Experimental methods in Physics. Electron Microscopy. Basic Techniques (MEP-I) SEM, TEM

Size: px

Start display at page:

Download "Experimental methods in Physics. Electron Microscopy. Basic Techniques (MEP-I) SEM, TEM"

Bernadette Miller
6 years ago
Views:

1 Experimental methods in Physics Electron Microscopy Basic Techniques (MEP-I) SEM, TEM Advanced Techniques (MEP-II) HR-TEM, STEM Analytical-TEM 3D-Microscopy Spring 2012 Experimental Methods in Physics Marco Cantoni Outline 1. High-Resolution TEM 2. STEM, Analytical EM 3. 3D Microscopy 4. Special Techniques, Trends Spring 2012 Experimental Methods in Physics Marco Cantoni 2

2 High Resolution TEM K. Ishizuka (1980) Contrast Transfer of Crystal Images in TEM, Ultramicroscopy 5,pages L. Reimer (1993) Transmission Electron Microscopy, Springer Verlag, Berlin. J.C.H. Spence (1988), Experimental High Resolution Electron Microscopy, Oxford University Press, New York. Pb Ti O Ti Pb Spring 2012 Experimental Methods in Physics Marco Cantoni High resolution.?! electron at 300keV: v = m/s (0.78 c) = nm diff = 10-3 rad Pb Ti Atomic resolution? Precipitate in a ceramic: PbTiO 3 Spring 2012 Experimental Methods in Physics Marco Cantoni 4

Field with rotational symmetry Lorenz Force : F = -e v ^ B e on optical axis: F = 0 e not on optical axis : deviated optical axis: symmetry axis The objective lens Scherzer 1936: Magnetic lens with

8Å Spring 2012 Experimental Methods in Physics Marco Cantoni 5 Image formation Source FEG Illumination coherent specimen exit wave objective lens Spherical aberration Cs Source: coherent and

3 Field with rotational symmetry Lorenz Force : F = -e v ^ B e on optical axis: F = 0 e not on optical axis : deviated optical axis: symmetry axis The objective lens Scherzer 1936: Magnetic lens with rotational symmetry: Aberration coefficients: C s : spherical C c : chromatical Always positive!! Resolution limit: D res 3/ 4 1/ Cs Example: = nm, C s = 1 mm D res = = 1.8Å Spring 2012 Experimental Methods in Physics Marco Cantoni 5 Image formation Source FEG Illumination coherent specimen exit wave objective lens Spherical aberration Cs Source: coherent and monochromatic Illumination: parallel Sample: thin, nicely prepared (no amorphization), orientation (zone axis) objective lens: aberrations, focus, stability! projection lens system (magnification) image Spring 2012 Experimental Methods in Physics Marco Cantoni 6

4 Image formation Source FEG Illumination coherente Illumination: parallel beam Sample: ( r) 0 exp weak phase object: weak phase object aproximation (WPOA) 2ik r Objective lens: specimen exit wave objective lens Spherical aberration Cs image Abbé s principle transfert function coherent transfer function (CTF) Image contrast (intensity) ( x) ( x) T( x) i * Ii( x) i ( x) i ( x) o Spring 2012 Experimental Methods in Physics Marco Cantoni 7 sample = phase objet Plane wave Cristal potential k Wave vector in vacuum: k 2me( E) h Wave vector in a potential: 2me( E V( r)) h 2 2 Exit wave Phase shift due to the cristal potential V p : Exit wave function: ( x) expiv ( x; z) o V p ( x, z) 2 E p Spring 2012 Experimental Methods in Physics Marco Cantoni 8

5 WPOA Weak phase object approximation: o iv ( x; z) 1 iv ( x; ) ( x) exp z p No absorbtion,effect of the object on the outgoing wave: only phase shift p The exit wave function contains the information about the structure of the sample Multi-slice calculation: Calculation of the exit wave function for complex structures: 0 1 V p1 1 V p V p3 The sample is cut into thin slices Spring 2012 Experimental Methods in Physics Marco Cantoni 9 Abbé s principle Spring 2012 Experimental Methods in Physics Marco Cantoni 10

6 Transfer Function The optical system (lenses) can be described by a convolution with a function T(x): Point spread function (PSF): describes how a point on the object side is transformed into the image. Transfer Fonction: Décrit comment une fonction d onde objet est transformé dans une fonction d onde image T(x) The image INTENSITY observed on a screen (or a camera / negative plate etc.) Spring 2012 Experimental Methods in Physics Marco Cantoni 11 Phase factors: Transfer Function i( h) ( h) ( ) T ( h) a( h)exp 2 E s E t h Spherical Aberration Defocus Amplitude factors: (objective) apertures spatial coherence enveloppe (non-parallel, convergent beam) Temporal coherence envelope (non monochromatic beam, instabilities of the gun and lenses) Spring 2012 Experimental Methods in Physics Marco Cantoni 12

