Application of statistical dynamical diffraction theory to highly defective ion implanted SiGe heterostructures

Abstract

The statistical dynamical diffraction theory (SDDT) provides a method for performing high resolution X-ray diffraction (HRXRD) analyses from materials that contain high levels of structural imperfection. SDDT is implemented by combining kinematical and dynamical diffraction formalisms into a single framework through the inclusion of two parameters (a static Debye-Waller factor and a correlation length) that can provide an adjustable coupling between the kinematic and dynamic extremes. Typically one of the prominent difficulties in implementing SDDT is the mathematical complexities that are characteristic of this theory. Recently we have demonstrated a simplified realization of SDDT [Shreeman and Matyi, J. Appl. Crystallogr. 43, 550 (2010)] that preserves the essential features of the theory while allowing it to be applied to a variety of structures. Here we show the viability of this approach by fitting various experimental HRXRD data from highly defective and partially relaxed Si 0.70 Ge 0.30 ion implanted heterostructures. This study demonstrates the capabilities the SDDT theory provides for HRXRD analyses of highly defective semiconductor materials.

Dynamical X‐ray diffraction theory: Characterization of defects and strains in as‐grown and ion‐implanted garnet structures

“…Since the ion implantation became a routine tool for purposeful modifying the structure of subsurface crystal layers, the various theoretical models have been developed to describe the X‐ray diffraction patterns, in particular, the rocking curves measured from such crystal structures with inhomogeneous strain fields. In whole, the most of these models could be subdivided into two groups, which make use of the semi‐kinematical or dynamical approximations , respectively. The first group of so‐called semi‐kinematical (or known also as kinematical ) models is characterized by the summation of kinematical scattering amplitudes from thin ion‐implanted layers and dynamical scattering amplitude from a thick substrate.…”

“…These analytical solutions have been obtained from both Takagi–Taupin equations in real space and wave equation in momentum space according to the Ewald–Bethe‐Laue approach, supposing the lamina are defect‐free and diffuse scattering is absent (except for Ref. ).…”

Modified statistical dynamical diffraction theory: analysis of model SiGe heterostructures

“…The use of this approach for the analysis of highly defective layers is not recommended, however. For example, fully relaxed silicon-germanium epitaxial layers grown with high Ge concentrations on silicon substrates are very poorly described using the dynamical diffraction theory (Shreeman & Matyi, 2010), as is structurally defective ion-implanted SiGe with a range of germanium concentrations (Shreeman & Matyi, 2011). A purely dynamical analysis strategy is not appropriate for the analysis of these cases of fully or partially relaxed samples.…”

“…We have found, however, that broadening effects due to the presence of defects in the substrate will have an impact on the diffracted amplitude and need to be incorporated into the SDDT model. This essential modification of the SDDT is detailed in recent work (Shreeman & Matyi, 2010, 2011Shreeman, 2012). In this approach the basic definition E c h ¼ R mÀ1 E c o is used, where the reflection coefficient from a given layer is defined in terms of the amplitude emerging from the material beneath.…”