Determination of threading dislocation density in hetero-epitaxial layers by diffuse X-ray scattering

An approach for the determination of dislocation densities in epilayers is presented, which is based on the analysis of the two-dimensional intensity distribution of diffuse X-ray scattering measured by triple-axis X-ray reciprocal-space mapping. A new formalism for the simulation of experimental iso-intensity contours is used, which assumes a defect model based on random elastic deformation due to the strain fields of dislocations. The simulation of the two-dimensional intensity contours yields the random strain field from which the energy density stored in the epilayer due to the presence of dislocations is calculated. On the other hand, the self-energy of threading dislocations is calculated assuming 60 degrees (for diamond or zincblende structure) or screw-type dislocations. The threading dislocation density is obtained by dividing the energy density by this self-energy. The method was applied for the analysis of SiGe layers grown on compositionally graded SiGe alloy buffer layers. The diffuse X-ray scattering analysis reproduces the increase in the dislocation densities in the buffer with higher Ge grading rates and yields upper limits for the threading dislocation densities.