X-ray measurement of deformation and dislocation density in semiconductor strained layers

Abstract

Double-crystal X-ray diffraction is commonly used to measure the misfit strain and relaxation of epitaxial semiconductor layers. In this paper, a framework is developed which links the measured parameters Δ d / d and Δø to the deformation tensor of a semicoherent layer. Isotropic elasticity theory and the Frank-Bilby equation are used to derive an analytical expression for this deformation. By combining X-ray measurements of different planes, it is possible to obtain the misfit strain and details of the misfit dislocation array in a strained layer grown on a substrate of arbitrary orientation. In (001) layers, it is shown that the misfit strain and relaxation can be found from just six rocking curves, although the most accurate measurements require twelve rocking curves.