Phase microscopy: Fresnel fringes in the TEM

Transcription

1 Phase microscopy: Fresnel fringes in the TEM Interferences between waves not being in phase overfocussed 2 waves propagating through different media (sample, vacuum) => difference of mean inner potentials => difference of optical paths => phase differences Transformed into intensity contrast by the objective lens underfocussed in focus Phase TEM relies on coherency of incident beam (energy spread, point source) => FEG

2 Phase microscopy: High Resolution Electron Microscopy Multi beam mode image: transmitted + several diffracted beams interfere => contrast = f (phase relationships of these beams) FT 11 FT image represents the crystalline structure of the specimen => structural characterization at the atomic scale phase differences result from: (i) interactions between the e beam and the electrostatic potential in the object (periodical lfor a crystal) tl) (ii) phase shift induced by the objective lens (transfer function) specimen thin enough => beam amplitude variations can be neglected ( phase object ) => phase shift proportional to the electrostatic potential at every point of the exit surface

3 High Resolution Electron Microscopy: WPO approx Transmission function of the sample: if small phase shift, Weak Phase Object (WPO) approximation q(x,y)= 1-iσΦ(x,y) Projected potential Image directly related to the projected potential of the object (atoms) after modification by the objective lens (filter) I(x,y)= ψ i (x,y) 2 = q (x, y)*t(x,y) 2 = 1+2σΦ(x,y) *s(x,y) Projected potential (object) Im. of t(x,y) (objective lens) s(x,y)=tf{o (u, v)sin(χ(u, v)} is the imaginary yp part of t(x,y) best reading of the projected potential when largest possible frequency bandwith objective lens is underfocussed by Δf=-1.2(Csλ) 1/2 (Scherzer condition)

4 High Resolution Electron Microscopy In all practical cases, WPO approximation is not valid => comparison HREM images/numerical simulation of the images for Df is necessary to access to the real structure of the sample (ex: where are the atomic columns?) However, although non linear, information regarding the atomic structure can be directly obtained in some cases: stacking sequences, extra plane, orientation relationship, presence of dislocations Good experimental conditions: thin thinspecimen (10 nmrange) incident beam // to a simple (low index) direction of the crystal => diffraction= known plane of the RS column perfectly aligned appropriate defocus of the objective lens (Schertzer condition) microscope resolution smaller than the distance between the atomic columns that you want to image! Never trust ONE image!

5 High Resolution Electron Microscopy Rod like defect in silicon B=[011] Si «dumbells» [-200] [-1-11] [-11-1] [-1-11] [-11-1] [11-1] [1-11][200] 0.14 nm [1-13] [1-11] [-111] [-3 3 2] with Cs corrector nm Houdellier 2005 Cherkashin 2005 Interfaces, precipitates, i defects, df phase identification, ifi i defects, df strain, etc

6 What else? Incident beam specimen Diffracted electrons 2Θ Transmitted electrons Energy loss electrons EELS

7 Electron Energy Loss Spectroscopy E V E F M L K BC BV Im(-1/ε) = ε 2 / (ε 1 2 +ε 2 2 ) intensity jumps ionization energy levels => edges =core level distributions Low-losses (the first few ten ev) Valence electrons (VEELS) Collective excitation : Plasmon Individual excitation :Interband Transition Thickness: I t /I zl =t/λ p Dielectric function ε = ε 1 + i ε 2 Optical parameters n, k, μ, R = f (ε 1, ε 2 ) Electronic structure ε 2 JDOS Core-losses (up to a few thousand ev) Inelastic interactions with inner or core level electrons Elemental l quantitative analysis Electronic structure I~Im(-1/ε) = ε 2 unoccupied DOS Energy Loss Near Edge fine Structure ELNES

8 Electron Energy Loss Spectroscopy

9 Electron Energy Loss Spectroscopy. Electron Energy Loss Spectroscopy Energy filtered TEM

10 TEM/EELS EELS adds one dimension to TEM imaging By probing the excitations ti of electrons bounded dto the solid with the electrons from the incident beam Gives information on: specimen thickness elemental chemical composition and spatial distribution of elements spatial distribution of first neighbors relative to an atomic site chemical bonding electronic band structure dielectric function with an energy resolution ranging between 1 ev and 0.3 ev with a spatial resolution ranging between 10 nm and 1 nm

11 Concept of holography Complex wave : amplitude and phase Take a picture : Ψ = Ae iϕ I = Ψ ² = A² You loose the phase ϕ!!! We want to retrieve the phase! Object Coherent photon wave Object wave Reference wave I = Ψ ref + Ψ object ² = Aref ² + Aobject² + 2Aref Aobject cos(2π R0 x + ϕobject ϕref )

12 Information in the phase E φ ( x) = C V ( x, z ) dz E φ M e x) = - B (x,z) dxdz h ( n T M φ = φ + φ E

13 Electron Holography in a TEM Sample ψ o= exp( ik.r) ψ s= As ( r)exp( i K.r+ ϕs( r)) Objective lens Focal plane V+ Image plane Projector lenses I = Ψ Ψ s* 2 2 Holo o =1+A +As (x,y ) + 2As(x,y)cos[ 2πR 0.x+ ϕs(x,y)]

14 GPA analysis of the hologram FT Mask FT 1 π < ϕ < π Image d amplitude A s (x, y) 2π jumps unwrapped Image de phase ϕ s (x,y)

15 Experimental aspects Coherent Electron Beam Field Emission Gun Fresnel fringes due to the high h coherence of the beam Elliptic illumination to increase the spatial coherence biprism meilleure cohérence

