Analytical Electron Microscopy

Transcription

1 Analytical Electron Microscopy Walid Hetaba Fritz-Haber-Institut der MPG MPI für Chemische Energiekonversion W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

2 1 Introduction 2 EDX 3 EELS 4 Conclusion W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

3 Introduction Analytical Electron Microscopy Imaging Diffraction Spectrometry Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

4 Introduction Mode of Operation Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

5 EDX Introduction to EDX Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

6 EDX Introduction to EDX Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

7 EDX Fluorescence Yield Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

8 Detectors EDX-Setup Detector area, collection angle SuperX (ChemiSTEM): 4 detectors Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

9 Detectors EDX Detectors Dead Time Live Time Clock Time Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

10 Detectors EDX Signal Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

11 Qualitative Analysis EDX-Spectra Cu from System Be for low background sample holder W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

12 Qualitative Analysis EDX-Spectra W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

13 Qualitative Analysis EDX-Spectra W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

14 Qualitative Analysis EDX-Maps W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

15 Qualitative Analysis EDX-Maps W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

16 Quantitative Analysis Cliff-Lorimer Ratio Technique C A /C B = k AB I A /I B k AB... Cliff-Lorimer factor C A + C B = 1 For thin specimen, absorption can be neglected k AB either measured using standards or calculated W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

17 Quantitative Analysis ζ-factor Method ρt = ζ A I A /C A C A /C B = (I A ζ A )/(I B ζ B ) ζ-factors either measured using standards or calculated For both techniques absorption correction (ZAF) possible W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

18 Electron Energy Loss Spectrometry EELS Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

19 Electron Energy Loss Spectrometry EELS Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

20 Electron Energy Loss Spectrometry Williams, Carter: Transmission Electron Microscopy - A Textbook for Materials Science, Springer 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

21 Electron Energy Loss Spectrometry Hetaba: Fine Structure and Site Specific Energy Loss Spectra of NiO, Diploma Thesis, TU Wien 2011 Schaffer et al., Phys. Rev. B, 79, (R), 2009 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

22 Electron Energy Loss Spectrometry NiO TiO 2 Cond. A Cond. B Cond. C Intensity [arb. u.] Energy Loss [ev] states / ev O p x O p y O p z Exp E - E F [ev] Hetaba: Fine Structure and Site Specific Energy Loss Spectra of NiO, Diploma Thesis, TU Wien 2011 Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

23 Classical Scattering Theory Elastic vs. inelastic scattering Differential scattering cross section dσ/dω to describe scattering Elastic Scattering Transfer of momentum Transfer of kinetic energy No change of internal energy of particle and target Inelastic Scattering Transfer of momentum Transfer of energy Internal energy of target changed W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

24 Elastic vs. Inelastic Scattering Schattschneider, Werner, Hébert: Lecture Notes Electron Beam Techniques for Nanoanalysis, TU Wien 2007 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

25 Elastic Scattering Classical scattering p 0 = p 1 + p 2 E 0 = p2 0 2m = p2 1 2m + p2 2 2M E = p2 2 2M = 4mM (M+m) 2 E 0 4 m M E 0, with m M Demtröder: Experimentalphysik 1, Springer 2013 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

26 Elastic Scattering Rutherford scattering dσ/dω = f (q) 2, f (q)... scattering factor f (q) proportional to FT [V (r)], V (r)... atomic potential Coulomb potential yields Rutherford cross section: dσ/dω = 4γZ 2 a 2 0 q4, q = 2k 0 sin(θ/2) W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

27 Elastic Scattering Egerton: Electron energy-loss spectroscopy in the electron microscope, Plenum Press 1996 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

28 Elastic Scattering Rutherford scattering dσ/dω = f (q) 2, f (q)... scattering factor f (q) proportional to FT [V (r)], V (r)... atomic potential Coulomb potential yields Rutherford cross section: dσ/dω = 4γZ 2 a 2 0 q4, q = 2k 0 sin(θ/2) Unscreended potential Overestimates elastic scattering at small θ (large b) W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

