Generation of X-Rays in the SEM specimen
The electron beam generates X-ray photons in the beam-specimen
interaction volume beneath the specimen surface.
Some X-ray photons emerging from the specimen have energies specific to
the elements in the specimen; these are the characteristic X-rays that
provide the SEM’s analytical capabilities
(give information about
composition).
Other photons have no relationship to specimen elements and constitute the
continuum background of the spectrum.
We can distinguish
Production of
Production of
bremsstralhung X-rays
characteristic X-rays
The X-rays we analyse in the SEM usually have energies between 0.1 and 20 keV
Continuum X-ray production (bremsstralhung)
Beam electrons can undergo
deceleration in the Coulombian field of
the specimen atoms which corresponds
to a loss in electron energy ∆E.
∆E is emitted as electromagnetic
radiation, that is as a photon (∆E = hυ,
υ = frequency of the electromagnetic
radiation).
Thi radiation is referred to as
bremsstalhung or braking radiation
Since the interactions are random, the electrons may lose any amount of
energy in a single deceleration event. Therefore, the bremsstalhung can
take on any energy value from zero up to the original energy of the
incident eletron (from 0 to E0), forming a continuous electromagnetic
spectrum.
The intensity of the continuum increases with beam current and energy.
Moreover, although the bremsstralhung radiation is generated by beam
electrons and it doen’t present specimen characteristics, its intensity
increases with specimen atomic number,
because of the increased
Colulombian field of the nuclei (more charge).
The intensity of the continuum radiation is important in analytical X-ray
spectrometry because it forms a background under the characteristic
peaks.
The dependence of intensity upon Z can cause artifacts in the spectra;
for this reason the identification of characteristic peaks should be
difficult and ambiguous.
Characteristic X-rays production
A beam electron can interact with tightly bound inner shell electrons of a
specimen atom, ejecting an electron from a shell. The atom is left as an ion
in an excited, energetic state.
The incident beam
electron leaves the
atom having lost at
least EK ( the
binding energy of
the electron to the
shell K)
The ejected orbital
electron leaves the
atom with a kinetic
energy of a few eV to
several keV, depending
on the interaction
The atom is left in an excited state with a missing inner shell electron. Then the
atom relaxes to its ground state within approximately 1 ps through a limited
set of allowed transitions of outer shell electrons filling the inner-shell vacancy.
The energy of electrons in the shells (atomic energy levels) are sharply defined
with values characteristic of a specific element. So the energy difference between
electron shells is a specific value for each element.
The excess energy can be released from the atom during relaxation in one of 2
ways:
In the Auger process,
the difference in shell
energies
can
be
transmitted to another
outer shell
electron,
ejecting it from the
atom with a specific
kinetic energy.
In the characteristic
X-ray process, the
difference in energy is
expressed as a photon
of
electromagnetic
radiation which has a
sharply defined energy.
X-ray involving the filling of a vacant state in the innermost electron shell
(K-shell) with an electron transition from outer shells are indicated as
K-series X-rays
Thus, as an example the energy of a Kα X-ray is equal to the difference in
energy between K and L shell.
In fact the situation is more complicated because the L and M shells are
splitted into subshells, as we will see shortly.
The partioning of the de-excitation process between X-ray and Auger
branches is described by the fluorescence yield (ω coefficient).
As an example, for the production of K radiation the fluorescence yield is:
ωK =
# K _ photons _ produced
# K − shell _ ionization
X-ray and Auger are competitive, anyway X-ray emission prevails at high
atomic number (Z), against the Auger electron emission.
For example: for the carbon K shell ωK∼ 0.005, whereas for the germanium K shell
ωK∼
0.5, increasing to near unity for heaviest elements.
In the figure
ωL ed ωM are shown, too.
Electronic shells
Electrons of an atom occupy electron shells around the atom that, in order of
increasing distance from the atomic nucleus, are designed with K, L, M,… (related to
quantum numbers of atomic physics).
The shells beyond K shell are divided into subshells: for example the L shell is
composed of three subshells (that are closely spaced in energy), the M shell has five
subshell,….
Electrons populate these subshells in a definite scheme (see below)
Energy-level diagram
In the figure below a representative energy level diagram is reported. The diagram
originate from the solution of the Schrödinger equation. The possible transitions are
shown.
Electron transitions
Characteristic X-ray lines result from transition between subshells; however, atomic
theory tells us that only transitions between certain subshelles are allowed (only those
indicated with x in the table).