16 Hologram with the object Reference hologram (without object) FT FT 20 nm FT -1 FT -1 Ιs = A i s e ϕs Ι R = A R e iϕ R Ιs Ι R = A s A R e i( ϕs ϕ R ) 20 nm Dérivée de la phase Normalised Amplitude A s A R = A N Phase shift due to the object only ϕs ϕ R = Δϕ

17 Non magnetic sample (B = 0) e ϕ(xϕ ( x, y) = C V ( x, y, z ) dz Bn ( x, y, z ) dxdz E h ϕelect ( x, y) = C V ( x, y, z)d dz E with : C E = 2π λ E + E 0 E(E + 2E 0 ) V(x,y,z) = V i (x,y,z) + V (x,y,z) V i (x,y,z) = Mean Inner Potential (MIP) V (x,y,z) = Local electric potential (junctions, CMOS, diode..) if V i et V are constants along the e-beam direction «z» : ϕ elect = C E (V i + V ) t t = sample thickness Need to perfectly know the sample thickness (sphere, cleaved sample, CBED thickness measurement...) to quantify V i and V

18 Mean Inner Potential (MIP) measurement ϕ elect = C E V i t Fe 0.5 Ni nm 10 nm

19 Fe 0.3 Ni nm Phase/radians s FeNi theory FeNi exp c 0 φ = c V t E Position/nm MIP measurement Composition analysis Morphological studies

20 Magnetic samples ϕ( x) = C e E V(x,z)dz Bn(x,z) dxdz h Pb. 1: The objective must be witched off. => use of Lorentz lens to get sufficient resolution Object in a magnetic field free area Field of view up to 1µm f = 30 mm Cs = 7430 mm (!!) Cc = 39 mm Point resolution # 2 nm

21 Magnetic samples Pb. 2: How to separate the magnetic and electrostatic contributions B and C E V i t? Phase shift induced bt the local electrostatic potential: ϕ elect ( x) E ) = C V ( x, z dz Phase shift induced by the local magnetic field : ϕ mag e ( x) = - Bn (x,z) dd dxdz h Total phase shift ϕ ( x) = ϕ (x) + ϕ (x) Tot ( elect mag

22 Pb. 2: How to separate the magnetic and electrostatic contributions B and C E V i t? 1/ Taking two holograms (4 with the reference holograms) switching upside down the sample => The sign of the magnetic contribution is reversed and the electrostatic one remains. t V i B V i B e ϕ 1 = C E V i. t B n ds e h ϕ 2 C. t + ϕ -ϕ 2 1 h e = 2 B ds n ϕ +ϕ = 2 1 = E V i B n ds h 2C E V t Problem : finding back the same area of interest 2/ Taking two holograms with two different high voltages 2π E + E0 CE = λ E(E + 2E 0 ) e ϕ 1 = C E V i. t B n ds ϕ -ϕ h V i t = e ( CE C E ) ϕ 2 = C E V i. t B n ds h Problem : keeping the same acquisition iiti conditions (magnification, alignment ) when changing the high voltage. i

23 3/ Using the high magnetic field of the objective (~2 Tesla) to saturate the magnetic sample in two opposite directions H Objective H Objective H Objective +Θ -Θ Back to Θ = 0 objective switch off t ϕ 1 = C E V.t e i.t. h B n (x). dx ϕ 2 = C E V.t+ e i.t. h B n (x). dx e ϕ - 2 ϕ ϕ + ϕ.t. B n (x).dx = 1 C E V i t = h ϕ 1 Magnetic contribution to the Electrostatic contribution to the phase shift phase shift

24 x 1 = = = Δ dz d z y B e y x y x n x ξ ξ ϕ ϕ ϕ ξ ),, ( ), ( ), ( h t x B e x x n ). ( ) ( h = ϕ The gradient of the phase is proportional to the in plane component of the magnetic induction B n The equiphase contour gives the direction of the magnetic induction B

25 Magnetic Configuration of an isolated Fe Nanocube al., Nano Lett Snoeck et a ), pp t., 2008, 8 (12 (a) TEM image, (b) Magnetic contribution to the phase shift, (c) Magnetic induction mapping, (d) micromagnetic simulation (OOMMF)

26 Magnetic Configuration of two neighbouring Fe Nanocubes (a) TEM image, (b) Magnetic contribution to the phase shift, (c) Magnetic induction () g,( ) g p, () g mapping, (d) micromagnetic simulation (OOMMF)

27 Magnetic Configuration of four neighbouring Fe Nanocubes (a) TEM image, (b) Magnetic contribution to the phase shift, (c) Magnetic induction mapping, (d) micromagnetic simulation (OOMMF)

28 Magnetic multilayers φ(x) = e/ħ B (x) t(x) dx dφ(x)/dx = (e / ħ). t. B (x) E. Snoeck, P. Baules, G. BenAssayag, C. Tiusan, F. Greullet, M. Hehn, A. Schuhl J. Phys.: Condens. Matter 20 (2008)

29 Sample preparation Cross Section glue specimen 1t 1st cut specimen Ar+ ions electrons 2nd cut Mechanical grinding (abrasive papers + dimpler) > µm + ion milling > hole Ready for TEM

30 Sample preparation Plan view Ar+ ions electrons 20 µm specimen mechanical grinding + dimpling ion milling > hole Ready for TEM

31 Sample preparation Sample preparation

32 Sample preparation: FIB

33 Sample preparation: FIB

34 Summary Good TEM results from 50% specimen preparation, 20% TEM s price 30% guy s experience