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3.1.3.2.2 Absorption (A) X-Rays are produced over a range of depth into a bulk sample. To be detected, they have to “travel” up to the detector. This propagation takes place along a finite path through the specimen to reach the detector, and they are subject to photoelectric absorption and scattering. As a consequence, the detected X-Ray intensity will be less than the generated intensity and this intensity reduction has to be taken into account in order to give the right chemical composition.

3.1.3.2.3 Fluorescence (F) It was seen previously that absorption of X-Rays on the way to the detector needs to be corrected for. There is is another effect: absorption of X-Rays causes the inner shell ionisation of the absorbing atoms and the subsequent generation of characteristic X-rays from the absorbing atoms. It raises the generated intensity over that produced by the direct action of the beam electrons. Therefore, the detected X-Ray intensity will be more than expected and this intensity increase has to be taken into account to yield the correct chemical composition. This effect can be induced by both characteristic X-Rays and Bremsstrahlung.

When the above three physical processes are taken into account in a quantitative analysis procedure, one is using the ZAF method. A separate correction factor is calculated for each effect (or matrix effects). The characteristic X-Rays measured from the specimen are ratioed to the intensity measured from a standard. The physical models yielding the correction factors Z, A and F described above are used to calculate iteratively inter-element matrix factors that multiply the unknown/standard intensity ratio to yield the concentration of the unknown relative to the standard [134]. Therefore, in a binary compound AB, A and B peak intensities are related to the concentrations of A and B by:

C_A

C_B = ZAF × I_A

I_B (3.2)

3.2 Electron Energy-Loss Spectroscopy (EELS)

Electron energy-loss spectroscopy provides a spectrometry complementary to EDX, en-abling much better light element detection. It consists of the analysis of the energy disribution of electrons that have interacted inelastically with the specimen. The scat-tered beam of electrons is spectroscopically analysed to give an energy spectrum for the electrons after the interaction. Energy and hence intensity from the incident electron beam are absorbed by the matter under study. The nature of this energy absorption will depend on the precise composition and electronic structure of the specimen under

3.2. Electron Energy-Loss Spectroscopy (EELS) 41

investigation. The general principle of EELS will first be explained before moving on to the description of the electron energy loss spectrum and the working principles of the spectrometer.

3.2.1 General principles

Electrons can interact in two manners with matter: elastically and inelastically. During scattering both the amplitude and phase of the incident electron wave may alter. When elastic scattering occurs, the direction of the electron velocity is changed, but its mag-nitude remains constant, so that the kinetic energy is unchanged. It is also generally coherent. Large angle scattering (greater than 5^◦) occurs through the coulombic inter-action between the incident electron and the nucleus of the atom. It is also known as Rutherford scattering. If the electrons travel much farther from the nucleus and only interact with the screened nuclear field (by electrons) of an atom, then small-angle (a few degrees) elastic scattering occurs.

During an inelastic scattering event, not only is energy transferred to the target atoms and electrons but also any phase relationships between scattered waves are lost (incoherent scattering). As a consequence, the kinetic energy of some beam electrons decreases giving rise to energy losses. An inelastically scattered electron undergoes only slight angular deviation (up to a few mrads/tens of degrees), which means that contrary to EDX, a large fraction of the total possible signal can be collected by an electron spectrometer placed in the forward-scattering direction. It is the energy analysis of these inelastically scattered electrons that forms the basis for EELS.

The main types of inelastic scattering mechanisms are:

• Phonon excitation (heat).

• Plasmon excitation (valence electrons in a solid).

• Single electron excitation (inner and outer shell scattering).

• Direct radiation losses (deceleration of the electron beam in the Coulomb field of an atom (Bremsstrahlung radiation)).

• Excitation of conducting electrons leading to secondary electron (low-energy) emissions.

These different mechanisms are all associated with different energy levels. Some of them cannot even be detected, like phonon excitation. Indeed, the energy resolution of the very best current EELS systems (0.1 eV) is much higher than the phonon scattering

3.2. Electron Energy-Loss Spectroscopy (EELS) 42

energy (0.03 eV) [135].

If the specimen is sufficiently thin to prevent any multiple inelastic scattering (or if the latter is corrected for), the majority of electrons suffers only a single inelastic scattering event during passage through the specimen. If not, there is a degradation of the ionisation edge information. ”Sufficiently thin” means that the specimen thickness must generally lie in the 25-100 nm range (depending on the average atomic number of the specimen and the beam energy). If the specimen thickness is less than 25 nm, surface effects are increasingly likely and can modify low-loss EELS spectra [136]. Thickness is sometimes given as a fraction of the inelastic mean free path (IMFP). This better represents the average distance travelled by an electron between two inelastic scattering events and is inversely proportional to the inelastic cross section. It can be calculated by the use of either classical physics or wave mechanics. A commonly used expression for the IMFP is given by Egerton [137]:

IM F P (nm) = 106 × [(1 + E₀/1022)/(1 + E₀/511)²× (E₀/E_m)]

ln(2βE₀/E_m) (3.3)

where E₀ is the incident beam energy (keV), E_m = 7.6 × Z^0.36 (Z is the average atomic number), β is the collection angle (mrad) and (1+E0/1022)/((1+E0/511)²is a relativistic correction factor. IMFP is expressed in nanometres.

