X-ray Analysisphybcb/teaching/DTU... · Scanning Electron Microscopy and X-ray Microanalysis Joseph...

X-ray AnalysisChris Boothroyd

Center for electron nanoscopy, Technical University of Denmark

Advanced TEM course, Thurs 16 Sept 2010

Thursday, 16 September 2010

1. Electron beam interactions and X-ray generation

2. Recording X-ray spectra: wavelength dispersive X-ray spectroscopy (WDX)

3. Recording X-ray spectra: energy dispersive X-ray spectroscopy (EDX)

4. Quantitative analysis: Quantification of X-ray spectra, detection limits, standards, spectrum fitting

OverviewX-ray Analysis in TEM


References

Electron Microscopy and AnalysisPeter J Goodhew, John Humphreys and Richard BeanlandChapter 6

Scanning Electron Microscopy and X-ray MicroanalysisJoseph Goldstein, Dale E Newbury, David C Joy, Charles E Lyman, Patrick Echlin, Eric Lifshin, LC Sawyer, JR Michael

Fundamentals of energy dispersive X-ray analysis! JC Russ

Transmission Electron Microscopy: A Textbook for Materials Science! DB Williams and C Barry Carter


Microanalysis is the determination of the composition of a specimen on a microscopic scale

General idea is to irradiate area of interest with electrons and measure the energy of the signals (X-rays or electrons) emitted

SEM and TEM do not give direct information on specimen composition

Need to determine composition on microscopic scale

X-ray spectroscopy and energy loss spectroscopy measure elemental concentrations

Why?

Quantitative analysis

Aims to give accurate elemental concentrations

...but is more difficult and requires an understanding of the processes involved

Introduction


1. Electron beam interactions and X-ray generation


Surface analysis techniques - input and output signals

1. Interaction of electrons with materials


Beam-specimen interactions: techniques

Technique Input signal Output signal

Depth sampled

Lateral resolution

Elemental range

Sample Detection limit

Wavelength dispersive X-ray spectroscopy (WDX, WDS)

Electron Photon(X-ray)

~1000 nm ~1000 nm Z ≥ 4 Flat polished surface

0.005% (50 ppm)

Energy dispersive X-ray spectroscopy in SEM (EDX, EDS)


~1000 nm ~1000 nm Z ≥ 5 Flat polished surface

0.1%

Energy dispersive X-ray spectroscopy in TEM or STEM (EDX, EDS)


10 to 100 nm (sample thickness)

1 nm Z ≥ 5 TEM foil 0.1%

Electron energy loss spectroscopy in TEM (EELS), EFTEM

Electron Electron 10 to 100 nm (sample thickness)

0.1 nm Z ≥ 3 TEM foil 0.1%



Beam-specimen interactions: electron microscopy (SEM and TEM)

Signals emitted when a beam of electrons hits a specimen

In analysis we use the X-rays, energy loss electrons and Auger electrons to determine composition

X-rays: Emitted in all directions from both SEM and TEM specimens

Energy loss electrons: transmitted through the specimen, TEM only



Distances depend strongly on material and beam energy.

Note SEM X-ray resolution, typically about 1µm, TEM X-ray resolution ~width of beam

Interaction volume for electrons in a bulk sample.

Distances are for 20 kV electrons in Cu. For Al, multiply by 3.

2. Interaction volume


3. X-ray generation

When an electron hits a material X-rays are formed by 2 processes giving rise to bremsstrahlung and characteristic X-rays

3a. Bremsstrahlung process

Caused by electrons being decelerated

Contains all energies from 0 to beam energy

Intensity given by Kramers law

€

i Z E −E0( )E

I ≈

where" i" =" beam current" " Z" =" average atomic number" " E0" =" incident electron beam" " " " energy


3b. Characteristic X-rays

Primary electron removes electron from inner shell of target atom giving an ion in excited state

Ion loses energy by outer shell electron falling into vacancy

K, L and M characteristic lines for Au.

