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Back-to-Basics tutorial: X-ray diffraction of thin films

Abstract

X-ray diffraction (XRD) is an indispensable tool for characterising thin films of electroceramic materials. For the beginner, however, it can be a daunting technique at first due to the number of operation modes and measurements types, as well as the interpretation of the resultant patterns and scans. In this tutorial article, we provide a foundation for the thin-film engineer/scientist conducting their first measurements using XRD. We give a brief introduction of the principle of diffraction and description of the instrument, detailing the relevant operation modes. Next, we introduce five types of measurements essential for thin film characterisation: \(2\theta /\omega\) scans, grazing-incidence scans, rocking curves, pole figures, and azimuth scans (or ϕ scans). Practical guidelines for selecting the appropriate optics, mounting and aligning the sample, and selecting scan conditions are given. Finally, we discuss some of the basics of data analysis, and give recommendations on the presentation of data. The aim of this article is to ultimately lower the barrier for researchers to perform meaningful XRD analysis, and, building on this foundation, find the existing literature more accessible, enabling more advanced XRD investigations.

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source and detector are ‘rocked’ during the scan

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Notes

  1. The case for transmission electron microscopy (TEM) as a comparatively useful tool could certainly be made but should be seen as a complementary technique for spatially resolved characterisation within films.

  2. Obviously, this is not strictly true, but is a useful working assumption.

  3. This is Siegbahn notation which describes the electron shell that loses an electron during ionisation, with \(K\) (\(n=1\), where \(n\) is the principal quantum number) being the innermost shell. Relaxation of an electron into the \(K\) shell from the second innermost shell (\(L\), \(n=2\)) is denoted by an \(\alpha\) subscript, and from the third innermost shell (\(M\), \(n=3\)) by a \(\beta\) subscript. The \(1\) and \(2\) subscripts denote the slight energy differences from electrons in the shell due to interactions between the spin and orbital momentum.

  4. Different materials such as Cr, Fe, Co, Ni, Mo, or Ag can also be used if the wavelength is more suitable for investigating a particular range of \(d\)-spacings. Cu \({K}_{\alpha }\) radiation will cause materials containing Fe and Co to fluoresce as they are irradiated, making use of a different anode material sometimes necessary.

  5. Different metal filters are used depending on the choice of anode material.

  6. The intensity of the peaks originating from W contamination will depend on the age of the X-ray tube.

  7. X-ray tubes also require substantial amounts of electrical power to operate.

  8. Sometimes other notation will be used that refers to similar types of measurement but with key differences. A \(\theta /2\theta\) scan is a symmetric or coupled scan about the surface normal of the sample and plotted as a function of \(2\theta\), which is most commonly used in power diffraction measurements. A \(\omega /2\theta\) scan is a symmetric or coupled scan about the crystallographic axis of the substrate, but plotted as a function of the \(\omega\) angle.

  9. Be careful not to oversaturate the detector. Use an attenuator if necessary.

  10. 2D detectors, which are becoming increasingly available, are capable in collecting a large \(\psi\) and \(2\theta\) range for a single φ scan. These can dramatically reduce the time needed to perform certain measurements, such as pole figures.

  11. Some sample stages are equipped with a \(x\)-\(y\)- \(z\) stage which allows for several samples to be placed together depending on their size. When placing several samples, one has to be aware of, or limit, the illuminated area with the corresponding set of slits and masks so one sample is illuminated at a time and none of the rest of the samples interferes in the measurement. It is a common practice not to place the samples in close proximity (leave at least 1 cm spacing between samples) and try to place them, if possible, at similar height (\(z\)-plane). The \(z\)-position and surface alignment should be carried out separately for each film.

  12. Precise sample height and surface normal alignments are particularly crucial for grazing incident measurements, for example X-ray reflectivity (XRR) or in-plane diffraction.

  13. Remember to use an attenuator!

  14. This is also particularly important if there is a miscut angle between the planes of the substrate and film and that of the surface normal, which is aligned using \(z\)-axis and \(\omega\)-axis scans. The miscut angle can vary from a few tenths of degrees to some degrees in vicinal substrates. This angle will also vary depending on the rotation of the single crystal surface via the azimuthal axis (φ).

