Simultaneous determination of tensile and shear strains of crystalline bilayers using three Bragg reflections of X-rays

A method for the simultaneous determination of nine strain coefficients, both shear and tensile, of crystalline bilayers is proposed and realized. The X-ray diffraction peak intensities along 2θ (vertical) and β (horizontal) scans relative to the plane of incidence of three Bragg reflections whose atomic planes are not parallel to each other can be used to obtain shear and tensile strain coefficients. The theoretical considerations and experimental examples for single-crystal GeSi/Si overlayers are reported. It is also demonstrated that, for GeSi/Si, the shear and tensile strain coefficients of the Si substrate tend to vanish when the GeSi layer is thicker than 40 nm.