Ultra-high Resolution Electron Microscopy- Diving into the World of Atoms. Knut W. Urban Jülich, Germany. I see you...

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1 Ultra-high Resolution Electron Microscopy- Diving into the World of Atoms Knut W. Urban Jülich, Germany I see you...

2 Real Intuitive SrTiO 3

3 Electrons see matter in their own way They are not interested in atoms but in potential Electrons are following quantum mechanics We are used and embossed to think in terms of light optics Images show Electron Currents and Electron-Wave Phase shifts Interpretation requires a brain understanding quantum mechanics: The computer.

4 The principles of atomic imaging

5 ψ () r = exp(2 πik r) 0 ρ r = ρi r δ r r ( ) ( ) ( ) i i V ( r ) unknown atomic structure

6 ψ () r = exp(2 πik r) 0 V ( r ) Stationary states of electrons inside the crystal (300 kev)? 232,900 kms -1 ; m=1.59m 0 ; 78 % c; relativistic: Dirac equation - low-angle approximation - Schrödinger form with relativistically corrected E, m, λ 2 2 h 2 * * 2mc 0 + eu + E V( r) ψ ( r) = 0 with E = E 2m 2 mc eu ( r ) exp( 2 igr ) V V π = g g ( 2 ) 0 +

7 ψ () r = exp(2 πik r) 0 ( j ) ( j ) ( j ) g g ( 0 ) ψ () r = ε C exp2πi k + g r j V ( r ) Eigenvalue problem: Solution in terms of lattice-periodic Bloch functions 2 2 h 2 * * 2mc 0 + eu + E V( r) ψ ( r) = 0 with E = E 2m 2 mc eu ( r ) exp( 2 igr ) V V π = g g ( 2 ) 0 +

8 ψ () r = exp(2 πik r) 0 ( j ) ( j ) ( j ) g g ( 0 ) r k g r ( ) ψ () = ε C exp2πi + j V r faster E kin k = 1 λ k 2 j=1 j=2

9 ψ () r = exp(2 πik r) 0 ( j ) ( j ) ( j ) g g ( 0 ) r k g r ( ) ψ () = ε C exp2πi + j V r oscillation faster E kin k = 1 λ k 2 j=1 j=2 ξ = k 1 k (1) (2) Extinction distance

10 ψ () r = exp(2 πik r) 0 ( j ) ( j ) ( j ) g g ( 0 ) ψ () r = ε C exp2πi k + g r j V ( r ) ( ) = ( )exp( 2πi ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ψ g gr ε k g r g g j exit-plane wave function (Fourier-)sum of plane waves

11 ψ () r = exp(2 πik r) 0 V ( r ) ( ) = ( )exp ψ ()( 2πi r = ) = ψ ( g)exp2πi ( j) C ( j) { 2πi gr( } d ( j) g 0 g+ ) g g j ψ r ψ g gr ε k g r g exit-plane wave function Object of optics

12 ψ () r = exp(2 πik r) 0 V ( r ) ( ) = ( )exp ψ ()( 2πi r = ) = ψ ( g)exp2πi ( j) C ( j) { 2πi gr( } d ( j) g 0 g+ ) g g j ψ r ψ g gr ε k g r g exit-plane wave function Object of optics

13 ( ) = ( )exp( 2πi ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ψ g gr ε k g r g g j exit-plane wave function Lens Object of optics aberrations { χ g } ψ ( g)exp 2πi ( ) χ( g) = C λ g + Zλg S 2 (aberration function) Image

14 ( ) = ( )exp( 2πi ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ψ g gr ε k g r g g j exit-plane wave function Lens Object of optics aberrations { χ g } ψ ( g)exp 2πi ( ) χ( g) = C λ g + Zλg S 2 Image spherical aberration defocus

15 ( ) = ( )exp( 2πi ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ψ g gr ε k g r g g j exit-plane wave function Lens Object of optics aberrations { χ g } ψ ( g)exp 2πi ( ) χ( g) = C λ g + Zλg S 2 Image

16 Spherical aberration Object P Lens Gaussian image plane R Point spread function χ max max S λ λ g ( g) = C g + Z g R = = C g + Z g χ λ λ aberration disk 4 S 2

17 Spherical aberration in light microscopy Object P Lens Gaussian image plane R 0 Point spread function χ max max S λ g λ 3 3 R = = C g + Z g quasi ideal image

18 Aberration-corrected electron microscopy 2 Δ B = 0 (Laplace s equation) B Lens I Always converging

19 The Rose Corrector (H. Rose, Optik 85, 19 (1990)) diverging lens Hexapoles M. Haider, H. Rose, K. Urban et al. Nature 392, 768 (1998)

