1. Electron Beam Analysis (EPMA, SEM-EDS) Warren Straszheim, PhD EPMA, Ames Lab, 227 Wilhelm SEM-EDS, MARL, 23 Town Engineering wesaia@iastate.edu 515-294-8187 wesaia@iastate.edu With acknowledgements to John Donovan of the University of Oregon

2. Instrumental Techniques Excite measure characteristic response quantify by comparison to standards

3. Bulk or microanalysis Can excitation be focused? Can detector be focused?

4. Electron beam microanalysis Excitation: focused electron beam Sample interactions  secondary electrons  backscattered electrons  auger electrons  cathodoluminescence  absorbed current  X-rays

5. Precise x-ray intensities High spectral resolution Sub-micron spatial resolution Matrix/standard independent Accurate quantitative chemistry Electron-Sample Interactions

6. characteristic emissions Be and heavier elements background (bremsstrahlung) X-rays

7. X-ray Lines - K, L, M K  X-ray is produced due to removal of K shell electron, with L shell electron taking its place. K  occurs in the case where K shell electron is replaced by electron from the M shell. L  X-ray is produced due to removal of L shell electron, replaced by M shell electron. M  X-ray is produced due to removal of M shell electron, replaced by N shell electron.

8. Ranges and interaction volumes It is useful to have an understanding of the distance traveled by the beam electrons, or the depth of X-ray generation, i.e. specific ranges. For example: If you had a 1 um thick layer of compound AB atop substrate BC, is EPMA of AB possible?

9. Differences between SEM and EPMA Many shared components Resulting from intent - imaging vs. analysis Stability (higher for EPMA) Current capability (higher for EPMA) Spatial resolution (higher for SEM) via smaller spot and limited aberration correction attached analyzer (EDS vs. WDS)

10. EDS vs. WDS technology – solid state crystal vs. wavelength spectrometer Resolution~126 eV vs 20eV P/B ratio Detection limit count rate limitations 500 kcps in total vs. 70 kcps/element parallel vs. serial operation

11. Spectral Resolution WDS provides roughly an order of magnitude higher spectral resolution (sharper peaks) compared with EDS. Plotted here are resolutions of the 3 commonly used crystals, with the x- axis being the characteristic energy of detectable elements. Note that for elements that are detectable by two spectrometers (e.g., Y L  by TAP and PET, V K  by PET and LIF), one of the two crystals will have superior resolution (but lower count rate). Reed, 1995, Fig 13.11, in Williams, Goldstein and Newbury (Fiori volume)

12. Spectrometer Efficiency The intensity of a WDS spectrometer is a function of the solid angle subtended by the crystal, reflection efficiency, and detector efficiency. Reed (right) compared empirically the efficiency of various crystals vs EDS. However, the curves represent generation efficiency (recall overvoltage) and detection efficiency. Reed, 1996, Fig 4.19, p. 63 Reed suggests that the WDS spectrometer has ~10% the collection efficiency relative to the EDS detector. How to explain the curvature of each crystal’s intensity function? At high Z, the overvoltage is presumably minimized (assuming Reed is using 15 or 20 keV). Low Z equates larger wavelength, and thus higher sin , and thus the crystal is further away from the sample, with a smaller solid angle.

13. Effect of voltage Excitation volume goes as V 1.7 Available X-ray lines 25kV 5um 15kV 2.5um 10kV 1.3um 5kV 0.4um

14. Typical steel spectrum, 15 kV

15. Lines available at low kV Note overlap of V, Cr, Mn, and Fe. Also, O has its line at 0.53 keV.

16. Effect of current spatial resolution reduced with high currents greater sensitivity with high currents detectability precision/repeatability

17. Overlap considerations Smaller issue for WDS – effects background choices Deconvolution option for EDS if statistics permit Statistics become problematic if trace element on major element background

18. EDS Overlap: S, Mo, Hg HgS stdLine TypeWt%Wt% SigmaAtomic % SK series13.380.1449.15 HgM series86.620.1450.85 Total100.00 Stoichiometry is on- the-mark - in this case.

