Electron Energy Loss Spectroscopy

R. Brydson

• Publisher: Garland Science
• Year: 2020
• ISBN:
  9781000144628
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biophysics
• Index: Biological Sciences

Electron Energy Loss Spectroscopy (EELS) is a high resolution technique used for the analysis of thin samples of material. The technique is used in many modern transmission electron microscopes to characterise materials. This book provides an up-to-date introduction to the principles and applications of EELS. Specific topics covered include, theory of EELS, elemental quantification, EELS fine structure, EELS imaging and advanced techniques.

1 Introduction

1.1 What is EELS?

Considering the large range of possible physical analysis techniques available, very few microscopically analytical techniques are currently in widespread use. There are some 10 or more possible primary probes (e.g. electrons, X-rays, ions, atoms, light, neutrons, sound etc.) which can be used to excite up to 10 secondary effects from the region of interest (e.g. electrons, X-rays, ions, light, neutrons, sound, heat etc.); the chosen secondary effects may then be monitored as a function of one or more of seven or eight variables (e.g. energy, temperature, mass, intensity, time, angle, phase etc.) as well as a function of position in the sample. This gives the possibility of around 700 single signal techniques as well as the technically more difficult multi-signal techniques. At present the number of techniques which have been tried is around 100. In this book we will mainly be concerned with those analytical techniques which are based in the electron microscope and hence we only consider those in which the primary probe is an electron beam.

Electron energy loss spectroscopy (EELS) is the general title and acronym for techniques whereby a beam of electrons is allowed to interact with matter (in principle, a solid, liquid or gaseous specimen) and the scattered beam of electrons is spectroscopically analysed to give the energy spectrum of electrons after the interaction. The EELS spectrum so formed can also be filtered and the filtered electrons recombined to form an image of the specimen — a technique known as electron spectroscopic imaging (ESI). In general terms this set of techniques may be classed as an absorption spectroscopy since energy and intensity from the incident electron beam is absorbed by the matter under study. As we shall see, the nature of this energy absorption will depend on the precise composition and electronic structure of the matter under investigation.

The subject of this book is the technique of EELS conducted in the environment of a transmission electron microscope (TEM), whereby a focused electron beam is allowed to traverse a thin solid sample (although gases are also sometimes studied) and the transmitted electron beam is spectroscopically analysed. Hence this may be termed transmission EELS and is known by the acronyms EELS or parallel EELS (PEELS) — the associated spectroscopic imaging mode being known as energy filtered TEM (EFTEM) or ESI. An alternative technique also known as EELS, or high-resolution EELS (HREELS), or even surface EELS (SEELS) is concerned solely with the interaction of an electron beam with a surface of a material with the backscattered electron beam being analysed. These surface specific techniques allow the study of surface adsorbates and surface layers; however, they will not concern us here and for further information the reader is referred to the book by Ibach and Mills (1982).

1.2 Interaction of electrons with matter

The use of electrons as a probe of the atomic and electronic structure of solids has many advantages. Firstly, electrons are relatively easy to produce via simple heating of say a tungsten filament. Secondly, there is a large interaction between the incident electron beam and the electrons in the solid, which may be used for the purpose of analysis. Finally, since electrons are charged particles they may be accelerated to high kinetic energies via the application of a high voltage and subsequently focused onto small areas using electromagnetic lenses so forming images or diffraction patterns at atomic-scale resolution.

1.2.1 Electronic structure of atoms and solids

A simplified picture of the structure of an isolated atom is shown in Figure 1.1. The dense positively charged nucleus is exactly neutralized by the surrounding negative electrons, which describe orbits around this central nucleus; these orbits are shown in Figure 1.1 as simple spherical Bohr shells. The set of electronic wavefunctions and associated electronic energy levels for the simple case of an isolated hydrogen atom, which consists of one proton and one electron, may be obtained by solving the Schrodinger equation for a single electron moving in the potential of the Hydrogen nucleus (Levine, 1991). The wavefunctions, Ψ, may be expressed as a radial part, governing the spatial extent of the wavefunction, multiplied by a spherical harmonic, which determines the exact shape. These localized atomic states are known as Rydberg states and may be described in terms of either simple Bohr shells or as combinations of the three quantum numbers n, l and m, known as electron orbitals. The Bohr shells (designated K, L, M etc.) correspond to the principal quantum numbers (n)equal to 1, 2, 3 et cetera. Within each of these shells, the electrons may exist in s,p, d, or f subshells, for which the angular-momentum quantum number (l) equals 0, 1, 2, 3, respectively. It is usual to define the zero-of-energy scale (the vacuum level) as the potential energy of a free electron far from the atom. The energies of the localized electrons are then negative (i.e. they are bound to the atom) as shown in Figure 1.1. Table 1.1 gives the ‘KLM’ and ‘spdf’ descriptions of the 16 lowest electron energy states in the atom, together with the number of electrons which each state can hold. The occupation of the states depends on the total number of electrons in the atom. In the hydrogen atom, which contains only one electron, the set of Rydberg states is almost entirely empty except for the 1s level which is half full. The energy spacing between these states becomes smaller and smaller and eventually converges to a value known as the vacuum level (n=∞)which corresponds to the ionization of the inner-shell electron. Above this energy the electron is free of the atom and this is represented by a continuum of empty states. In fact the critical energy to ionize a single isolated hydrogen atom is equal to 13.61 eV and is termed a Rydberg.

Figure 1.1. The Bohr shell electronic structure and associated energy level diagram of an isolated magnesium atom.

Table 1.1. Electron states in the atom including the standard nomenclature for the EELS ionization edge involving transitions from these initial states

Solving the Schrödinger equation for higher atomic number atoms, with more than one electron, is difficult due to the problem of electron—electron interactions in the expression for the potential. However, one method is to assume that the wavefunctions have a similar form to those derived for the simple H atom (known as hydrogenic-like solutions). The wavefunctions and energies are then derived self-consistently. Assuming a starting potential, initial solutions of the Schrodinger equation are derived which are, in turn, fed back to construct a new and improved potential function. The calculation is iterated until a minimum-energy solution is derived. This approach is known as the variation principle. The final results are self-consistent field (SCF) atomic wavefunctions and they have a qualitatively similar form to those obtained for hydrogen, which leads to the basis for the periodic classification of the elements in the Periodic Table.

When atoms come into close proximity with other atoms in a solid, most of the electrons remain localized and may be considered to remain associated with a particular atom, however, some outer electrons will become involved in bonding with neighbouring atoms. Upon bonding the atomic energy level diagram in Figure 1.1 becomes modified (Cox, 1991). Briefly, the well-defined outer electron states of the atom overlap with those on neighbouring atoms and become broadened into energy bands. One convenient way of picturing this is to envisage the solid as large molecule. Figure 1.2 shows the effect of increasing the number of atoms on the electronic energy levels of a one-dimensional solid (i.e. a linear chain of atoms). For a simple diatomic molecule, the two outermost atomic orbitals (AOs) overlap to produce two molecular orbitals (MOs) which can be viewed as a linear combination of the two atomic orbitals.

Figure 1.2. Schematic representation of the electron energy level diagram on going from an isolated atom to a gradually larger linear chain of n atoms. As n increases the number of molecular orbitals correspondingly increases and the outer energy levels progressively become more closely spaced until they form an overlapping energy band.

One MO, formed from the in-phase overlap of the AOs, is lower in energy than the corresponding AOs and ...