Model-independent determination of the strain distribution for aSi0.9Ge0.1/Si superlattice using x-ray diffractometry data

The strain distribution in a ${\mathrm{Si}}_{0.9}$ ${\mathrm{Ge}}_{0.1}$/Si superlattice is determined from x-ray diffractometry data with a 25 Å depth resolution. A logarithmic dispersion relation is used to determine the phase of the structure factor with information available a priori on the sample structure. Phase information is obtained from the observed reflection intensity via a logarithmic Hilbert transform and the a priori information is used to select the zeros to be included in the solution. The reconstructed lattice strain profile clearly resolves SiGe and Si layers of 90–160 Å thickness alternately stacked on a silicon substrate. The SiGe layer is found to have a lattice spacing in the surface-normal direction significantly smaller than predicted by Vegard’s law. The result gives simulated rocking-curve profiles in very good agreement with the observation. The apparent deviation from Vegard’s law could be confirmed by chemical analysis. © 1996 The American Physical Society.