# Introduction

Grazing incidence X-ray diffraction (GIXRD or GIXD) is a non-destructive analysis method that is considered a common characterization technique for thin films. Conventional X-ray diffraction methods are not suitable for thin film studies, as they produce only weak signals from the thin film materials and huge interference from the substrate. Low penetration of X-rays in the matter in GIXRD is achieved using a low angle of incidence close to the critical angle (see X-Ray Reflection).

When using very small angles, the technique is often referred  as Grazing Incidence Small-Angle Scattering (GISAXS). This can provide precise morphological information of the surface comparable to methods such as TEM or SEMWhen using wide angles, the technique might be referred as Grazing Incidence Wide Angle Scattering (GIWAXS) or just GIXRD. This provides crystallographic information of the surface structure. By moving the detectors over multiple axes, information can be obtained out of a plane and in-plane.Information from both planes can be used to gain more complete picture of the thin film structure. Different planes are depicted in Figure 1.

Grazing incidence diffraction technique was originally proposed by W. C. Marra and A. Y. Cho back in 1979 in a study of GaAs and Al thin films grown on a GaAs substrate.

Figure 1. Schematic diagram of GIXRD setup for out-of-plane and in-plane measurements. (Figure: Alexi Sirén)

# Principle behind GIXRD

The theory behind X-ray diffraction is Bragg’s law:

$n\lambda = 2dsin\theta$

where n is an integer, λ is the wavelength of the X-rays, d is the space between the reflective layers and θ is the diffraction angle(see Figure 2).

A sample is exposed to a beam of X-rays at an angle θ. The crystalline structure of the sample causes interference in the incident x-rays causing a diffraction pattern. The diffraction pattern is recorded over the range 2θ with detectors. From the collected data the d-spacings of the samples crystalline structure can be defined. Since each compound has a unique d-spacing (and thus unique diffraction pattern), the compound can be identified by comparing the collected data to well established XRD-databases.

In GIXRD the incidence angle is fixed at a small angle exceeding the critical angle of total reflection, typically < 3°.  The low angle limits the penetration of x-rays in the sample, making the method suitable for thin films. The angle of the detector is varied over the range 2θ similar to traditional XRD methods.

Figure 2. Diagram of Bragg's diffraction. (Figure: Alexi Sirén)

Some advantages of the GIXRD method discussed in the literature are described below.

1. As the method uses X-rays, it is non-destructive. However high intensity X-rays obtained with synchrotron might damage some organic thin films.

2. Signal from the substrate under a thin film or other surface layer can be reduced or completely suppressed. Thus the method is suitable for thin films.

3. When studying the surface, no sample preparation is needed.
4. The measurement can be averaged over larger areas, even millimetres, compared to microscopical methods that are restricted to hundreds of nanometers.
5. By performing multiple measurements with different incident angles, it is possible to control the depth of penetration and gain information on different depth levels. This can be used for depth profiling of buried interfaces or multilayered structures.
6. The method can be applied in various environments, which can enable real-time monitoring of surface reactions.

# Applications

## GIXRD in examining Nb:TiO2 thin films

Grazing incidence X-ray diffraction was used to analyze the crystallinity of ALD-fabricated thin films of niobium-doped TiO­­2 anatase which has a large band gap of 3.2 eV and low resistivity of 2 ×10-4 Ω cm which means that it is a very promising conductive oxide in applications such as solar cells and blue LEDs.

Nb:TiO­­thin films are typically deposited in higher temperatures which leads to smaller grain size and thus higher resistivity. Typically higher Nb doping-concentration is used to gain acceptable grain size and resistivity at the expense of other properties. In the study, lower deposition temperatures were used to obtain higher grain size and lower resistivity reducing the need for excess Nb-doping. But since low deposition temperatures lead to amorphous Nb:TiO­­2 thin films, annealing was used to gain a crystalline structure in the thin films.

# References

 1 1 G, Renaud, Oxide surfaces and metal/oxide interfaces studied by grazing incidence X-ray scattering, Surface Science Reports, 1998, 32(1-2), 5-90 (https://doi.org/10.1016/S0167-5729(98)00005-3). 2 1 2 3 4 5 G. Renaud, R. Lazzari, & F. Leroy, Probing surface and interface morphology with Grazing Incidence Small Angle X-Ray Scattering, Surface Science Reports, 2009, 64(8), 255-380 (https://doi.org/10.1016/j.surfrep.2009.07.002) 3 1 W. C. Marra, P. Eisenberger, & A. Y. Cho. X‐ray total‐external‐reflection–Bragg diffraction: A structural study of the GaAs‐Al interface. Journal of Applied Physics, 1979, 50(11), 6927-6933 (https://doi.org/10.1063/1.325845) 4 1 2 A. A. Bunaciu, E. G. Udristioiu & H. Y. Aboul-Enein, X-Ray Diffraction: Instrumentation and Applications, Critical Reviews in Analytical Chemistry, 2015, 45(4), 289-299 (https://doi.org/10.1080/10408347.2014.949616) 5 1 2 A. Pandey, S. Dalal, S. Dutta, & A. Dixit, Structural characterization of polycrystalline thin films by X-ray diffraction techniques, Journal of Materials Science: Materials in Electronics, 2021, 32, 1341-1368 ( 6 1 A. Neuhold, J. Novák, H.-D. Flesch, A. Moser, T. Djuric, L. Grodd, S. Grigorian, U. Pietsch, R. Resel, X-ray radiation damage of organic semiconductor thin films during grazing incidence diffraction experiments, Nuclear instruments & methods in physics research, 2012, 284, 64-68 (https://doi-org.libproxy.aalto.fi/10.1016/j.nimb.2011.07.105) 7 1 2 3 D. Simeone, G. Baldinozzi, D. Gosset, S. Le Caer, J-F. Bérar, Grazing incidence X-ray diffraction for the study of polycrystalline layers, Thin Solid Films, 2013, 530, 9-13 (https://doi.org/10.1016/j.tsf.2012.07.068). 8 1 R. van Rijn, M. D. Ackermann, et al., Ultrahigh vacuum/high-pressure flow reactor for surface x-ray diffraction and grazing incidence small-angle x-ray scattering studies close to conditions for industrial catalysis, Review of Scientific Instruments, 2010, 81(1), 014101 (https://doi.org/10.1063/1.3290420) 9 1 Q. Hu, L, Zhao, J. Wu et al., In situ dynamic observations of perovskite crystallization and microstructure evolution intermediated from [PbI6]4 cage nanoparticles, Nature Communications, 2017, 8, 15688 (https://doi.org/10.1038/ncomms15688) 10 1 2 3 4 5 J-P. Niemelä, Y. Hirose, K. Shigematsu, M. Sano, T. Hasegawa, & M. Karppinen, Suppressed grain-boundary scattering in atomic layer deposited Nb:TiO2 thin films, Applied Physics Letters, 2015, 107(19), 192102 (https://doi.org/10.1063/1.4935425).

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