Spectrum Imaging

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Spectrum Imaging
Charles Lyman Lehigh University, Bethlehem, PA
Based on presentations by John Hunt (Gatan,
Inc.), John Titchmarsh (Oxford University), and
Masashi Watanabe (Lehigh University)
2
Spectrum Imaging (SI)

• Collect entire spectrum at each pixel
• No a priori of specimen knowledge required
• Can detect small amounts of elements in local
  regions of x-y images
• Away from microscope
• Repeatedly apply sophisticated spectrum
  processing
• Mine the data cube for features
• Concept
• Jeanguillaume Colliex, Ultramicroscopy 28
  (1989), 252
• Demonstration
• Hunt Williams, Ultramicroscopy 38 (1991), 47

3
Elemental Maps from Data Cube
Elemental X-ray map
X-ray Spectrum
Specimen polished granite
Data courtesy of David Rohde
4
Quantitative Phase Analysis

• Sum spectra for pixels within box
• Enough counts for quatitative analysis

Specimen polished granite
Data courtesy of David Rohde
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Compositional Maps in TEM/STEM

• Collection by
• STEM X-ray
• Sequentially acquire EDS x-ray spectrum at each
  pixel (original concept)
• Each x-ray entering detector assigned
  x-y-energy tag (Mott Friel, 1999)
• STEM EELS
• Sequentially acquire EELS spectrum at each pixel
• EFTEM (Energy-filtered imaging)
• Sequentially acquire images at specific energies
• One energy window for each energy channel in
  spectrum (DE)

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A few Words about EFTEM Elemental Maps without
Employing Spectrum Imaging
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EFTEM In-Column and Post-Column Energy Filters
Omega Filter
Gatan Imaging Filter (GIF)
From Williams and Carter, Transmission Electron
Microscopy, Springer, 1996
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Energy-Filtered TEM (EFTEM) Element Maps - Not
Spectrum Images
Elemental Maps of a SiC/Si3N4 ceramicShort
Acquisition Time (3 maps, 250K pixels) 50s
RGB composite
Oxygen
Carbon
Nitrogen
Courtesy John Hunt, Gatan
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Energy-Filtering TEM

• Images of only a small range of energies
• Energy window of 1-100eV
• Just above or just below energy-loss edge
• EFTEM compositional mapping
• Elemental maps using multiple energy-filtered
  images
• 2 images to determine background before edge
• Scale background and subtract to obtain elemental
  signal
• 1 image to collect elemental signal (edge above
  background)
• Only one electron energy can be precisely in
  focus
• All other energies will be suffer resolution loss
  (blurring)
• The blurr is given by
• d Cc b DE/E
• Cc chromatic aberration constant
• b the acceptance angle of the objective
  aperture
• DE range of energies contributing to the image
• Blurr will be especially large for thick, high-Z
  specimens.

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EFTEM Elemental Mapping

• Three-Window Method
• Subtract edge background using two pre-edge
  images (dotted line)
• Element concentration proportional to area of
  edge above background (outlined in red)
• Absolute concentration can be determined if
  thickness and elemental cross-sections are known

Courtesy John Hunt, Gatan
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EFTEM Elemental Mapping Example 1
Aluminum
Titanium
6 layer metallization test structure 3 images
each around O K edge _at_ 532 eV Ti L23 edge _at_
455 eV Al K edge _at_ 1560 eV
1 µm
Oxygen
Superimpose three color layers to form RGB
composite
O
Al
Ti
Courtesy John Hunt, Gatan
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EFTEM Elemental Mapping Example 2
N
BF image
Color composite of all 5 elemental maps displayed
on the left,showing the device construction.
Unfiltered bright-field TEM image of
semiconductor device structure and elemental maps
from ionization-edge signals of N-K, Ti-L, O-K,
Al-K, and Si-K.
Courtesy John Hunt, Gatan
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EFTEM detection limits

• Typically 2-5 local atomic concentration of most
  elements
• 1 is attainable for many elements in ideal
  samples
• 10 for difficult specimens that are thick or of
  rapidly varying thickness
• Sensitivity limited by
• Diffraction contrast
• Small number of background windows
• Signal-to-noise
• Thickness
• Artifacts
• If you can see the edge in the spectrum, you can
  probably map it
• EFTEM spectrum image can map lower concentrations
  than the 3-window method
• Better background fits because there are more
  fitting channels

