Dynamical X-ray Diffraction from In x Ga1-x As Heterostructures with Dislocations

High-resolution x-ray diffraction is an important nondestructive tool for structural characterization of semiconductor heterostructures, and the diffraction intensity profiles contain information on the depth profiles of strain, composition, and defect densities in device heterostructures. Much of this information remains inaccessible because the lack of phase information prevents direct inversion of the rocking curves. The current practice is to use dynamical simulations in conjunction with a curve-fitting procedure to indirectly extract the profiles of strain and composition, but such dynamical simulations have been based on perfect, dislocation-free laminar crystals, which renders the analysis inapplicable to highly mismatched structures containing dislocation densities greater than about 10(6) cm(-2). In this work we present a dynamical model for Bragg x-ray diffraction in semiconductor device structures with nonuniform composition, strain, and dislocation density, which is based on the Takagi-Taupin equation for distorted crystals and accounts for the diffuse scattering arising from the strain mosaicity and angular mosaicity associated with dislocations. We show theoretically that the x-ray diffraction profiles from In (x) Ga1-x As/GaAs (001) heterostructures are strongly affected by the depth distribution of the dislocation density as well as the composition and strain, so that in principle all three distributions may be obtained by the analysis of the measured diffraction profiles.