Shape-fitting analyses of two-dimensional X-ray diffraction spots for strain-distribution evaluation in a β-FeSi₂ nanofilm

New fitting analyses for peak shapes in a 2D reciprocal-space map are demonstrated to evaluate the strain, strain distribution and domain size of a crystalline ultra-thin (15 Å) film of β-FeSi₂(100) grown epitaxially on an Si(001) substrate, using grazing-incidence X-ray diffraction. A 2D Laue-fit analysis taking into account instrument broadening and the double-domain effect provides residual maps as a function of the inequivalent strains [epsilon]_b and [epsilon]_c along the b and c axes of β-FeSi₂, respectively (and domain size D), reflecting the probability of existence of homogeneous domains with fixed [epsilon]_b, [epsilon]_c and D, in addition to the most probable minimum residual. A 2D Laue fit with an inhomogeneous domain distribution provides a population map with [epsilon]_b and [epsilon]_c, reflecting strain components contributing to the film. The population map also leads to a reference residual as a guide for the strains contributing to the residual map. The advantages of the 2D Laue fits are discussed by comparison with the Scherrer, Williamson–Hall and Gaussian fitting methods for equivalent systems. The analyzed results indicate that the β-FeSi₂ nanofilm was considerably small strained, which was also confirmed by transmission electron microscopy, implying a weak interface interaction between the film and the substrate.