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FYS4340 Summary lecture 3 Energy dispersive X-ray analysis November 19th 2015 Energy dispersive X-ray spectroscopy (EDS) Introduction and basic physics [W&C chap. 4.1-4.2] Instrumentation [W&C chap. 32] Quantification

  1. FYS4340 Summary lecture 3 Energy dispersive X-ray analysis November 19th 2015

  2. Energy dispersive X-ray spectroscopy (EDS) • Introduction and basic physics [W&C chap. 4.1-4.2] • Instrumentation [W&C chap. 32] • Quantification and spectrum imaging [W&C chap. 33-35] • Spatial resolution [W&C chap. 36] • Fultz & Howe chapter 5.6 + 5.7

  3. Electron beam – sample interaction W&C

  4. Energy transfer processes The main energy transfer processes are: • Brehmsstrahlung • Single electron excitations • Collective excitations (plasmons) The first two processes are observed both in energy dispersive X- ray spectroscopy (EDS) and in electron energy loss spectrscopy (EELS). The last process is only observed in EELS.

  5. Brehmsstrahlung The change in trajectory is caused by an acceleration of the electron. The spectrum of the photons generated is given by the Fourier transform of a(t) for the electron. F&H

  6. Brehmsstrahlung Kramer’s cross section for production of bremsstrahlung Single bremsstrahlung event Several events Many events W&C F&H

  7. Single electron excitations 1: Incident 2: The atom is left electron transfers in an excited state energy to a with a core hole. «core» electron of the atom, which exits the sample. 3b:…or by 3a: The atom can relax to the ground emitting an state either by Auger-electron emitting a photon (characteristic X- ray )…

  8. Nomenclature Atomic shell Main quantum Orbital quantum Total spin Spectroscopic number n number l quantum number notation j 1s 1 0 +1/2, -1/2 K 2s 2 0 +1/2, -1/2 L 1 2p 1/2 2 1 1/2 L 2 2p 3/2 2 1 3/2 L 3 3s 3 0 +1/2, -1/2 M 1 3p 1/2 3 1 1/2 M 2 3p 3/2 3 1 3/2 M 3 3d 3/2 3 2 3/2 M 4 3d 5/2 3 2 5/2 M 5

  9. More on nomenclature Siegbahn notation is most commonly used to name the transitions generating X-rays. However, this can get quite complicated as seen in the figure on the left. The International Union of Pure and Applied Chemistry (IUPAC) recommends an alternative system that is simpler, but unfortunately not widely in use. W&C

  10. R. Jenkins et al. X-Ray Spectrometry 20 (3), 149-155 (1991).

  11. Copper K lines

  12. Copper K lines E b (K) = -8979 eV E b (L 3 ) = -933 eV E b (L 2 ) = -952 eV E b (M 2,3 ) = -76 eV L 3 -> K transition (K α 1 ) E=h n = E b (L 3 )- E b (K) = 8.046 keV L 2 -> K transition (K α 2 ) E=h n = E b (L 2 )- E b (K) = 8.027 keV M 2,3 -> K transition (K b ) E=h n = E b (M 2,3 )- E b (K) = 8.903 keV

  13. Threshold/critical energy In order to generate X-rays, the electron beam must have an energy E 0 larger than the critical energy E c of the process. Usually not a problem in TEM E 0 > 100 keV; E c < 20 keV BUT: with C s correctors, low voltage operation has become more common. 60 keV, 40 keV, even down to 30 keV. For heavy elements this may limit which characteristic X-rays are generated

  14. Ionization cross section Non-relativistic (Bethe) cross section for ionization • E 0 : energy of electrons • E c : critical energy of excitation • E 0 / E c : Overvoltage

  15. The fluorescence yield The probability for generating a characteristic X-ray is given by the fluorescence yield w The probability of generating an Auger electron is the 1- w. F&H

  16. The detector and electron/hole-pair generation • Characteristic X-rays are generated in the specimen and enter the detector • There, they generate a number of electron/hole-pairs depending on their energy • The electron/hole-pairs are separated by an applied bias, and the current measured W&C

  17. The detector and electron/hole-pair generation • Historically, the most common detectors have been the Si(Li) detectors • The so-called Silicon-drift detectors (SDD) have been used for SEM for quite a while, and are becoming more common also for TEM • The detectors are usually cooled to avoid – diffusion of dopants in the strong applied bias – thermal noise • Si(Li) detectors are usually cooled to LN 2 temperatures (-196  C) • SDD detectors can make do with only Peltier cooling (~-30  C) W&C

  18. Windows • Detectors that are cooled to LN 2 temperature «need» to be protected from contamination • Water, hydrocarbons • A «window» is used for protection • Beryllium, thin polymer, thin polymer with support • But is the window transpararent «enough»? W&C

