Chapter 5
Electron spectroscopy
5.1 Electron interactions
Effects upon bombardment of material with electron beam:
• material processing: cleaning (desorption), activation energy for chemical and physical processes,
electron lithography
• heating: evaporation
• reflection, transmission
• diffraction (scattering)
• excitation of photons (x-ray, chatodoluminescence)
• emission of true secondary electrons
Total electron current from a substance is the current of secondary electrons on reflection or
transmission. Different processes that lead to this current are depicted in Fig. 5.1. The true
secondary electrons are part of it. The secondary electron yield depends on many factors, and is
generally higher for high atomic number targets, and at higher angles of incidence. In Fig. 5.2,
there is a general division of different characterization methods that uses emitted electrons.
1
2 CHAPTER 5. ELECTRON SPECTROSCOPY
Figure 5.1: Electron emission: (a) without interaction, (b) elastic scattering (diffraction on passage),
(c) elastic reflection (diffraction on reflection), (d) inelastic reflection (characteristic energy
loss), (e) backscatter electron, (f) electron transmission with the possibility to emit others and (g)
electron transmission with secondary electron emission.
Figure 5.2: Overwiev of measuring methods that use emitted electrons.
5.1. ELECTRON INTERACTIONS 3
The ration between this current Is and primary Ip is called secondary emission coefficient
σ = Is/Ip. Looking at the energy distribution of the secondary electrons (Fig. 5.3) we can identify
individual interactions:
• the highest maximum of primary energy level ⇒ elastic reflection of e−
interaction with the atom like a whole, there is no change in energy but, the electron momentum
can be changed dramatically. For higher energies (≥ 5 keV), it can be described by
Rutherford scattering
dQ(θ)
dΩ
=
1
4
e2
(Z − F(θ))
4π 0 mred g2
2
1
sin4
(θ/2)
, (5.1)
where F(θ) is the screening effect of electrons. F(θ) is insignificant at high angles θ and
strong scattering can occur only in heavy atoms (used for TEM contrast). When the target
is a crystalline material diffraction and channelling occurs. When electron scattering
from crystal lattice is coherent, amplification in those direction occurs, which is represents
Bragg law:
nλ = 2dhkl sin θ, (5.2)
where n is a integer dhkl is is the spacing between the planes in the atomic lattice expressed
with Miller indexes. This method is used to examine the bulk crystalline structure (E ≈
10 keV) or the surface structure using low-energy electron diffraction (LEED) or very small
angle relection in reflection high-energy electron diffraction (RHEED).
• smaller peaks on the left exhibit energy shift together with the maximum of elastic scattered
electrons ⇒ electrons which suffered some characteristic energy loss:
Figure 5.3: Electron energy distribution.
4 CHAPTER 5. ELECTRON SPECTROSCOPY
– excitation of vibrational states in adsorbed molecules ∆E ≈ 50–500 meV;
– individual interaction with valence e−
, ∆E ≈ 3–20 eV but this interaction does not
have a sharp value because the valence band has a width of several eV
– interaction with the cloud of e−
having characteristic oscillation frequency - excitation
of plasmon with the frequency of
ωp =
1
0
n0e2
m
(5.3)
for plasmon in volume, or
ωs =
ωp
√
1 + r
=
ω
√
2
(5.4)
for excitation of the surface plasmon. ∆E is between 5 and 60 eV.
• broader peak at low energies - true secondary electrons, usually defined with the condition
E < 45 − 50 eV
• Usually, electrons undergo many inelastic interactions (phonon excitations, inter and intra
band transitions, plasmon excitations, inner shell ionizations) and when emitted as “back
diffusion” they do not bring a specific information (background signal that also includes
a small part of fast true secondary electrons). Small part of electrons are emitted after
undergoing only one such interaction - only electrons emitted from a thin surface layer or
through a thin specimen ⇒ electron energy loss spectroscopy (EELS).
• smaller peaks on the signal of true secondary electrons (left part of the EEDF) - do not shift
with energy of primary beam ⇒ Auger e−
which have for each substance a characteristic
position.
The process is following. Primary e−
removes a core e−
(e.g. from K shell) creating 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. The Auger energy released
Ek = EK − EL − EV − Eaf. (5.5)
The EV is not equal with the original level energy EV, because the e−
on the level V moves
in a potential and the e−
on the level L is missing. The Auger requires the existence of at
least two energy levels to three electrons. That is why it can not measure H and He. The
elements with atomic number between 3 and 14 have KLL line, elements between 14 and 40
have LMM line, between 40 and 79 are MNN line and for heavier elements NOO line exists.
5.2. SPECTROSCOPIC METHODS INVOLVING ELECTRONS 5
5.2 Spectroscopic methods involving electrons
Dispersive electron spectroscopies:
• UPS - Ultraviolet Photoelectron Spectroscopy using VUV radiation, especially from synchrotron;
excitation of electrons from valence band;
• XPS - X-ray Photoelectron Spectroscopy (ESCA - Electron Spectroscopy for Chemical Analysis)
using soft X-rays; excitation of electrons from core levels;
• AES - Auger Electron Spectroscopy (remember Auger electron effect discussed before);
• EELS - Electron Energy Loss Spectroscopy, used in the case of internal excitation of electron
levels (inter and intraband transitions, plasmons, excitation of phonons) or IS - Ionization
Spectroscopy (energy losses due to the excitation of core electrons);
• INS - Ion Neutralization Spectroscopy (slow ions neutralize after impingment and transmit
part of the energy to electrons that are emitted)
• FES - Field Electron Spectroscopy, energy distribution measurements of field-emitted elec-
trons
Notice: The method called XAS (X-ray absorption spectroscopy) does not belong to electron
spectroscopies but uses the principles of UPS and XPS - absorption of photons due to excitation
of electrons.
6 CHAPTER 5. ELECTRON SPECTROSCOPY
Figure 5.4: Overwiev of different dispersive electron spectroscopy methods. UPS - Ultraviolet
Photoelectron Spectroscopy, XPS - X-ray Photoelectron Spectroscopy, AES - Auger Electron
Spectroscopy, EEELS - Electron Energy Loss Spectroscopy, used in the case of internal excitation
of electron levels, also known as IS - Ionization Spectroscopy, INS - Ion Neutralization Spectroscopy,
FES - Field Electron Spectroscopy, energy distribution measurements of field-emitted
electrons
Figure 5.5: Schematic drawing of method’s differences.
5.3. ELECTRON SPECTROSCOPY CONDITIONS 7
Figure 5.6: Overwiev of different APS methods
Appearance potential spectroscopies:
• XXAPS, XEAPS - X-ray X-ray Appearance Potential Spectroscopy, X-ray Electron Appearance
Potential Spectroscopy. Methods in which X-rays are generated from the sample. They
are practically not used since electron generation is much easier.
• SXAPS - Soft X-ray APS, electrons impact the sample and emitted X-rays are detected.
• DAPS - Disappearance Potential Spectroscopy, used to measure the surface electrons current.