  15. Since the penetration depth of X-rays is much larger than the typical thickness of films which are generally below a few microns, the diffracted signal from the substrate is more intense than for film peaks. The exceptions being for grazing incidence geometries, highly absorbent materials, and very thick films. If the substrate peaks are not present or very weak, then aligning the sample using the film peaks is advisable.

  16. Some commercial single-crystal substrates might not have the expected quality, and display peak splitting in the \(2\theta /\omega ,\) \(\omega\), and \(\psi\) alignment, which implies twinning or multiple crystal domains are present. In this situation, it is usually best to align to the most intense peak.

  17. The La Bail and Rietveld refinement methods are powerful techniques for determining the crystal structure from power diffraction methods, but have limited use for thin film analysis.

  18. Databases of crystal structures of inorganic materials that can be used to generate powder diffraction patterns are available, such as the Inorganic Crystal Structure Database (ICSD), the International Centre for Diffraction Data (ICDD), and the Crystallography Open Database (COD), the latter of which is free to access.

  19. When selecting reference patterns from a database, it is important to check the conditions under which the data were obtained that was used to calculate the reference crystal structure. Some structures come from XRD data taken at high temperatures, high pressures, or reducing conditions, and others come from simulations. It is also worth bearing in mind the reliability and precision of the diffraction data used to calculate the structures. Some databases have an indicator for the quality of the data the structure is calculated from.

  20. Although this is generally the case, in some instances, there may be subtle changes in the crystal symmetry that affects the structure factor and relates to changes in relative intensities of the peaks. In some layered compounds changes in the stacking sequence during film growth can cause the absence of some peaks, which may be erroneously interpreted as preferential orientation. If in doubt, performing rocking curves of the reflections present should allow one to determine the orientation of the domains.

  21. In films with a complex microstructure consisting of a collection of domains with different orientation (twin domains, different orientation variants, i.e. a/c-oriented domains of tetragonal structure) or different shear distortions (monoclinic and triclinic structures) the accurate cell parameter determination requires first a model for the domain tilt. Once these tilts are taken into account the cell parameters can be extracted.

  22. \({\beta }_{\tau }=(B-b)\) where \(B\) is the FWHM of the film peak and \(b\) the FWHM of a perfect crystal due to instrumental broadening.

  23. If \({\beta }_{\tau }\) refers to the integral breadth of the peak rather than the FWHM, then for spherical grain with cubic crystal symmetry K = 0.89.

  24. \({\beta }_{\varepsilon }={({B}^{2}-{b}^{2})}^{1/2}\) where \(B\) is the FWHM of the film peak and \(b\) the FWHM of a perfect crystal due to instrumental broadening.

  25. As previously discussed, cell parameters may vary as a function of slight deviations in composition. It is often observed in electroceramics that chemical composition may vary at the microscale, i.e. from the core to the boundary of a single grain, or even at nanoscale, i.e. typical in morphotropic phase boundaries of ferroelectric materials, or martensitic structures. This may represent a source of “chemical” micro-strain difficult to distinguish from any other source.

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Acknowledgements

We gratefully acknowledge D. Klotz and H.L Tuller for critically reading the manuscript. GFH acknowledges support from The Japanese Science and Technology Agency (JST) through its Center of Innovation Program (COI Program, grant number: JPMJCE1318) and the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), supported by MEXT, Japan. ICN2 is funded by the CERCA programme/Generalitat de Catalunya and by the Severo Ochoa programme of the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, grant no. SEV-2017-0706). The datasets generated during and analysed during the current work are available from the corresponding author on reasonable request.

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Harrington, G.F., Santiso, J. Back-to-Basics tutorial: X-ray diffraction of thin films. J Electroceram 47, 141–163 (2021). https://doi.org/10.1007/s10832-021-00263-6

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Keywords

  • X-ray diffraction
  • Thin films
  • Methodology
  • Tutorial
  • Guidelines
  • Back-to-Basics