Editing Auger electron spectroscopy (section)

==Electron transitions and the Auger effect==

The Auger effect is an electronic process at the heart of AES resulting from the inter- and intrastate transitions of electrons in an excited atom. When an atom is probed by an external mechanism, such as a photon or a beam of electrons with energies in the range of several&nbsp;[[Electronvolt|eV]] to&nbsp;50 keV, a core state electron can be removed leaving behind a hole. As this is an unstable state, the core hole can be filled by an outer shell electron, whereby the electron moving to the lower energy level loses an amount of energy equal to the difference in orbital energies. The transition energy can be coupled to a second outer shell electron, which will be emitted from the atom if the transferred energy is greater than the orbital binding energy.<ref name="carlson"/><ref name="briggs_sheah1983"/><ref name="thompson1985"/><ref name="davis1980"/><ref name="feldman_mayer">{{cite book |last=Feldman |first=Leonard C. |author2=James W. Mayer |year=1986 |title=Fundamentals of Surface and Thin Film Analysis |location=Upper Saddle River |publisher=[[Prentice Hall]] |isbn=0-13-500570-1}}</ref><ref name="oura2003">{{cite book |last=Oura |first=K. |author2=V. G. Lifshits |author3=A. A. Saranin |author4=A. V. Zotov |author5=M. Katayama  |year=2003 |title=Surface Science: An Introduction |location=Berlin |publisher=Springer |isbn=3-540-00545-5}}</ref> An emitted electron will have a kinetic energy of:

:<math>E_{\text{kin}}=E_{\text{Core State}}-E_B-E_{C}'</math>

where <math>E_{\text{Core State}}</math>, <math>E_B</math>, <math>E_C'</math> are respectively the core level, first outer shell, and second outer shell electron binding energies (measured from the vacuum level) which are taken to be positive. The apostrophe (tic) denotes a slight modification to the binding energy of the outer shell electrons due to the ionized nature of the atom; often however, this energy modification is ignored in order to ease calculations.<ref name="briggs_sheah1983"/><ref>[http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_1/4_1_3.html Auger spectroscopy] {{Webarchive|url=https://web.archive.org/web/20180110175852/http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_1/4_1_3.html |date=2018-01-10 }} National Physical Laboratory: Kaye & Laby, Tables of Physical and Chemical Constants</ref> Since orbital energies are unique to an atom of a specific element, analysis of the ejected electrons can yield information about the chemical composition of a surface. Figure 1 illustrates two schematic views of the Auger process.

[[Image:Auger Process.svg|thumb|340px|Figure 1. Two views of the Auger process. (a) illustrates sequentially the steps involved in Auger deexcitation. An incident electron creates a core hole in the 1s level. An electron from the 2s level fills in the 1s hole and the transition energy is imparted to a 2p electron that is emitted. The final atomic state thus has two holes, one in the 2s orbital and the other in the 2p orbital. (b) illustrates the same process using [[X-ray notation]], <math>KL_1L_{2,3}</math>.]]

The types of state-to-state transitions available to electrons during an Auger event are dependent on several factors, ranging from initial excitation energy to relative interaction rates, yet are often dominated by a few characteristic transitions. Because of the interaction between an [[Electron magnetic moment|electron's spin]] and [[Angular momentum operator#Orbital angular momentum operator|orbital angular momentum]] (spin-orbit coupling) and the concomitant energy level splitting for various shells in an atom, there are a variety of transition pathways for filling a core hole. Energy levels are labeled using a number of different schemes such as the j-j coupling method for heavy elements ([[Atomic number|''Z'']] ≥ 75), the Russell-Saunders L-S method for lighter elements (''Z'' < 20), and a combination of both for intermediate elements.<ref name="briggs_sheah1983"/><ref name="kittel1996">{{cite book |last=Kittel |first=Charles |author-link=Charles Kittel |year=1996 |title=[[Introduction to Solid State Physics]] |edition= 7th |location=New York |publisher=John Wiley & Sons |isbn=81-265-1045-5}}</ref><ref name="ashcroft_mermin">{{cite book |last=Ashcroft |first=Neil |author2=Mermin, N. David |author-link2=David Mermin  |year=1976 |title= Solid State Physics|location=Ithaca |publisher=Thomson Learning |isbn=0-03-049346-3}}</ref> The [[Angular momentum coupling#jj coupling|j-j coupling]] method, which is historically linked to [[X-ray notation]], is almost always used to denote Auger transitions. Thus for a <math>KL_1L_{2,3}</math> transition, <math>K</math> represents the core level hole, <math>L_1</math> the relaxing electron's initial state, and <math>L_{2,3}</math> the emitted electron's initial energy state. Figure 1(b) illustrates this transition with the corresponding spectroscopic notation. The energy level of the core hole will often determine which transition types will be favored. For single energy levels, i.e. ''K'', transitions can occur from the L levels, giving rise to strong KLL type peaks in an Auger spectrum. Higher level transitions can also occur, but are less probable. For multi-level shells, transitions are available from higher energy orbitals (different ''n, ℓ'' quantum numbers) or energy levels within the same shell (same ''n'', different ''ℓ'' number).<ref name="carlson"/> The result are transitions of the type LMM and KLL along with faster [[Coster–Kronig transition]]s such as LLM.<ref name="carlson"/><ref name="briggs_sheah1983"/> While Coster–Kronig transitions are faster, they are also less energetic and thus harder to locate on an Auger spectrum. As the [[atomic number]] Z increases, so too does the number of potential Auger transitions. Fortunately, the strongest electron-electron interactions are between levels that are close together, giving rise to characteristic peaks in an Auger spectrum. KLL and LMM peaks are some of the most commonly identified transitions during surface analysis.<ref name="briggs_sheah1983"/> Finally, valence band electrons can also fill core holes or be emitted during KVV-type transitions.

Several models, both phenomenological and analytical, have been developed to describe the energetics of Auger transitions. One of the most tractable descriptions, put forth by Jenkins and Chung, estimates the energy of Auger transition ABC as:

:<math>E_{ABC}=E_A(Z)-0.5[E_B(Z)+E_B(Z+1)]-0.5[E_C(Z)+E_C(Z+1)]</math>

<math>E_i(Z)</math> are the binding energies of the <math>i</math>th level in element of atomic number ''Z'' and <math>E_i(Z+1)</math> are the energies of the same levels in the next element up in the periodic table. While useful in practice, a more rigorous model accounting for effects such as screening and relaxation probabilities between energy levels gives the Auger energy as:

:<math>E_{ABC}=E_A-E_B-E_C-F(BC:x)+R_{xin}+R_{xex}</math>

where <math>F(BC:x)</math> is the energy of interaction between the ''B'' and ''C'' level holes in a final atomic state ''x'' and the ''R'''s represent intra- and extra-atomic transition energies accounting for electronic screening.<ref name="briggs_sheah1983"/> Auger electron energies can be calculated based on measured values of the various <math>E_i</math> and compared to peaks in the secondary electron spectrum in order to identify chemical species. This technique has been used to compile several reference databases used for analysis in current AES setups.