Influence of first-order approximations in the incidence parameter on the simulation of symmetric and asymmetric X-ray rocking curves of heteroepitactic structures

Abstract

The simulation of the experimental symmetric X‐ray rocking curve of a coherent heteroepitactic structure, using first‐order expressions in the incidence parameter, is shown to give a strain‐depth profile not consistent with asymmetric rocking curves taken on the same sample. Two different expressions are suggested for the incidence parameter to attain internal consistency among all the rocking curves. The former involves second‐order approximations and considers both normal and parallel lattice mismatches. The latter is the result of an exact derivation and takes into account only the normal mismatch. These models make the data from rocking‐curve simulation reliable, provided that the angle between the surface and the planes corresponding to the nominal crystallographic orientation is not ignored.

X-ray Rocking-Curve Analysis of Crystals with Buried Amorphous Layers. Case of Ion-Implanted Silicon

“…Moreover, the above f parameter [(3)], suitable only for e_L values below 1%, was replaced by the exact expression already used in a previous study (Servidori, Cembali, Fabbri & Zani, 1992) for the general case of an asymmetric reflection. The new expression for the incidence parameter for symmetric reflection, which includes the exact deformation term, is…”

Strain Relaxation of Si/Ge Multilayers Investigated by Transmission Electron Microscopy and High-Resolution X-Ray Diffractometry

“…From these experiments we measure the average multilayer lattice parameter in the growth direction (outplane), as well as in the interface plane (in-plane), which are related to the angular distances between the zero-order superlattice satellite and the substrate peak. A simple tetragonal distortion (with respect to the Si substrate) of the epilayer unit cell has been considered for data analysis using a 2nd-order approximation of the strain function in the Takagi-Taupin equation [29]. The superlattice period (ASL) was measured from the angular separation between the superlattice satellites peaks [30].…”

Structural and analytical characterization of Si1-x Gex /Si heterostructures by Rutherford backscattering spectrometry and channeling, analytical electron microscopy and double crystal X-ray diffractometry

“…The intensity values were recorded with a single channel analyzer regulated in order to avoid any contribution of the A/n harmonies to the counting rate. The degree of reliability of the intensity values and the angular positioning of the samples was verified by obtaining perfect matching between experimental and calculated RCs of a high quality [001] silicon crystal aligned according to the 004 symmetric and 224 grazing incidence, asymmetric reflections [27].…”

“…Hence, it was replaced by the second order expression [27] (25) The angle -y between surface and diffracting planes corresponding to the nominal crystallographic orientation was measured by a Seifert MZ VI diffractometer equipped with an Eulerian cradle and was kept as a fixed parameter in the simulation program. AU these items must be taken into account in order to avoid differences between the mismatch profiles obtained by simulating the symmetric and asymmetric RCs of the same sample [27].…”

“…Hence, it was replaced by the second order expression [27] (25) The angle -y between surface and diffracting planes corresponding to the nominal crystallographic orientation was measured by a Seifert MZ VI diffractometer equipped with an Eulerian cradle and was kept as a fixed parameter in the simulation program. AU these items must be taken into account in order to avoid differences between the mismatch profiles obtained by simulating the symmetric and asymmetric RCs of the same sample [27]. Moreover, as the dynamical model used [28] calculates only the diffracted intensity as a function of the angular setting of the sample, the thermal and Compton diffuse intensities, scattered from a thick, perfect Si crystal outside its range of total-reflection, were measured and taken into account, following the method previously described [29].…”