Multiple reflection optimization package for X-ray diffraction

Abstract

A new software package titled Multiple Reflection Optimization for X-ray Diffraction (MROX) to simulate and fit multiple reflections simultaneously, as well as single reflections is presented. The simulation employs the recursive solution of the dynamical theory of X-ray diffraction to derive the deformation profile as a function of depth, ε_⊥. It is applied to argon ion implanted 650 nm thick aluminium gallium nitride layers grown on c-sapphire substrates. The implantation is performed on five different pieces of the as-grown sample normal to the sample surface with increasing energy of between 25 keV and 250 keV. The individual as-grown pieces reveal very good crystalline quality. In contrast to the standard single reflection mode, the multiple reflection mode allows inferring negligible strain/compositional, Debye–Waller and thickness heterogeneities of the individual layers within the same as-grown piece. Moreover, the single reflection mode neglects the effects of decreasing penetration depth and increasing sample probed area, with the increasing scattering order resulting in higher ε_⊥ closer to the surface and thinner strained regions for the as-implanted samples. Therefore, the multiple reflection mode is suggested to be used to model the strain field propagation in implanted species. The Gaussian-like shape profile deduced for ε_⊥ follows the normalized density of vacancies derived via simulations of radiation of ions in matter (SRIM) at the surface while reaching the end of range of the ions deeper inside the ternary layer. Diffusion of point defects is thus suggested not only towards the surface but also towards the end of range of the ions. Furthermore, the effect of the broadenings of the main Bragg peak due to the thickness of the relaxed region of the as-implanted sample and due to the instrumental function is discussed.