| Dynamical diffraction theory, which is based on solution of Maxwell's equations in a periodic medium, differs from kinematical diffraction theory for a particular subset of crystal features. Dynamical diffraction is used for studying diffraction from thick single crystals since coherent scattering from different regions of a thick crystal invalidates the assumptions lying under kinematical theory. This thesis performs a rigorous analysis of the diffraction process from single crystals. First, a dynamical diffraction theory which is valid for both symmetric and asymmetric reflections is developed from Maxwell's equations. Then, this theory is generalized to distorted crystals. Through the analysis of this formulation, dynamical to kinematical transition and the validity of real space methods for strain determination are investigated. Free space propagation of diffracted waves from the crystal to the detector is analyzed, and it is proved that the propagation distance causes a fundamental change in the nature of the measured diffraction data. A parameter called "Angular Fresnel Number" which is useful to characterize the measured diffraction data as near-field or far-field is introduced. A numerical method to estimate strain quantitatively in thin-film/substrate systems relying on dynamical diffraction theory is developed and successfully applied to Si3N 4 stressor features on Silicon. Through these studies, we define a rigorous framework to describe diffraction measurements and interpret their results. |