Excess energy emitted as either an X-ray or an Auger electron

Probability of X-ray emission given by fluorescence yield,ωk, ωl, ωm

ω small for low Z

3. X-ray generation


Fluorescence yield

Fluorescence yield (ω) as a function of atomic number for the K, L and M shells Goldstein (1st ed) p101

Fluorescence yield is small for low Z

e.g.

C (Z=6) ωK ≈ 0.001 Ge (Z=32) ωK ≈ 0.5

3. X-ray generation


2. Recording spectra:Wavelength dispersive X-ray

spectroscopy (WDX)


Recording spectra

Wavelength dispersive X-ray spectroscopy (WDX)

To record X-ray spectrum need to measure X-ray energy and count number of X-rays at each energy

In WDX use a crystal spectrometer

WDX is slow as need to measure each X-ray wavelength individually

It has good wavelength resolution & a good detection limit

Less common except in SEM based electron probe microanalysers (EPMA)


Example spectrum

Wavelength dispersive X-ray spectroscopy (WDX)

Ni Kβ


3. Recording spectra: Energy dispersive X-ray

spectroscopy (EDX)


Recording spectra

1. Basis of EDX

In EDX use a Si chip both to measure the X-ray energy and to count the X-rays.

EDX is fast because can count all energies in parallel (cf WDX)

The Si chip is made from “lithium drifted Si” or Si(Li). It is effectively undoped Si

It must be kept cold by liquid nitrogen to reduce thermal noise

When an X-ray hits the Si chip, it creates electron-hole pairs.

These electron-hole pairs are counted by an amplifier, resulting in a pulse whose height is proportional to the X-ray energy.

The pulses are counted as a function of energy and displayed on a computer.


Recording spectra

X-ray detector

Enlargement of Si(Li) detector

1. Basis of EDX


2. Hardware2a. Detector

Cross-section of Si(Li) crystal and end of EDX detector.


2. Hardware

The detection of X-rays takes place in the intrinsic layer in the middle of the detector.

In intrinsic silicon, all the electrons are in the valence band with none in the conduction band.

An X-ray ejects a photoelectron in the Si which loses its energy by promoting electrons from the valence band to the conduction band forming electron-hole pairs.

A reverse bias of 500 to 1000 volts is used to ensure that most of the electron-hole pairs are collected.

It is not possible to make silicon pure enough to be intrinsic - it usually contains acceptor impurities and thus acts as a p-type semiconductor.

The acceptor sites are thus “filled” with Li, and the Si is then called “lithium drifted silicon” or Si(Li).

2a. Detector



The energy gap for Si is 1.1 eV, but normally on average 3.8 eV is required to form an electron-hole pair as not all of the energy creates electron-hole pairs.

Thus, for example, a single Cu Kα X-ray will create

8040/3.8! =! 2300 electron-hole pairs

! ! ! =! 10-16 C.

This is a very small signal to measure!



The signal needs to be amplified by a factor of about 1010.

Hence, there is a need to minimise noise.

The detector and preamplifier are thus cooled with liquid nitrogen in order to:

reduce thermally generated electron-hole pairs

prevent the Li atoms from diffusing which would otherwise occur under the applied bias

reduce noise in the FET preamplifier.


2a. Detector

2. Hardware

Silicon drift detectors (SDD)Relatively new type of detectorHigh count rate (>100,000 counts/sec)Good resolution (~130eV at 5.9kV)Does not need liquid nitrogen cooling

http://www.amptek.com/drift.htmlThursday, 16 September 2010

2b. Window

2. Hardware

The Si chip is normally protected from the microscope by a window. This window absorbs some X-rays

Be window

Thin (~10µm) of Be. Can withstand atmospheric pressure but absorbs X-rays from Z < 11 (Na)

Ultrathin window

Thin (<100nm) film of polymer, diamond, boron nitride or silicon nitride. Mostly can withstand atmospheric pressure. Better than Be but absorb some low energy X-rays

