X-Ray Diffraction Methods for the Determination of Stresses and Strains in Multilayer Monocrystal Films

Abstract

Abstract Basic equations relating to the anisotropic theory of elasticity for multilayer heterostructures are presented. These equations account for the plastic deformation and the layer lattice parameters mismatch with respect to the substrate. Special attention is given to take into account the variation in the components of the elastic stiffness tensor in the layers of various compositions. A solution of the one-dimensional problem of elastically and plastically deformed state is cited for heterostructures of the cubic system. Particular cases of a two-layer heterostructure with variable components of elastic stiffness tensor were studied in the absence of plastic deformations, as well as with constant components of elastic stiffness tensor in the presence of dislocations in the heterostructure. The most promising non-destructive double and triple-crystal X-ray diffraction methods for the measurement of components of the strain tensor and heterostructure curvature are discussed. Particular attention is paid to the determination of a number of structural features of epitaxial systems: viz., the critical thicknesses of pseudomorphous layers, the strain gradient in the films of heterogeneous solid solutions, recovering of proper deformation profiles on the basis of measured results for heterostructure curvature with its layer by layer elimination, determination of lattice parameter mismatch, determination of concentration in heterostructures of four-component solid solutions, and determination of the thickness of the transition width on the heteroboundary of a two-layer heterostructure. A calculation of stresses in the layers of a five-layer double heterostructure with two consistent layers of solid solutions, and in the layers of epitaxial superlattice, has been carried out. In conclusion, X-ray diffraction methods allowing one to measure deformation in ultrathin surface layers are discussed.