Refinement of high-resolution X-ray diffraction data in characterizing epitaxial layers and multiple-quantum wells by the peak separation technique

Abstract

The process of determining the strain and composition in epitaxial layers by the X-ray rocking curve technique involves the measurement of peak separations between the substrate and the epilayer for specific reflections. The resulting interplanar spacings are combined and solved for the in-plane and perpendicular lattice parameters and hence for the strain. However, lattice parameters computed from different combinations of reflections often differ by amounts as large as several hundred parts per million, whereas much smaller errors of near ten parts per million are expected. This leads to an ambiguity in separating discrepancies from true experimental errors. To remove this ambiguity, a simple, analytical, and versatile method is proposed, which forces the X-ray reflection equations towards internal consistency by making small adjustments to each measurement. A least-squares version of the method is described, and applied to several common systems of interest, although any other assumed relationship among the adjustments may also be utilized. The concepts of inconsistency and experimental error are distinguished, and an index of consistency is defined. This definition does not absolve the requirement of repeated measurements for determining the experimental error, but gives a quantitative gauge of fit among individual measurements from various diffracting planes.