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 〈100〉 GaAs and 〈100〉 GaSb substrates, respectively. In the former, the thickness of the period was 676 Å 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 Å 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 Å 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 Å thick) at the interface with the substrate. The net number of edge dislocations was calculated to be ∼1×104/cm2. 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 Å, 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.

Erratum: Rocking curve peak shift in thin semiconductor layers [J. Appl. Phys. 66, 985 (1989)] The statement "a wrong boundary condition, saying that the amplitude X is zero deep inside the substrate crystal" on page 986 is incorrect. In fact, our boundary condition Eq. (2) can be obtained from Halliwel's analytical formula for a single-crystal layer' by setting X = 0 at the back side of the crystal layer and assuming the layer thickness to be infinite in her formula. Therefore, our Eq. (2) and the above boundary condition yield the same result. The above statement, however, does not affect any other contents and conclusions of our paper. 'M. A. Halliwel, M. H. Lyons, and M. J. Hill, J. Cryst. Growth 68, 523 (1984).Erratum: Dynamical x-ray diffraction from nonuniform crystalline films: Application to x-ray rocking curve analysis [J. Appl. Phys. 59, 3743 (1986)]

The velocities of individual dislocations of edge and mixed types in pure aluminum single crystals were determined as a function of applied-resolved shear stress and temperature. The dislocation velocities were determined from measurements of the displacements of individual dislocations produced by stress pulses of known duration. The Berg-Barrett x-ray technique was employed to observe the dislocations, and stress pulses of 15 to 108 !'sec duration were applied by propagating torsional waves along the axes of [111} oriented cylindrical crystals. Resolved shear stresses up to 16X 10 6 dynes/em• were applied at temperatures ranging from -150° to +70°C, and dislocation velocities were found to vary from 10 to 2800 em/sec over these ranges of stress and temperature. The experimental conditions were such that the dislocation velocities were not significantly influenced by impurities, dislocation curvature, dislocation-dislocation interactions, or long-range internal stress fields in the crystals. The velocity of dislocations is found to be linearly proportional to the applied-resolved shear stress, and to decrease with increasing temperature, Qualitative comparison of these results with existing theories leads to the conclusion that the mobility of individual dislocations in pure aluminum is governed by dislocation-phonon interactions. The phonon-viscosity theory of dislocation mobility can be brought into agreement with the experimental results by reasonable choices ot the values of certain constants appearing in the theory.

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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.