7 Transfer Function T ( h) exp 2i ( h) 4 ( h) 0.25C h 0.5zh 3 s 2 Spherical aberration defocus Object plane z image plane Spring 2012 Experimental Methods in Physics Marco Cantoni 13 Image formation Source FEG Illumination ( r) 0 exp 2ik r Illumination coherent specimen exit wave objective lens Spherical aberration Cs Sample o objective lens Image, contrast ( x) ( x) T( x) i iv ( x; z) 1 iv ( x; ) ( x) exp z o p i( h) avec ( h) 0.25C h 0.5z T ( h) exp 2 s h p image * Ii( x) i ( x) i ( x) Spring 2012 Experimental Methods in Physics Marco Cantoni 14

8 The «magic» of image contrast Espace Fourier Spring 2012 Experimental Methods in Physics Marco Cantoni 15 but. For a direct and simple interpretation of the image contrast: the imaginary part (sin) of the transfer function exp[2pi(h)] should be ~1 The only free parameter in the microscope is: the defocus z Spring 2012 Experimental Methods in Physics Marco Cantoni 16

9 CTF CTF: contrast transfer function («useful» = V p ) 3 4 CTF( k) sin Cs k z k 2 2 Spring 2012 Experimental Methods in Physics Marco Cantoni 17 With z scherzer z 4 3C s Scherzer defocus The CTF has a wide pass band D scherzer 3/4 1/ Cs The first zero crossing of the CTF defines the «point-to-point» resolution of an electron microscope The atom columns appear as dark areas on a bright background Spring 2012 Experimental Methods in Physics Marco Cantoni 18

10 Spatial and temporal coherence i( h) ( h) ( ) T ( h) a( h)exp 2 E s E t h CM300UT FEG Field emission C s : 0.7mm z= 44nm Résolution (point to point): 1.7Å Information limit : ~1.2Å Resolution (Scherzer) Information limit Spring 2012 Experimental Methods in Physics Marco Cantoni 19 A good microscope CM300UT FEG Emmission à éffet de champs C s : 0.7mm z= 44nm Résolution (point à point): 1.7Å Limite d information: ~1.2Å CM30ST LaB6 Emmission thermionique C s : 2mm z= 76nm Résolution (point à point): 2.1Å Limite d information: ~1.9Å Spring 2012 Experimental Methods in Physics Marco Cantoni 20

11 Pass bands z=44nm z=84nm directe z=67nm z=98nm Spring 2012 Experimental Methods in Physics Marco Cantoni 21 Super microscopes.. Cs=0.2mm Cs=0.01mm Dilemma: Cs=0mm: no more contrast. Spring 2012 Experimental Methods in Physics Marco Cantoni 22

Problems: defocusing for contrast: delocalization of information, information limit not used image image of projected potential thickness

12 HRTEM image formation Source FEG specimen project. pot. atom pos. phase of exit wave Illumination coherent specimen exit wave objective lens Spherical aberration Cs projected potential Transfer Function Problems: defocusing for contrast: delocalization of information, information limit not used image image of projected potential thickness defocus Spring 2012 Experimental Methods in Physics Marco Cantoni 23 Wave funct. Defocus defocus proj. pot. scherzer 1. p.b. 2. p.b. 3. p.b. Au [100], thickness 20nm Spring 2012 Experimental Methods in Physics Marco Cantoni 24

13 Variation of the contrast with: thickness, defocus Au, face centered cubic Spring 2012 Experimental Methods in Physics Marco Cantoni 25 Spring 2012 Experimental Methods in Physics Marco Cantoni 26

14 Through-focus series Spring 2012 Experimental Methods in Physics Marco Cantoni 27 Through-focus series Spring 2012 Experimental Methods in Physics Marco Cantoni 28

15 Simulation of image contrast Spring 2012 Experimental Methods in Physics Marco Cantoni 29 Comparison: experiment and simulation Spring 2012 Experimental Methods in Physics Marco Cantoni 30

104 ºC cubic 135 ºC excellent dielectric, electrostrictive, and pyroelectric properties for high performance sensors and actuators nanoscale chemical

16 Limitation of atomic resolution: HRTEM of cationic ordering in Pb(Mg 1/3,Ta 2/3 )O 3 Ti O Pb Spring 2012 Experimental Methods in Physics Marco Cantoni 31 rhombohedral What is the secret of a relaxor? 104 ºC cubic 135 ºC excellent dielectric, electrostrictive, and pyroelectric properties for high performance sensors and actuators nanoscale chemical inhomogeneity in the B-site sublattice direct observation of the B-site cationic order in the ferroelectric relaxor Pb(Mg 1/3 Ta 2/3 )O 3 by high-resolution Transmission Electron Microscopy Spring 2012 Experimental Methods in Physics Marco Cantoni 32

