Lattice-mismatch induced-stress in porous silicon films

We have studied the stress in porous silicon films with different porosities at the interface with the substrate. Micro-Raman spectra were measured along a cleaved cross-section to sample different layer depths. Each spectrum was fit to the phonon confinement model, with the bulk phonon frequency as a free parameter to remove phonon confinement effects. At the interface this frequency increases sharply, indicating a compressive stress on the porous silicon pillars. The stress is due to the lattice mismatch, measured by X-ray diffraction, between the porous film and the bulk silicon substrate. For porosities between 50 and 85% the stress and the lattice mismatch vary, respectively, between 4 and 10 kbar, and between 2.9×10 −3 and 3.5×10 −3. Finally, from the dependence of stress on the lattice mismatch we obtain a microscopic Young's modulus of 156 GPa. This magnitude, mostly dependent on atomic bonding, is close to the bulk silicon value and is much larger than the macroscopic modulus, strongly dependent on the porous structure, reported in the literature.