29 Elastic Scattering Yukawa potential Screened potential: V (r) = (Ze/4πɛ 0 r) exp(r/r 0 ) dσ dω = 4γ2 Z 2 1 a0 2k4 0 (θ 2 +θ0 2)2 Characteristic scattering angle: θ 0 = (k 0 r 0 ) 1 Screening radius: r 0 = a 0 Z 1/3 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

30 Elastic Scattering Schattschneider, Werner, Hébert: Lecture Notes Electron Beam Techniques for Nanoanalysis, TU Wien 2007 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

31 Elastic Scattering Diffraction and channelling effects Bragg scattering in crystals Modifies scattering cross section Channelling effects: redistribution of electron flux inside crystal Elastic scattering changes probabilites for inelastic scattering W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

32 Elastic Scattering Schattschneider, Werner, Hébert: Lecture Notes Electron Beam Techniques for Nanoanalysis, TU Wien 2007 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

33 Elastic Scattering Diffraction and channelling effects Bragg scattering in crystals Modifies scattering cross section Channelling effects: redistribution of electron flux inside crystal Elastic scattering changes probabilites for inelastic scattering W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

34 Inelastic Scattering Inelastic differential scattering cross section { } dσ i dω = 4γ2 Z 1 1 a0 2q4 [1+(qr 0 ) 2 ] 2 q 2 = k 2 0 (θ2 + θ 2 E ) θ E = E/(γm 0 v 2 ), characteristic inelastic scattering angle θ 0 = (k 0 r 0 ) 1 θ E < θ < θ 0 : dσ/dω θ 2 θ > θ 0 : dσ/dω θ 4 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

35 Inelastic Scattering Egerton: Electron energy-loss spectroscopy in the electron microscope, Plenum Press 1996 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

36 Quantum Mechanical Description Double differential scattering cross section W i f = 2π Ψ f ˆV Ψ i 2 dv f δ ( ) E Ψf E Ψi dj = dσ(e, Ω) j i 2 σ E Ω = ( ) 2π 4 m 2 k f k i i p i f ψ f f ˆV i ψ i 2 δ ( E f E i E ) W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

37 Models for the DDSCS Single plane wave ψ i,f (r) = 1 (2π) 3/2 exp[ik i,f r] 2 σ E Ω = 4γ2 k f 1 a0 2 k i Q i p 4 i f j f e iq R j i 2 δ ( E f E i E ) Dynamic Form Factor (DFF): S(Q, E) = i p i f e iq R j f j 2 σ E Ω = 4γ2 k f 1 a0 2 k i S(Q, E) Q 4 i 2 δ ( E f E i E ) W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

38 Models for the DDSCS Superposition of plane waves ψ i = a 1 k 1 + a 2 k 2, a a 2 2 = 1 2 σ E Ω = 4γ2 a0 2 [ k f k i a S(Q, E) + a Q ] ] [ +2R a 1 a2 1 S(Q, Q 2 Q 2 Q, E) Q 4 S(Q, E)+ Mixed Dynamic Form Factor (MDFF): S(Q, Q, E) = i f f eiq R i i e iq R f δ ( E f E i E ) W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

39 Models for the DDSCS k 0 θ θ' k' k G I A A R[A 1A 2 exp i(φ 1 φ 2 )] q q' 0 G A B C Demtröder: Experimentalphysik 1, Springer 2013 Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

40 Models for the DDSCS Bloch waves 2 σ E Ω = 4γ2 k f a0 2 k i x j,j,l,l X jlj l (x) S g,g,h,h g hg h x (Q,Q,E) Q 2 Q 2 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

