ADSORPTION STRAINS IN POROUS SILICON

X-ray-diffraction observations of strains induced by vapor adsorption are reported for porous silicon single-crystal samples. Two types of porous silicon ($p$ and ${p}^{+}$) with very different pore structure are investigated. A low-pressure contraction is observed in $p$-type samples with spherical pores of about 3-nm diameter. In ${p}^{+}$-type samples, where the pores are cylindrical with a larger diameter of about 10 nm, a minimum of the lattice parameter versus the vapor pressure is observed when capillary condensation occurs with a distinct hysteresis between increasing and decreasing vapor pressure. Finally, an expansion is observed for complete wetting. These results are discussed for the different pressure ranges in relation to previous experimental and theoretical studies on adsorption strains. The analogous features observed for very different materials could have a common origin. The expansion is easily explained by the decrease of surface energy due to adsorption and wetting. It appears that the low-pressure contraction is partially related to the attractive van der Waals interactions induced by vapor adsorption in nanometer-size cavities. The softening of the elastic constants observed in porous silicon is discussed in order to explain the magnitude of the observed strains.