Lecture 4 - Spectroscopy

1. Lecture 4 - Spectroscopy Analytical Electron Microscopy (AEM), Energy Dispersive Spectroscopy (EDS), Electron Energy Loss Spectroscopy (EELS),, EDS-EELS Spectrum Imaging, Energy Filtered TEM (EFTEM)

36. What we are mostly interested in measuring by EELS in the TEM is inelastic electron scattering Elastic scattering Phonon scattering (few meV) Quasi-elastic Thermal diffuse scattering Plasmon excitation (10-30 eV) Collective excitation of conduction electrons Valence electron excitation Inner-shell ionization Core losses Absorption edges Most useful for: Composition Bonding

37. Gatan parallel-collection electron energy-loss spectrometer (PEELS)Attaches to base of camera/viewing chamber of TEMAdditional ports for scintillator and PMT for on-axis STEM detector

38. Gatan electron energy-loss spectrometer (EELS)Old-style serial-collection; newer parallel-collection (PEELS)Latest PEELS (Enfina) uses a CCD detector instead of a photodiode array

39. Gatan parallel-collection electron energy-loss spectrometer (PEELS)curved pole piece entrance/exit faces; double-focusing 90° magnetic prism

40. Information from energy-loss spectrum

41. Nomenclature for inner-shell ionization edges

42. L3 and L2 white lines for 3d transition metals Transitions from 2p to unfilled 3d states Similar M5 and M4 white lines for Lanthanides (unfilled 4f states)

43. Anatomy of an electron energy-loss spectrum(TiC, 100kV, b = 4.7 mrad, a = 2.7 mrad, t/l = 0.52)from Disko in Disko, Ahn, Fultz, Transmission EELS in Materials Science, TMS, Warrendale PA, 1992 I0 zero loss or elastic peak low-loss region <40eV, dominated by bulk plasmon at 23.5 eV Carbon K edge, 285 eV, 1s shell electron excited Titanium L23 edge, 455 eV, 2p shell

44. Low-loss regionPlasmons and thickness determination • Plasmons are collective excitations of valence electrons • Lifetime 10-15 s, localized to <10 nm • Ep = hwp/2p = h/2p (ne2/e0m)0.5 h is Planck’s constant, n is free-electron density, • e and m are electron charge and mass, 0 is permittivity of free space • Characteristic scattering angles are small <1 mrad • Thickness (t) determination: • t/l = ln (IT/I0) • l is inelastic scattering mean free path (average distance between scattering events) • and is inversely proportional to scattering cross section • IT is total intensity, I0 is zero-loss intensity • (nm) = 106 F (E0/Em) / ln (2b E0/Em) E0 is in kV, b in mrad, F is a relativistic correction factor ~1 for E0 < 300 kV, Em is the average energy loss in eV Em = 7.6 Z0.36 where Z is average atomic number F = {1 + (E0/1022)} / {1 + (E0/511)2} Java script at Nestor’s web site http://tpm.amc.anl.gov/NJZTools/NJZTools.html

47. Quantitative microanalysis with core-loss EELS(TiC spectrum from Disko)Isolation of core-loss intensities that scale with atomic concentrationsAtomic fractions or atoms/area with use of atomic scattering cross sections Least squares fit of form AE-r to model background ~50 eV before each edge Extrapolated to higher energy losses Integrated counts above extrapolated background give shaded core-edge intensities in energy windows width D IC(D,b) = NCsC(E0,D,b) I(D,b) NC carbon atoms/area IL(D,b) = total spectrum intensity up to an energy loss D sC = partial ionization cross section at incident beam energy E0 up to a maximum scattering angle b (collection semiangle) No need for I0(D,b) if use element ratios: NC/NTi = {IC(D,b) / ITi(D,b)} {sTi(E0,D,b) / sC (E0,D,b)}

48. Quantitative microanalysis with core-loss EELSSelection and measurement of acquisition parameters The sample must be thin ! Typically t/l 0.3 to 0.5 The collection angle b should be set to an appropriate value wrt the characteristic scattering angle  = E/2E0 (E0 should be relativistic) Typically b ~ few times  (few mrad) If b is too large: S/B decreases (just extra background) Include diffracted beams But b should be larger than the incident beam convergence semi-angle  Joy proposed a correction to reduce s(D,b). Reduction factor R = [ln{1+(/)2} b] / [ln{1+(b/)2} ]

49. Background fitting Background comes from tails of (multiple) plasmons and core edges at lower energy losses (especially outer-shells) Inverse power law, IB = AE-r Least squares fit to ln(I) versus ln(E) A and r valid over a limited energy range r is typically between 2 and 5, and decreases for increases in t, b, and E For E < ~200 eV, AE-r commonly fails to give a good fit and extrapolation Working with 3dTM borides in the early 80’s we developed the log-poly background fitting for B. It is the most useful and reliable alternative to AE-r. Polynomials do not extrapolate sensibly - do not use them. Usually a quadratic, sometimes a third order polynomial, will cope with the small curvature in ln(I) versus ln(E) Mike Kundmann wrote a log-poly function for Gatan’s EL/P software. JK Weiss included it in ESVision as nth order power law fit (select n).

50. Cross sectionsCalculated (Egerton, Rez), parameterized (Joy)Measured from standards, similar to k-factors in EDS Egerton’s SIGMAK and SIGMAL used in EL/P (Fortran) code listed in Egerton’s book Hydrogenic model but works well A white-line correction is also selectable in EL/P, but best to define D beyond WLs EL/P v3 also has Rez’s Hartree-Slater models (includes M edges)