• AEAPS - Auger Electron APS, records the secondary electrons current.
5.3 Electron spectroscopy conditions
All methods except FES require a monochromatic source - more or less focused, a analyser
and a detector (electron multiplier). All this system must be kept under high vacuum conditions
(≤ 10−7
Pa). If the surface sensitivity is greater, i.e. information depth is smaller, the vacuum
conditions must be stronger. The most stringent conditions for surface are for UPS and not so for
XPS. The device is equipped with a surface cleaning systems (Ar+
sputtering and baking) or for
preparation of clean surfaces in situ (cleaving or applying of layers).
5.3.1 Sources of primary particles
X-rays: soft X-rays are generated by bombardment of a suitable material (Al, Mg, Mo, Co, W)
with sufficient e−
energy ⇒ characteristic X-rays.
• Line width limits the resolution (Ek = hν − EB − eφ). Natural line width provides the
resolution of ≈ 1.0 eV, monochromatized sources provide better resolution.
• The energy must be high enough in order to obtain emission of photoelectrons from the bulk
of material.
8 CHAPTER 5. ELECTRON SPECTROSCOPY
• In addition, the anode material needs to be capable of manufacturing into the shape of anode
and stable under e−
bombardment.
⇒ Mg Kα (E = 1253.6 eV, δE = 0.7 eV), Al Kα (E = 1486.6 eV, δE = 0.85 eV).
Photoemission starts at e−
energies equal with electron ionization threshold for the inner shell and
growing rapidly with increasing energy. Therefore, devices allow e−
acceleration up to 15 keV.
Figure 5.7: Scheme of X - ray source.
The e−
source as close as possible to the anode. The X-ray source is often composed of two
anodes. For continuous operation at 1–8 kW, a rotating anode is required. Beside the characteristic
lines (Kα for Mg and Al), satellite, Kβ and continuous spectrum (Bremsstrahlung) lines exists.
Monochromatic radiation is used to get rid of other signals and also to improve the resolution:
Bragg diffraction from a crystal - suitable material is quartz (suitable distance of crystal planes,
possible to bend into a shape of Rowland focusing sphere with the radius of 0.5 m).
Synchrotron radiation
If the charged particles are accelerated, they radiate energy which covers an area of electromagnetic
radiation from hard X-rays up to IR. The synchrotron is a particular type of cyclic
particle accelerator in which the magnetic field (to turn the particles so they circulate) and the
electric field (to accelerate the particles) are carefully synchronised with the travelling particle
beam. Synchrotron radiation has many advantages: a broad spectrum, natural collimation, high
intensity, coherence, the source is under vacuum. Maximum intensity is at the critical wavelength
(0.1–0.4 nm) that is related to curvature of e−
path. The intensity decreases rapidly for lower
5.3. ELECTRON SPECTROSCOPY CONDITIONS 9
wavelengths.
Sources of electrons thermionic or field-emission guns. AES does not need a monochromatic
e−
source, only electrons with the sufficient energy to ionize the core levels. Energy width of the
beam is important for EELS, max. 0.3–0.5 eV, which is too large for HREELS equiring special
monochromatic electron sources.
5.3.2 Electron energy analysers
The electron spectroscopy uses electrostatic analysers. The measured values can be divided into
• retarding field analyzers - recording the total current of particles,
• dispersive analyzers - selecting only certain e−
energies by changing the trajectories.
When choosing the analyser following parameters are considered:
• resolution R = E/∆E - indicates the spectrum energy resolution;
• intensity (brightness) - affects the intensity of the output signal (signal-to-noise ratio);
• analyzer size - because it needs to be placed in the vacuum chamber;
• complexity - economic factor
The final solution is a compromise because the individual requirements have a contradictory
character.
Analysers with retarding field
The operation principle is based on the application of a potential barrier Vb. The flux of particles
over the barrier is divided into fast and slow components. Only the faster ones are usually recorded:
J(E) =
∞
E
N(E )dE , (5.6)
where N(E ) is the energy distribution of particles, E = eVb is the lower energy limit and the
symbol ∞ upper limit (maximum energy of particles). The energy distribution function can be
obtained from the derivative of the above equation.
Planar analyser
The analyzed beam is usually selected by an entrance slit which properties are crucial for the
accuracy of the energy measurements. Since it divides the space without and with the decelating
field it forms electrostatic diverging lens (field inhomogeneities cause that the particles from parallel
beam gain perpendicular velocity, maximum divergence for edge points of the slit). Around
the threshold energy E = eVb, the resolution is:
10 CHAPTER 5. ELECTRON SPECTROSCOPY
Figure 5.8: Scheme of planar analyser
Rr0 =
16d2
r2
0
. (5.7)
The basic parameter is the diameter of the solid angle Ω, under which the beam enters the
detector (effective area). Impute increases with the slit and Ω.
Spherical analysers
Compact electrode system often use a system of 3 or 4 grids (collectors). Total energy
analysis is carried out in a radial trajectory of the particles. It can be used for LEED if the
Figure 5.9: Scheme of spherical analyser
5.3. ELECTRON SPECTROSCOPY CONDITIONS 11
system in equipped with a fluorescent screen or a small movable detector. Retarding fields are
generated between the 1st and 2nd (or 2nd and 3rd) grids. The resolution is given by the field
inhomogeneity (mesh size, number of grids). Analyzer throughput is high because it can detect
particles from a large solid angles (120◦
or 180◦
).
Dispersion analyzer (deflectors)
Figure 5.10: Scheme of dispersion analyzer
The parallel beam entering the analyzer is divided into different trajectories (Fig. 5.10) depending
on the energy. The detector is either able to monitor signals at different positions (channel
plate, screen) or it is tuned to detect particles with a certain energy E0 (multiplier, Faraday cup).
In the latter, a characteristic parameter is the main trajectory, i. e. the trajectory between the
input and output slits. Properties of the analyzer are given by the dispersion
D(E) = E0 ∂x/∂E,
i. e. by the quantity expressing the difference in the position in the dependence on the energy. The
dispersion with other parameters covering field focusation properties and some construction parts
determines energy resolution of the analyzer.
Energy resolution can be estimated by detail analysis of particle trajectories in dependence on
their input parameters: energy, coordinates of input slit, input angle. In most cases it is enough
to use a rough estimate of the resolution as made below.
Let us irradiate the entrance slit s1 by monoenergetic parallel beam that is imaged at the
output slit with the magnification M. If the beam will be slightly divergent, each point of the
entrance slit will be imaged by a line in each directions in which the focusation takes place. The
length of this line is approximately
Σ
.
= a1α + a2α2
+ a3α3
+ . . . + b1β + b2β2
+ b3β3
+ . . . . (5.8)
12 CHAPTER 5. ELECTRON SPECTROSCOPY
Figure 5.11: Understanding the energy resolution.
The angle 2α is divergence of the beam in the plane of the main trajectory, 2β in the plane
perpendicular. The focusation order expresses how many coefficients a1, a2, . . . , an or b1, b2, . . . , bn
are equal to zero.