41 MDFF for Crystals MDFF for Crystals S(Q, Q, E) = i λ λ 4π(2l + 1) ν mm λλ µµ LMS L M S (2L + 1)(2L + 1)(2λ + 1)(2λ + 1) Y µ λ (Q/Q) j λ (Q) νnjls Y µ λ (Q /Q ) j λ (Q ) νnjl S ( ) ( L λ l L λ ) ( ) ( l L λ l L λ ) l M µ m M µ m ( ) ( ) l 1 ( 1) M+M (2j + 1) 2 j l 1 2 j m S j z m S j z j z (D ν LMS ) (D ν L M S )δ(e f E i E) Löffler: Study of real space wave functions with electron energy loss spectrometry, PhD Thesis, TU Wien 2013 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

42 WIEN2k Simulations Features of WIEN2k Density Functional Theory, Kohn-Sham equation Electronic properties of crystal Electron density Bandstructure DOS TELNES.3 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

43 Density Functional Theory Kohn-Sham equation Ĥ = 2 2 N i 1 4πɛ 0 2 Ri N i,j M i 2 2 N i 2 r i m e e 2 Z i R i r j + 1 8πɛ 0 N i j e 2 r i r j + 1 8πɛ 0 N i j e 2 Z i Z j R i R j Ĥ KS = ˆT + ˆV H + ˆV xc + ˆV ext = 2 2 i + e2 2m e 4πɛ 0 i ρ( r ) r r d r + ˆV xc + ˆV ext W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

44 Calculated Spectra NiO G20 GGA LDA+U B3PW91 PBE0 G20 mbjlda Intensity [a.u.] Intensity [a.u.] Energy Loss [ev] Energy Loss [ev] Hetaba: Fine Structure and Site Specific Energy Loss Spectra of NiO, Diploma Thesis, TU Wien 2011 Hetaba et al., Phys. Rev. B 85, , 2012 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

45 Applications Oxidation State W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

46 Applications Oxidation State W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

47 Applications Crystallographic Structure - Coordination Egerton: Electron energy-loss spectroscopy in the electron microscope, Plenum Press 1996 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

48 Applications EMCD Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

49 Applications Channelling effects states / ev O p x O p y O p z TELNES E - E F [ev] Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

50 Applications Channelling effects Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 Hetaba et al., Micron 63, 15-19, 2014 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

51 Applications Channelling effects Intensity [arb. u.] Cond. A Cond. B Cond. C Energy Loss [ev] θ θ' k 0 k G k' 0 q q' G A B C Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 Hetaba et al., Micron 63, 15-19, 2014 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

52 Applications Channelling effects Cond. A Cond. B Cond. C O p x O p y O p z Intensity [arb. u.] states / ev Energy Loss [ev] E - E F [ev] Hetaba: The Theory and Application of Inelastic Coherence in the Electron Microscope, PhD Thesis, TU Wien 2015 Hetaba et al., Micron 63, 15-19, 2014 W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

53 Conclusion EDX and EELS complimentary techniques Understanding of theory necessary for interpretation Lots of different properties accessible Analytical Electron Microscopy versatile tool W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

54 Literature Useful books (linked) Analytical electron microscopy in general: Williams, Carter: Transmission Electron Micrsocopy - A Textbook for Materials Science Everything about EELS: Theory: Egerton: Electron energy-loss spectroscopy in the electron microscope Schattschneider: Fundamentals of Inelastic Electron Scattering Schattschneider: Linear and Chiral Dichroism in the Electron Microscope W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

55 Literature Links to cited articles and EELS Databases Schaffer et al., Phys. Rev. B, 79, (R), 2009 Hetaba et al., Phys. Rev. B 85, , 2012 Hetaba et al., Micron 63, 15-19, 2014 Demtröder: Experimentalphysik 1, Springer 2013 PhD thesis Löffler PhD thesis Hetaba EELS Database: Gatan EELS.info, EELS-Atlas EELS Data Base W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23

56 Acknowledgments M. Willinger R. Farra G. Algara-Siller R. Schlögl P. Schattschneider S. Löffler M. Stöger-Pollach A. Hütten W. Hetaba (FHI, MPI-CEC) Analytical Electron Microscopy / 23