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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). Incident electron probe. Scan. x. y. E. “x-y-energy” data cube. Spectrum Imaging (SI). - PowerPoint PPT Presentation
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PASI - Electron Microscopy - Chile
1Lyman - Spectrum Imaging
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)
PASI - Electron Microscopy - Chile
2Lyman - Spectrum Imaging
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
x
E
Scan
y
Incidentelectron
probe
“x-y-energy” data cube
PASI - Electron Microscopy - Chile
3Lyman - Spectrum Imaging
Elemental Maps from Data Cube
Data courtesy of David Rohde
Specimen: polished granite0
200400
600800
10001200
14001600
18002000
Energy
x
y
x
y
Energy
ElementalX-ray map
X-ray Spectru
m
PASI - Electron Microscopy - Chile
4Lyman - Spectrum Imaging
Quantitative Phase Analysis
Sum spectra for pixels within box » Enough counts for quatitative analysis
Data courtesy of David Rohde
Specimen: polished granite
PASI - Electron Microscopy - Chile
5Lyman - Spectrum Imaging
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 (E)
PASI - Electron Microscopy - Chile
6Lyman - Spectrum Imaging
A few Words about EFTEM
Elemental Maps without
Employing Spectrum Imaging
PASI - Electron Microscopy - Chile
7Lyman - Spectrum Imaging
EFTEM: In-Column and Post-Column Energy Filters
Omega Filter Gatan Imaging Filter (GIF)
From Williams and Carter, Transmission Electron Microscopy, Springer, 1996
PASI - Electron Microscopy - Chile
8Lyman - Spectrum Imaging
RGB compositeOxygenNitrogenCarbon
Elemental Maps of a SiC/Si3N4 ceramic
Short Acquisition Time (3 maps, 250K pixels) = 50s
Energy-Filtered TEM (EFTEM) Element Maps - Not Spectrum Images
Courtesy John Hunt, Gatan
PASI - Electron Microscopy - Chile
9Lyman - Spectrum Imaging
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 * *E/E
– Cc = chromatic aberration constant– = the acceptance angle of the objective aperture– E = range of energies contributing to the image
» Blurr will be especially large for thick, high-Z specimens.» Reduce blurr by:
– Using a small energy window (E) – Select energy loss E by changing the gun voltage (vary kV)
PASI - Electron Microscopy - Chile
10Lyman - Spectrum Imaging
EFTEM Elemental Mapping
Courtesy John Hunt, Gatan
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
PASI - Electron Microscopy - Chile
11Lyman - Spectrum Imaging
O AlTi
Aluminum
Superimpose three color layers to form RGB composite
Titanium
Oxygen
6 layer metallization test structure
3 images each around:
O K edge:@ 532 eVTi L23 edge: @ 455 eVAl K edge: @ 1560 eV
EFTEM Elemental Mapping: Example 1
1 µm
Courtesy John Hunt, Gatan
PASI - Electron Microscopy - Chile
12Lyman - Spectrum Imaging
EFTEM Elemental Mapping: Example 2
O
N
Si
Ti
Al
BF image
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.
Color composite of all 5 elemental maps displayed on the left,showing the device construction.
Courtesy John Hunt, Gatan
PASI - Electron Microscopy - Chile
13Lyman - Spectrum Imaging
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
PASI - Electron Microscopy - Chile
14Lyman - Spectrum Imaging
STEM & EFTEM EELS Spectrum Imaging
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15Lyman - Spectrum Imaging
STEM spectrum image acquisition
STEM spectrum image» acquired by stepping a focused
electron probe from one pixel to the next
EDXSTEM
EELSDF
Specimen
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
x
y
ECourtesy John Hunt, Gatan
PASI - Electron Microscopy - Chile
16Lyman - Spectrum Imaging
yx
E
image at E1
image at E2
image at Ei
.
.
.
.
.
.
.
.
.
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
PASI - Electron Microscopy - Chile
17Lyman - Spectrum Imaging
STEM EELS spectrum imaging
EELS STEM SI acq. at 200keV (cold FEG)» xy: 50*29 pixels» E: 1024 channels (75eV, =0.5eV)» Acquisition time: ~ 5 minutes» Processing time: ~ 5 minutes
Courtesy John Hunt, Gatan
PASI - Electron Microscopy - Chile
18Lyman - Spectrum Imaging
Quantitative EFTEM Spectrum Imaging
EFTEM Spectrum Image» 2.9 nm resolution» Si-L23 : 75-150eV
{3eV 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
PASI - Electron Microscopy - Chile
19Lyman - Spectrum Imaging
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
PASI - Electron Microscopy - Chile
20Lyman - Spectrum Imaging
X-ray Spectrum Imaging
PASI - Electron Microscopy - Chile
21Lyman - Spectrum Imaging
Mining the SI Data Cube
Masashi Watanabe Lehigh University
Nb(wt%)
1.5
0
Nb(wt%)
1.5
0
Multivariate Statistical Analysis of X-ray Spectrum Images
PASI - Electron Microscopy - Chile
22Lyman - Spectrum Imaging
X-ray Spectrum Imaging
Collection of SIHuge data set e.g. 256x256 = 65,536 spectra each spectrum 1024 channels cannot analyze manuallyNoisier spectrum for XEDS than EELSMany possible variables composition, thickness, multiple phases
100 nm
NiK
TiKAlK CrK
FeKWhat can we do?
