 GPa. The anisotropy factor, η=1.50 indicates that the porous layer is elastically anisotropic.

Modeling macroscopic elasticity of porous silicon

“…However, excepting some simple empirical relations [2], a general theoretical modeling tool able to recover experimental data and to predict material properties at particular pore sizes and shapes is still missing. As the continuum theory fails to apply at the length scale of pores in nano-PSi we propose a discrete homogenization model and show that under certain regularity assumptions (such as uniformity of shapes and distributions of the pores) the method predicts a mechanical macroscopic behavior that fits remarkably well the experimental data reported in [3][4][5][6] for a wide range of porosities. The method can be easily extend in order to include much more complicated situations such as: other porous semiconductors, more complex microscopic symmetries, compositional effects (like back-bond oxidation) and mechanical related behavior including joint bulk and surface effects.…”

“…The simplest pore shape is the union of three cylinders with equal square cross-section, described by P = [3][4][5][6]. Only in the case of a pore with cubic symmetry the macroscopic response has the same symmetry as the bulk Si.…”

“…where R = C 12 /C 11 while, experimental data for the Young modulus are those reported in [3][4][5][6] obtained respectively using: X-ray diffraction, acoustic methods, nano-indentation and Brillouin spectroscopy. We remark that:…”

Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance

“…(12) for constant V SW . Since no evidence of such surface mode dispersion was reported in previous studies on singlelayer p-Si films, 20,39,40 it is conceivable that this dispersive jj for (a) superlattice A and (b) superlattice B. Filled circles: data collected from the superlattices; filled squares: duplicate measurements taken from superlattice B; solid (dashed) curves: calculations using Eq.…”

Mechanical properties of sintered meso-porous silicon: a numerical model

“…Only few researchers investigated the mechanical properties of this material. Characterizations of PSi mechanical properties were performed employing very different techniques, e.g., nanoindentation [2], Brillouin scattering [3], phase velocity scanning [4], and microechography [5], but each of these works dealt with open-porosity PSi.…”