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X-ray rocking curve analysis of superlattices

Speriosu, V. S. and Vreeland, T., Jr. (1984) X-ray rocking curve analysis of superlattices. Journal of Applied Physics, 56 (6). pp. 1591-1600. ISSN 0021-8979. doi:10.1063/1.334169.

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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 ~1×10^4/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 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.

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Additional Information:Copyright © 1984 American Institute of Physics. Received 16 March 1984; accepted 7 May 1984. Dr. Bruce M. Paine contributed in a major way to the setting up of our diffractometer and data acquisition and analysis system. During the initial critical stages of the development, Dr. Paine guided us successfully through a morass of hardware and software problems. Since then we have relied on him for general troubleshooting and advice on programming. We are grateful to John Melvin for supplying us with an initial graphics package and to Frank Cosso and Prakash Kasiraj for systems programs. Professor M-A. Nicolet encouraged us at every step of this study. The work was supported by the Defense Advanced Research Projects Agency (S. Rooslid) under Contract6 (MDA 903-82-C-0348).
Issue or Number:6
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ID Code:10206
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Deposited On:16 Apr 2008
Last Modified:08 Nov 2021 21:06

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