This review paper presents the applications of X-ray diffraction to routine measurements and the procedures for extending its capabilities of analysis to undertake a detailed structural investigation of low-dimensional structures. The uses and limitations of the familiar double-crystal diffractometer are discussed as are the advantages of 'reciprocal space mapping' with a multiple-crystal diffractometer. In general X-ray diffraction has been used for composition and thickness measurement in low-dimensional structures (LDS) and these aspects are covered, as well as the avoidance of the pitfalls associated with their determination. The possibilities for the use of X-ray diffraction methods to determine interface quality, the evolution of lattice relaxation, the detailed microstructure, etc, are discussed, with an indication of the limits of the techniques.

https://iopscience.iop.org/article/10.1088/0268-1242/8/11/001/pdf

X-ray diffraction from low-dimensional structures

A dynamical model for the general case of Bragg x-ray diffraction from arbitrarily thick nonuniform crystalline films is presented. The model incorporates depth-dependent strain and a spherically symmetric Gaussian distribution of randomly displaced atoms and can be applied to the rocking curve analysis of ion-damaged single crystals and strained layer superlattices. The analysis of x-ray rocking curves using this model provides detailed strain and damage depth distributions for ion-implanted or MeV-ion-bombarded crystals and layer thickness, and lattice strain distributions for epitaxial layers and superlattices. The computation time using the dynamical model is comparable to that using a kinematical model. We also present detailed strain and damage depth distributions in MeV-ion-bombarded GaAs(100) crystals. The perpendicular strain at the sample surface, measured as a function of ion-beam dose (D), nuclear stopping power (Sn), and electronic stopping power (Se) is shown to vary according to (1–kSe)DSn and saturate at high doses.

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Dynamical x‐ray diffraction from nonuniform crystalline films: Application to x‐ray rocking curve analysis

The dislocation densities, surface morphology, and strain of Ga1−xInxAs/GaAs epitaxial interfaces as a function of indium composition and layer thickness have been investigated by transmission electron microscopy, medium energy ion blocking, and double‐crystal x‐ray diffractometry. The electron microscopy shows that in the thinnest dislocated films (90 and 160 nm, x=0.07) 60° α dislocations form first in one 〈110〉 direction at the interface. Surprisingly, however, an asymmetry in residual layer strain is not detected in these samples, suggesting that the dislocations have the same Burgers vector or are evenly distributed between two Burgers vectors. Orthogonal arrays of dislocations are observed in films thicker than 300 nm (60° and edge‐type, x=0.07). In this case, dislocation densities in each 〈110〉 direction are equal to within experimental error while an asymmetry in in‐plane strain is measured (18% and 30% for x=0.07, 300, and 580 nm thick, respectively). An unequal distribution of Burgers vectors of...

Asymmetries in dislocation densities, surface morphology, and strain of GaInAs/GaAs single heterolayers

Epitaxial TiN/V0.3Nb0.7N superlattices with a 1.7% lattice mismatch between the layers were grown by reactive magnetron sputtering on MgO(001) substrates. Superlattice structure, crystalline perfection, composition modulation amplitudes, and coherency strains were studied using transmission electron microscopy and x-ray diffraction. Hardness H and elastic modulus were measured by nanoindentation. H increased rapidly with increasing Λ, peaking at H values ≍75% greater than rule-of-mixtures values at Λ ≍ 6 nm, before decreasing slightly with further increases in Λ. A comparison with previously studied lattice-matched TiN/V0.6Nb0.4N superlattices, which had nearly identical composition modulation amplitudes, showed a similar H variation, but a smaller H enhancement of ≍50%. The results suggest that coherency strains, which were larger for the mismatched TiN/V0.3Nb0.7N superlattices, were responsible for the larger hardness enhancement. The results are discussed in terms of coherency strain theories developed for spinodally decomposed materials. Nanoindenter elastic modulus results showed no significant anomalies.

Structure and mechanical properties of epitaxial TiN/V0.3Nb0.7N(100) superlattices

The structural and optical properties of lattice-matched InAs0.911Sb0.089 bulk layers and strain-balanced InAs/InAs1−xSbx (x ∼ 0.1–0.4) superlattices grown on (100)-oriented GaSb substrates by molecular beam epitaxy are examined using X-ray diffraction, spectroscopic ellipsometry, and temperature dependent photoluminescence spectroscopy. The photoluminescence and ellipsometry measurements determine the ground state bandgap energy and the X-ray diffraction measurements determine the layer thickness and mole fraction of the structures studied. Detailed modeling of the X-ray diffraction data is employed to quantify unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattices. A Kronig-Penney model of the superlattice miniband structure is used to analyze the valence band offset between InAs and InAsSb, and hence the InAsSb band edge positions at each mole fraction. The resulting composition dependence of the bandgap energy and band edge positions of InAsSb are described using the bandgap bowing model; the respective low and room temperature bowing parameters for bulk InAsSb are 938 and 750 meV for the bandgap, 558 and 383 meV for the conduction band, and −380 and −367 meV for the valence band.

/pdf/measurement-of-inassb-bandgap-energy-and-inas-inassb-band-31sbyogp7x.pdf

Measurement of InAsSb bandgap energy and InAs/InAsSb band edge positions using spectroscopic ellipsometry and photoluminescence spectroscopy

We present detailed analyses of x-ray double-crystal rocking curve measurements of superlattices. The technique measures depth profiles of structure factor, and profiles of perpendicular and parallel strains relative to the underlying substrate. In addition to providing a detailed picture of the state of stress, the profiles are a direct measure of the composition modulation. The thickness of the period of modulation and the average strain are determined with a precision of ~1%. The detailed structure of the period is determined to ~5%. We obtain an expression relating the structure of the rocking curve to the structure of the period. This expression allows analytic determination of the structure without Fourier transformation or computer fitting. We show the influence of small random fluctuations in layer thicknesses and strains. The technique is applied to a 15-period GaAlAs/GaAs and a ten-period AlSb/GaSb superlattice grown on GaAs and GaSb substrates, respectively. In the former, the thickness of the period was 676 A and the perpendicular strain varied between zero for the GaAs layer and 0.249% for the layer with peak (93%) Al concentration. Transition regions, ~100 A thick, with continuously varying composition, were found between the GaAs and the Ga0.07 Al0.93As layers. Fluctuations in structural properties were less than 5% of the average. The AlSb/GaSb superlattice had a period of 610 A with sharp transition regions between the layers and negligible fluctuations from period to period. The perpendicular strains were −0.03% and 1.25%, respectively, for the GaSb and AlSb layers. A uniform parallel strain of 0.03% was found throughout the superlattice. Nonzero parallel strain indicates that a small fraction of the misfit between the superlattice and the substrate is plastically accommodated by net edge dislocations lying in a narrow region (a few hundred A thick) at the interface with the substrate. The net number of edge dislocations was calculated to be ~1×10^4/cm^2. The measured perpendicular strains were in excellent agreement with the values calculated from bulk lattice parameters, elastic properties, and the parallel strain. For both superlattices, the standard deviation of random atomic displacements away from perfect crystal sites was below 0.1 A, in agreement with reported ion channeling and electron diffraction measurements of superlattices. The rocking curve method is a major tool for quantitative analysis of superlattices.

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V. S. Speriosu

Papers

X‐ray rocking curve analysis of superlattices