Atomic Structure Based Simulation of X-Ray Scattering from Strained Superlattices

Abstract

The X‐ray scattering from strained superlattices is simulated using the positions of all individual atoms, determined by minimizing the strain energy of the structure, and the kinematic approximation (atomistic kinematic theory, AKT). For thin epilayers the agreement with dynamical diffraction theory (DT) is very close in the vicinity of a reciprocal lattice point, even in the case of large strain. Serious flaws in two of the five tested, widely used commercial DT simulation programs are revealed. DT in the two‐beam approximation yields incomplete large angle diffraction scans since the solution is developed around only one reciprocal lattice vector, while in AKT all possible scattering vectors are (implicitly) considered.

Determination of strain state and composition of highly mismatched group-III nitride heterostructures by x-ray diffraction

“…where k o,h are the wavevectors of the incident and diffracted beams, h is the reciprocal lattice vector of the specific reflection, and n is the surface unit vector. Most x-ray simulation programs (for an overview of the faults of commercially available programs, see [8]) rely on a first-order approximation for α [6,9,16,17] namely…”

“…Expressions (2)-( 4) are reasonable approximations for an angular range of at most 0.2˚around the substrate reflection. Several researchers have recognized this deficiency and have resorted to either improved, dynamically corrected incidence parameters [6], (see footnote 2) purely kinematical models [8], or to second-order expansions [10,11]. Here, we do not resort to any approximations but use the kinematically exact expressions.…”

“…The former model is a significant improvement over those commonly used, but is conceptually questionable 2 . The latter model is generally valid (except for situations involving more than one Bragg reflection) [8] but is difficult to implement, poses significant numerical problems, and is computationally very intensive.…”

“…We focus on zincblende and wurtzite systems of arbitrary orientation. Our approach is based on the standard (two-beam) Takagi-Taupin equations, and is thus not valid for diffraction close to total internal or external reflection [7,9], or for situations involving more than one Bragg reflection [8]. Our model, however, features an exact incidence parameter, as well as an exact calculation of the changes of Bragg angle and lattice plane inclination due to strain.…”

Effect of H-implantation in the local elastic properties of silicon crystals

“…Simulations of the XRD curves, to reconstruct the depth-distribution of strain in the materials, were done using a web-based code provided by the Argonne National Laboratory. 31 The in-plane strain e k developed in the implanted region is associated with an in-plane stress r k . Provided that the implantation process modifies a superficial region which is thin compared to the thick substrate, we can use Stoney's equation 32 to calculate the mean value of stress in the layer r mean k by measuring the curvature of the implanted wafers.…”