19. WDS “overlap”: HgS, PbS, Mo Note that signal drops to background in between most peaks. Mo tail interferes with S.

20. Rare earths by EDS and WDS Pr peak fits between Ce L  and L  peaks. Er Dy Tb

22. EDS Atomic fraction CompoundFeYCePrNdGdTbDyHoErLu D5 Y2Fe1788.4911.51 B4 Ce2Fe1789.0510.95 B5 Pr2Fe1788.3911.61 C1 Nd2Fe1788.8111.19 C2 Gd2Fe1790.129.88 C5 Tb2Fe1786.2113.79 D1 Dy2Fe1788.4311.57 D2 Ho2Fe1787.5912.41 D3 Er2Fe1784.6915.31 E2 Lu2Fe1789.7710.23 2/19 = 10.53%

23. Suitable samples solid/rigid stable under beam conductive (while under beam) nonconductive samples can be coated with C or metal (e.g., Au, Pt, Ir) (coating obscures features and elements but only a little)

24. Samples include Metals Geologic samples Ceramics Poly mers Experimental materials

25. Quantitative Considerations Homogeneous (within excitation volume) Thick (enclosing interaction volume); therefore, problems with layered samples Known geometry (preferably “flat” compared to excitation volume; thus, polished); therefore problems with rough samples Be smart with construction (e.g., glass vs. Si) Standards collected each time vs. Standardless and normalization

26. Matrix effects Z-A-F or Phi-Rho-Z corrections accounting for penetration depth, absorption, secondary fluorescence Accuracy depends on well known curvature. Alternatively, need standard in region for better results.

27. Range of Quantitation 100% down to 0.05% (500 ppm) EDS, 0.001% (10s of ppm) WDS Limited by statistics, differentiation from background More counts help!

28. Mapping and Line-scans Point analysis are most sensitive to concentration differences (30s/point) Line scans are next (500 ms/pixel) Mapping is least sensitive (12 ms/pixel) Graphics convey much information quickly (i.e., a picture is worth a thousand words)

29. Digital image showing regions of analysis and line-scan

30. Mg portion of overlapped peak

31. Ge portion of overlapped peak

32. Line-scan using typical windows Ge-Mg overlap causes problems

33. Line-scan using deconvolution Ge contribution is stripped from Mg profile

34. Mapping using deconvolution

36. EDS-WDS comparison

37. “Harper’s Index” of EPMA 1 nA of beam electrons = 10 -9 coulomb/sec 1 electron’s charge = 1.6x 10 -19 coulomb ergo, 1 nA = 10 10 electrons/sec Probability that an electron will cause an ionization: 1 in 1000 to 1 in 10,000 ergo, 1 nA of electrons in one second will yield 10 6 ionizations/sec Probability that ionization will yield characteristic X-ray (not Auger electron): 1 in 10 to 4 in 10. ergo, our 1 nA of electrons in 1 second will yield 10 5 x-rays. Probability of detection: for EDS, solid angle < 0.03 (1 in 30). WDS, <0.001 ergo 3000 x-rays/sec detected by EDS, and 100 by WDS. These are for pure elements. For EDS, 10 wt% = 300 X-rays; 1 wt% = 30 x-rays; 0.1 wt % = 3 x-ray/sec. ergo, counting statistics are very important, and we need to get as high count rates as possible within good operating practices. From Lehigh Microscopy Summer School

38. Raw data needs correction This plot of Fe Ka X- ray intensity data demonstrates why we must correct for matrix effects. Here 3 Fe alloys show distinct variations. Consider the 3 alloys at 40% Fe. X-ray intensity of the Fe-Ni alloy is ~5% higher than for the Fe-Mn, and the Fe-Cr is ~5% lower than the Fe- Mn. Thus, we cannot use the raw X-ray intensity to determine the compositions of the Fe-Ni and Fe-Cr alloys. (Note the hyperbolic functionality of the upper and lower curves)

40. n = principal quantum number and indicates the electron shell or orbit (n=1=K, n=2=L, n=3=M, n=4=N) of the Bohr model. Number of electrons per shell = 2n 2 l = orbital quantum number of each shell, or orbital angular momentum, values from 0 to n –1 Electrons have spin denoted by the letter s, angular momentum axis spin, restricted to +/- ½ due to magnetic coupling between spin and orbital angular momentum, the total angular momentum is described by j = l + s In a magnetic field the angular momentum takes on specific directions denoted by the quantum number m <= ABS(j) or m = -l… -2, -1, 0, 1, 2 … +l Rules for Allowable Combinations of Quantum Numbers:  The three quantum numbers (n, l, and m) that describe an orbital must be integers.  "n" cannot be zero. "n" = 1, 2, 3, 4...  "l" can be any integer between zero and (n-1), e.g. If n = 4, l can be 0, 1, 2, or 3.  "m" can be any integer between -l and +l. e.g. If l = 2, m can be -2, -1, 0, 1, or 2.  "s" is arbitrarily assigned as +1/2 or –1/2, but for any one subshell (n, l, m combination), there can only be one of each. (1 photon = 1 unit of angular momentum and must be conserved, that is no ½ units, hence “forbidden transitions) No two electrons in an atom can have the same exact set of quantum numbers and therefore the same energy. (Of course if they did, we couldn’t observably differentiate them but that’s how the model works.) One slide Schrödinger Model of the Atom

41. Origin of X-ray Lines for K and L Transitions