The high background in the EELS spectrum generally restricts the relative detection limit to 1% or higher [134]. Quantitative analysis is based on physical models of inelastic electron scattering with empirical corrections for instrumental effects. The next section will detail the different regions of the electron energy loss spectrum.

3.2.2 The Electron Energy Loss Spectrum

The electron energy loss spectrum is composed of two main parts: a low loss and a high loss part. The first region extends from 0 to about 50 eV with several noticeable features.

It contains a zero-loss peak (ZLP) which is made up from those electrons which have (1) not been scattered by the specimen, (2) suffered only phonon scattering (±0.03 eV) or (3) been elastically scattered. The energy width of the zero-loss peak is caused by the energy spread of the electron source (up to ±2 eV for a thermionic W filament) and the energy resolution of the spectrometer. It is an excellent measurement of the energy resolution of a given experiment. A lower intensity peak is observed in the 20-30 eV region. It is associated with bulk plasmon excitations corresponding to collective, resonant oscillations of the valence electrons. Its energy is given by:

3.2. Electron Energy-Loss Spectroscopy (EELS) 43

where N is the valence electron density, h the Planck constant, me the electron mass, e the electron charge and ε₀ the permittivity of free space.

Plasmon scattering has the largest cross section and it is by far the most common inelastic interaction occurring in materials [138]. The typical mean free path for the generation of a plasmon is about 50 nm, resulting in many electrons suffering from single-plasmon losses: only thicker specimens would show additional peaks at multiples of the plasmon energy, corresponding to the excitation of more than one plasmon by the incident electron.

Plasmons can be imagined as soundwaves, since they are longitudinal oscillations which create regions of varying electron density. Other types of plasmons can be observed depending on the material under investigation or its geometry. Samples thinner than 20 nm or nanoparticles generally show surface plasmons. The presence of interfaces parallel to the beam direction (including possible contamination layer(s)) can give rise to interface losses such as interface plasmons [139] and gap states [140]. The low-loss region is generally used for thickness and electron density measurement. It is also used for deriving the dielectric function after Kramers-Kronig analysis of the single scattering distribution (SSD) obtained after zero-loss peak and multiple scattering deconvolution of the low-loss spectrum. It can then be correlated with optical measurements and band gap determinations in semiconductors/insulators.

The second region extends from about 50 eV to 2000 eV. Above a certain critical ioniza-tion energy Ec, excitation of electrons from well localised orbitals (core shells) at a single atomic site to previously unoccupied electron energy levels just above the Fermi level of the material arises. This region reflects the atomic character of the specimen, so that com-positional data can also be derived. A continuous background on which the characteristic ionisation edges (rather than peaks in the low-loss range) are superimposed is particular to this region. Such a background arises from tails of plasmon excitation(s) combined with those of ionisation edges at lower threshold energies. Qualitative elemental analysis can be carried out simply by measuring the energies of the edges and comparing them with tabulated energies. A classification of EELS ionisation edges can be found in [141].

Since the ionisation process can impart more than the critical ionisation energy E_cneeded by the core electron to escape the attraction of the nucleus, the final state of the excited electron will be in the range of possible energy levels above the Fermi level (E_F) giving rise to Energy-Loss Near Edge Structures (ELNES). Some electrons gain enough energy to

3.2. Electron Energy-Loss Spectroscopy (EELS) 44

leave the atom and act as an electron wave which can be diffracted by the surroundings atoms. In the spectrum, it is seen as weak oscillations and fine structures beyond the first 30-40 eV of an edge and known as Extended Energy Loss Fine Structures (EXELFS).

Analysis of this part of the spectrum can be performed to obtain the Radial Distribution Function (RDF).

3.2.3 The electron spectrometer

The intensity of the various electrons, i.e. those transmitted without loss of energy and those that have been inelastically scattered and lost energy, is obtained by dispersing the electrons with a magnetic prism, which separates spatially the electrons of different energies. This is the main feature of an electron spectrometer.

Several types of electron spectrometers are curently in use: the sector magnet spectrom-eter, the Castaing-Henry prism, the Ω filter and the Mollenstedt analyser. The sector magnet spectrometer is the most commonly used as it can be easily fitted to any TEM column. It consists of a sector magnet generating a homogenous magnetic field normal to the electron beam. According to the Lorentz equation, this causes the electron to bend with a radius R where R=mv/eB due to the magnetic force F defined as F=Bev where v is the electron velocity, B the magnetic vector value and e the electron charge.

Therefore, electrons with different kinetic energies undergo a different Lorentz force and hence emerge from the spectrometer spatially dispersed. The object plane of the spectrometer is either the final projector crossover in TEM mode or the virtual image of the specimen in STEM mode. The spectrometer has a focusing action which results in the formation of a line spectrum at the spectrometer image plane and can be thought of as an optical component with its own properties and aberrations. Such aberrations have to be corrected by the user through quadrupole and sextupole magnetic lenses at the entrance and exit faces of the magnet. At the image plane is an array of silicon photodiodes where the whole spectrum is recorded at once in parallel. Like any other photodiode, they need to be calibrated before exposure to electron radiation. A schematic of a sector magnet spectrometer is shown in Fig. 3.4.