Lattice distortions perpendicular to the surface in thin surface layers of ion-implanted (111) silicon crystals have been mapped as a function of depth and lateral position with resolutions of 0.05 and 0.65gm, respectively. X-ray triple-crystal diffractometry data were collected near the fundamental 111 and satellite reflections from samples with periodic superstructure modulations in the lateral direction. 300 keV B + ions implanted through surface mask windows are found to produce lattice distortions in a very thin layer of 0.15 gm thickness at 1.05 gm depth below the surface, with interplanar lattice spacings normal to the surface increased by several parts in 104 . The distortions are appreciably extended in the lateral direction, suggesting diffusion of the ions. A 0.5 gm-thick thermaloxide strip is found to contract the interplanar spacing of substrate silicon crystal under the strip region by a few parts in 104, while the strain field created by the parallel oxide edges extends beyond a depth of 3 Bm. A practical procedure is also described for arriving at a solution of the phase problem in the case of a strain field involving heavily distorted layers.
A new method for unambiguous reconstruction of crystal-lattice strains in epitaxially grown layers from high-resolution x-ray diffraction data is proposed. The technique uses x-ray diffracted intensity profiles collected for two different radiation wavelengths. We enhance the theory for the previously developed algorithm for model-independent determination of crystal-lattice strain profiles in single crystals with epitaxially grown top-surface layers. The method relies on the retrieval of the scattered x-ray wave phase from its intensity profile via a logarithmic Hilbert transform. This phase-retrieval technique is always associated with the problem of complex polynomial root finding. A practical procedure for the mapping of complex polynomial roots is proposed to distinguish true and virtual zeros. This allows the phase of the diffracted x-ray wave to be retrieved unambiguously. The method was applied to determine physical dimensions and concentration composition of a Si/Si1−xGex/Si alloy multilayer structure typical for SiGe heterobipolar transistor device.
The strain distribution in a Si 0.9 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.
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