The cation ordering on the B-site of Pb(Mg 1/3,Ta 2/3 )O 3 perovskite

different B-sites disordered Mg and Ta occupy alternatively the

Experimental Methods in Physics Marco Cantoni 33 Chemical ordered

time annealing Small and diffuse ordered regions Relaxor long time

17 The cation ordering on the B-site of Pb(Mg 1/3,Ta 2/3 )O 3 perovskite Ti O Pb [110] zone axis Mg and Ta randomly distributed on the different B-sites disordered Mg and Ta occupy alternatively the different B-sites ordered 1:1-type superstructure Spring 2012 Experimental Methods in Physics Marco Cantoni 33 Chemical ordered regions in Pb(Mg 1/3,Ta 2/3 )O 3 DF image of ordered regions Short time annealing Small and diffuse ordered regions Relaxor long time annealing Large ordered regions Ferroelectric Spring 2012 Experimental Methods in Physics Marco Cantoni 34

Ta Mg Chemical ordered regions in Pb(Mg1/3,Ta2/3)O3, two different models Ta Mg Ta Mg/Ta Ta Ta Ta [110] direction Ta Ta Space-charge model: perfect 1:1 ratio in ordered regions 1:2+ 1:1 Mg : Ta = 1:1

first-principles total energy calculations: random-layer model is an energetically stable ground state structure Random-site model (also called random layer) Perfect overall stochiometry 1:2 1:2 1:2

18 Ta Mg Chemical ordered regions in Pb(Mg1/3,Ta2/3)O3, two different models Ta Mg Ta Mg/Ta Ta Ta Ta [110] direction Ta Ta Space-charge model: perfect 1:1 ratio in ordered regions 1:2+ 1:1 Mg : Ta = 1:1 1:1 1:1 1:1 1:1 1:1 Mg : Ta = 1:2 B. P. Burton and E. Cockayne, Ferroelectrics 270, 1359 (2002). B. P. Burton J. Phys. Chem. Solids 61, 327 (2000). first-principles total energy calculations: random-layer model is an energetically stable ground state structure Random-site model (also called random layer) Perfect overall stochiometry 1:2 1:2 1:2 1:2 Spring 2012 Experimental Methods in Physics Marco Cantoni 35 Chemical ordered regions in 0.95Pb(Mg 1/3,Ta 2/3 )O PbZrO 3 In dark field (DF) images with a ½(111) reflection (left image) the chemically ordered regions form well defined domains separated by a narrow disordered regions. The disordered matrix becomes visible in DF images with a principal (100) reflection (right image). Spring 2012 Experimental Methods in Physics Marco Cantoni 36

Fourier filtering HR_TEM of (110) zone axis Fourier filtered image,

region and the disordered matrix can be seen.

19 Fourier filtering HR_TEM of (110) zone axis Fourier filtered image, superlattice due to chemical ordering High-Resolution TEM image of a (110) zone axis. Even in the raw image the contrast difference between the ordered region and the disordered matrix can be seen. Spring 2012 Experimental Methods in Physics Marco Cantoni 37 Antiphase boundaries (211) zone axis Spring 2012 Experimental Methods in Physics Marco Cantoni 38

20 Different zone axes Spring 2012 Experimental Methods in Physics Marco Cantoni 39 HRTEM image simulation with JEMS Space Charge [110] Random layer Spring 2012 Experimental Methods in Physics Marco Cantoni 40

Image contrast simulation [211] zone axis Random layer model thickness Space

experimental image compared to simulations Ta Pb Mg Pb Space-charge Random-site

Direct observation of the B-site cationic order in the ferroelectric relaxor

21 Image contrast simulation [211] zone axis Random layer model thickness Space charge model defocus Spring 2012 Experimental Methods in Physics Marco Cantoni 41 experimental image compared to simulations Ta Pb Mg Pb Space-charge Random-site Cantoni, M; Bharadwaja, S; Gentil, S; Setter, N Direct observation of the B-site cationic order in the ferroelectric relaxor Pb(Mg1/3Ta2/3)O-3. JOURNAL OF APPLIED PHYSICS 96 (7): Spring 2012 Experimental Methods in Physics Marco Cantoni 42

Image formation. Image formation

Image formation. Image formation Image formation Source FEG Illumination coherent specimen exit wave objective lens Spherical aberration Cs Source: coherent and monochromatic Illumination: parallel Sample: thin, nicely prepared (no amorphization),