3.4.1 Grazing incidence x-ray diffraction
X-ray diffraction (XRD) is a non-destructive method used to study atomic structure of a crystalline matter. Crystal symmetry, lattice parameters, lattice strain, qualitative and quantitative phase composition as well as preferred orientation (texture) of grains in polycrystalline materials can be obtained by means of XRD analyses [199], [200], [201]. This technique makes use of an x-ray wave interference on the periodic arrays of atoms in a crystal, which serve as a diffraction grating. This interaction becomes possible due to x-rays wavelength being of the same order of magnitude (1-100 Å) as the interatomic and interplanar distances in crystals. A constructive interference occurs only at certain diffraction angles determined by a specific crystal structure of a material, its crystal symmetry and lattice
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3.4 Microstructural analyses
parameters. The condition of a constructive interference is described by the Bragg’s law [200]:
2dh k lsinh k l , (3.7)
where dhkl is the spacing between the series of parallel lattice planes with Miller indices (h, k, l) responsible for a particular diffraction peak; θhkl is the diffraction angle – the angle, which the incident and the reflected beams make with the (h k l) planes; and λ – the wavelength of the incident x-ray beam. The Miller indices define the crystallographic orientation of planes as well as spacing d between them in combination with the lattice parameters. Different crystallographic planes are characterised by a different interplanar spacing, which alter the θ angle of the corresponding diffraction peak. A diffraction pattern – a set of allowed diffraction angles and corresponding relative peak intensities, is unique for each crystalline matter. A large diffraction data base is available from the international centre for diffraction data (ICDD). It contains experimentally collected as well as theoretically calculated powder diffraction patterns for different materials and their polymorphs. These can be used as reference patterns for identification of the phase composition of the studied sample. Figure 3.11 (a) shows an experimental diffraction scan obtained on a 10 nm Si:HfO2 film
embedded between two TiN layers together with reference patterns of a tetragonal HfO2 phase
with a space group P42/nmc [202] and a cubic TiN (Fm3m) [203].
20 30 40 50 60 70 80 90 TiN cubic 0 12 Inte nsit y (count s/) 1 21 0 20 0 02 1 12 1 10 011 R el at iv e I 2 (deg) tetragonal P42/nmc
Figure 3.11 (a) Experimental diffraction data for a 10 nm thick polycrystalline Si:HfO2 film embedded
between TiN layers (top) and reference powder diffraction patterns for the tetragonal HfO2 phase of a
space group P42/nmc (bottom) [202] and the cubic TiN (Fm3m) [203]; (b) Schematics of a GI-XRD
Detector Soller slits Incident x-ray beam Normal to the diffracting lattice planes Thin film 1 2 3 (a) (b)
3 Characterisation methods
Grazing incidence x-ray diffraction (GI-XRD) is an advanced XRD measurement technique, utilised for investigation of thin films with thicknesses in the range of a few nanometres [200]. The penetration depth of an x-ray beam in a standard symmetric geometry achieves 10 – 100 m depending on the absorption properties of the material. In this case the diffraction signal comes primarily from the substrate, whereas the contribution from the nanometre thick films is negligibly small. In the GI-XRD method (Figure 3.11 (b)) the incoming beam enters the sample under a very small angle of incidence (ω) of a few degrees or even less. This enables to increase the path travelled by the incoming beam within a studied thin film, so that the diffraction signal is magnified, while the signal coming from substrate is significantly reduced or even completely eliminated. The GI-XRD spectra are recorded with a constant incidence angle. The position of the x-ray source remains the same in respect to the sample, whereas the detector moving around the sample and collects the diffraction data from different diffraction angles.
GI-XRD was exploited in this work for studying the crystal structure and identification of phase composition in thin ferroelectric Si:HfO2 films. The GI-XRD experimental
diffraction data were collected using a Bruker D8 Advance diffractometer with Cu-Kα radiation (λ = 1.5418 Å) with an incidence angle of 0.5º.
3.4.2 X-ray photoelectron spectroscopy
X-ray photoelectron spectroscopy (XPS) is a non-destructive analytical method, which provides qualitative and quantitative information about chemical composition of solid materials within the topmost few nanometres (1 – 10 nm) of the surface [204]. This method is based on the photoemission of electrons from the surface of a sample exposed to monochromatic x-ray radiation. The kinetic energies and number of photoemitted electrons corresponding to different energy levels are being measured. The kinetic energy can be transformed into the electron binding energy using a law of energy conservation [204]. The set of binding energies is characteristic for each chemical element, whereas the number of emitted electrons (XPS peak intensities) is directly related to the amount of the element present within the studied sample.
By means of XPS technique the Si-content within the Si:HfO2 thin films was analysed.
XPS measurements were performed at Fraunhofer Center Nanoelectronic Technologies Dresden with a REVERA VeraFlex production metrology system using Al-Kα excitation and 141.2 eV pass-energy. The intensities of characteristic peaks for hafnium (Hf-4f) and silicon (Si-2p) were determined. The Si-content was subsequently obtained as cation fraction (cat%) by applying the tool specific calibration factors and weighting the areas of the respective XPS peaks.
3.4 Microstructural analyses
3.4.3 Transmission electron microscopy
Transmission electron microscopy (TEM) is a microscopy technique enabling to study the sample’s microstructure with sub-nanometre resolution. Utilisation of electrons with significantly smaller de Broglie wavelength (λ < 0.05 Å) instead of the visible light (λ in the range 3900 – 7000 Å) provides a considerably higher resolution capability of TEM in comparison with the light microscopy. By using TEM, both images and diffraction patterns of the specific specimen area can be obtained. These are formed by electrons transiting through a thin specimen. Due to interaction of transmitted electrons with the matter of the specimen, they contain information about its microstructure. Three main principles of the contrast formation in TEM images are distinguished [205]: mass-thickness contrast, diffraction contrast and phase contrast. The latter is utilised by a high-resolution TEM to image material structure on the atomic scale. More information about principle of image formation and imaging system of the high-resolution TEM can be found in [205], [206]. The samples studied with TEM should be thin enough (less than 100 nm) in order to obtain sufficient intensity of the transmitted electron beam. Therefore, specific specimen preparation from the bulk samples prior to actual TEM analyses is required. Mechanical thinning, electrochemical thinning or ion milling can be exploit for this purpose [204].
High-resolution TEM was used to study the microstructure of the polycrystalline Si:HfO2 films. Thin specimens of different film regions were prepared for TEM analysis by
means of focused ion beam (FIB) technique, a special type of ion milling, which utilises highly energetic gallium ions. High-resolution TEM measurements were performed by Dr. Thomas Gemming at Leibniz Institute of Solid State and Material Research Dresden.