Windowless

Best collection efficiency, but need good vacuum to prevent contamination of Si chip


X-ray detector efficiencyWilliams and Carter p 561

2. Hardware2b. Window


2c. Detector electronics

Detector charge to voltage converter and pulse shape linear amplifierGoldstein p 318

2. Hardware


Output of charge-to-voltage converter after a series of photonsGoldstein p 318

2. Hardware2c. Detector electronics



The stages in processing are:

Preamplifier

This consists of a field effect transistor (FET), mounted close to the Si crystal and cooled to ~100 K along with the Si crystal to minimise stray capacitance and noise pick up.

The Si detector produces a short current pulse proportional to the incident X-ray energy.

The preamp acts as a charge to voltage converter and integrates this signal.

This means that its output rises with time and must be reset.

A resistor is too noisy, so use “pulsed opto-feedback” to reset when the voltage gets too high.

The typical pulse width at this stage is 150 ns.



Amplifier

The amplifier converts the stepped output of the preamp of a few millivolts into shaped pulses of several volts in height and around 20 µs in width.

The time constant of this amplifier determines the trade off betweenX-ray energy resolution and maximum count rate.

Short time constants (e.g. 10 µs) allow higher count rates before the detector is saturated, while long time constants (e.g. 40 µs) allow better energy resolution.

This time constant can usually be set manually.


2. Hardware2c. Detector electronicsProcessing

There are various stages involved in processing the pulses, including:

Pulse pile-up rejecter:This rejects overlapping peaks by terminating processing if another pulse arrives while one is being processed.

For this, a second amplifier is used with a short time constant.

If two pulses arrive too close together, then both of them are ignored.

Noise peak or zero energy strobe:The natural electronic noise can be allowed through into the final spectrum.

This allows the zero energy to be calibrated accurately and the electronic noise to be measured.

Analogue to digital converter (ADC):This converts pulse height (proportional to X-ray energy) into a digital signal.

For accurate digitisation this may take up to 10 µs per pulse.



Processing

Multi-channel analyser (MCA) or computer:Typically 1024 channels of 20 eV width to cover 0 to 20 keV.

Each pulse is digitised and 1 added to the corresponding bin in the MCA.

For a given X-ray pulse the X-ray energy it is assigned to depends on the gain of the amplifier which can drift over time.

Thus the system must be calibrated by acquiring a spectrum from a known element such as Co or Cu.

Most EDX software includes calibration using the zero strobe and a known element when the system is started.


3a. Ionisation statistics

3. Energy resolution

Ideally, each X-ray photon of the same energy would give the same number of electron-hole pairs:

N = E/ε

where! ε = electron-hole pair energy = 3.8 eV for Si

and! E = X-ray energy

Electron-hole pair formation is somewhere between ideal and random (Poisson)

Standard deviation for N pairs:

σN =

where! F = Fano factor, typically about 0.125 for Si.€

NF


3a. Ionisation statistics


Converting this formula to energy gives:

σE = εσN =

If the peak is gaussian, then its full width at half maximum (fwhm) is

ΔEionisation = ! ! =

Thus,! ΔEionisation → 0 as E → 0

For a Si X-ray detector:

ΔEionisation ≈ 125 eV at the energy of Mn Kα (5.898 keV)

This is the fundamental limit of resolution

The only way to improve it is to reduce ε, i.e. to reduce the energy per electron-hole pair, and thus to increase the number of electron-hole pairs - for example by using a Ge detector instead of a Si detector.

€

EFε

€

8 ln2σE

€

2.355 EFε


3b. Noise


Noise is caused by:

DC leakage current in the Si detector;

Thermal noise in the Si and the FET;

Electronic noise in the amplifiers.

It can be measured from the width of the strobe peak.

