Charles Lyman Lehigh University, Bethlehem, PA 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) x E Collect entire spectrum at each pixel Scan y Incident electron probe “x-y-energy” data cube 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 X-ray map x y Energy 200 400 600 800 1000 1200 1400 1600 1800 2000 Energy x y X-ray Spectrum Specimen: polished granite Data courtesy of David Rohde

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 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

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 Elemental Maps of a SiC/Si3N4 ceramic Short Acquisition Time (3 maps, 250K pixels) = 50s Carbon Nitrogen Oxygen RGB composite Courtesy John Hunt, Gatan 3

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) This is an introductory slide. More in-depth discussion is given further on in this presentation.

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

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

EFTEM Elemental Mapping: Example 2 BF image N Ti O Al Si 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

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 spectrum image acquisition 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 EDX STEM EELS DF Specimen x y E Courtesy John Hunt, Gatan

EFTEM spectrum image acquisition 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 y x E image at E1 image at E2 image at Ei . Courtesy John Hunt, Gatan

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 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 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

Masashi Watanabe Lehigh University 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

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 (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)

Nb map in Ni-base superalloy original MSA-processed Nb(at%) Nb(at%) 1 1 100 nm Multivariate Statistical Analysis identify specific features in the spectrum image reduce random noise Courtesy M. Watanabe

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) 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

Practical Operation of PCA eigenanalysis or SVD original data score loading nE nE nE nX D T PT line profile PCA = nX * nY nX x nY nX x nY nE eigenvalues 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 matrix NiKa FeKa CrKa g’ NiKa NbLa AlKa TiKa M23C6 CrKa spectrum image: 256x256x1024 dwell time: 50 ms 20 eV/channel 100 nm Courtesy M. Watanabe Reconstructed spectra

Results of PCA 1 #1: average #2: M23C6 scree plot #3: g’ Score Loading STEM-ADF Score Loading #1: average Cr Ka Ni Ka 200 nm #2: M23C6 scree plot Cr Ka Ni Ka #3: g’ Fe Ka Ni Ka Noise Cr Ka Al Ka Ti Ka Courtesy M. Watanabe

Results of PCA 2 #4: absorption #5: noise scree plot #6: noise Score STEM-ADF Score Loading #4: absorption Cr Ka Ni Ka Ni La 200 nm #5: noise scree plot #6: noise Noise Courtesy M. Watanabe

Compositional fluctuations below 2 wt% can be revealed Comparison of Maps Al Nb wt% wt% 2 1.5 Original wt% wt% 2 1.5 Reconstructed 100 nm Compositional fluctuations below 2 wt% can be revealed Courtesy M. Watanabe

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)

Application to Fine Precipitates in Steel Burke et al. J. Mater. Sci. (in press) STEM ADF Thickness Fe Cr 50nm 10 20 85 95 1 5 (nm) (wt%) (wt%) Ni Mn Cu Mo 8 2 3 0.5 1 (wt%) (wt%) (wt%) (wt%) Too noisy

Application of MSA to Fine Precipitates Burke et al. J. Mater. Sci. (in press) STEM ADF Thickness Fe Cr 50nm 10 20 85 95 1 5 (nm) (wt%) (wt%) Ni Mn Cu Mo 8 1.5 3 0.8 1 (wt%) (wt%) (wt%) (wt%)

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 Spectrum Imaging Mining the data cube 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)