Practical XRD with Confidence

Webinar summary

In this webinar, the third in the series Practical XRD with Confidence, Keisuke discusses how thin-film X-ray diffraction requires different measurement choices depending on whether the film is polycrystalline, textured, or epitaxial. A key challenge is preferred orientation. In a powder sample, crystallites are randomly oriented, so a conventional scan can capture many diffraction peaks needed for phase identification. In a thin film, crystallites often align in specific directions because of epitaxial growth on a single-crystal substrate or because low-surface-energy planes tend to align parallel to the surface during deposition. As a result, only certain reflections may appear, making phase identification more difficult.

For polycrystalline thin films, the first recommended measurement is a symmetric 2θ/θ scan. This scan is similar to a powder diffraction scan, but thin-film measurements typically use parallel-beam optics, such as an X-ray mirror, to control the incident beam. In this geometry, the scattering vector is perpendicular to the sample surface, so the scan mainly probes lattice spacings, phase information, and preferred orientation in the out-of-plane direction. The major drawback is penetration depth: X-rays can penetrate deeply, so signals from the substrate or thicker underlying layers can dominate and obscure the signal from a very thin surface layer.

Grazing-incidence methods are used to make XRD more surface sensitive. In an in-plane XRD scan, the X-ray beam strikes the sample at a shallow incident angle, often below one degree, while the detector scans parallel to the sample surface. This makes the scattering vector nearly parallel to the film surface, allowing analysis of in-plane lattice spacings, phase information, and preferred orientation. Changing the incident angle can provide depth-dependent information because it changes how deeply the X-rays penetrate.

Grazing-incidence diffraction, or GID/GIXRD, is another surface-sensitive option. In this approach, the incident angle remains shallow while the detector scans out of plane. It can be performed with a parallel-slit analyzer or with faster one-dimensional detector methods. However, the scattering vector is tilted, and that tilt changes with 2θ, which complicates interpretation when the film has strong preferred orientation. For non-textured thin films, both in-plane XRD and GID can be useful; for textured or oriented films, in-plane XRD is preferred.

A thin-film iron oxide example illustrates the need to choose scan geometry carefully. The surface iron oxide layer was only 5 nm thick, while the underlying copper oxide layer was much thicker. A symmetric 2θ/θ scan was dominated by copper oxide peaks and substrate-related features, although broad peaks from the iron oxide were also visible. Peak widths were used with the Scherrer equation to estimate crystallite size. Copper oxide peaks corresponded to crystallites of about 11 nm, while iron oxide peaks corresponded to about 5 nm crystallites. A sharp feature near 33° was attributed not to a normal silicon 002 reflection, which is forbidden, but to multiple diffraction from the silicon substrate.

Surface-sensitive measurements clarified the iron oxide phase information. By calculating penetration depth near the critical angle for total reflection, the incident angle could be selected to limit penetration to only a few nanometers. An in-plane scan at the critical angle greatly reduced the copper oxide signal and emphasized the iron oxide layer. Magnetite and maghemite were difficult to distinguish because their diffraction patterns are similar in thin-film form, and wüstite could not be confirmed confidently because of peak overlap. However, beta iron oxide was detected in the surface-sensitive scan even though it was not observed in the out-of-plane scan. GID scans at different incident angles showed that higher incident angles penetrated deeper and produced stronger copper oxide peaks, while shallower angles emphasized broad iron oxide peaks.

Instrumental broadening must be considered when crystallite size is estimated from peak width. The measured full width at half maximum contains contributions from the sample and the instrument. Instrument broadening can be determined by measuring a standard reference material, such as silicon, lanthanum hexaboride, or another standard powder, using the same configuration. The corrected peak broadening should be converted from degrees to radians before being used in the Scherrer equation. For thin films, a shape factor of 1.0 is more appropriate than the common powder value of 0.9 because film crystallites are often oriented and not spherical.

Detector resolution is only one contributor to the final diffraction peak width. A detector pixel size of about 0.02° does not automatically mean that peaks separated by 0.02° can be confidently resolved. The observed profile is a convolution of contributions from the X-ray source, optics, slits, sample, and detector. If the incident beam divergence or sample broadening is larger than the detector contribution, the detector pixel resolution alone will not determine peak separability.

High-resolution XRD is mainly used for epitaxial thin films. In this context, the incident angle is usually described as omega rather than theta, because omega may differ from half of 2θ. High-resolution measurements require monochromating the X-ray beam, often down to Cu Kα1, using two-bounce or four-bounce germanium monochromators. Two-bounce monochromators provide higher intensity but more dispersion, while four-bounce monochromators provide more stable resolution over a wider angular range but lower intensity. Analyzer crystals on the receiving side can provide very high 2θ resolution, but they reduce intensity and are most useful when the sample has significant mosaicity.

Several high-resolution scan types provide complementary information. A symmetric 2θ/ω scan probes the out-of-plane lattice parameter and can show thickness fringes or satellite peaks, which can be used to calculate film thickness. An omega scan, or rocking curve, probes mosaicity caused by deviations in crystal orientation, often related to dislocations from lattice mismatch. Reciprocal space mapping combines angular scans to map intensity around reciprocal lattice points, allowing determination of both in-plane and out-of-plane lattice parameters, strain, relaxation, symmetry, and domain structure.

A perovskite thin-film example demonstrates how high-resolution measurements reveal structure. A 45 nm L5BO film on an LSAT substrate was examined using 00L scans and reciprocal space maps. The 00L scan showed layer peaks and clear thickness fringes. The out-of-plane lattice mismatch was calculated from the layer/substrate peak separation as about 0.471%, and the layer lattice parameter was about 0.387 nm. The film thickness calculated from fringe spacing was about 44.2 nm, close to the expected 45 nm. Higher-angle reflections provided better separation between closely spaced substrate and film peaks.

Reciprocal space maps provided additional structural information that could not be obtained from a simple out-of-plane scan. Mapping around a tilted reflection showed multiple layer peaks, indicating multiple domain orientations. The analysis showed a monoclinic structure with an in-plane lattice parameter of about 0.387 nm, a slightly elongated c-axis, and a beta angle about 0.5° away from 90°. Four domains were identified, separated by 90° rotations in the in-plane direction.

Rocking-curve information can be extracted from reciprocal space maps. Around a surface-normal reflection such as 004, the rocking-curve direction is nearly parallel to the QX direction over a small region. Extracting intensity along QX and converting ΔQX/QZ to angular width gave a rocking-curve width of about 0.02°. Separate rocking-curve measurements confirmed this value when a sufficiently narrow receiving slit was used. A wide receiving slit mixes broadening from QX and QZ; because QZ broadening is strongly affected by finite film thickness, a wide slit can make the measurement reflect thickness-related broadening rather than true mosaicity.