Specimen: Ni-based superalloy
Courtesy M. Watanabe
PASI - Electron Microscopy - Chile
23Lyman - Spectrum Imaging
Multivariate Statistical Analysis
Problems for which MSA may be useful 1. Investigation of data of great complexity2. Handling large quantities of data3. Simplifying data and reducing noise4. Identifying specific features (components) can be interpreted in useful ways E.R. Malinowski, Factor Analysis in Chemistry, 3rd ed. (2002)
Multivariate statistical analysis (MSA) is a group of processing techniques to:
(1) identify specific features from large data sets (such as a series of XEDS and EELS spectra, i.e. spectrum images) and
(2) reduce random noise components efficiently in a statistical manner.
PASI - Electron Microscopy - Chile
24Lyman - Spectrum Imaging
Nb map in Ni-base superalloy
Nb(at%)
1
0
Nb(at%)
1
0100 nm
original MSA-processed
Multivariate Statistical Analysis• identify specific features in the spectrum image• reduce random noise
Courtesy M. Watanabe
PASI - Electron Microscopy - Chile
25Lyman - Spectrum Imaging
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
PASI - Electron Microscopy - Chile
26Lyman - Spectrum Imaging
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
PASI - Electron Microscopy - Chile
27Lyman - Spectrum Imaging
Practical Operation of PCA
nXnY
nE
spectrum image
PCAD
nE
nX x nY
= T
PT
*
nX x nY
nE
D = T * PT D: original data matrix (nX x nY x nE)T: score matrix (related to magnitude)PT: loading matrix (related to spectra)
line profile
nEnX
original data score loading
eigenanalysisor SVD
eigenvalues
Courtesy M. Watanabe
PASI - Electron Microscopy - Chile
28Lyman - Spectrum Imaging
Spectrum Image of Ni-Base Superalloy
100 nm• spectrum image: 256x256x1024• dwell time: 50 ms• 20 eV/channel
matrix
’
M23C6
NiK
CrK FeK
NiK
CrK
TiKAlK
NbL
Reconstructed spectraCourtesy M. Watanabe
PASI - Electron Microscopy - Chile
29Lyman - Spectrum Imaging
Results of PCA 1
0 10 20
10–2
10–1
100
Component
Eig
enva
lue
STEM-ADF
200 nm
LoadingScore
scree plot
#1: average
#2: M23C6
#3: ’
Ti K
Al K
Ni KFe K
Cr K
Cr K
Ni K
Cr K Ni K
Courtesy M. Watanabe
Noise
PASI - Electron Microscopy - Chile
30Lyman - Spectrum Imaging
Results of PCA 2
0 10 20
10–2
10–1
100
Component
Eig
enva
lue
STEM-ADF
200 nm
LoadingScore
scree plot
#4: absorption
#5: noise
#6: noise
Ni K
Ni L
Cr K
Noise
Courtesy M. Watanabe
PASI - Electron Microscopy - Chile
31Lyman - Spectrum Imaging
Comparison of Maps
Alwt%
2
0
wt%
2
0
wt%
1.5
0
wt%
1.5
0
Nb
100 nm Compositional fluctuations below 2 wt% can be revealed
Reconstructed
Original
Courtesy M. Watanabe
PASI - Electron Microscopy - Chile
32Lyman - Spectrum Imaging
Application to Fine Precipitates
Irradiation-induced hardening in low-alloy steelis caused by fine-scale precipitationAverage precipitate size: 2-5 nmX-ray mapping in VG HB 603 300 keV STEM
100 nm
BF-STEM image ADF-STEM image
Burke et al. J. Mater. Sci. (in press)
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33Lyman - Spectrum Imaging
Application to Fine Precipitates in Steel
(wt%)
Thickness
10 20(nm)
STEM ADF Fe Cr
Ni Mn Cu
50nm 85 95 5
0 8 2 3 0 0.5 1
(wt%)(wt%)(wt%)
(wt%) (wt%)Mo
0
1
Too noisy
Burke et al. J. Mater. Sci. (in press)
PASI - Electron Microscopy - Chile
34Lyman - Spectrum Imaging
Application of MSA to Fine Precipitates
(wt%)
Thickness
10 20(nm)
STEM ADF Fe Cr
Ni Mn Cu
50nm 85 95 5
0 8 1(wt%)
(wt%) (wt%)Mo
0
1
1.5 3(wt%)
0 0.8(wt%)
Burke et al. J. Mater. Sci. (in press)
PASI - Electron Microscopy - Chile
35Lyman - Spectrum Imaging
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: M&M 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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36Lyman - Spectrum Imaging
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)