Modified Statistical Dynamical Diffraction Theory: A Novel Metrological Analysis Method for Partially Relaxed and Defective Carbon-doped Silicon and Silicon Germanium Heterostructures.

摘要

The statistical dynamical diffraction theory, which has been initially developed by late Kato remained in obscurity for many years due to intense and difficult mathematical treatment that proved to be quite challenging to implement and apply. With assistance of many authors in past (including Bushuev, Pavlov, Pungeov, and among the others), it became possible to implement this unique x-ray diffraction theory that combines the kinematical (ideally imperfect) and dynamical (the characteristically perfect diffraction) into a single system of equations controlled by two factors determined by long range order and correlation function within the structure. The first stage is completed by the publication (Shreeman and Matyi, J. Appl. Cryst., 43, 550 (2010)) demonstrating the functionality of this theory with new modifications hence called modified statistical dynamical diffraction theory (mSDDT). The foundation of the theory is also incorporated into this dissertation, and the next stage of testing the model against several ion-implanted SiGe materials has been published: (Shreeman and Matyi, physica status solidi (a)208(11), 2533-2538, 2011). The dissertation with all the previous results summarized, dives into comprehensive analysis of HRXRD analyses complete with several different types of reflections (symmetrical, asymmetrical and skewed geometry). The dynamical results (with almost no defects) are compared with well-known commercial software. The defective materials, to which commercially available modeling software falls short, is then characterized and discussed in depth. The results will exemplify the power of the novel approach in the modified statistical dynamical diffraction theory: Ability to detect and measure defective structures qualitatively and quantitatively. The analysis will be compared alongside with TEM data analysis for verification and confirmation. The application of this theory will accelerate the ability to quickly characterize the relaxed/partially relaxed/fully strained semiconductors using non-destructive HRXRD metrology.