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Energy-Dispersive X-ray
Microanalysis in the TEM
Anthony J. Garratt-Reed
Neil Rowlands
•One result of the interaction of an
electron beam with matter is the
emission of x-rays
•One result of the interaction of an
electron beam with matter is the
emission of x-rays
•The energy and wavelength of the Xrays is different for, and characteristic
of, each element
•One result of the interaction of an
electron beam with matter is the
emission of x-rays
•The energy and wavelength of the Xrays is different for, and characteristic
of, each element
•Analysis of the X-rays can, therefore,
be used as a tool to give information
about the composition of the sample
In today's talk:
In today's talk:
i. X-ray emission from materials
In today's talk:
i. X-ray emission from materials
ii. X-ray detectors (brief!)
In today's talk:
i. X-ray emission from materials
ii. X-ray detectors (brief!)
iii. Quantitative chemical analysis
In today's talk:
i. X-ray emission from materials
ii. X-ray detectors (brief!)
iii. Quantitative chemical analysis
iv. Spatial Resolution
X-ray emission from
materials
X-ray emission from
materials
• 2 independent processes
X-ray emission from
materials
• 2 independent processes
• Characteristic X-rays (discrete
energies)
X-ray emission from
materials
• 2 independent processes
• Characteristic X-rays (discrete
energies)
• Bremsstrahlung (continuum)
Characteristic X-rays
• 2-step process involving the atomic
electrons
Characteristic X-rays
• 2-step process involving the atomic
electrons
• Firstly, the atom is excited by ionization of
one of the core-level electrons
Characteristic X-rays
• 2-step process involving the atomic
electrons
• Firstly, the atom is excited by ionization of
one of the core-level electrons
• This is followed by an outer-shell electron
losing energy by emission of a photon (the
X-ray), and dropping to the core state
Bremsstrahlung
• “Braking radiation”
Bremsstrahlung
• “Braking radiation”
• All charged particles radiate energy when
accelerated
Bremsstrahlung
X-ray detectors
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
Used since around 1970 on SEMs
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
Used since around 1970 on SEMs
• Silicon Drift detector
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
Used since around 1970 on SEMs
• Silicon Drift detector
Over the last 5 years
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
Used since around 1970 on SEMs
• Silicon Drift detector
Over the last 5 years
• Crystal detectors – Electron Microprobe
X-ray detectors
• Lithium-drifted Silicon (Si(Li))
Used since around 1970 on SEMs
• Silicon Drift detector
Over the last 5 years
• Crystal detectors – Electron Microprobe
Different characteristics
Si(Li) crystal
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
•About 3mm thick and 3-6 mm diameter
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
•About 3mm thick and 3-6 mm diameter
•Electrodes plated on front and back
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
•About 3mm thick and 3-6 mm diameter
•Electrodes plated on front and back
•Front electrode is thin to allow X-rays to
enter
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
•About 3mm thick and 3-6 mm diameter
•Electrodes plated on front and back
•Front electrode is thin to allow X-rays to
enter
•Biased by a voltage of 3-500V
Si(Li) crystal
•Crystal of pure silicon, with lithium diffused
in to compensate for any residual carriers
•About 3mm thick and 3-6 mm diameter
•Electrodes plated on front and back
•Front electrode is thin to allow X-rays to
enter
•Biased by a voltage of 3-500V
•Cooled to Liq. N2
Si(Li) crystal
•Energy of an x-ray generates electronhole pairs
Si(Li) crystal
•Energy of an x-ray generates electronhole pairs
•These are swept from the crystal by the
bias voltage, and are detected in the
external circuitry as a pulse of charge
Si(Li) crystal
•Energy of an x-ray generates electronhole pairs
•These are swept from the crystal by the
bias voltage, and are detected in the
external circuitry as a pulse of charge
•Since the average energy required to
create an electron-hole pair is constant and
predictable (about 3.8eV), the external
