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)]

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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.

The depth profiles of metamorphic In x Al 1−x As ͑0.05Ͻ x Ͻ 1͒ buffer layers grown on GaAs substrates were characterized using the x-ray reciprocal space mapping. Three types of metamorphic samples were investigated and compared: step grade, single-slope linear grade, and dual-slope linear grade. The lattice mismatch, residual strain, crystallographic tilt, tilt azimuth, and the full width at half maximum were obtained from the reciprocal space maps. The tilt angle of linearly graded buffer layers stayed low at low In compositions until InϷ 60%, at which composition the tilt angle increased abruptly. All linear-grade samples had an untilted relaxed structure in the low In region ͑below 60% In͒ and a tilted structure in the upper, high In region ͑above 60% In͒. The average lattice mismatch between the untilted relaxed structure and the tilted structure determines the tilt angle. The tilt angle of the step-graded layers increased at a near-linear rate as the In composition was increased. The tilt azimuth was intermediate between the ͗100͘ and ͗110͘ in-plane directions. The x-ray full width at half maximum generally increased with the In composition, but tended lower toward surface. We suggest a possible design strategy for the linear-grade metamorphic buffer layer based on our result.

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