X-ray diffraction (XRD)

XRD is a non-destructive technique to determine the structural composition of the samples. In a conventional XRD laboratory, the X-rays can be generated by electrons bombarding metal anodes such as Cu. The selected monochromatic X-ray wavelengths generally share similar magnitude (∼1 Å) with the interplanar distances in the crystal lattices, thus are very suitable for probing the atomic structure of materials.¹

When X-rays travel through the sample, they are scattered by the electron clouds of the atoms.^1,2 Diffraction occurs when two scattered X-rays have integer wavelength difference (constructive interference), defined by Bragg’s law in

nλ =2dsinθ (2.1)

where n is an integer,λ is the wavelength of the incident light,dis the interplanar distance in the crystal lattice, andθ is half of the angle between incident and scattered X-rays, as displayed in Figure 2.3a. In this way, the incident angleθ is related inversely to the spacings of atomic planes d.¹

Fig. 2.3(a) Schematic diagrams illustrating how the X-ray diffraction occurs when Bragg’s Law is satisfied for constructive interference between the scattered light beams from the atomic planes. (b) Comparison of the different diffraction phenomena for polyscrystalline and single crystal samples. (c) Different scan modes could be achieved using different diffraction geometries by varying the anglesω,φ,χ and 2θ. S stands for the sample normal. (d) Illustration of the diffraction geometries forθ-2θ scan and GIXRD.

An X-ray diffraction pattern, or a diffractogram, is typically plotted as the intensity of diffracted X-rays versus varied detector angles 2theta (2θ). Each specific set of crystal planes, identified with Miller indices (hkl), attributes to one diffraction reflection; as a result, the XRD pattern is formed as an addition of diffraction peaks reflecting the phases present in the material of interest.

Thus, one can obtain information of the atomic arrangements within the crystal from the Bragg reflections for phase identification, crystallinity evaluation, etc. From the peak position and height, crystal structure could be solved for phase determination, quantitative phase analysis and calculation of lattice parameters. Besides, peak areas, widths and shapes of the Bragg reflections give additional structural information of the investigated materials in terms of crystallite size and strain, etc.²

For example, depending on the crystallinity, a materiel could be i) single crystal with long-range ordered atoms throughout the volume of the material, ii) polycrystalline with randomly distributed crystallites with all-orientations, or iii) fully amorphous with short-range ordered atoms. As is depicted in Figure 2.3b, different diffraction phenomena would happen depending on the crystallinity of the studied sample, thus they can be distinguished in XRD. More specifically, for a polycrystalline sample containing crystallites with all orientations, diffraction cones are formed;

for a single crystal sample with only one crystallographic orientation, the Bragg condition is met once at a time resulting in isolated diffraction beams; for amorphous samples, only broad humps

with low intensities would be observed due to the short range order.

Different scan types, e.g. θ-2θ scan, grazing incidence X-ray diffraction (GIXRD), φ scan, rocking curve, etc, can be realized with different XRD geometries by varying the four angles in a 4-circle diffractometer displayed in Figure 2.3c. Specifically,ω is the angle that the incoming X-rays strikes sample surface, 2θ corresponds to the angle between the incident and diffracted X-ray beams,φ indicates rotation of the sample around the surface normal S, whileχ refers to the angle that the sample plane is rotated with respect to the incident X-ray beams. In the following, we introduce the main principles ofθ-2θ scan and GIXRD which were used in this study.

θ-2θ scan is a very common scan type in XRD, which is oftentimes referred to as Bragg-Brentano parafocusing geometry. During the measurements, ω equalsθ, so that the incident angle and the detector are rotated in a synchronized motion, see Figure 2.3d, upper panel.¹This can be achieved by either rotating the X-ray source tube or or by rotating the sample. Under this configuration, only atomic planes that are parallel to the sample surface could be detected. If the film is textured,i.e.c-axis oriented, only (00l) planes will be observed in the diffraction spectra.

2Dθ-2θ patterns can be acquired using a two-dimensional (2D) areal detector. It allows much faster data collection within the diffraction cone comparing to the conventionalθ-2θ measure-ments that are confined in a diffraction plane. As can be imagined, polycrystalline samples would generate a GADDS frame with diffraction rings, or arcs, depending on the crystallinity and film texture, while single crystal samples would result in diffraction patterns with isolated spots.

GIXRD is a very useful surface-sensitive XRD technique for studying ultrathin films. The reason is that in XRD measurements that use large incidence angles, the penetration depth of X-rays are in the order of micrometers, thereby the diffractogram could be dominated with substrate contributions that hinder the weak signals of the thin films. The use of grazing incident X-rays in GIXRD could maximize the diffraction contributions from film surfaces and lowers intensities from the bulk background.^2,3In this technique,ω is fixated to small angles (<2º) and the spectrum is collected by moving the detector along the 2theta circle (ω ̸=θ), as is shown in Figure 2.3d, lower panel. For non-textured polycrystalline film, the diffraction pattern will reproduce the intensities as in the reference powder spectrum. However, this configuration is not suitable to identify film epitaxy.

In this study, for investigating phase purity and crystallinity of the ALD thin films, various XRD studies were performed includingθ-2θ scan, GIXRD and 2Dθ-2θ pattern. The diffractometers employed in this study include a Siemens D5000 diffractometer for standardθ-2θ scan, a Bruker GADDS diffractometer with two-dimensional (2D) areal AXS HI-STAR detector for texture analysis and a Bruker D8 Discover A25 diffractometer for high resolutionθ-2θ scan and GIXRD

study, shown in Figure 2.4, respectively. In all cases, the X-ray was generated with Cu K_α radiation source (K_α=1.5406 Å).

Fig. 2.4The three diffractometers located at ICMAB that are employed in this thesis: (a) Siemens D5000 diffractometer, (b) Bruker GADDS diffractometer and (c) Bruker D8 Discover A25 diffractometer.⁴

Herein,θ-2θ scans were performed in the 2θ range of 20º - 80º. The GADDS patterns were acquired using standardθ-2θ scan in the 20º-50º, 50º-80º range. The GIXRD measurements were performed using the incident angle of 1º in 20º-80º 2θ range.