Courtesy John Hunt, Gatan
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STEM EFTEM EELS Spectrum Imaging
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STEM spectrum image acquisition

• The spectrum image data cube is filled one
  spectrum column at a time
• In STEM it is possible to collect x-ray, EELS,
  BF, and ADF simultaneously
• Use of the ADF or SE signal during acquisition
  permits spatial drift correction

• STEM spectrum image
• acquired by stepping a focused electron probe
  from one pixel to the next

EDX
Courtesy John Hunt, Gatan
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EFTEM spectrum image acquisition

• EFTEM spectrum image
• Acquire an image containing a narrow range of
  energies
• The spectrum image data cube is filled one energy
  plane at a time
• Image plane retains full spatial resolution of
  TEM image

Courtesy John Hunt, Gatan
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STEM EELS spectrum imaging

• EELS STEM SI acq. at 200keV (cold FEG)
• xy 5029 pixels
• E 1024 channels (75eV, D0.5eV)
• Acquisition time 5 minutes
• Processing time 5 minutes

Courtesy John Hunt, Gatan
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Quantitative EFTEM Spectrum Imaging

• EFTEM Spectrum Image
• 2.9 nm resolution
• Si-L23 75-150eV3eV steps (1.5 min)
• N-K, Ti-L, O-K 350-650eV
  5eV steps (8 min)
• FEI CM120 BioFilter
• 120keV
• Corrections x-rays, MTF, spatial drift
• Scaled by hydrogenic x-sections

Courtesy John Hunt, Gatan
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STEM vs. EFTEM Spectrum Imaging

• Quantitative elemental mapping
• Both STEM SI and EFTEM SI can do this
• EELS STEM Spectrum Imaging
• Good quality spectra
• All artifacts / instabilities correctable
• Usually safer w/unknowns
• EFTEM Spectrum Imaging
• Fast mapping
• Uncorrected artifacts / instabilities are very
  dangerous
• Very useful for well characterized systems
• Excellent spatial resolution

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X-ray Spectrum Imaging
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Mining the SI Data Cube
Multivariate Statistical Analysis of X-ray
Spectrum Images
Nb(wt)
Nb(wt)
1.5
1.5
0
0

• Masashi Watanabe
• Lehigh University

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X-ray Spectrum Imaging
Specimen Ni-based superalloy
Collection of SI Huge data set e.g. 256x256
65,536 spectra each spectrum 1024 channels
cannot analyze manually Noisier spectrum
for XEDS than EELS Many possible variables
composition, thickness, multiple phases
100 nm
NiKa
AlKa
CrKa
What can we do?
TiKa
FeKa
Courtesy M. Watanabe
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Multivariate Statistical Analysis

• Multivariate statistical analysis (MSA) is a
  group of processing techniques to
• identify specific features from large data sets
  (such as a series of XEDS and EELS spectra, i.e.
  spectrum images) and
• reduce random noise components efficiently in a
  statistical manner.

• Problems for which MSA may be useful
• Investigation of data of great complexity
• Handling large quantities of data
• Simplifying data and reducing noise
• Identifying specific features (components) can be
  interpreted
• in useful ways
• 
  E.R. Malinowski, Factor Analysis in
  Chemistry, 3rd ed. (2002)

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Nb map in Ni-base superalloy
MSA-processed
original
Nb(at)
Nb(at)
1
1
100 nm
0
0

• Multivariate Statistical Analysis
• identify specific features in the spectrum image
• reduce random noise

Courtesy M. Watanabe
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The Data Cloud

• Find greatest variancein data
• x1, x2, x3 are first three channels of spectrum
  or image
• Manipulate matrices
• Principal component analysis finds new axes for
  data cloud that correspond to the largest changes
  in the data
• These few components can represent data

