Spectrum Imaging

1. 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. 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

3. 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

4. Quantitative Phase Analysis • Sum spectra for pixels within box • Enough counts for quatitative analysis Specimen: polished granite Data courtesy of David Rohde

5. 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)

6. A few Words about EFTEM Elemental Maps without Employing Spectrum Imaging

7. EFTEM: In-Column and Post-Column Energy Filters Omega Filter Gatan Imaging Filter (GIF) From Williams and Carter, Transmission Electron Microscopy, Springer, 1996

8. 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

9. 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)

10. 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

11. 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

12. 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

13. 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

14. STEM & EFTEM EELS Spectrum Imaging

15. 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

16. 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

17. 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

18. 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

19. 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

20. X-ray Spectrum Imaging

21. 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

22. 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

23. 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)

24. 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

25. 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

26. 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

27. 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. 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

29. 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

30. 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

31. 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

32. 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)

33. 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

34. 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%)

35. 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)

36. 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)