For a typical EDX system:

ΔEnoise ≈ 80 to 85 eV


3c. Overall resolution

€

ΔEnoise2 + ΔEionisation

2

€

ΔEnoise2 + 2.3552EFε


The overall resolution of the detector depends on the sum of both the ionisation statistics and detector noise resolution limits.

Resolution ΔEfwhm! =

! ! ! =


Reimer SEM p 205

EDX resolution (ΔEfwhm) measured as the full width half maximum of the Gaussian peak of an X-ray line of energy Ex for different levels of amplifier noise


For a modern detector the overall resolution at the energy of Mn Kα (5.898 keV) is 130 to 150 eV.

3c. Overall resolution


4. Dead time

The time constant τ is the time that the detector takes to process a pulse. It is typically from a few to 40 µs and can usually be changed by the user.

A short value of τ allows higher count rates to be processed. A longer value of τ gives better energy resolution, as the electronics have more time to process the pulse.

The detector cannot process further pulses while one is being processed, hence it is “dead” for this time. If a further pulse arrives while the first is being processed, then the dead time is increased.


Williams and Carter p 567

4. Dead time

Relation between output count rate and input count rate.The output count rate takes account of the dead time


WDX EDX

Energy resolution 10 eV 140 eV

Max count rate 50,000 counts/sec on one peak

3,000 counts/sec over all spectrum

Spectrum acquisition time 30 min 1 min

Detection limit 0.005% 0.1%

Peak to background ratio 1000 50

Artefacts Higher order lines Sum peaksEscape peaks

Si K internal fluorescenceetc

5. Comparison of WDX and EDX

Approximate values of parameters for WDX and EDX spectrometers:


Comparison of WDX and EDX spectra from BaTiO3.

The broad peaks are from EDX and the sharp peaks from WDX.

5. Comparison of WDX and EDX



EDX spectrum from glass test specimen Goldstein p 356

6. Interpretation of EDX spectra


6. Interpretation of EDX spectra

Steps to interpret an EDX spectrum of an unknown material:

1. Ensure that the incident beam energy is high enough.

For quantitative work: Beam energy > 2 × Highest peak energy.

2. Ensure that the spectrum is reliable.

Repeat the spectrum from the same area or from a similar area;

Ensure there are enough counts, so that peaks are not lost in the noise of the background;

Ensure the count rate is not too high (< 3000 counts/sec) and that the dead time is below 50% to minimise sum and escape peaks.


6. Interpretation of EDX spectra3. Use prior knowledge of the sample to know which elements are likely to be present and which are unlikely to be present.

4. Confirm elements by looking for other peaks from that element.

5. Work from high energy to low energy identifying peaks.

At high energy, there are fewer peaks - and it is easier to resolve neighbouring peaks.

6. Peak shapes and energies:

For the energy range 0 - 20kV (typical of most spectrometers):

K series:Elements B (Z = 4) to Ru (Z = 44);If Z > ~16 (S) look for Kβ peak (intensity 10-20% of Kα);Kα1 and Kα2 not resolvable;Gaussian peak shape with a shoulder when Kβ peak just resolvable.


6. Interpretation of EDX spectraL series:

Elements Cl (Z = 17) and higher.If Z > ~ 42 (Mo), look for Lβ and others.Relative intensities:

Ll! 4%Lα1! 100%Lβ1! 70%Lβ2! 20%Lγ1! 8%Lγ3! 3%

M series:Elements ~Ag (Z = 47) and higher.Highest M peak for U (Z = 92) at 3.2kV.M alpha and beta peaks not resolvable.Peaks are gaussian in shape, with a small shoulder for highest Z.

7. Beware of peak overlaps eg

S K 2.31 keV!! Mo L 2.29 keV! ! Pb M 2.35 keVN K 0.39 keV! Ti L 0.45 keV


1. Escape Peaks

7. Artefacts

Escape peaks occur when a Si K X-ray escapes from the Si detector.

The energy recorded is reduced by the energy of a Si K X-ray.

An extra peak appears 1.74 keV below any intense peak.