During anayzer tuning the image in output plane is moving. It is detected if some part of it
falls into the output slit s2. Its geometrical width is
∆xB = Ms1 + s2 + Σ (5.9)
where s1 and s2 are the slit sizes for input and output, M is the magnification (∼1) and Σ is the
blur due to the input divergence. ∆xB is connected with energy width of the image in the vicinity
of E0 by
∆xB =
∂x
∂E
∆EB =
D
E0
∆EB. (5.10)
It means that image of monoenergetic beam source is the peak with final width. If we have two
such sources with close energies, they will be imaged with similar sensitivity as two close peaks
(Fig. 5.11). They are expected as resolved if the minimum valey inbetween them is at 20 % of
their maximum, i. e. they intersect at 40 % of their height. Their distance in energies ∆E will be
approximately half of their energy base ∆EB and we can write for the resolution R
R =
E0
∆E
.
=
2E0
∆EB
=
2D
∆xB
=
2D
Ms1 + s2 + Σ
. (5.11)
From this expression is observed the decrease of R with the increase of slit size directly (Ms1 +s2),
and indirectly with Σ.
Dispersion analysers are divided into mirror and sector analyzers.
Mirror analyser
The beam enters through field lines at an different angle than π/2; the velocity component perpendicular
to the field direction is maintained, v is gradually changed to the opposite direction
5.3. ELECTRON SPECTROSCOPY CONDITIONS 13
⇒ symmetrical axis trajectory to the field. The input and output slits are places in the positive
potential electrode. The entrance angle is chosen with regard to the position of the source and
the detector.
• planar - two parallel electrodes focusing only the deflection plane a. Two arrangements (a)
φ0 = π/4, source and detector in the entrance and exit slits, (b) φ0 = 30◦
, source and
detector tangent to field.
• cylindrical (CMA) - it is frequently used because allows the construction of high resolution
systems. It consists of to concentric cylinders, with a positive potential between.
Figure 5.12: Scheme of planar mirror analyzer, T is sample, D is detector.
Figure 5.13: Scheme of CMA analyzer
Sectors analyzer
The beam enters ⊥ to the field. The main trajectory is a circle, where the centrifugal force
associated with the kinetic energy compensates the centripetal force. The incident and reflected
14 CHAPTER 5. ELECTRON SPECTROSCOPY
angles is determined by the focus and position of the source and detector. It is mainly used in the
differentiated angular spectroscopy:
• cylindrical - two cylindrical sector analyser and to pairs of planar electrodes (in front and
lateral); in the frontal one are located the slits. Deflection potential V1 − V2 is inserted
between the cylinders (inner potential is positive), both planar electrodes are isolated and
maintained on the potential V0 = (V1 +V2)/2. The analyser is focusing only in one direction.
Sector angle is Φ = π/
√
2 = 127, 3◦
therefore ⇒ the name of 127◦
analyser.
• spherical (CHA - concentric hemispherical analyser) - two concentric spherical segments;
input and output electrodes are radial slices are maintained at median surface potential V0.
The spherical deflector is capable of spatial focusing. Angle or the sector is usually Φ = 180◦
.
Conclusion
Analysing the energy of electrons has some other associated phenomena such as reflection and
secondary emission. It is advantageous to use electron optics in order to increase the input angle,
to obtain the image in a suitable place in the optimal regime area of the analyser, finely tune
the input angle for slow electrons. The relative resolution of the analyser is constant ⇒ absolute
intensity will decrease with the decrease of energy.
5.3. ELECTRON SPECTROSCOPY CONDITIONS 15
Figure 5.14: Scheme of cylindrical sector analyzer.
Figure 5.15: Scheme of spherical sector analyzer.
Figure 5.16: 3D view of sector analyzers.
16 CHAPTER 5. ELECTRON SPECTROSCOPY
5.4 Ultraviolet photoelectron spectroscopy
• If the photon energy is < 3 eV (VIS radiation), photoemission can occur only for substances
with very low φ and the energy spectrum is narrow because e−
are emitted only from the
highest occupied level ⇒ information only about φ.
• If the photon energy is higher (UV radiation) electrons from the valence band can be emitted
(UPS) ⇒ distribution of densities of states in valence band can be obtained.
• In addition to energy distribution is possible to measure the angular distribution (ARUPS).
In an isolated atom, the electrons occupy certain energy levels. In a solid, the levels involved
in bonding ’the valence states’, become blurred, and electrons can occupy a range of energies
called bands. The energy of an electron in the solid depends on its momentum. Hence, by
detecting photoelectrons emitted from a surface at different emission angles, the energy of
the electrons as a function of the momentum vector may be determined. This process is
known as "band mapping" and is a powerful probe of the electronic structure of crystalline
materials.
• The mean free path in the case of UPS is only 0.5–2 nm ⇒ surface characterization method.
Photoemission
The first paper of Burglund and Spicer (1964) worked out what is called the three-step model for
photoemission, and the second applied it to new data on Cu and Ag. The three-step model uses
this picture in considerable detail to predict the spectrum of photoelectrons from a given band
structure. This spectrum sometimes resembles the density of occupied electronic states weighted
by a function that varies smoothly with energy. This model assumes the photoemission process
can be described by three sequential processes:
• photoexcitation of an electron (photoabsorbtion) - general theory based on Fermi‘s golden
rule, which determines the transition probability between two electron states of the same
Hamiltonian HN
, if the disturbance ∆ is small.
w =
2π
¯h
| < ψN
f |∆|ψN
i >2
δ(EN
f − EN
i − ¯hω) (5.12)
• transport of that electron to the surface without inelastic scattering
• scape of the electron into the vacuum
The law of energy conservation must be applied (Ekin = Eu
f − eΦ = Eu
i + ¯hω − eΦ) and the
wavelength vector. Overall, the wave-vector is not maintained because the emitted electron escapes
into vacuum, and the system achieve three-dimensional symmetry. The surface has only twodimensional
translation symmetry of the surface reciprocal lattice vector GS:
kvn
= ku
f + GS (5.13)
5.4. ULTRAVIOLET PHOTOELECTRON SPECTROSCOPY 17
Inside the crystal the wave-vector is preserved:
ku
f = ku
i + GB, (5.14)
where GB is the reciprocal lattice volume vector. Dispersion relation for free e−
:
Ekin =
¯h2
2m
(k2
+ k2
⊥). (5.15)
If we don‘t know the dispersion relation within the crystal we are able to directly measure the band
structure, but if we know the initial dispersion or the final states, we can limit the dispersion or
the initial conditions. For surface conditions these restrictions do not apply ⇒ layered materials
with two-dimensions periodicity exists: TaS2, GeS or graphite, where the bulk band structure
E(k ) will be explored.
k =
2m
¯h2 Ekin sin θ, (5.16)
where θ is the angle between the surface normal and the axis of the detector. The UPS method
can be applied to absorb on substrate system like CO on Ni
Several modes exist for the evaluation of the emitted electrons:
• the number of emitted electrons is measured as the function of the final-state energy Ef
(kinetic energy Ek = Ef − Esurf−barrier=Ef −eΦ is measured) for a fixed photon energy and
a fixed mutual position of the source and the surface elementary cell - energy distribution
curve (EDC). EDC can be measured as integral or differential function of the emission angle.
