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). Incident electron probe. Scan. x. y. E. “x-y-energy” data cube. Spectrum Imaging (SI).

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Spectrum Imaging

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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)


Spectrum imaging si

Incident

electron probe

Scan

x

y

E

“x-y-energy” data cube

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


Elemental maps from data cube

y

Energy

x

Energy

2000

1800

1600

1400

1200

1000

y

800

600

x

400

200

0

Elemental Maps from Data Cube

Elemental

X-ray map

X-ray Spectrum

Specimen: polished granite

Data courtesy of David Rohde


Quantitative phase analysis

Quantitative Phase Analysis

  • Sum spectra for pixels within box

    • Enough counts for quatitative analysis

Specimen: polished granite

Data courtesy of David Rohde


Compositional maps in tem stem

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)


A few words about eftem elemental maps without employing spectrum imaging

A few Words about EFTEM Elemental Maps without Employing Spectrum Imaging


Eftem in column and post column energy filters

EFTEM: In-Column and Post-Column Energy Filters

Omega Filter

Gatan Imaging Filter (GIF)

From Williams and Carter, Transmission Electron Microscopy, Springer, 1996


Energy filtered tem eftem element maps not spectrum images

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

Carbon

Oxygen

Nitrogen

Courtesy John Hunt, Gatan


Energy filtering tem

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.

    • Reduce blurr by:

      • Using a small energy window (DE)

      • Select energy loss DE by changing the gun voltage (vary kV)


Spectrum imaging

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


Spectrum imaging

EFTEM Elemental Mapping: Example 1

Aluminum

Titanium

6 layer metallization test structure

3 images each around:

O K edge:@ 532 eV

Ti L23 edge:@ 455 eV

Al K edge:@ 1560 eV

1 µm

Oxygen

Superimpose three color layers to form RGB composite

O

Ti

Al

Courtesy John Hunt, Gatan


Spectrum imaging

Ti

O

Al

Si

EFTEM Elemental Mapping: Example 2

BF image

N

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


Eftem detection limits

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


Stem eftem eels spectrum imaging

STEM & EFTEM EELS Spectrum Imaging


Stem spectrum image acquisition

STEM spectrum image

acquired by stepping a focused electron probe from one pixel to the next

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

x

y

Specimen

DF

EELS

E

STEM spectrum image acquisition

EDX

Courtesy John Hunt, Gatan


Eftem spectrum image acquisition

x

y

image at E1

image at E2

.

.

.

.

.

.

.

.

.

image at Ei

E

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


Stem eels spectrum imaging

STEM EELS spectrum imaging

  • EELS STEM SI acq. at 200keV (cold FEG)

    • xy: 50*29 pixels

    • E: 1024 channels (75eV, D=0.5eV)

    • Acquisition time: ~ 5 minutes

    • Processing time: ~ 5 minutes

Courtesy John Hunt, Gatan


Quantitative eftem 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


Stem vs eftem 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


X ray spectrum imaging

X-ray Spectrum Imaging


Mining the si data cube

Mining the SI Data Cube

Multivariate Statistical Analysis of X-ray Spectrum Images

Nb(wt%)

Nb(wt%)

1.5

1.5

Masashi Watanabe

Lehigh University

0

0


X ray spectrum imaging1

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


Multivariate statistical analysis

Multivariate Statistical Analysis

Multivariate statistical analysis (MSA) is a group of processing techniques to:

identify specific featuresfrom large data sets (such as a series of XEDS and EELS spectra, i.e. spectrum images) and

reduce random noisecomponents 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)


Spectrum imaging

Nb map in Ni-base superalloy

MSA-processed

original

Nb(at%)

Nb(at%)

1

1

100 nm

0

0

Multivariate Statistical Analysis

  • identify specific featuresin the spectrum image

  • reduce random noise

Courtesy M. Watanabe


The data cloud

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


Principal component analysis pca

Principal Component Analysis (PCA)

PCA is one of the basic MSA approaches and can

extractthe 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


Practical operation of pca

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


Spectrum image of ni base superalloy

100 nm

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


Results of pca 1

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


Results of pca 2

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


Comparison of maps

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


Application to fine precipitates

Application to Fine Precipitates

Irradiation-induced hardening in low-alloy steel

is caused by fine-scale precipitation

Average 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)


Spectrum imaging

Application to Fine Precipitates in Steel

Burke et al. J. Mater. Sci. (in press)

STEM ADF

Thickness

Fe

Cr

50nm

5

1

95

85

20

10

(wt%)

(wt%)

(nm)

Mo

Cu

Ni

Mn

1

0

0.5

3

8

0

2

0

(wt%)

(wt%)

(wt%)

(wt%)

Too noisy


Application of msa to fine precipitates

Application of MSA to Fine Precipitates

Burke et al. J. Mater. Sci. (in press)

Cr

Thickness

STEM ADF

Fe

50nm

5

1

95

85

20

10

(nm)

(wt%)

(wt%)

Ni

Cu

Mn

Mo

1

3

0

1.5

0.8

0

8

0

(wt%)

(wt%)

(wt%)

(wt%)


Some references to msa procedures

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)


Summary

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)


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