The effects of lattice misfit strain in epitaxial GeSn/Ge/Si(001) heterostructures on Sn incorporation, misfit dislocations (MDs), and the critical thickness were investigated using high-resolution x-ray diffraction. By performing a simulation of the x-ray reciprocal space maps measured in the vicinity of an asymmetrical reflection, we determined the strong correlation between the strain relaxation, density of MDs, and Sn content in the GeSn alloy for a compositional range of 4 to 15 at. %. Herein, we quantitatively describe the phenomenon of strain-suppressed Sn incorporation in GeSn, leading to the formation of top Sn-rich, middle compositionally graded, and bottom Sn-poor regions at fixed growth conditions. It is shown that the thicknesses of the bottom Sn-poor region at which the composition spontaneously changes are correlated with the theoretically predicted critical thickness for the nucleation of MDs. Depending on the degree of strain relaxation in the bottom GeSn layer, the density of MDs at the GeSn/Ge interface varies in the range of $\sim$ 2–5 × 10⁵ cm⁻¹ as the Sn content increases from 4 to 12 at. %. The thickness of the compositionally graded region, 160 ± 25 nm, corresponds to the thickness at which the GeSn layer fully relaxes through the interaction/multiplication of MDs. These results contribute to the fundamental understanding that strain engineering is not only crucial to tune the bandgap of Sn-containing group-IV semiconductors but also a key factor for the growth of Sn-rich metastable GeSn layers for mid-infrared photonic devices.

In this work, the influence of micro- and macro-deformation profiles in GaN nanowires (NWs) on the angular intensity distribution of X-ray diffraction are studied theoretically. The calculations are performed by using kinematical theory of X-ray diffraction and assuming the deformation decays exponentially from the NW/substrate interface. Theoretical modeling of X-ray scattering from NWs with different deformation profiles are carried out. We show that the shape of the (002) 2θ/ω X-ray diffraction profile (XDP) is defined by initial deformation at the NW's bottom and its relaxation depth given by the decay depth of the exponential deformation profile. Also, we demonstrate that macro-deformation leads to XDP shift, whereas micro-deformations are the cause of XDP's asymmetry and its symmetrical broadening. A good correlation between calculated and experimental XDP from self-assembled GaN NWs on Si(111) substrate was achieved by taking into account all parameters of micro- and macro-deformation profiles.

The strain relaxation, depth profiles of composition and density of dislocations in GeSn epilayers were studied by using the x-ray diffraction. Regions with uniform and graded composition, different levels of strain relaxation, and dislocation density were found in the GeSn layers grown at fixed growth conditions. At the initial stage of growth, the GeSn layer is under ∼8 × 10 ^–3 compressive strain, and the Sn composition is close to the target value of 6.6%. With increasing layer thickness, the Sn content is enhanced by 0.85 ± 0.12% due to the relief of compressive strain down to ∼5.0 × 10 ^–4 . The plastic strain relaxation is dominated by 60° misfit dislocations at the GeSn/Ge interface, where their density is 3 × 10 ⁵ cm ⁻¹ . The relaxed GeSn layer serves as a buffer for the high-quality GeSn overlayer with uniform and enhanced Sn composition. The laboratory-based x-ray diffraction is shown as a non-destructive reliable technique for strain, composition, and defects characterization, as an alternative to secondary ion mass spectrometry and transmission electron microscope techniques.

A new approach is described that is applicable for structural characterization of any heteroepitaxially grown (strained or relaxed) III-nitride superlattices (SLs). The proposed method utilizes X-ray reciprocal space mapping measured in the vicinity of an asymmetrical reflection to determine the SL period, thickness, and strain state of a quantum well/barrier. On the example of a GaN/AlN SL, it is demonstrated that the structure parameters obtained from the proposed method agree very well with the parameters revealed by the currently preferred approach that is based on the measurements of ω/2θ X-ray diffraction profiles. Furthermore, it is shown that the shape of the reciprocal lattice points measured in the asymmetrical diffraction geometry contains additional information about the density of threading dislocations (TDs) in the GaN substrate and in the GaN/AlN SL. The comparison of the density of TDs in the substrate and in the SL allows analysis of the relaxation mechanism and development of new techniques for the improvement of the structural quality of the SL.

Superlattices (SLs) consisting of symmetric layers of GaN and AlN have been investigated. Detailed X-ray diffraction and reflectivity measurements demonstrate that the relaxation of built-up strain in the films generally increases with an increasing number of repetitions; however, an apparent relaxation for subcritical thickness SLs is explained through the accumulation of Nagai tilt at each interface of the SL. Additional atomic force microscopy measurements reveal surface pit densities which appear to correlate with the amount of residual strain in the films along with the appearance of cracks for SLs which have exceeded the critical thickness for plastic relaxation. These results indicate a total SL thickness beyond which growth may be limited for the formation of high-quality coherent crystal structures; however, they may indicate a growth window for the reduction of threading dislocations by controlled relaxation of the epilayers.