The latter is called angular resolved UPS (ARUPS).
• By scanning photon energy hν and holding fixed the energy windows of the electron spectrometer,
one measures the constant final-state spectra (CFS), N(hν, Ef fixed). Unlike in
EDC, the energy and wave vector are the same in every point of the spectra.
• By synchronously scanning hν and Ef , so that hν − Ef , is held fixed, one measures the
constant-initial-state spectra (CIS), N(hν, hν − Ef fixed).
EDC
Přenesení počáteční hustoty stavů na hustotu prázdných konečných stavů vzdálených o ¯hω. Hlavní
obtíž spočívá v oddělení příspěvků počátečních a koncových stavů. Tuto eliminaci je možné
dostatečnou energií budící energie, aby e−
byly excitovány do oblasti, kde hustota tvoří prakticky
kontinuum. Při energiích nad 100 eV to však vede ke ztrátě informací o impulzu e−
. Pro energie
30–100 eV jde o spektra zobrazující hustotu počátečních stavů a zachovávající možnost určení
disperzních relací ⇒ synchrotronové záření. Musíme znát pásovou strukturu konečných stavů ⇒
aproximace model téměř volných e−
; kritické je umístění dna paraboly na energetické stupnici.
CFS
Elektrony jsou excitovány do jednoho zvoleného stavu ⇒ dává užitečné informace o výběrových
pravidlech a symetrii stavů; pokud je okénko nastaveno tak, že leží mimo dovolené přechody
18 CHAPTER 5. ELECTRON SPECTROSCOPY
Figure 5.17: Angular resolved UPS.
5.4. ULTRAVIOLET PHOTOELECTRON SPECTROSCOPY 19
v objemu, dominuje ve spektru příspěvek od povrchových stavů. Technika CFS je pro studium
pásové struktury výhodnější než postup EDC, protože dovoluje snímat spektra s k =konst i mimo
normálu. Opět je nutné určit k⊥ vně PL a dát ji do souvislosti s odpovídající složkou vl. vektoru
e−
v konečném stavu uvnitř PL ⇒ postup obdobný jako u EDC.
CIS
Není tak rozšířena jako předchozí dvě techniky, protože byly vyvinuty jiné metody umožňující
spektroskopii prázdných stavů v oblasti těsně nad dnem vodivostního pásu. U fotoemisních měření
totiž nemohou e−
excitované do energetických pásů pod hladinou vakua přispívat k fotoproudu.
Navíc se zvyšující se energií se zvětšuje energetické rozmazání pásů, a tím je velice obtížné získat
informace o momentu e−
z úhlově rozlišených měření.
20 CHAPTER 5. ELECTRON SPECTROSCOPY
5.5 Spectroscopic nomenclature of electronic states
Molecules can possess several types of angular momentum. Electrons possess orbital and
spin angular momenta, rotation of the molecule generates angular momentum, degenerate
vibrations may give rise to vibrational angular momentum, and nuclei may also have spin angular
momentum. Interactions (coupling) between these various types of angular momentum can have
important implications for interpreting spectra, particularly high resolution spectra, and so it
is important to be familiar with some basic results from the quantum theory of angular momentum.
The angular momentum is a vector quantity and a simple vector model provides a useful
visual recipe for assessing how different angular momenta interact. There are more powerful
and rigorous mathematical approaches to angular momentum coupling than that described here.
These more comprehensive treatments deal explicitly with the angular momenta as mathematical
operators, and the coupling behaviour then follows from the properties of these operators when
added vectorially. The simple vector picture is use to emphasize the physical principles underlying
the coupling of angular momenta, focussing on electronic angular momentum.
The magnitude of the orbital angular momentum for a single electron in an atom is given by
the expression ¯h l(l + l) where l is the orbital angular momentum quantum number with allowed
values 0, 1, 2, . . . Similarly, the magnitude of the spin angular momentum vector is given by
¯h s(s + l) where s is the spin quantum number which, for a single electron, can only take the value
1/2. For an electron with both orbital and spin angular momenta, the total angular momentum
vector j will be the sum of the two constituent vectors j = l + s. The magnitude of this vector is
¯h j(j + l), where j is the corresponding quantum number, and according to the quantum theory
of angular momentum this can only take on the values j = l + s, l + s − 1, ..., |l − s|. Series such as
this are called Clebsch – Gordan series and arise when the total angular momentum results from a
system composed of any two sources of quantized angular momentum. In the general case, if two
angular momenta, say j1 and j2, can interact then the allowed values for the angular momentum
quantum number for the resultant total angular momentum will be given by the Clebsch – Gordan
series j = j1 + j2, j1 + j2 − 1, ..., |j1 − j2|
5.5.1 L-S (Russell-Saunders) coupling
In the Russell – Saunders limit the coupling between the orbital angular momenta is strong.
The source of the coupling is the electrostatic interaction between two electrons. Electron
spins can also couple together, although spin is a magnetic phenomenon and therefore the
coupling is via magnetic fields,which tends to be a weaker effect than electric field coupling. In
Russell – Saunders coupling the interaction between the orbital and spin angular momenta of
a given electron is assumed to be small compared with the coupling between orbital angular
momenta. In this limit the principal torque causes the orbital angular momenta to precess
about a common direction, the axis of the total orbital angular momentum of all electrons.
The spin angular momenta also couple together through the magnetic interaction of electron spins.
The vector model described above can be employed to see the effect of coupling on atoms.
5.5. SPECTROSCOPIC NOMENCLATURE OF ELECTRONIC STATES 21
Figure 5.18: Forming the total angular momentum.
For illustration, consider an atom with two electrons outside its closed shell. The orbital angular
momenta of these electrons are represented by l1 and l2, and the corresponding spin momenta by
s1 and s2. The coupling of orbital angular momenta dominates and they form a resultant total
orbital angular momentum L = l1 + l2. In the same way, the spin momenta also couple to form
S = s1 + s2. When this coupling case is valid, the individual orbital angular momenta l1 and l2
precess rapidly around L, and s1 and s2 precess rapidly around S. L and S can themselves couple
with each other, but this coupling, known as spin – orbit coupling, is assumed to be relatively weak.
As a result, L and S precess slowly around the resultant total angular momentum J = (L + S).
