GROWTH AND CHARACTERIZATION
2.3 Complementary experimental and theoretical tech- niques
2.3.1 Nanoindentation
Nanoindentation is a technique which uses an indenter that penetrates the sample and by measuring the penetration depth along with the measured applied load one can de- termine the hardness of the specimen. From the experimental load-displacement curve, other mechanical properties (as the elastic modulus) can be obtained.
The three-sided Berkovich indenter tip is usually used in nanoindentation in- stead of the more familiar Vickers tip, and the reason is that a sharper tip can be ob- tained when the tip is grounded. With four-sided Vickers pyramidal tip there is always an undesirable line of conjunction at the tip. With a three-sided Berkovich indenter is much easier to grind the faces of the indenter to meet a single point, rather than a line. A representative trace left on a film after nanoindentation with a Berkovich tip is shown in Figure 2.11. The hardness of the studied film can be determined by performing a se- ries of indentations at increasing depths and then plotting the clalculated hardness against the indentation depth.
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Figure 2.11: Representative trace of a Berkovich tip used for nanoindentation.22
2.3.2 X-Ray Diffraction (XRD)
X-ray diffraction finds the geometry or shape of a molecule using x-rays. X-ray diffrac- tion techniques are based on the elastic scattering of x-rays from structures that have long range order. The most comprehensive description of scattering from crystals is given by the dynamical theory of diffraction. XRD has variations from which different information about the studied material is obtained. From the various XRD techniques available, the following were used in this thesis for extracting information for the crystal structure, grain, mosaicity and strain of the studied samples.
1. Single-crystal X-ray diffraction is a technique used to solve the complete structure of crystalline materials.
2. Thin film diffraction is used to characterize the crystallographic structure and pre- ferred orientation of substrate-anchored thin films.
3. High-resolution x-ray diffraction is used to characterize thickness, crystallographic structure, and strain in thin epitaxial films. It employs parallel-beam optics.
4. X-ray rocking curve analysis is used to quantify grain size and mosaic spread in crys- talline materials.
2.3.3 Raman Spectroscopy
Raman spectroscopy is a technique used to observe low-frequency modes in a material.
It relies on inelastic scattering (Raman scattering) of monochromatic light usually from
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a laser in the visible, the IR or the UV range. The light interacts with excitations in the system (e.g. phonons) resulting in the energy shift of the laser photons which gives in- formation about the vibrational modes in the system.
Raman spectroscopy is applied for characterization of solid materials such as its crystallographic orientation through its characteristic phonon modes. Also it can be used to observe other low frequency excitations of the solid (plasmons). The Raman signal gives information on the population of a given phonon mode in the ratio between the Stokes (downshifted) and anti-Stokes (upshifted) intensity. Raman scattering by an anisotropic crystal gives information on the crystal orientation by studying the polariza- tion of the scattered light with respect to the crystal and the polarization of the laser light.
2.3.4 Empirical potential calculations using Molecular Dynamics (MD)
Molecular Dynamics (MD) is a computer simulation technique which studies the physi- cal movements of atoms and molecules in the context of N-body simulation in which the atoms and molecules are allowed to interact for a period of time.
In general a force field is the mathematical function that describes a system in correlation with its structure. In order to define the empirical potential the following assumption has to be taken into account; that a solid consists of well-defined isolated atoms that interact in desirable distances and angles. This hypothesis does not consider the role of the electrons on the cohesion of a solid. Despite this, this assumption can be justified if the Born-Oppenaheimer approximation is taken into consideration that states that “the motion of the dislocation cores and the electrons can be distinguished”.
Then, in order to be able to manipulate the atoms and their bonds, the ball and spring models can employed. The atoms are considered as the balls (which are placed as the center of the atom cores) and the springs correspond to the interaction force between the atoms. Then the forces that are applied in the system atoms can be described in terms of potential energy functions that contain the various system characteristics such as the bond length, the angles between the bonds etc.
Hence, the force field, that is a linear combination of potential energy functions that derived from the atoms interactions, is called empirical potential. The interaction force is given by an analytical expression (energy functional), which is the difference between the total energy of the system and the energy of the ideal structure which is the following:
E=Ebonded+Enon-bonded (2.17) where Ebonded=Ebond-stretch+Eangle-bend+Erotate-along-bond (2.18)
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and Enon-bonded=Evan-der-waals+Eelectrostatic +… (2.19)
in the above expressions the Ebond-stretch term is due to bond length changes, the Eangle-bend
term corresponds to bond bending and Erotate-along-bond is the term due to the rotation along the bond length.
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