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Principal Component Analysis (PCA)
PCA is one of the basic MSA approaches and can
extract the smallest number of specific features
to describe the original data sets.
The key idea of PCA is to approximate the
original huge data matrix D by a product of two
small matrices T and PT by eigenanalysis or
singular value decomposition (SVD)
D T PT
D original data matrix (nX x nY x nE) T score
matrix (related to magnitude) PT loading matrix
(related to spectra)
Courtesy M. Watanabe
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Practical Operation of PCA
eigenanalysis or SVD
original data
loading
score
nE
nE
nE
nX
D
T
PT
line profile
PCA

nX

nY
nX x nY
nX x nY
eigenvalues
nE
D original data matrix (nX x nY x nE) T score
matrix (related to magnitude) PT loading matrix
(related to spectra)
D T PT
spectrum image
Courtesy M. Watanabe
28
Spectrum Image of Ni-Base Superalloy
matrix
NiKa
FeKa
CrKa
g
NiKa
NbLa
AlKa
TiKa
M23C6
CrKa

• spectrum image
• 256x256x1024
• dwell time 50 ms
• 20 eV/channel

Reconstructed spectra
Courtesy M. Watanabe
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Results of PCA 1
Loading
Score
STEM-ADF
1 average
Ni Ka
Cr Ka
200 nm
2 M23C6
scree plot
Cr Ka
Ni Ka
3 g
Fe Ka
Ni Ka
Cr Ka
Noise
Al Ka
Ti Ka
Courtesy M. Watanabe
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Results of PCA 2
Score
Loading
STEM-ADF
4 absorption
Cr Ka
Ni Ka
Ni La
200 nm
5 noise
scree plot
6 noise
Noise
Courtesy M. Watanabe
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Comparison of Maps
Al
Nb
wt
wt
2
1.5
Original
0
0
wt
wt
2
1.5
Reconstructed
0
0
100 nm
Compositional fluctuations below 2 wt can be
revealed
Courtesy M. Watanabe
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Application to Fine Precipitates
Irradiation-induced hardening in low-alloy
steel is caused by fine-scale precipitation Averag
e precipitate size 2-5 nm X-ray mapping in VG HB
603 300 keV STEM
BF-STEM image
ADF-STEM image
100 nm
Burke et al. J. Mater. Sci. (in press)
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Application to Fine Precipitates in Steel
Burke et al. J. Mater. Sci. (in press)
Thickness
STEM ADF
Fe
Cr
50nm
5
1
20
85
95
10
(wt)
(wt)
(nm)
Ni
Mn
Cu
Mo
1
0
8
2
3
0
0.5
0
(wt)
(wt)
(wt)
(wt)
Too noisy
34
Application of MSA to Fine Precipitates
Burke et al. J. Mater. Sci. (in press)
Cr
Thickness
STEM ADF
Fe
50nm
5
85
95
1
10
20
(nm)
(wt)
(wt)
Ni
Mn
Cu
Mo
1
0
1.5
3
8
0
0.8
0
(wt)
(wt)
(wt)
(wt)
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Some References to MSA Procedures

• Multivariate statistical analysis in general
• S.J. Gould The Mismeasure of Man, Norton, New
  York, NY, (1996).
• E.R. Malinowski Factor Analysis in Chemistry,
  3ed ed., Wiley, New York,
• NY, (2002).
• P. Geladi H. Grahn Multivariate Image
  Analysis, Wiley, West Sussex,
• UK,
  (1996).
• For microscopy applications
• P. Trebbia N. Bonnet Ultramicroscopy 34
  (1990) 165.
• J.M. Titchmarsh S. Dumbill J. Microscopy 184
  (1996) 195.
• J.M. Titchmarsh Ultramicroscopy 78 (1999) 241.
• N. Bonnet, N. Brun C. Colliex Ultramicroscopy
  77 (1999) 97.
• P.G. Kotula, M.R. Keenan J.R. Michael MM 9
  (2003) 1.
• M.G. Burke, M. Watanabe, D.B. Williams J.M.
  Hyde J. Mater. Sci. (in press).
• M. Bosman, M. Watanabe, D.T.L. Alexander, and
  V.J. Keast Ultramicroscopy
• 
  
  (in press)

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Summary

• Spectrum Imaging
• the way serious microanalysis should be done
• Mining the data cube
• MSA is applicable for large data sets such as
  line
• profiles and spectrum images
• The large data sets can be described with a few
• features by applying MSA
• PCA is useful for noise reduction of data sets.
• Be aware -- MSA can provide only hints of
  significant
• features in the data sets (abstract components)