A rigorous comparison of X-ray diffraction thickness measurement techniques using silicon-on-insulator thin films

Abstract

Thickness data from semiconductor‐grade silicon‐on‐insulator thin‐film samples determined from high‐resolution X‐ray diffraction (HRXRD) data using the Scherrer equation, rocking‐curve modeling, thickness fringe analysis, Fourier analysis and the Warren–Averbach method, as well as with cross‐sectional transmission electron microscopy and X‐ray reflectivity measurements, are presented. The results show that the absolute accuracy of thin‐film thickness values obtained from HRXRD data is approximately 1 nm for all techniques if all sources of broadening are correctly identified, while their precision is one or two orders of magnitude smaller. The use of multiple techniques is required to determine the various contributions to peak broadening.

Crystallinity of tellurium capping and epitaxy of ferromagnetic topological insulator films on SrTiO3

“…The lattice constant obtained from the peak positions is c  = 30.66 ± 0.19 Å for CBST and a  = 4.47 ± 0.03 Å for Te, slightly larger than that of bulk Te. The Scherrer equation uncorrected for instrumental broadening, with a Scherrer constant of 0.88527, provides the crystalline thickness of 67.2 ± 0.7 Å for CBST and 108.7 ± 1.9 Å for Te, consistent with their nominal thicknesses of 6 nm and 10 nm. Furthermore, the measured ratios of the scattering intensities of the CBST (0 0 0 3n) and Te (n 0 -n 0) reflections are also consistent with a calculation assuming perfect crystalline films of the nominal thicknesses.…”

Applied and Residual Stress Determination Using X‐ray Diffraction

“…The Bragg angle, θ B (not shown), is one half of the angle between the transmitted beam (the extension of I 0 through the sample) and the diffracted beam The angles φ, ψ are settable on the diffractometer and are assumed to be known exactly. From Equations (6.1), (6.2) and (6.3) one obtains: 11 cos 2 φsin 2 ψ + ε 12 sin 2φsin 2 ψ + ε 22 sin 2 φsin 2 ψ + ε 33 cos 2 ψ + ε 13 cos φ sin 2ψ + ε 23 sin φ sin 2ψ (6.4) which is the fundamental equation for X-ray strain determination. It is important to note that, Equations (6.2) and (6.3) have no explicit or implicit assumptions about the type of material.…”

“…If the perfect crystal sample is thinner along the scattering vector than the relevant extinction depth, or has severe mosaic and dislocation distributions, kinematical diffraction theory [11] can adequately represent the diffraction process. This approach is also adequate for most polycrystalline samples and is the basis of almost all commercial diffraction analysis codes.…”

“…2) Scattering removes a negligible amount of energy from the transmitted X-ray beam. Under these assumptions the dependence of scattered intensity on the scattering angle depends only on the structure factor of the reflection in use (which depends on the symmetry of the particular unit cell) and on the size and shape distributions of the diffracting volumes [11]. The penetration depth of the X-rays into the sample in such cases depends on the diffraction geometry and the linear absorption coefficient, μ, of the X-rays of the particular energy within the sample under investigation.…”

“…11 Depth-averaged out-of-plane strain measured in the SOI layer underneath the 1.0 μm wide Si 3 N 4 feature and comparison to mechanical modeling results. Reproduced with permission from[20], Copyright 2008 American Institute of Physics…”