charge is proportional to the x-ray energy
Quantitative Analysis
Quantitative Analysis
• Different techniques for:
Quantitative Analysis
• Different techniques for:
• SEM
Quantitative Analysis
• Different techniques for:
• SEM
• Organic thin sections
Quantitative Analysis
• Different techniques for:
• SEM
• Organic thin sections
• Materials thin sections
Quantitative Analysis
• Different techniques for:
• SEM
• Organic thin sections
• Materials thin sections – Today's talk!
Characteristic X-rays
• 2-step process involving the atomic
electrons
• Firstly, the atom is excited by ionization of
one of the core-level electrons
• This is followed by an outer-shell electron
losing energy by emission of a photon (the
X-ray), and dropping to the core state
Characteristic X-rays
• 2-step process involving the atomic
electrons
• Firstly, the atom is excited by ionization of
one of the core-level electrons
• This is followed by an outer-shell electron
losing energy by emission of a photon (the
X-ray), and dropping to the core state Fluorescence
Ionization cross-section
Ionization cross-section
•The Ionization cross-section is defined as
the probability of ionizing a single atom in a
region of uniform current density of
electrons.
Ionization cross-section
•The Ionization cross-section is defined as
the probability of ionizing a single atom in a
region of uniform current density of
electrons.
•Usually denoted by “QA” where the “A”
denotes the particular element of interest
Ionization cross-section
•The Ionization cross-section is defined as
the probability of ionizing a single atom in a
region of uniform current density of
electrons.
•Usually denoted by “QA” where the “A”
denotes the particular element of interest
• It has units of area
Ionization cross-section
• Units are generally Barns, where
1 Barn=10-24 square centimeters
Ionization cross-section
• Units are generally Barns, where
1 Barn=10-24 square centimeters
• Typical values of the cross-section are
100-1000 Barns.
Ionization cross-section
• Units are generally Barns, where
1 Barn=10-24 square centimeters
• Typical values of the cross-section are
100-1000 Barns.
• For practical purposes, the cross-section
can be regarded as a function of the
electron energy alone, and is independent
of the chemical surroundings.
Ionization cross-section
• For practical purposes, the cross-section
can be regarded as a function of the
electron energy alone, and is independent
of the chemical surroundings.
• Various equations have been proposed to
predict the value of the ionization crosssection for all the elements at different
beam voltages
Characteristic X-rays
• 2-step process involving the atomic
electrons
• Firstly, the atom is excited by ionization of
one of the core-level electrons
• This is followed by an outer-shell electron
losing energy by emission of a photon (the
X-ray), and dropping to the core state Fluorescence
Fluorescence Yield
Fluorescence Yield
• Generally given the symbol “wA” where,
again, the subscript “A” denotes the
particular element.
Fluorescence Yield
• Generally given the symbol “wA” where,
again, the subscript “A” denotes the
particular element.
•For practical purposes again, the
fluorescence yield can be considered to be
a constant for a particular transition. (No
significant dependence on chemical
bonding, for example)
Fluorescence Yield
• For practical purposes again, the
fluorescence yield can be considered to be
a constant for a particular transition.
• The fluorescence yield has been
measured for a wide range of lines; an
equation has been developed to fit these
measurements to predict the fluorescence
yield in those cases where measurements
have not been made.
Putting this together --
Putting this together -• We can write, for a sample of thickness t
and density r:
No i p
IA 
  r  t  C A  QA  w A  s A t
AA e
where IA is the number of x-rays generated, ip is the probe
current in Amps, e is the electron charge, CA is the
concentration (weight fraction) of element A in the sample,
AA is the atomic weight of element A, s is a partition function
to account for the fraction of x-rays in the detected line, and
t is the analysis time in seconds.
Writing the same equation for
element B and dividing:
I A AB Q A  w A   A  s A C A