For example, for the K
series, only those
electrons coming from
LIII and LII subshells
can fill the vacancy in
the K shell, so only the
Kα1 and Kα2 X-rays are
emitted
Critical ionization energy
Because the energy of each shell and subshell is sharply defined, the
minimum energy to remove an electron from a specific shell has a sharply
defined value as well. This energy is called critical ionization or excitation
energy, Ec, which is function, for each shell or subshell, of atomic number.
As an example, consider the wide range in Ec for the K, L and M shells and
subshells of platinum (Pt, Z = 78)
A 20-keV beam can ionize the L and M shells, but not the K shell.
As Z decreases (Z(Nb)=41 and Z(Si)=14), the critical ionization energies
decrease.
The critical ionization energy is an important parameter in calculating
characteristic X-ray intensity and to have quantitative information about the
elemental composition of the specimen.
For X-ray microanalysis the SEM typically operate at energies two to three
times Ec of the element of interest.
Moseley’s law
The energy of the electron shells vary in a discrete fashion with Z. In
particular the difference in energy between shells changes in regular steps
when Z changes by one unit.
This law was discovered by Moseley and can be expressed in the form of an
equation:
E = A(Z − C )
2
where E is the energy of the X-ray line, and A and C are constant which
differ for each series (for example: C = 1.13 for the K series and
approximately 7 for the L series).
Thus Moseley’s law may be used to find the energy of any element K or L line
and forms the basis for qualitative analysis, that is, the identification of
elemental constituent.
Families of characteristic lines
For elements with Z ≥ 11 (sodium), the shell structure is sufficiently complex
that when an ionization occurs in the K shell, the transition to fill the vacant
stage can occur from more than one outer shell.
Following ionization of a K-shell
electron, a transition to fill the
vacant state can occur from
either L or M shell.
X-rays resulting from transition
of electrons from the M shell
are designed Kβ X-rays; for
transitions from the L shell the
X-rays are designed Kα X-rays.
Because the difference of
energy between the K and M
shells is larger than between K
and L shells, the Kβ rays energy
is larger than that of the Kα.
Within the SEM beam energy range, each element can emit X-rays, of the K
series only (light elements), the K and L series (intermediate elements) and L
and M series (heavy elements)
Kα
Kβ
Some series (L series) are not resolved
because their energies are very close
and the resolution of the instrument is
low.
When a beam electron has sufficient
energy to ionize a particular electron
shell
in
an
atom
to
produce
characteristic X-ray lines, all other
characteristic X-ray of lower energy
for the atom will also be excited,
provided there are electrons available
for such transition.
Typical EDS spectra for increasing Z
This occurs because of
1 direct ionizazion
2 propagation of the vacant state as
the atom returns to groud state
Weights of lines
Although many possible electron transitions can occur giving rise to the
families of X-rays, the probability (called “weight of lines”) for each type of
transition vary considerably.
The weights of lines are dependent upon atomic nimber and vary in a complex
fashion, but, in general:
The greater the energy difference in the electron transition
The less probable and less intense is the X-ray line
Thus the Kα lines are more intense than the Kβ lines.
Although the values in the table are not exact for a specific element, these
wieights are a useful guide in interpreting spectra and assigning peak
identification in energy dispersive X-ray spectrometry.
Anyway peaks belonging to different elements cannot be compared on the
basis of the emission probability (weights of line) because intensity depends
on a variety of factors (including the fluorescent yield, absorption and
excitation energy)
Cross section for inner shell ionization
Numerous cross sections expressing the probability for inner shell ionization
can be found in literature; anyway the basic form is that derived by Bethe:
Q = 6.51× 10 − 20
nS bS
ln (cSU )
2
UEc
nS is the number of electrons in a shell or subshell (e.g., nS = 2 for K shell)
bS e cS are constant for a particular shell
Ec is the critical ionization energy (keV)
U is the “overvoltage”
U = E0/Ec
Cross section for the K-shell
ionization for silicon (it has a
maximum at U ∼ 3, that is
E0≥ 3Ec)
X-ray peak-to-backgroud ratio
The most important factor in determing the limits of detection in X-ray
spectrometric analysis is the presence of the continuum background, whose
contribution can be calculated by:
I Peak
I Background
1  E0 − Ec 

= 
Z  Ec 
n −1
It would seem to be advantageous to make E0 as large as possible to increase the
peak signal with respect to tha background.
In fact, beam electrons penetrate deeper into the specimen as the beam energy
E0 increases. Correspondingly, X-rays are produced deeper into the specimen.
As a consequence, there are
a) the degradation of the spatial resolution of analysis and
b) the increasing of X-ray absorption, which reduces the measured X-ray
intensity.
For a thick, bulk specimen there is an optimum beam energy beyond which
further increases in beam energy actually degrade analytical performance. This
limit depends on the energy of the characteristic X-ray and the composition of
the specimen.