5.5.2 jj coupling
The Russell–Saunders scheme describes the electronic states of light atoms rather well but breaks
down for heavier atoms, particularly for the lanthanides and actinides. This is due to increasing
coupling between the orbital and spin angular momenta of individual electrons to the point where
it is no longer negligible, as was assumed in the Russell – Saunders case. In the limit of very strong
coupling between orbital and spin angular momenta, the appropriate coupling scheme is known
as jjcoupling. A dominant spin – orbit torque will first couple the spin and orbital momenta of
each electron to form resultants, j1 = l1 + s1 and j2 = l2 + s2. The vectors j1 and j2 interact more
weakly, forming the total angular momentum J = j1 + j2. In jj coupling, l1(l2) and s1(s2) precess
rapidly around j1(j2), while jj1 and j2 precess slowly around their resultant J. As a result, only
j1, j2, J and the projection of J(MJ ) are good quantum numbers, i.e. the quantum numbers L
and S in the Russell – Saunders scheme have no significance in jj coupling. Of course it is also
possible that the spin–orbit coupling is neither weak enough for Russell–Saunders to be applicable,
nor strong enough for true jj coupling.
22 CHAPTER 5. ELECTRON SPECTROSCOPY
5.6 Auger electron spectroscopy
5.6.1 Auger effect
Auger electrons were named after Pierre Auger who, together with Lise Meitner, discovered Auger
electron emission in 1920s. When a high-energy electron (or X-ray photon) strikes an inner shell
electron of an atom, the energy of the incident particle can be high enough to knock out the inner
shell electron. Thus, the atom becomes ionized and in an excited state. The atom will quickly
return to its normal state after refilling the inner electron vacancy with an outer shell electron.
In the meantime, the energy difference between the outer shell electron and the inner shell may
cause emission of either an Auger electron from an electron shell or a characteristic X-ray photon.
The kinetic energy of an Auger electron is approximately equal to the energy difference between
binding energies in the electron shells involved in the Auger process. For example, the kinetic
energy of an Auger electron is approximated by the following equation:
EKL1L2,3 = EK − EL1 − E∗
L2,3, (5.17)
where Ei is the binding energy and E∗
L2,3 is mark with asterisk because the energy levels L∗
2,3
differs slight from the energy levels of L2,3.
The notation for kinetic energy of Auger electron describes its origin, but the nomenclature is
rather complicated. For example, the kinetic energy of an Auger electron is from a following
process: an incident electron knocks out a K shell electron, a L1 shell electron refills the K shell
vacancy, and a L2,3 shell electron is ejected as the Auger electron. Auger electron spectroscopy
(AES) identifies chemical elements by measuring the kinetic energies of Auger electrons. In an
AES spectrum, an individual kinetic energy peak from an Auger electron is marked with an
elemental symbol and subscripts indicating the electron shells or sub shells involved, for example,
in aluminium oxide case, AlKLL, OKLL. . .
A typical AES spectrum is a plot of intensity versus kinetic energy; most commonly,it is a plot
of the first derivative of intensity versus the kinetic energy. The primary electrons ejected from
a solid surface by inelastic scattering comprise the background of an AES spectrum in the region
of high kinetic energies while the secondary electrons comprise the background in the region of
low kinetic energies. The number of Auger electrons ejected from a sample is much less than that
of scattered primary electrons and secondary electrons. Thus, the direct-mode spectrum is not
favoured except for quantitative analysis.
5.6.2 Fine Auger structure
A recent interest is concerned with the fine structures in the neighbourhood of Auger lines,
denoted by EXAFS (extended X-ray absorption fine structure). It is a powerful nondestructive
technique that provides structural information on metal or metal oxide phases highly dispersed
on inorganic supports under reaction conditions. Bond lengths and coordination numbers of
X-ray absorbing material can be determined. When single crystals are employed as supports,
characterization of metal sites on them can be achieved separately in two different bonds parallel
5.6. AUGER ELECTRON SPECTROSCOPY 23
and normal to the surface by polarized X-ray radiation.
In transmission mode, the EXAFS signal of surface species on solid substrates can not be
detected because of the large adsorption by the substrate. To determine surface structures, it is
possible to measure EXAFS spectra by detecting the reflected X-rays from sample, but usually
the sensitivity is worse.
24 CHAPTER 5. ELECTRON SPECTROSCOPY
5.7 X-ray photoelectron spectroscopy
The X-ray photoelectron is an electron ejected from an electron shell of an atom when the atom
absorbs an X-ray photon. An incident X-ray photon can have sufficient energy (a value of hν)
to knock out an inner shell electron, for example from the atom’s K shell. In such a case, the
K-shell electron would be ejected from the surface as a photoelectron with kinetic energy EK.
Knowing the kinetic energy EK, we can calculate the binding energy of the atom’s photoelectron
(EB) based on the following relationship:
EB = hν − EK − φ (5.18)
The value of φ depends on both the sample material and the spectrometer. The binding energies
(EB) of atomic electrons have characteristic values, and these values are used to identify elements,
similar to the way that characteristic X-ray energy is used in X-ray spectroscopy. X-ray photoelectron
spectroscopy (XPS) identifies chemical elements from the binding energy spectra of X-ray
photoelectrons.
Inner shell
• depending on how deep is, we obtain atomic number and the energy of X-rays
• doublet separations in photoelectron lines ⇐ spin-orbital coupling jj. Splitting distance is
directly proportional with < 1/r3
> for a given orbit, so it increases for higher Z or lower l
(at constant n).
subshell value of j area ratio
s 1
2
–
p 1
2
,3
2
1:2
d 3
2
,5
2
2:3
f 5
2
,7
2
4:4
• Relative intensities are given by the photoemission cross section, analyser transmission and
very little by the X-ray energy
• peak width (FWHM) is determined by
∆E = (∆E2
n + ∆E2
p + ∆E2
a )1/2
, (5.19)
where ∆En is the natural width of the inner surface, ∆Ep is the width of the X-rays ∆Ea is
the analyser resolution (in all cases Gaussian distribution).
– ∆En associated with the lifetime τ
Γ =
h
τ
. (5.20)
where τ is related with the photoemission of X-rays, emission of Auger electrons or
special type Auger electron (Coster-Kronig transition), which prefers l and is very fast.
Width for light elements (1s, 2p) increases with the atomic number.
5.7. X-RAY PHOTOELECTRON SPECTROSCOPY 25
– ∆Ea is constant for all peaks in "constant analyser energy" (CAE) mode, but changes
in "constant retard ratio" (CRR), because ∆E/E ratio remains constant.
Valence shell
Electrons with low binding energy (0–20 eV). They are very close to each other ⇒ band structure.
At high resolution spectrum scanning can show the band structure and a sharp decrease of
intensity for EF.
Auger series
Kinetic e−
energy from Coster-Kronig transition is very low; four basic series exists:
• KLL - from boron to magnesium(with Mg Kα) or aluminium (with Al Kα),
• LMM - from sulphur to germanium (with Mg Kα) or selenium (with Al Kα),
• M4,5N4,5N4,5 - from molybdenum to neodymium (with Mg Kα),
• M4,5N6,7N6,7 - only for high energy X-rays (e.g. Ag Lα, 2984 eV).
