energy-dispersive x-ray microanalysis in the tem anthony j. garratt-reed neil rowlands

Energy-Dispersive X-ray Microanalysis in the TEM

Anthony J. Garratt-ReedNeil Rowlands

•One result of the interaction of an electron beam with matter is the

emission of x-rays


emission of x-rays•The energy and wavelength of the X-rays is different for, and characteristic

of, each element


emission of x-rays•The energy and wavelength of the X-rays 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:


ii. X-ray detectors (brief!)

In today's talk:



iii. Quantitative chemical analysis

In today's talk:



iii. Quantitative chemical analysis

iv. Spatial Resolution

X-ray emission from materials


• 2 independent processes


• 2 independent processes• Characteristic X-rays (discrete energies)


• 2 independent processes• Characteristic X-rays (discrete energies)• Bremsstrahlung (continuum)

Characteristic X-rays

• 2-step process involving the atomic electrons


• 2-step process involving the atomic electrons• Firstly, the atom is excited by ionization of one of the core-level electrons


• 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. N

2

Si(Li) crystal

•Energy of an x-ray generates electron-hole pairs

Si(Li) crystal


•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


•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


• Different techniques for:


• Different techniques for:• SEM


• Different techniques for:• SEM• Organic thin sections


• Different techniques for:• SEM• Organic thin sections• Materials thin sections


• Different techniques for:• SEM• Organic thin sections• Materials thin sections – Today's talk!


• 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


• 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


•The Ionization cross-section is defined as the probability of ionizing a single atom in a region of uniform current density of electrons.


•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


•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


• Units are generally Barns, where 1 Barn=10-24 square centimeters


• Units are generally Barns, where 1 Barn=10-24 square centimeters• Typical values of the cross-section are 100-1000 Barns.


• 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.


• 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 cross-section for all the elements at different beam voltages


• 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 “A” where,

again, the subscript “A” denotes the particular element.

Fluorescence Yield

• Generally given the symbol “A” 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 :

where IA is the number of x-rays generated, i

p is the probe

current in Amps, e is the electron charge, CA is the

concentration (weight fraction) of element A in the sample, A

A 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 is the analysis time in seconds.

AAAAp

A

oA sQCt

e

i

A

NI

Writing the same equation for element B and dividing:

B

A

BBBB

AAAA

A

B

B

A

C

C

sQ

sQ

A

A

I

I

Writing the same equation for element B and dividing:

orB

A

BBB

AAA

A

B

B

A

C

C

sQ

sQ

A

A

I

I

ABB

A

B

A kC

C

I

I.

Since the detector sensitivity varies for different elements,

where the I’s are now the measured x-ray intensities for the

various elements

ABB

A

B

A

B

Ak

C

C

I

I.

'

'

Since the detector sensitivity varies for different elements,

where the I’s are now the measured x-ray intensities for the

various elements

ABB

A

B

A

B

Ak

C

C

I

I.

'

'

The Cliff-Lorimer equation

Limitations of Cliff-Lorimer

• Valid for “thin” samples only

The more common reality!


• Valid for “thin” samples only• Variations of detector parameters (espec. ice)


• Valid for “thin” samples only• Variations of detector parameters (espec. ice) • Only works when all elements can be detected


• Valid for “thin” samples only• Variations of detector parameters (espec. ice) • Only works when all elements can be detected• Spectral Processing


• 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• 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


10 secs, low count rate


100 secs, low count rate


100 secs, high count rate

Statistics

• Counting of x-rays is a random phenomenon• In counting N events, there is an uncertainty (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 (the standard deviation) which is equal to the square root of N• N has a 95% probability of being within +-2 of the “Correct” answer

Statistics

• N has a 95% probability of being within +-2 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 +-2 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

• 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 :

where IA is the number of x-rays generated, i

p is the probe

current in Amps, e is the electron charge, CA is the

concentration (weight fraction) of element A in the sample, A

A 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 is the analysis time in seconds.

AAAAp

A

oA sQCt

e

i

A

NI

But …

3

2

3

82

4 s

p

C

Bdi

(B is brightness of electron source, Cs is spherical aberration coefficient of objective lens)

Source Brightness:

Source Brightness:

•Inherent function of emitter

Source Brightness:


•Thermionic W: 5 Vo A/cm2/Sr

Source Brightness:



•Thermionic LaB6: 200 Vo A/cm2/Sr

Source Brightness:



•Thermionic LaB6: 200 Vo A/cm2/Sr

•Field Emitter: 5000 Vo A/cm2/Sr

AND

• Beam Broadening:

2/32/1

51025.6 tAE

Zb

o

Spatial Resolution

AND

• Beam Broadening:

2/32/1

51025.6 tAE

Zb

o

Inserting values:

Z=26 (Iron), =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)

energy-dispersive x-ray microanalysis in the tem anthony j. garratt-reed neil rowlands

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