The intensity is about 0.2 - 2% of the main peak.

Escape peaks are most often seen for elements between P K (2.0 keV) and Zn Kα (8.6 keV).


Escape peak in Cu, 1.74 keV below the Cu Kα peakWilliams and Carter p 568

7. Artefacts1. Escape Peaks


Sum peak in Mg for various dead times.No sum peak is present for 14% dead time and below.


7. Artefacts2. Sum peaks

Sum peaks appear when two X-rays arrive at the same time


3. Stray radiation peaks, secondary fluorescence

7. Artefacts

There are many possible sources of stray radiation:

X-rays can be collected from various parts of the microscope chamber, detector, sample holder, or parts of the sample away from the area of interest.

They can be created due to backscattered electrons and/ or X-rays hitting parts of the specimen and/ or chamber, and exciting secondary X-rays.

This is especially a problem for TEM, where there is much less space.

For this reason, it is important to remove the objective aperture, which is particularly good at scattering electrons back onto the specimen.


Sources of stray X-rays generated in a TEM when the electron beam is scattered by a tilted specimen.


7. Artefacts3. Stray radiation peaks, secondary fluorescence


EDX spectrum from an amorphous Ni-Nb film on a Cu TEM grid.Cu peak present even though the beam passes through the middle of a grid square.

7. Artefacts3. Stray radiation peaks, secondary fluorescence


4. Si fluorescence peak

Si internal fluorescence peak in a spectrum from pure C obtained with a Si(Li) detector.Williams and Carter p 569

7. Artefacts


5. Coherent bremsstrahlung

7. Artefacts

Two or three small peaks at low energy, which can be mistaken for low Z elements, e.g. Si or S.

Appear in crystalline materials when the beam is at a zone axis.


6. Rough or bent specimens

7. Artefacts

If the surface is rough, then the angle at which the beam hits the specimen is different from the angle that the specimen is tilted to.

This changes the absorption length, and if the specimen is very rough (SEM) or bent (TEM), it may obscure the direct line from the point at which the beam hits the specimen to the detector.


4. Quantitative Energy dispersive X-ray spectroscopy


Quantitative analysis

In qualitative analysis, we are just interested in finding the elements present in our sample and getting a rough idea of how much of each is present.

This can be done just by looking at and identifying the peaks in the X-ray spectrum.

In quantitative analysis, we want to measure the proportion of each element present as accurately as possible, by measuring the areas under the X-ray peaks.


1. Background subtraction and peak integration1a. Measure background on either side of peak

This is the simplest and most obvious method:

Measure the background intensity in a window on either side of the peak of interest, and linearly interpolate under the peak to find the background.

It relies on the background being linear (which is often not the case due to absorption, and the background is often curved at low energies).

It also relies on there being some background with no other peaks nearby, and no peak overlap.

It is simple and reliable, and can be done by hand.



1. Background subtraction and peak integration1a. Measure background on either side of peak

Background subtraction by averaging background measured in two windows on either side of peak.There must be no other peaks near the background windows. Most useful for WDX.


Use Kramers relation to model the background:

! I! =!

where! E! =! X-ray energy! E0! =! beam energy! Z! =! atomic number! k! =! constant

1b. Background modelling

€

k Z E −E0( )E

1. Background subtraction and peak integration


Goldstein p 372Background subtraction by bremsstrahlung plus absorption by specimen.

1. Background subtraction and peak integration1b. Background modelling


1c. Fourier filtering


The background is slowly varying, and thus contains mostly low frequencies.

The peaks are sharp, and thus contain high frequencies.

So:

Fourier transform the spectrum, remove the low frequencies, and back transform.

The result is a spectrum without the background.


1d. Top hat filtering


This is similar to Fourier filtering.

The method is to convolute the spectrum with a top hat filter.

This gives approximately the second differential of the spectrum, with some smoothing.

This removes the background completely if it is linear and sloping, but not if it is curved.

