Date of Completion


Embargo Period



Rajeev Bansal, Faquir Jain

Field of Study

Electrical Engineering


Master of Science

Open Access

Open Access


High-resolution x-ray diffraction is a valuable non-destructive tool for the structural characterization of semiconductor heterostructures, and measured diffraction profiles contain information on the depth profiles of strain, composition, and defect densities in device structures. Much of this information goes untapped because the lack of phase information prevents direct inversion of the diffraction profile. A common practice is to use dynamical simulations in conjunction with a curve-fitting procedure to extract the profiles of strain and composition in the depth of the material. Prior to this work, the dynamical simulations have been based on perfect, dislocation-free laminar crystals, and this renders the analysis inapplicable to many real structures which contain dislocation densities greater than about 106 cm-2. In this work we present two novel dynamical models for Bragg x-ray diffraction in semiconductor crystals with arbitrary, nonuniform composition, strain, and dislocation density: the Phase Invariant Model for Dynamical Diffraction (PIDDM) and the Mosaic Crystal Model for Dynamical Diffraction (MCDDM), which improves upon the former with greater accuracy and better computation times. The framework for dynamical diffraction calculations is based on the Takagi-Taupin equation, but modified for distorted crystals by accounting for the angular and strain broadening introduced to the lattice by the presence of dislocations.

In this thesis we cover dynamical diffraction from perfect crystals then provide a description of both PIDDM and MCDDM models. We present results for each of these using the Si1-xGex / Si (001), ZnSySe1-y / GaAs (001), and InxGa1-xAs / GaAs (001) material systems in multilayer, superlattice, step-graded, and linearly-graded heterostructures. We also compare the MCDDM to experimental measurements of an InxAl1-xAs / GaAs (001) metamorphic device structure. Lastly we provide a comparison of the two models with InxGa1-xAs heterostructures. We show that these two models for defected crystals extend the usefulness of the x-ray diffraction characterization method and should in principle allow depth profiling of dislocation densities in arbitrary heterostructures.

Major Advisor

John E. Ayers