20 What is it what we see? formation of contrast

21 Amplitude contrast Phase manipulated contrast

22 Amplitude contrast

23 The principles of imaging ψ ( r) = exp(2 πin r/ λ) Object Lens 0 V ( r) ρ r = ρ r δ r r i i ( ) ( ) ( ) i unknown structure exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration corrected instrument aberration-induced phase shifts ψ ( g)exp 2πi ( ) { { χ g } } χ( g) 0 Image I r ( ) ψ 2

24 Amplitude contrast in atomic resolution imaging (channelling) sample thickness ( ) = ( )exp( 2πi ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ψ g gr ε k g r Lens g g j Image C.L. Jia, K. Tillmann

25 Electron diffraction channelling high Z low Z ~ ξ, Z

26 Video sample thickness ξ = (1) (2) k k V Z n Extinction distance Sr 38 Lens Ti 22 O 8 I ( r ) ψ 2 SrTiO 3 [011] Image C.L. Jia, K. Tillmann

27 Amplitude contrast Phase manipulated contrast

28 Phase-manipulated contrast sample thickness very thin sample little localisation at atoms poor (amplitude) contrast Lens Image

29

30 Phase-manipulated contrast sample thickness there is phase information but forming 2 ψ phase information is lost Lens { χ g } ψ ( g)exp 2πi ( ) χ( g) = C λ g + Zλg S Image manipulating phase of individual plane waves exploiting aberration function (Scherzer phase contrast) ~ Zernike technique

31 Phase-manipulated contrast ( ) = ( j) C ( j) exp 2πi( ( j) + g 0 ) ψ r ε k g r exit-plane wave function g j Lens ( { } j ) ( ) ( ) C j ( j g 0 ) ( ) ( ) ψ r = exp 2πχ i g ε exp 2πi k + g r g ( ) ( 4 2 g... S ) j 1 1 ( j) ( j) ( j) { C g Z } Cg ( 0 ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Image

32 Phase-manipulated contrast (Scherzer s theory) 1 1 ( j) ( j) ( j) { C g Z } Cg ( 0 ) ( ) ( 4 2 g... S ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Otto Scherzer, 1949 Image

33 Phase-manipulated contrast (Scherzer s theory) C S = const. Contrast sin χ( g) 1 Z g d S S S = - = = ( 4 ) 3 C λ S 1 2 ( 3 C λ ) 2 3 g 1 S S sin χ(g) 0-1 g S χ( g) = C λ g + Zλg S 2 g I g 1 1 ( j) ( j) ( j) { C g Z } Cg ( 0 ) ( ) ( 4 2 g... S ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Image

34 Phase-manipulated contrast (Scherzer s theory) image object P R + point spread function χ 3 3 R= max = max Cλ g + Zλg 3d S g S

35 Phase-manipulated contrast (Scherzer s theory) image object P R + point spread function χ 3 3 R= max = max Cλ g + Zλg 3d S g S

36 Phase-manipulated contrast (C.L. Jia and M. Lentzen) 1 1 ( j) ( j) ( j) { C g Z } Cg ( 0 ) ( ) ( 4 2 g... S ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Image

37 Phase-manipulated contrast (C.L. Jia and M. Lentzen) C S, opt =+ λ ( 3 4 ) g 1 I Contrast sin χ( g) 1 Z opt = 16 9 ( 2 ) λ g 1 I 0 g S g Ig R opt g I M. Lentzen et al., Ultramicroscopy 92, 233 (2002) ( j) ( j) ( j) { C g Z } Cg ( 0 ) ( ) ( 4 2 g... S ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Image

38 Phase-manipulated contrast (C.L. Jia and M. Lentzen) image object P R + point spread function χ 3 3 R= max = max C 1 S λ g + Zλg 2 d g

39 Phase-manipulated contrast (C.L. Jia and M. Lentzen) C S, opt =+ λ ( 3 4 ) g 1 I Z opt = 16 9 ( 2 ) λ g 1 I R opt g I Weakening each other Phase image Amplitude image

40 Phase-manipulated contrast (C.L. Jia and M. Lentzen) C S, opt = ( 3 4 ) λ g 1 I Contrast sin χ( g) 1 Z opt = ( 2 ) λ g 1 I 0 g S g Ig R opt g I C.L. Jia, M. Lentzen & K. Urban, Science 299, 870 (2003) ( j) ( j) ( j) { C g Z } Cg ( 0 ) ( ) ( 4 2 g... S ) ψ r = exp 2πi λ + λ + ε exp 2πi k + g r g j Image

41 Phase-manipulated contrast (C.L. Jia and M. Lentzen) C S, opt = ( 3 4 ) λ g 1 I Z opt = ( 2 ) λ g 1 I R opt g I Enhancing each other Phase image Amplitude image

42 Phase-manipulated contrast and amplitude contrast (C.L. Jia and M. Lentzen) Negative spherical aberration BaTiO SrTiO 33 The NCSI technique (negative spherical aberration imaging) BaTiO 3 Positive spherical aberration