5.7.1 Energy scale calibration
For meaningful measurements it is important to ensure the instrument is calibrated. For example,
to identify chemical constituents from the peak energy correctly, the energy scale needs to be
calibrated. To provide quantitative information, use sensitivity factors and compare with other
instruments, while the intensity scale needs to be linear and also corrected for the intensity
response function. The intensity response function (IRF) includes the angular acceptance of the
analyser to electrons, the transmission efficiency of electrons and the detection efficiency.
• for metals is possible to observe directly the Fermi level in the valence lines;
• the semiconductors are sufficiently conductive in order to offset the EF. It is yet difficult to
determine the exact location of line since the Fermi level depends on doping, surface states
and defects;
• in the analysis of dielectrics the surface charge and energy shift occurs. The most commonly
used method is called internal standard - a reference line from photoemission with a known
binding energy from other measurements. It is based on the fact that often the sample is
contaminated with hydrocarbons (C1s = 284,6–285,2 eV).
Cu and Au samples set with their angle of emission ≤ 56◦
are sputtered clean, and the
measured energies of the peaks are compared with the energy values given in the table. As
for AES, the peak energy for the calibration is evaluated from the top of the peak without
background subtraction. For gold line 4f7/2 the energy is 83.95 eV. The lineshapes and energies
of the Kα1 and Kα2 X-rays that characterize hν appear to be the same in all unmonochromated
instruments. However, the lineshapes and energies of the Kα X-rays, when monochromated
vary significantly and depend on the set-up of the monochromator and its thermal stability. By
26 CHAPTER 5. ELECTRON SPECTROSCOPY
altering the monochromator settings, the measured energies of the peak may be moved over a
kinetic energy range of 0.4 eV without too much loss of intensity.
Use of the standard with a modern, well-maintained spectrometer should result in calibration
within tolerance limits of ±0.2 eV over four months or ±0.1 eV over one month before recalibration
is required. For many purposes ±0.2 eV is satisfactory.
5.7.2 Primary structure information
Inner shell line
The binding energy is influenced by interactions with other electrons → chemical shift. The exact
calculation of the binding energy is very difficult and limited to small molecules → approximate
methods, such as electrostatic model - the model potentials(charge Potential model)
EB = E0
B + kqi +
i=j
qj
4π 0rij
, (5.21)
where E0
B has significant calibration factor , k s a constant indicating an average repulsion
between inner shell and valence e−
, qi is the atom i charge and sum of potentials of neighbouring
atoms j, also called Madelung potential, where rij are the internuclear distances.
Valence band peak
The valence electrons are directly involved in bond formation and molecular interactions, so the
intensity and energy of the valence band peaks depend on their bonding environment. Thus,
quantitative interpretation of the valence band spectrum for most materials requires a full
molecular orbital calculation. For multi-component materials or those containing a large number
of atoms per structural unit (e.g. polymers) this requires computer calculations.
Valence band analysis is worth pursuing because it can provide electronic structure information
that cannot be obtained from typical core level analysis. Also, it is sometimes possible to extract
useful structural information from valence band spectra.
In metals the information about the valence band and the Fermi energy give the opportunity to
observe the transformation of the material from dielectric to metal (VO2 non-conductor x metal
at 65◦
, NaxWO3 non-conductor x metal when changing x).
Auger chemical shift
To identify the oxidation state of an element is often preferable to use the Auger parameter:
α = EK(jkl) − EK(i) = EK(jkl) + EB(i) − hν, (5.22)
where EK(jkl) and EK(i) is the kinetic Auger energy. α does not depends on the reference surface
or the sample charge. The Auger parameter is modified
α = α + hν = EK(jkl) + EB(i). (5.23)
Auger line shapes
Auger lines can be readily distinguished from photoemission lines by changing X-ray sources (e.g.
5.7. X-RAY PHOTOELECTRON SPECTROSCOPY 27
using a Mg Kα source instead of an Al Kα source). If the Auger process causes the formation of
at least one hole, then the distribution of Auger lines intensities strongly depends on the type of
molecule.
5.7.3 Final state effects
X-ray satellites and ghost peaks
Satellites appear together with the less intensive X-ray characteristic peaks. The main peak
Kα1,2 corresponding to the 2p3/2,1/2 → 1stransition, satellites are Kβ, valence bands → 1s or
multi ionized atoms.
Ghosts appear due to excitation of surface contaminants. Often, Al Kα1,2 from the Mg Kα (due
to the aluminium window), followed by Cu Lα and O Kα.
Multiplet splitting
A requirement for this splitting of the s photoemission peak into a doublet is that there be unpaired
orbitals in the valence shells. Complex peak splitting can be observed in transition metal ions and
rare earth ions when multiplet splitting occurs in p and d levels.
∆E = (2Sv
+ 1)Ksd a
I(Sv
+ 1/2)
I(Sv − 1/2)
=
Sv
+ 1
Sv
, (5.24)
where Sv
is the total spin of a unpaired valence electron and Ksd is the s-d exchange integral.
Shake-up satellites
It represents photoelectrons that have lost energy through promotion of valence electrons from
an occupied energy level (e.g. a π level) to an unoccupied higher level (e.g. a pi∗
level). Shake-up
peaks (also called "loss peaks" because intensity is lost from the primary photoemission peak) are
most apparent for systems with aromatic structures, unsaturated bonds or transition metal ions.
In contrast to the continuum of reduced energies seen in the inelastic scattering tail, shake-up
peaks have discrete energies (∼ 6.6eV higher binding energy than the primary peak in C1s spectra
of aromatic-containing molecules) because the energy loss is equivalent to a specific quantized
energy transition (i.e., the π → π∗
transition).
Asymmetric metal lines
The metal lines may change with the degree of surface charging during data acquisition. With
asymmetric metal lines as encountered with many transition metals, this effect may mimic the
presence of metal ions, The line broadening is , most likely, due to varying degree of differential
charging, since it is paralleled in the widths of the support elements.
Asymmetric non-metal lines
Appears only at high resolution. The asymmetry occurs due to fine vibrational structure of
molecules. After ionization there is a change in interatomic distances and narrowing the potential
curves of the molecule.
28 CHAPTER 5. ELECTRON SPECTROSCOPY
Shake-off satellites
If the departing photoelectron transfers sufficient energy into the valence electron to ionize it into
the continuum, the photoemission loss peak is called a "shake-off" peak. The shake-off satellite
peaks of the photoemission peak can have a wide range of possible energies (of course, always with
a lower KE than the photoemission peak). This energetically broad feature is typically hidden
within the background signal and is usually not detected or used analytically.
5.7.4 Angular effects
1. Enhancement of system sensitivity and depth profile
Almost all electrons (95 %) come on a path equal with 3λ. If e−
are detected at angle θ
different from normal, the thickness of the analysed layer is:
d = 3λ sin θ (5.25)
For the substrate (s) with homogeneous layer (v), the change of intensity in the ideal case
is:
Is
(d) = Is
0 e−d/λ sin θ
and Iv
(d) = Iv
0 (1 − e−d/λ sin θ
). (5.26)
In practice, however, the geometry of the system also exhibits a angular response dependence
function ⇒ measured values for Iv
/Is
2. Single-crystal studies
Measuring the absolute core electron intensity from a single-crystal surface, depending on
the angle θ gives modulated intensity. Similar modulation is observed for fixed θ and rotation
of surface plane. ⇒ X-ray photoelectron diffraction XPD
5.8 Quantitative analysis in AES and XPS
Quantitative elemental analysis in electron spectroscopy is similar to that in X-ray spectroscopy.