I B AA Q B  w B   B  s B C B
Writing the same equation for
element B and dividing:
I A AB QA  w A  s A C A



I B AA QB  w B  sB CB
or
I A CA

.k AB
I B CB
Since the detector sensitivity 
varies for different elements,
I ' A CA  A

 .k AB
'
I B CB  B
where the I’s are now the
measured x-ray intensities for the
various elements
Since the detector sensitivity 
varies for different elements,
I ' A CA  A

 .k AB
'
I B CB  B
where the I’s are now the
measured x-ray intensities for the
various elements
The Cliff-Lorimer equation
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
The more common reality!
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
• Variations of detector parameters (espec.
ice)
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
• Variations of detector parameters (espec.
ice)
• Only works when all elements can be
detected
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
• Variations of detector parameters (espec.
ice)
• Only works when all elements can be
detected
• Spectral Processing
Limitations of Cliff-Lorimer
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
• Variations of detector parameters (espec.
ice)
• Only works when all elements can be
detected
• Spectral Processing
• Spurious effects -
Spurious effects:
• Fluorescence
Spurious effects:
• Fluorescence
• Escape peaks
Spurious effects:
• Fluorescence
• Escape peaks
• Coherent Bremsstrahlung
Spurious effects:
• Fluorescence
• Escape peaks
• Coherent Bremsstrahlung
• Detector imperfections
Spurious effects:
• Fluorescence
• Escape peaks
• Coherent Bremsstrahlung
• Detector imperfections
• Etc., etc.
Limitations of Cliff-Lorimer
Limitations of Cliff-Lorimer
• Valid for “thin” samples only
• Variations of detector parameters (espec.
ice)
• Only works when all elements can be
detected
• Spectral Processing
• Spurious effects
• Statistics!
Statistics
• Counting of x-rays is a random
phenomenon
Why do we need counts?
2 sec, low count rate
Why do we need counts?
10 secs, low count rate
Why do we need counts?
100 secs, low count rate
Why do we need counts?
100 secs, high count rate
Statistics
• Counting of x-rays is a random
phenomenon
• In counting N events, there is an
uncertainty s (the standard deviation) which
is equal to the square root of N
Statistics
• Counting of x-rays is a random
phenomenon
• In counting N events, there is an inherent
uncertainty s (the standard deviation) which
is equal to the square root of N
• N has a 95% probability of being within +2s of the “Correct” answer
Statistics
• N has a 95% probability of being within +2s of the “Correct” answer
• Hence if 1% precision is required 95% of
the time, 40,000 counts must be acquired
Statistics
• N has a 95% probability of being within +2s of the “Correct” answer
• Hence if 1% precision is required 95% of
the time, 40,000 counts must be acquired
•Likewise for 0.1% precision, 4,000,000
counts are required
Statistics
• Likewise for 0.1% precision, 4,000,000
counts are required
• Approximately half the counts are in the
major peak of an element, so 8,000,000
counts must be acquired in the spectrum
Statistics
• Likewise for 0.1% precision, 4,000,000
counts are required
• Approximately half the counts are in the
major peak of an element, so 8,000,000
counts must be acquired in the spectrum
• Maximum count rate for Si(Li) detector is
about 30,000cps, so this will take about 250
seconds (SDD will count at 250,000 cps)
Spatial Resolution
Spatial Resolution
Spatial Resolution
• There is no single definition of “Spatial
Resolution”
Spatial Resolution
• There is no single definition of “Spatial
Resolution”
• Analyzing a small particle on a thin support
film has very different requirements from
analyzing a diffusion gradient in a foil
Spatial Resolution
• There is no single definition of “Spatial
Resolution”
• Analyzing a small particle on a thin support
film has very different requirements from
analyzing a diffusion gradient in a foil
• Consider the diffusion example:
Spatial Resolution
Putting this together -• We can write, for a sample of thickness t
and density r:
No i p
IA 
  r  t  C A  QA  w A  s A t
AA e
where IA is the number of x-rays generated, ip is the probe
current in Amps, e is the electron charge, CA is the
concentration (weight fraction) of element A in the sample,
AA is the atomic weight of element A, s is a partition function
to account for the fraction of x-rays in the detected line, and
t is the analysis time in seconds.
But …
ip 
8
3
 d B
2
4C s 
2
3
(B is brightness of electron source, Cs is spherical
aberration coefficient of objective lens)
Source Brightness:
Source Brightness:
•Inherent function of emitter
Source Brightness:
•Inherent function of emitter
•Thermionic W: 5 Vo A/cm2/Sr
Source Brightness:
•Inherent function of emitter
•Thermionic W: 5 Vo A/cm2/Sr
•Thermionic LaB6: 200 Vo A/cm2/Sr
Source Brightness:
•Inherent function of emitter
•Thermionic W: 5 Vo A/cm2/Sr
•Thermionic LaB6: 200 Vo A/cm2/Sr
•Field Emitter:
5000 Vo A/cm2/Sr
AND
• Beam Broadening:
Z
b  6.25 10 
Eo
5
r
 
 A
1/ 2
 t 3/ 2
Spatial Resolution
AND
• Beam Broadening:
Z
b  6.25 10 
Eo
5
r
 
 A
1/ 2
 t 3/ 2
Inserting values:
Z=26 (Iron), r=8gm/cc, A=56, t=4E-6 cm (40 nm),
Eo=200KV
We find that b= 2.4x10-7 cm (2.4 nm)
Optimizing,
• We can estimate a spatial resolution of
about 2 nm with 1% analytical precision
Optimizing,
• We can estimate a spatial resolution of
about 2 nm with 1% analytical precision
• Or, much better resolution if the required
precision is not so high
Optimizing,
• We can estimate a spatial resolution of
about 2 nm with 1% analytical precision
• Or, much better resolution if the required
precision is not so high
• Requires VERY good sample! (e.g.
thickness of ~10nm)