43 strontium titanium oxygen SrTiO 3 C.L. Jia

44 N N GaN L. Houben

45 N N Si 3 N 4 [001], Z. Zhang & U.Kayser, Uni Ulm nm

46 Sr Ti O Objective lens current Sample thickness [110]

47 Objective lens current Sample thickness

48 Objective lens current Sample thickness

49 Our eyes cannot be trusted in the quantum mechanical world

50 Our brain treats visual impressions always as light optical elements The computer is the brain that comprehends quantum mechanics

51 Quantum-mechanical and optical image calculation

52 Backward: From images to structure ψ () r ρ r = ρ r δ r r i i ( ) ( ) ( ) i Object Lens V ( r) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

53 Backward: From images to structure ψ () r ρ r = ρ r δ r r i i ( ) ( ) ( ) i Object Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) V ( r) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

54 Reconstruction of exit-plane wave function Focal series: r Z χ( g)= C λ g + λg S 2 Z -12 Z -11 Z -10Z-9 Z -8 Z -7 Z -6 Z -5 Z -4 Z -3 Z -2 Z -1 Z 0 Z +1 Z +2 Z +3 Z +4 Z +5

55 Reconstruction of exit-plane wave function by TrueIMAGE TM Start wave function Ψ j Calculate image I nj Experimental image I nj Ψ j+1 =Ψ j + δψ j Correction δψ j A. Thust, TrueIMage, FEI Eindhoven W.M. Coene, A. Thust, M. Op de Beeck & D. Van Dyck, Ultramicroscopy 64, 109 (1996) Differences δι nj Ψ N 2 r S = δi ( g) dg 2 1 N n= 1 n

56 Backward: From images to structure ψ () r ρ r = ρ r δ r r i i ( ) ( ) ( ) i Object Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) V ( r) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

57 Backward: From images to structure ψ () r ρ r = ρ r δ r r i i ( ) ( ) ( ) i Object Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) V ( r) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

58 Backward: From images to structure Multi-slice solution of Dirac equation ψ () r (Cowley&Moody) ρ r = ρ r δ r r i i ( ) ( ) ( ) i Object Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) V ( r) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) first guess model { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

59 The challenge in atomic dimensions ρ ρ i r = r r r δ i i ( ) ( ) ( ) Object Lens Image Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) ( ) V r exit-plane wave function ψ () r = ψ ( g)exp2πi { gr} d g g aberration-induced phase shifts ψ ( g)exp 2πi χ ( g) ( ) I r ψ { } χ C λ Zλ S ( g) = 4 g + 2 g l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

60 The challenge in atomic dimensions? ρ r = ρ r δ r r i i ( ) ( ) ( ) V ( r) i Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

61 The challenge in atomic dimensions?? ρ r = ρ r δ r r i i ( ) ( ) ( ) V ( r) i Lens Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) { { } χ( g) = C λ g + Zλg +... } S 2 Image I ( r ) ψ 2

62 The challenge in atomic dimensions Solution Dirac equation (Cowley&Moody) ρ r = ρ r δ r r i i ( ) ( ) ( ) V ( r) i Lens Image Exit-plane wave function reconstruction (Coene, Thust, van Dyck Kirkland et al.) Ultra-high resolution does not produce images, exit-plane wave function ψ () r = ψ ( g)exp2πigr dg g aberration-induced phase shifts ψ ( g)exp 2πi χ( g) it produces an atomic model on the computer I ( r ) { { } χ( g) = C λ g + Zλg +... ψ 2 } S 2

63 How to display / use the results? Z -12 Z -6 Z 0 1) Projected potential approximation 2) Select similar image from series Z +4

64 How to display / use the results? Z -12 Z -6 Z 0 1) Projected potential approximation 2) Select similar image from series Z +4

65 How to display / use the results? 1) Projected potential approximation 2) Select similar image from series 3) Measurements in computer model

66 How good is the original data? The weak point: The CCD-Camera Problem of the Stobbs factor A. Thust, Phys. Rev. Lett. 102, (2009)

67

68 Stobbs factor Modulation transfer function (A. Thust 2009) CCD Chip f (units of f Nyquist )

69 Stobbs factor Modulation transfer function (A. Thust 2009) CCD Chip 1 1 Real MTF f (units of f Nyquist )

70 Matching Simulation/Experiment A. Thust, Phys. Rev. Lett. 102, (2009) SrTiO 3

71 Resolution & precision

72 Rayleigh-resolution and precision Rayleigh Δ

73 Rayleigh-resolution and precision resolution information limit: corrected microscope Δ= pm

74 Rayleigh-resolution and precision 2σ = 1-5 pm Gaussians Precision ~ signal-to-noise ratio resolution information limit: corrected microscope Δ= pm A. J. Den Dekker et al. J. Microscopy 194, 95 (1999) A. J. Den Dekker et al. Ultramicroscopy 104, 83 (2005) S. Van Aert et al. Ultramicroscopy 104, 107 (2005) L. Houben, A. Thust, K. Urban, Ultramicroscopy 106, 200 (2006).

