Elastic properties of porous silicon studied by acoustic transmission spectroscopy

Abstract

The porosity dependence of the elastic properties of porous silicon in different crystallographic directions is studied. The velocity of longitudinal acoustic waves in porous silicon layers electrochemically etched in (100), (110), and (111) oriented wafers has been measured by acoustic spectroscopy in the gigahertz frequency range. This non-destructive method was used for porous silicon layers with porosity of 25-85% obtaining velocities in the range of about 1 to 7 km s-1. The implication of constant Poisson’s ratio of porous silicon is examined. The effect of velocity dispersion due to multiple scattering is considered. The c11 stiffness constant can be obtained from the velocity measurement in the [100] direction of a cubic crystal. We show that, using the results for velocity in [110] or [111] directions and Keating’s relation, the stiffness constants c12 and c44 can be obtained. The velocity dependence on porosity was fitted as v=v0(1-φ)κ, where v0 is the velocity in bulk silicon, φ is porosity, and κ is a fitting parameter. It is shown that with other conditions being equal: (i) the porosity dependence of the acoustic velocity is related to the doping level of the wafer from which the porous silicon was etched (κ depends on wafer resistivity); (ii) acoustic velocities in different crystallographic directions have the same dependence on porosity (κ is independent of wafer orientation). This requires that all three stiffness constants c11, c12 and c44 have the same dependence on porosity: cij=cij0(1-φ)m; and (iii) the morphology of porous layers depends on the HF concentration in the etchant (κ is used as an indicator for the disorder of the porous structure).