Analysis quantifies the concentrations of chemical elements on a sample surface from the peak
intensities of the spectra. In theory, the quantitative relationship between the intensities of electron
signals and atomic fractions of elements can be calculated. In practice, for quantification in both
XPS and AES, most parameters for calculations are not available.
Sensitivity factor method: the Auger current is described by
Iα,XYZ = Ipγα,XYZ T(Eα,XYZ)D(Eα,XYZ)
Ep
Eα,X
σtotal
α,X (E)dE
∞
0
nα(z)e
− z
λM(Eα) cos θ
dz (5.27)
where Ip is the excitation current, γα,XYZ is the Auger efficiency, σtotal
α,X (E) is the ionization cross
section X the element α, Ep is the energy of the primary electron nα(z) is the density of element α
at depth z. The transmittance of the spectrometer is T(Eα,XYZ) and the sensitivity of the detector
is D(Eα,XYZ).
5.8. QUANTITATIVE ANALYSIS IN AES AND XPS 29
Figure 5.19: The physical processes occuring when an electron strikes a solid surface.
Ionization is caused not only by the electrons but also by the backscattered energy which has
the distribution n(E)
σtotal
α,X = σα,X(Ep) +
Ep
Eα,X
σα,X(E)n(E)dE (5.28)
This relation can be approximated as:
σtotal
α,X = σα,X(E)[1 + rM
(Eα,XYZ, ψ] (5.29)
which can be simplified for homogeneous material
Iα,XYZ = Ipγα,XYZ T(Eα,XYZ)D(Eα,XYZ)σα,X(E)[1 + rM
(Eα,XYZ, ψ]nαλM
(Eα) cos θ (5.30)
The sensitivity factor Sα,XYZ is defined as:
Iα,XYZ = Ipnα cos θ Sα,XYZ (5.31)
and the atomic concentration α in the M matrix
cα =
nα
α
nα
=
Iα,XYZ
Sα,XYZ α
Iα ,XYZ
Sα ,XYZ
(5.32)
The sensitivity factor must be determined either theoretically or directly experimentally. Common
practice is to use the sensitivity factors from published handbooks with certain corrections
according to the instrument characteristics, because it is not feasible to compile a set of in-house
sensitivity factors.
30 CHAPTER 5. ELECTRON SPECTROSCOPY
Standard method: For simplicity, a binary alloy αβ is selected. No contamination on the
surface or segregation phenomena exists:
Iα
Is
α
Is
β
Iβ
=
nα
nβ
ns
α
ns
β
λαλs
β
λβλs
α
(1 + rα)(1 + rs
β)
(1 + rβ)(1 + rs
α)
=
nα
nβ
K (5.33)
and the elemental concentration α is
cα = 1 +
IβIs
α
IαIs
β
1
K
−1
. (5.34)
The matrix correction factor K describes the influence of the αβ alloy. When K = 1, we assume
that the influence on matrix is negligible.
Quantitative analysis - old text for XPS
The intensity of the photoemission line i
Ii
A ∼ QA cAσi
Aλi
Ti
Li
Af(φ, θ), (5.35)
where Q is the photon flux [cm−1
s−1
], A effective are of the sample, cA concentration of A, σi
A is
the partial ionization cross section, λi
mean free path, Ti
the transmission, Li
A angular asymmetry
coefficient and f(φ, θ) function, depending on the geometry of the experiment. The above equation
does not detect the absolute concentration of elements. The intensities of the lines for individual
measured elements under the same conditions can determine the relative atomic composition.
When a solid is homogeneous within the analysed depth for all elements of interest (A and B for
example), the uncertainties can be partially cancelled by considering relative atomic values. We
obtain:
Ii
A
Ij
B
=
cAσi
Aλi
Ti
Li
A
cBσj
BλjTjLj
B
=
cAσi
ALi
A
cBσj
BLj
B
R. (5.36)
If the kinetic energy differs by more than ∼ 400 eV, correction of T and λ should be performed.
the correction used for transmission:
T ∼ 1/Ek for constant energy (CAE) (5.37)
and
T ∼ Ek for constant resolution (CRR). (5.38)
To calculate the mean free path, the typically used equation is
λ = aE−2
k + bE
1/2
k . (5.39)
One of the major problem in quantitative analysis is the integral of photoemission intensity
lines. When using the theoretical values σ we have determine the overall intensity of lines including
the contributions of all satellites and inelastic electron scattering. For practical purposes we can
use the equation:
Ii
A
Ij
B
=
cASi
A
cBSj
B
. (5.40)
5.9. NUMERICAL DATA ANALYSIS 31
The intensity of the photoemission line i
Ii
A ∼ QA cAσi
Aλi
Ti
Li
Af(φ, θ), (5.41)
where Q is the photon flux [cm−1
s−1
], A effective are of the sample, cA concentration of A, σi
A is
the partial ionization cross section, λi
mean free path, Ti
the transmission, Li
A angular asymmetry
coefficient and f(φ, θ) function, depending on the geometry of the experiment. The above equation
does not detect the absolute concentration of elements. The intensities of the lines for individual
measured elements under the same conditions can determine the relative atomic composition.
When a solid is homogeneous within the analysed depth for all elements of interest (A and B for
example), the uncertainties can be partially cancelled by considering relative atomic values. We
obtain:
Ii
A
Ij
B
=
cAσi
Aλi
Ti
Li
A
cBσj
BλjTjLj
B
=
cAσi
ALi
A
cBσj
BLj
B
R. (5.42)
If the kinetic energy differs by more than ∼ 400 eV, correction of T and λ should be performed.
the correction used for transmission:
T ∼ 1/Ek for constant energy (CAE) (5.43)
and
T ∼ Ek for constant resolution (CRR). (5.44)
To calculate the mean free path, the typically used equation is
λ = aE−2
k + bE
1/2
k . (5.45)
One of the major problem in quantitative analysis is the integral of photoemission intensity
lines. When using the theoretical values σ we have determine the overall intensity of lines including
the contributions of all satellites and inelastic electron scattering. For practical purposes we can
use the equation:
Ii
A
Ij
B
=
cASi
A
cBSj
B
. (5.46)
5.9 Numerical data analysis
Simple operation with data:
(a) integration and determination of area, (b) noise removal, (c) satellites removal, (d) background
subtraction, (e) addition and subtraction of spectra, (f) search for lines maxima, (g) conversion
to the binding energy after calibration.
background subtraction
• linear background: straight line between the first and last point of the spectrum
• integral background: the integral is calculated over the hole line area and a calibrated curve
thus obtained is subtracted from the peak area
32 CHAPTER 5. ELECTRON SPECTROSCOPY
• background based on the elastic and inelastic processes
Signal to noise ratio
The noise is characterised in three different ways: peak-to-peak (p.t.p.), root-mean-square (r.m.s.),
standard deviation. If the spectrometer is limited to statistical noise, the signal to noise ratio
(S/N) can be defined like:
S/N =
S + B
F
, (5.47)
where S is the height of the line above background B, is the background B and F is the intensity
factor
F =
(S/B + 1)(S/B + 2)
(S/B)2
. (5.48)
If we desire S/N constant
t2/t1 = F2/F1. (5.49)
Smoothing
• fitting the data with a suitable smooth function (polynomial, fractional polynomial, exponential,
Fourier and splines)
• convolution data using a suitable algorithm, which leads to a smoothing
ysm
r =
m
r=−m
Cryr
NORM
, (5.50)
where Cr is the convolution number and NORM is the normalizing factor. Savitsky-Golay
convolution is recursive. the convolution function represented by lest squares fitting of an
polynomial(cubic-quadratic) to m points on either side of each data point.