75 Summary of Part I: 1. Aberration corrected lenses 2. Atomic contrast by amplitude and phase 3. NCSI technique 4. Inverting the imaging problem 5. CCD camera MTF has to be measured 6. Precision/Resolution

76 Three examples: Diving into the real world of atoms

77 Three examples: Diving into the real world of atoms 90 tilt grain boundary in YBa 2 Cu 3 O 7

78 90 o Tilt boundary in YBa 2 Cu 3 O 7 (L. Houben, A. Thust) amplitude phase

79 90 o Tilt boundary in YBa 2 Cu 3 O 7 (L. Houben, A. Thust) nm nm 44 pm amplitude phase a=0.382 nm

80 Detailed quantitative measurements

81 Precision Ba Y Ba Ba Ba Ba Regression analysis (2x2σ); 95 % 4pm σ σ

82 Magnetocardiography using superconducting SQUIDs SQUID

83 Σ3 {111} twin boundary in BaTiO3

84 Σ3 {111} twin boundary in BaTiO 3 C.L. Jia 2 nm Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

85 Σ3 {111} twin boundary in BaTiO 3 C.L. Jia Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

86 Σ3 {111} twin boundary in BaTiO 3 C.L. Jia 0 occupancy 1 Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

87 Point spread R conventional P aberration corrected

88 Point spread P R 0 conventional aberration corrected

89 BaTiO 3 Intensity (arbitrary units) BaO 100 % O 100 % 50 % bulk bulk 0.8 C.L. Jia, M. Lentzen & K. Urban, Science 229, 870 (2003) C.L. Jia & K. Urban, Science 303, 2001(2004) Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

90 Σ3 {111} twin boundary in BaTiO 3 C.L. Jia Mean occupancy: 0.68 ± 0.02 Number of columns Oxygen occupancy Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

91

92 Measurement of vertical atomic distances C.L. Jia Σ3 {111} twin boundary 0.4 nm nm TiO 6 Ti 2 O 9 cubic hexagonal corner to edge sharing oxygen octahedra nm Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

93 Measurement of the vertical atomic separations Ti-Ti separation: Ti-Ti nm + 35 ± 5 pm BaO plane Ba-Ba separation: nm - 17 ± 5 pm W.T. Geng, Y.J. Zhang & A.J. Freemann Phys. Rev. B 63, R (2006) Ti - Ti: nm Ba-Ba: nm

94 Ferroelectric domain walls in PZT

95 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l PbZr 0.2 Ti 0.8 O 3 (PZT) Zr/Ti + Pb + O - T C T > T c (centrosymmeric tetragonal) T < T c Pb + Zr/Ti + O - P S (non-centrosymmeric tetragonal)

96 PbZr 0.2 Ti 0.8 O 3 (PZT) Prepared by PLD at 700 C, MPI Halle SrTiO 3 PbZr 0.2 Ti 0.8 O 3 SrTiO 3 SrTiO 3 I. Vrejoiu, M. Alexe, D. Hesse et al. Advanced Mater. 18, 1657 (2006)

97 Ferroelectric domain walls in Pb(Zr 0.2 Ti 0.8 )O 3 PbO ZT O δ O P S δ Zr/Ti PbO ZT O δ Zr/Ti P S δ O 2 nm C.L. Jia et al. Nature mat. 7, 57 (2008)

98 Ferroelectric domain walls in Pb(Zr 0.2 Ti 0.8 )O Longitudinal Charged P S + P S + Transversal Uncharged

99 Transversal domain wall in Pb(Zr 0.2 Ti 0.8 )O 3 [011] PS P S 0.5 nm 2 a = 0.55 nm

100 Longitudinal domain wall in Pb(Zr 0.2 Ti 0.8 )O 3 P S I Longitudinal charged Geometrical central plane II 1 nm P S

101 Longitudinal domain wall in Pb(Zr 0.2 Ti 0.8 )O 3 c (nm) Domain II Domain I c c a (nm) ±5pm O a Zr/Ti Pb c/a bulk Distance (in units of c)

102 Longitudinal domain wall in Pb(Zr 0.2 Ti 0.8 )O 3 10 c δ (nm) ±5pm atomic δ Zr/Ti δ Zr/Ti δ O δ O O Zr/Ti 80 Domain I Pb P S (μc/cm 2 ) integral/macroscopic Domain II Distance (in units of c)

103 We have learned to see with the eyes of electrons

104 Ernst Ruska-Center for Microscopy and Spectroscopy with Electrons