A theory has been developed describing x-ray diffuse scattering from misfit dislocations in epitaxial layers. This approach has been used for explaining the origins of diffuse x-ray scattering from SiGe layers with linearly graded Ge content. The distribution of the diffusely scattered intensity in reciprocal plane measured by triple-axis x-ray diffractometry has been compared with theoretical predictions and a good agreement has been achieved. It is demonstrated that the main part of the diffusely scattered intensity originates from random strains caused by misfit dislocations at the substrate–epilayer interface or in the relaxed part of the compositionally graded layers. The contribution of the threading dislocation segments to the diffuse scattering is rather small.

We have studied the strain relaxation in Si1−xGex/Si (001) structures with high electron mobility grown by molecular beam epitaxy. The structures contain a Si1−xGex layer with linearly graded composition, followed subsequently by a uniform composition buffer Si1−yGey, a thin Si layer serving as two-dimensional electron gas channel, and a modulation n-doped Si1−xGex layer. We found that a major part of the graded layer is basically completely strain relaxed, whereas a very thin layer close to the graded-uniform layer interface, as well as the uniform alloy buffer, are just partly relaxed. We performed also model calculations of the strain status of a graded-uniform two-layer system using an equilibrium approach. It is found that for our Si0.7Ge0.3 systems, the residual strains of the samples with different composition, grading rate, and a uniform buffer thickness of 0.6 μm is almost the same at equilibrium. However, experiments show a clear dependence of the residual strain on the grading rate of the graded buffer. The higher the grading rate, the higher is the residual strain in the constant composition alloy buffer. This indicates that with a lower grading rate, the structure is closer to equilibrium, and is thus, thermally more stable. Furthermore, lower grading rates produce also smoother surfaces.

High-resolution x-ray reciprocal space mapping was employed to determine the in-depth strain distribution of Si1−xGex films with linear composition gradings between 4.2% and 15% Ge per μm, and thicknesses between 0.4 and 1.7 μm. The variation of grading and thickness parameters of the samples provides a complete picture of the overall relaxation behavior of linearly graded epilayers. The x-ray data show a top layer of grading-dependent residual strain whereas the lower parts of the films are completely and/or partly relaxed with respect to the Si substrate.

X-ray reciprocal space mapping has been used to investigate the strain status of microgun-pumped blue and blue-green laser structures. The devices exploit graded-index, separate confinement Zn1−xCdxSe/ZnSe heterostructures grown on InGaAs or GaAs substrates by molecular-beam epitaxy. The location of the reciprocal lattice point of the ZnSe buffer layer within a normally forbidden region of reciprocal space indicates that the ZnSe buffer layer is unusually strained, with an appreciable biaxial tensile strain despite the smaller lattice parameter of the III–V substrate relative to ZnSe. We associate such a phenomenon with the presence of the highly strained laser structure coupled with preferential strain relaxation at the II–VI/III–V heterointerface.

Transition from planar to island growth mode in SiGe structures fabricated on SiGe/Si (001) strain-relaxed buffers Appl. Phys. Lett. 101, 151601 (2012); 10.1063/1.4758486High-quality strain-relaxed SiGe films grown with low temperature Si buffer Strain relaxation of Ge films grown on a Si(001)2×1 surface by molecular beam epitaxy