• frequency filter for Fourier transformation (mathematical equivalent of convolution algo-
rithm).
Analysis of overlapping spectral lined
• spectra derivation (background removal, separation of overlapping lines), negative lines in
the second derivative correspond to approximately the position of overlapping lines ⇒ noise
problems ⇒ smoothing with derivation
• deconvolution, mostly for the shape of the line
ym
j =
N
i=1
yt
i gj−1 + nj, (5.51)
where nj is the noise. The instrument function g can be determined by line measurement of
Ag 4 eV from the Fermi level with a monochromatic X-ray source.
5.9. NUMERICAL DATA ANALYSIS 33
• fitting with Gaussian or Lorentz function. It can either be used the Voigt convolution or a
mix Gauss-Lorentz function
f(E) =
A
[1 + M(E − E0)2/β2] exp([1 − M][ln 2(E − E0)2]/β2)
, (5.52)
wheree M is mixing ration (1 for pure Lorentz shape) and β is a parameter, which is nearly
0.5 FWHM.
34 CHAPTER 5. ELECTRON SPECTROSCOPY
5.10 Electron energy loss spectroscopy
Metoda EELS je založena na nepružném rozptylu primárních e−
pevnou látkou, při níž
dochází k vybuzení e−
nebo skupiny e−
(vybuzení plazmonů) pevné látky do vyššího stavu.
Hodnoty energie primárních e−
jsou několik desítek eV ⇒ povrchová metoda.
Elektrony přecházejí do vyšších hladin téhož pásu (vnitropásové přechody), do jiného pásu
(mezipásové přechody) nebo do povrchových stavů. ⇒ Měřením ztrát získáme představu o elektronové
struktuře PL - neobsazených stavech. Musíme mít ovšem nezávislou informaci o rozdělení
a polohách zaplněných stavů, např. z fotoelektronové spektroskopie.
Hodnoty energetických ztrát jsou 1–20 eV.
The laws of energy and impulse conservation forms
E (k ) = E0(k) − ¯hω, (5.53)
k = k − q ± g , (5.54)
where E0(k) is the incident e−
energy with momentum ¯hk, E (k ) is the backscattered e−
energy
with momentum ¯hk , ¯hω is e−
energy loss in the transmission, q is the transferred momentum g is
the lattice reciprocal vector.
EELS modifications: AREELS - Angle Resolved EELS, HREELS - High Resolution EELS
(rozptyl na fononech povrchových vibrací, ztráty jsou ≈ 0.1 eV.), pro vysokou energii primárních
e−
(několik desítek keV) je možno měřit i v transmisním módu.
Experiment: HV nebo UHV (pro výzkum povrchů), zdroj primárních e−
(v případě HREELS
monochromatizovaných) a kolektor rozptýlených e−
(čtyřmřížkový analyzátor s brzdným polem
užívaný pro LEED nebo válcový zrcadlový analyzátor CMA používaný pro Augerovskou spektroskopii).
AREELS lze provádět v optice LEED za pomoci bodového fotometru nebo úpravou
jednoduššího systému s rovinnými mřížkami a stínítkem a elektronovým násobičem. Měření
rozptylu rychlých e−
lze s výhodou provádět v transmisních elektronových mikroskopech.
Jsou možné tři nezávislé způsoby měření spekter:
1. Měření při konst. úhlech θ, θ a konst. hodnotě energetické ztráty ¯hω v závislosti na primární
energii e−
, tzv. energetické profily ztrát
2. Měření vybrané ztráty ¯hω při konst. k v závislosti na úhlu rozptylu θ .
3. Měření při konst. k rozptýlených e−
v daném směru v závislosti na velikosti energetické
ztráty, tzn. proměřování spektra ztrát energie při dané energii a směru dopadajících e−
ve
směru daném detektorem.
Základním problémem po naměření spekter je přiřazení naměřených ztrát energie rozptylovým
mechanismů. Nejprve se sanžíme určit plazmové ztráty a pak mezi zbývajícími maximy rozlišit
objemové (ozn. E) a povrchové procesy (ozn. S). Často jsou zastoupena i maxima odpovídající
ionizaci hlubších hladin (např. “d”).
EELS poskytuje informace o struktuře PL a doplňuje tak informace získané jinými povrchově
citlivými metodami, např. XPS.
5.11. THRESHOLD TECHNIQUES 35
5.11 Threshold techniques
An alternative form of core level spectroscopy is based on the detection of the onset on ionization
as the exciting beam energy passes through such a threshold (equal to the binding energy of the
core level relative to the Fermi level of the solid). A technique of this kind involves sweeping the
exciting energy beam and detecting the onset of emission of photons or Auger electrons associated
with the refilling of the core hole thus created. These different modes of detection form a group
under the general heading of APS (Appearance Potential Spectroscopy). In principle, either incident
electrons or photons could be used but the photon calls for a tunable light source in the
50–2000 eV range, only possible using synchrotron radiation.
All three modes of the incident electron technique have been used, however, the thresholds either
being detected by fall in the elastically scattered electron flux (Disappearance Potential
Spectroscopy - DAPS), by the onset of photons emission (Soft X-ray Appearance Potential Spectroscopy
- SXAPS) or by the onset of the new Auger electron emission channel (Auger Electron
Appearance Potential Spectroscopy - AEAPS). Note that in all of these techniques the surface
sensitivity is guaranteed by inelastic scattering of the incident electron beam.
Primary energy Ep is determined by:
Ep = eVp + φ + kT. (5.55)
By applying the conservation of energy
Ep − E1 = EB + E2, (5.56)
where E1 is the primary electron energy level, EB is the binding energy of the electron on the
surface E2. At the threshold energy can be captures just above the Fermi level i.e.E1 = E2 = 0 and
Ep=EB. If instead of thermionic cathode we have tunnel cathode, the eVp = EB. The probability
of excitation of the inner layers is:
W(Ep) ≈
Ep
0
ψ(E − EB)
Ep+E
0
(5.57)