Question

Assume an atom has K, L, and M electrons and the energies for K, L, and M shells are -5000, -500, and -50 eV. Please give all possible energies of Auger electrons and characteristic X-rays.

Answer 1

Auger Electron Spectroscopy

Auger Electron Spectroscopy (Auger spectroscopy or AES) was developed in the late 1960's , deriving its name from the effect first observed by Pierre Auger, a French Physicist, in the mid-1920's. It is a surface specific technique utilising the emission of low energy electrons in theAuger process and is one of the most commonly employed surface analytical techniques for determining the composition of the surface layers of a sample.

PHYSICAL BASIS

Auger spectroscopy can be considered as involving three basic steps :

(1) Atomic ionization (by removal of a core electron)

(2) Electron emission (the Auger process)

(3) Analysis of the emitted Auger electrons

The last stage is simply a technical problem of detecting charged particles with high sensitivity, with the additional requirement that the kinetic energies of the emitted electrons must be determined.

We will therefore concern ourselves only with the first two processes - before starting, however, it is useful to briefly review the electronic structure of atoms and solids, and associated nomenclature.

Electronic Structure - Isolated Atoms.

The diagram below schematically illustrates the energies of the various electron energy levels in an isolated, multi-electron atom, with the conventional chemical nomenclature for these orbitals given on the right hand side.

However, scientists working with x-rays tend to use the alternative nomenclature on the left and it is this nomenclature that is used in Auger spectroscopy. The designation of levels to the K,L,M,… shells is based on their having principal quantum numbers of 1,2,3,… respectively.

It is convenient to expand the part of the energy scale close to the vacuum level in order to more clearly distinguish between the higher levels ....

The numerical component of the KLM.. style of nomenclature is usually written as a subscript immediately following the main shell designation.

Levels with a non-zero value of the orbital angular momentum quantum number ( l > 0), i.e. p,d,f,.. levels, show spin-orbit splitting. The magnitude of this splitting, however, is too small to be evident on this diagram - hence, the double subscript for these levels (i.e. L_2,3represents both the L₂ and L₃ levels).

Electronic Structure - Solid State

In the solid state the core levels of atoms are little perturbed and essentially remain as discrete, localised (i.e. atomic-like) levels. The valence orbitals, however, overlap significantly with those of neighbouring atoms generating bands of spatially-delocalised energy levels.

The energy level diagram for the solid is therefore closely resemblant of that of the corresponding isolated atom, except for the levels closest to the vacuum level.

The diagram below shows the electronic structure of Na metal :

The Auger Process & Auger Spectroscopy

Now let us return to the subject of Auger spectroscopy - in the following discussion, the Auger process is illustrated using the K, L₁ & L_2,3levels. These could be the inner core levels of an atom in either a molecular or solid-state environment.

I. Ionization

The Auger process is initiated by creation of a core hole - this is typically carried out by exposing the sample to a beam of high energy electrons (typically having a primary energy in the range 2 - 10 keV). Such electrons have sufficient energy to ionise all levels of the lighter elements, and higher core levels of the heavier elements.

In the diagram above, ionisation is shown to occur by removal of a K-shell electron, but in practice such a crude method of ionisation will lead to ions with holes in a variety of inner shell levels.

In some studies, the initial ionisation process is instead carried out using soft x-rays ( hν = 1000 - 2000 eV ). In this case, the acronym XAES is sometimes used. As we shall see, however, this change in the method of ionisation has no significant effect on the final Auger spectrum.

II. Relaxation & Auger Emission

The ionized atom that remains after the removal of the core hole electron is, of course, in a highly excited state and will rapidly relax back to a lower energy state by one of two routes :

1. X-ray fluorescence , or
2. Auger emission

We will only consider the latter mechanism, an example of which is illustrated schematically below ....

In this example, one electron falls from a higher level to fill an initial core hole in the K-shell and the energy liberated in this process is simultaneously transferred to a second electron ; a fraction of this energy is required to overcome the binding energy of this second electron, the remainder is retained by this emitted Auger electron as kinetic energy. In the Auger process illustrated, the final state is a doubly-ionized atom with core holes in the L₁ and L_2,3 shells.

We can make a rough estimate of the KE of the Auger electron from the binding energies of the various levels involved. In this particular example,

KE = ( E_K - E_L1 ) - E_L23

[ Why is this answer not likely to be very accurate ? ]

Note : the KE of the Auger electron is independent of the mechanism of initial core hole formation.

The expression for the energy can also be re-written in the form :

KE = E_K - ( E_L1 + E_L23 )

It should be clear from this expression that the latter two energy terms could be interchanged without any effect - i.e. it is actually impossible to say which electron fills the initial core hole and which is ejected as an Auger electron ; they are indistinguishable.

An Auger transition is therefore characterized primarily by :-

1. the location of the initial hole
2. the location of the final two holes

although the existence of different electronic states (terms) of the final doubly-ionized atom may lead to fine structure in high resolution spectra.

When describing the transition, the initial hole location is given first, followed by the locations of the final two holes in order of decreasing binding energy.

i.e. the transition illustrated is a KL₁L_2,3 transition .