Strain-profile determination in ion-implanted single crystals using generalized simulated annealing

Abstract

International audienceA novel least-squares fitting procedure is presented that allows the retrieval of strain profiles in ion-implanted single crystals using high-resolution X-ray diffraction. The model is based on the dynamical theory of diffraction, including a B-spline-based description of the lattice strain. The fitting procedure relies on the generalized simulated annealing algorithm which, contrarily to most common least-squares fitting-based methods, allows the global minimum of the error function (the difference between the experimental and the calculated curves) to be found extremely quickly. It is shown that convergence can be achieved in a few hundred Monte Carlo steps, i.e. a few seconds. The method is model-independent and allows determination of the strain profile even without any ‘guess' regarding its shape. This procedure is applied to the determination of strain profiles in Cs-implanted yttria-stabilized zirconia (YSZ). The strain and damage profiles of YSZ single crystals implanted at different ion fluences are analyzed and discussed

Interplay between atomic disorder, lattice swelling, and defect energy in ion-irradiation-induced amorphization of SiC

“…The curves were then, as mentioned in sect. II.1., fitted using the procedure described in [23,24]. In the latter case, the kinematical theory was sufficient due to the nanoscopic structure of the simulation cells.…”

“…Disorder was derived from the evaluation of peak intensity lowering through the so-called static Debye-Waller factor [23,24]. This evaluation does not require the usual assumption of normally distributed atomic displacements, which is probably not justified within collision cascades.…”

“…The experimental curves were simulated (see thin solid lines in Fig. 1) with a procedure that allows the determination of both the lattice strain (homogeneous lattice displacements) and lattice disorder (random atomic displacements) depth profiles in the irradiated region [23,24]. The corresponding strain profiles are provided in the inset of Fig.…”

Analysis of the stability of InGaN/GaN multiquantum wells against ion beam intermixing

“…XRD 2 / curves were simulated using the dynamical theory of X-ray diffraction 12 . The influence of the implantation is taken into account by including the Debye-Waller parameter on the structure factor of individual layers, thus attenuating the derived intensity and considering a c-lattice expansion following the work of Boulle and Debelle 13 .…”

Modeling of X-ray rocking curves for layers after two-stage ion-implantation

“…The kinematical [13][14][15][16][17][18] and generalized dynamical theory [21,22] of X-ray diffraction were used in combination with the dynamical approach in case of the Takagi-Topens approximation [11,12,19,20], for the ω/2Θ scans simulation for ion implanted layers. The kinematical and the dynamical approaches are used for thin implanted layers and high-quality bulk material, respectively.…”