An overvoltage of 2-3 is usually optimum for a given element.
Characteristic X-rays can be produced in almost all the interaction volume, in
particular within that portion of the electron trajectories for which the
energy exceeds Ec for a particular X-ray line, whereas bremsstralhung Xrays continue to be produced until the electron energy equals zero.
Scheme of the
interaction volume
and of the regions
from which the
electron beam
induced signals come
Energy and wavelength of the most intense X-rays
X-ray fluorescence
For some element pairs (A, B) in the specimen, the primary X-ray
of element A created by the electron beam can generate a
secondary X-ray of element B by fluorescence (photoelectric
effect) :
An electron of element B absorbs a primary photon from A and is
ejected leaving B atom in an excited state. Then B follows
deexcitation, producing either Auger electrons or (secondary)
characteristic X-ray (SECONDARY FLUORESCENCE).
Secondary radiation can be generated also by bremsstrahlung
photons.
Because the X-ray photon causing fluorescence must have at least
as much energy as the critical excitation energy of the atom in
question, the energy of secondary radiation will always be less than
energy of the photon that is responsible for ionizing the inner
shell.
X-ray detectors
Chemical analysis in the SEM is performed by measuring the energy and
intensity distribution of the X-ray signal generated by a focused electron
beam
There are two main kinds of spectrometers:
Energy Dispersive
Spectrometer (EDS)
Wavelength Dispersive
Spectrometer (WDS)
Energy Dispersive Spectrometer (EDS)
They are the most common, althoug the most recent.
The spectrometer is composed of a Silicon crystal (doped with Litium)
covered with a Gold evaporated layer.
Each photon, penetrating inside the
crystal, generates electron-hole pairs.
The number of pairs is proportional to
the energy photon.
The electrons, produced in the detector
are collected and converted, through
an amplification circuit, in an electric
signal with intensity proportional to the
number of electrons, and, consequently,
to the photon energy.
The output, is an energetic spectrum
with peaks in correspondence of the
photon energy and height (intensity)
dependent on the number of detected
photons.
The Au layer is very thin (about 20 nm)
in order to minimize the X-ray
absorption.
The detector is protected by a Be
window,
to
prevent
possible
contaminations.
To reduce the noise due to the thermal
agitation, the detector is held at about
77 K (liquid nitrogen) or, in the latest, is
cooled by Peltier method.
The Be window, although is only of some microns, absorbs a significant fraction
of the low-energy photons that go through it.
So it is impossible to detect X-rays with energy lower than 1 keV and,
therefore, to analyse elements having Z lower than that of Na.
Nowadays, detectors without window or with very thin polymeric windows are
avilable; so it is possible to broaden the analysis down to Boron.
This state solid detector is very efficient (about 100% of X-rays
entering the detector produce a pulse – is detected).
Anyway, the main drawback is the resolution that is very low (about one
hundred of eV); therefore the spectra are characterized by broaden peaks
and not by narrow lines.
This can make ambiguous the identification of the peaks, and of the
elements to which they belong, but, above all, precise quantitative analyses
are very difficult.
Wavelength Dispersive Spectrometer (WDS)
Differently from EDS detectors, WDS detectors can reveal without
problems light elements and are characterized by a high energetic resolution.
The detector geometry is shown in figure:
The X-rays emitted from the
sample are reflected by the
analyzing
crystal
(dispersive
element) and sent towards the
detector.
If d is the distance between the
crystal planes and θ the angle that
X-rays form with the crystal
surface, only the photons with
λ=
2d sin θ
n
are sent to the detector.
The crystal behaves like a filter which selects a well-defined wavelenght.
By varying θ, the wavelenght of the photon impinging the detector changes.
The detector doesn’t distinguish photons with different energy, but counts
the number (proportional counter).
Detector, specimen and crystal stay on a circle (Rowland circle).
This spectrometer is bulky, with a very complex mode of operation and
very often θ can vary only in a narrow range. So, to cover all the X-ray
wavelenght range, more crystals, with different d, are necessary.
Some instruments are equipped with different spectrometers or with
one spectrometer, but with interchangeable crystals
Another drawback is that, being the collecting angle very small, the
efficiency is almost low (< 30%). Morever the cost is quite high.
Finally, although the detector is very fast, the fact that it reveals one
wavelenght at a time makes this technique lengthy and complex.
Anyway, as analytical instrument it is interesting because of the:
• high spectral resolution
• high peak/background ratio
• possibility to reveal light elements
In conclusion:
The Energy Dispersive Spectrometers are faster and suitable for
qualitative analyses,
the Wavelenght Dispersive Spectrometer are more lengthy but give
more precise information for quantitative analyses.