The method works well, and is used in some commercial X-ray spectrometers, such as those from Link (now Oxford) .


Background subtraction by top hat filtering.The original spectrum is convoluted with a top hat filter.

1. Background subtraction and peak integration1d. Top hat filtering



When using top hat filtering:

To find peak areas, standard peaks that have been filtered in the same way are needed for each element .

A multiple least-squares fitting method is then used to decompose the experimental filtered spectrum into fractions of each filtered standard peak.

1d. Top hat filtering


2. Converting peak areas to concentrations2a. Standards (Castaing)

Once the background has been subtracted and the areas of the X-ray peaks measured, it is now necessary to convert these into elemental concentrations.

Historically, this was first done by Castaing.

It is difficult to predict the X-ray intensity that will be emitted from a given alloy directly, so Castaing used a standard of known composition.


If I is the X-ray intensity and Ci the concentration of element i , then:

where K is a sensitivity factor that takes into account the difference between the generated and measured X-ray intensities for the standard and the unknown specimen.

K depends on:

Z! - The atomic number of all the elements in the specimen

A! - The absorption of X-rays in the specimen

F! - The amount of fluorescence within the specimen.

As a result these are known as “ZAF” corrections.

The original method, as described, suffers from the need for standard specimens for each element of interest.

€

CiCi( std )

= K IiIi ( std )

2. Converting peak areas to concentrations2a. Standards (Castaing)


2b. Cliff-Lorimer ratio technique

2. Converting peak areas to concentrations

This technique was originally developed for TEM, where specimens are thin and absorption and fluorescence corrections are small.

Nowadays, the absorption and fluorescence corrections are included as well.

The above equation is now rewritten:

where A and B are two elements in the unknown alloy.

kAB is called the Cliff-Lorimer k factor or just the "k-factor".

It is not a constant, but is related to the atomic number correction factor (Z).

Note that no standards are needed.

€

CACB

= kABIAIB


Since measuring k factors for every pair of elements would be tedious, they are measured with respect to one element - usually Si.

Si was originally chosen because many minerals contain Si, and its K edge has a high enough energy to be detected on the Be window detectors then available (c.f. oxygen, the other obvious choice).

Then:

To work out the ZAF corrections (and background modelling), the sample composition needs to be known.

But, this is what we are trying to determine.

Hence, an iterative approach is needed.

€

kAB = kASikBSi

2. Converting peak areas to concentrations2b. Cliff-Lorimer ratio technique


3. Doing quantitative analysis

Quantitative analysis works only if:

The sample is of uniform composition over the area that the beam spreads to, plus adjacent areas that the X-rays pass through;

The sample is flat and oriented at the angle given to the program (i.e., the surface is not rough);

All of the elements in the specimen are considered by the program;

The program only looks at one peak (e.g., K, L or M) per element.

2b. Cliff-Lorimer ratio technique


4a. Random errors

4. Errors in peak area

Generally, random errors are around ±1 at%.

At best, with long counting times, ±0.1 at% may be possible.

Hence, all (except possibly the first) decimal place can be ignored when measuring compositions.

Random errors can be estimated, as shown above.

To get an idea of the random errors, analyse the same area a few times, and analyse similar areas in other parts of the specimen.


4b. Systematic errors

4. Errors in peak area

Systematic errors cannot be estimated. Examples of systematic errors are:

Incorrect k-factors (Z correction), which are calculated and not measured

Incorrect absorption and fluorescence correction because the specimen surface is either rough or not uniform.

Systematic errors are usually greater than random errors.

To overcome systematic errors, compare the composition of an unknown area with an adjacent area of known composition.

Such comparisons are much more accurate than absolute measurements, as many systematic errors cancel.


5. Practical limitations

Probe size: how big is it really? Contamination?

Secondary fluorescence: peaks from Cu grid, Si substrate, etc

X-rays & ions in column: measure hole count

Crystalline specimens: stay away from zone axes



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