  19. Detector-microscope interface W&C

  20. It may be necessary to tilt the sample towards the detector to avoid shadowing. But this also has drawbacks.

  21. Spurious and system X-rays • Spurious X-rays from the specimen, but not the region of interest • System X-rays from the sample holder, specimen support grid, microscope itself (Cu, Fe) W&C

  22. Example: LaNbO4 doped with Sr

  23. Absorption and fluorescence in the sample • The X-rays generated in the primary event must travel through the specimen to reach the detector • The longer the path, the greater the likelihood of absorbtion … • …and fluorescence • Might skew the ratio of element A and B X-rays detected • TEM samples are thin • Absorption is mainly a problem for low Z elements (e.g. O) • Fluorescence is rarely a problem at all • But still: be aware of these effects! W&C

  24. Detector artefacts • Escape peaks • Internal fluorescence • Sum peaks • Energy resolution

  25. Escape peaks • The detector determines the photon energy by measuring the charge pulse from the electron- hole pairs generated • Some times, fluorescence occurs in the detector, and a Si K  photon is generated • This photon can leave the detector, taking with it some of the energy that «should» have gone into making electron-hole pairs • The detector then sees a smaller charge pulse, which is interpreted as a lower energy of the incoming photon giving a peak at E-1.74 keV • Usually a small effect, but be aware when counting for a long time W&C

  26. Internal fluorescence • The reverse of the previous problem • Incoming X-rays can excite the Si atoms in the detector (dead layer) making a Si K  • If this photon enters the «active» region of the detector, it will be detected A small Si K  peak appears in the • spectrum • Usually a small effect, but be aware when counting for a long time W&C

  27. Sum peaks Two photons enter detector with small  t E=E 1 EDS detector E=E 2 Detector «sees» one photon with E=E 1 +E 2 Mainly a problem when count rates are very high (>> 10 kcps). Some K  sum May be mistaken for another element peaks

  28. Peak overlap, energy resolution • Typical energy resolution is ~130 eV • Measured as FWHM of Mn K  • You may easily see only one peak where in reality there are many

  29. WDS vs EDS • Uses a diffraction grating (crystal) to select X-rays with particular energy (wavelength) • Braggs law • Wavelength dispersive, in stead of energy dispersive • Excellent energy resolution • Low background, no detector artefacts • Good for light elements • Serial detection • Movable parts • Low effective detection angle

  30. Quantification from EDS spectra • How to get from a spectrum to composition • Assumptions usually made in EDS in TEM • Cliff-Lorimer k-factor method • Limits of the CL-method and the assumptions made • Statistical errors Williams & Carter chapter 35 30

  31. The thin film approximation In the SEM In the TEM 31 F&H

  32. The Cliff-Lorimer equations Binary system 𝑑 𝐵 + 𝑑 𝐶 = 1 𝑑 𝐵 𝐽 𝐵 𝑑 𝐶 = 𝑙 𝐵𝐶 𝐽 𝐶 𝑙 𝐵𝐶 = 𝑑 𝐵 𝐽 𝐶 𝑑 𝐶 𝐽 𝐵 1 = 𝑑 𝐶 𝐽 𝐵 = 𝑙 𝐶𝐵 𝑙 𝐵𝐶 𝑑 𝐵 𝐽 𝐶 Ternary system 𝑑 𝐵 + 𝑑 𝐶 + 𝑑 𝐷 = 1 𝑑 𝐶 𝐽 𝐶 𝑑 𝐷 = 𝑙 𝐶𝐷 𝐽 𝐷 𝑙 𝐵𝐷 = 𝑙 𝐵𝐶 𝑙 𝐶𝐷 32 F&H

  33. k-factors are not constants 33 W&C

  34. 34 Sheridan (1989)

  35. k-factors are not constants Depend on: • Acceleration voltage • Detector • Analysis conditions • Background subtraction • Peak-integration k-factors are a sensitivity factor for the particular system. For the best accuracy you the k-factors must be determined for the particular experimental setup. Usually not done today, calculated k-facors used in stead. Less reliable (+/- 20%) 35

  36. Limits to the thin film approximation 36 F&H

  37. Limits to the thin film approximation 37 F&H

  38. Background removal – simple fitting 38 W&C

  39. Background removal – modeling 39 W&C

  40. Peak integration vs modeling • Simply integrating the peak intensity and subtracting the background works well in many cases • But what about peak overlap? • The integration would add the two peaks together • Inaccurate results 40 W&C

  41. Peak integration vs modeling 41

  42. Peak integration vs modeling • In stead, model the known peaks e.g. with Gaussian funtions • Look at the residual • Are there unexplained discrepancies? • Perhaps another element is present? 42 W&C

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