It was noted that grazing-incidence X-ray diffraction methods permitted the direct measurement of the in-plane lattice parameters of SiGe films that were too thin to yield good results when using normal-geometry triple-axis techniques. An X-shaped pattern was seen in the H-K reciprocal space maps of the diffracted X-ray intensity from films that had relaxed via a modified Frank-Read mechanism. Contours of intensity were seen, along <110> directions from the (4¯00) reciprocal lattice peak, upon introducing the first dislocations. At higher dislocation densities, the X-shaped contours were anisotropically distorted and a satellite peak which corresponded to the lattice parameter for a partially relaxed film could be identified at lower H. On the other hand, the H-K reciprocal space contours from thin films that had relaxed, via roughening and the subsequent random nucleation of dislocations, exhibited broad oval contours that were centered at the (4¯00) reciprocal lattice point. Numerical simulations of the grazing-incidence X-ray diffraction from various dislocation arrangements were carried out in order to explain the origin of the X-shaped pattern. It was shown that this pattern arose from an array of long misfit dislocations which ran in <110> directions. The anisotropic distortion of the X-shaped pattern at higher dislocation densities was attributed to the orthogonal intersection of dislocations with equal Burgers vectors. The latter were characteristic of the dislocation networks that were generated by a modified Frank-Read mechanism. It was concluded that measured values of the in-plane lattice parameter, together with out-of-plane lattice parameters which were deduced from symmetrical (004) reflections, permitted accurate calculations to be made of compositions and strains in these layers.

J.L.Jordan-Sweet, P.M.Mooney, M.A.Lutz, R.M.Feenstra, J.O.Chu, F.K.LeGoues: Journal of Applied Physics, 1996, 80[1], 89-96