Microscopia elettronica in trasmissione di nanostrutture

Microscopia elettronica in trasmissione di 

nanostrutture 

Mauro Gemmi 

Dipartimento di Scienze della Terra ”A. Desio” 

Universita’ di Milano 

Mauro Gemmi Scuola GNM 2004 Otranto 14-18 Giugno 2004

Summary 

• 1. Inroduction 

• 2. Electron diffraction 

• 3. Imaging 

• 4. Probe techniques 

• 5. Examples 


1. Introduction 


Source (Gun) 

It can be thermionic or field emission 

Illumination system 

Two condenser lenses C1 and C2 

C1 : different spot sizes 

C2 : convrgence of the beam 

Objective Lens 

It creates the first image of the sample 

Projection system 

Intermediate lens: to change from 

image mode to diffraction mode 

Projection lens: to change the 

magnification 

Screen 

CCD or Photographic plates 


Microscope as an electron source 

-Electron diffraction: 

Selected area (SAD) 

Convergent beam (CBED) 

Micro and nano diffraction 

- High resolution electron imaging (HREM) 

- EDS (X-ray maps, microanalysis with high spatial resolution) 

- EELS electron energy loss spectroscopy 

- STEM Scanning Transmission Electron microscopy: 

imaging with backscattered electrons 

high angle anular dark field (HAADF) imaging 


Image resolution 

With TEM microscopes we can obtain images of crystalline 

materials with atomic resolution: 

Acceleration voltage (kV) Point resolution (Å) 

120 ~3 

200 2.0 

300 1.7 

We can see nano-crystals 


Brightness and beam size 

FEG Guns have a higher brightness (10 3 ): 

we can use beams with a smaller diameter having 

enough current for obtaining a detectable signal 

Thermionic 

FEG 

Smallest beam size 10nm

Back focal plane 

Image plane 

e - 

θ 

Object (sample) 

Lens 

Diffraction 

(Fourier transform) 

Image 


SAD Mode 

HREM Mode 


SAD 

HREM 

Reciprocal space 

Direct space 


2. Electron Diffraction 


Laue conditions k i 

-k d 

=h 

Electron diffraction 

Bragg law 2d h 

sinθ=nλ k=2π/λ 

S(r) 

r 

{ V(r) r 

crist 

r 

ρ e 

(r) 

for electrons 

for x ray 

r 

F h 

r r r 

= iφ I h 

Electron structure factor 

Stronger scattering! 

r r r 

f h : f h ≈ 1 : 10 

( ) F( h) exp( ( h 

) = [ S(r) ] 

F 

r 

( h ) ( ) e 

F h X 

≠ ( ) ( ) 

3 

X 

e 


• Dynamical effects 

Electron diffraction is far from being 

kinematical 

( ) 

Iexp ≈ Fh 

r 2 

(200) 

forbidden 

(111) 

allowed 

(111) 

(200) 

(111) 

Si [011] spg Fd3m 

(h00) allowed only if h=4n 


Electron diffraction 

VOLTAGE λ IN Å 

IN KV 

100 0.0370 

300 0.0197 

1000 0.0087 

The Ewald sphere is flat! 

In one shot we record a reciprocal 

lattice plane 


Polycrystal 

Fe oxides 

Modulated 

structures 

Bi 6 

Pb 2 

O 11 

Example of SAD patterns 

Single 

crystal 

[111] BaCuO 2 

Quasicrystal 

AlPdMn Alloy 


3 .Imaging 


Amplitude and phase contrast 

2 

2 

Ψ( r ) = A( x, 

y) 

r r r 

Ψ( ) = exp( −iu 

⋅ 

) 

e - 

Ψ( r ) = A( x, 

y)exp( −iφ( 

x, 

y) 

) 

2 

Ψ( r ) = 1 

r r r 

Ψ( ) = exp( 

−iu 

⋅ 

) 

e - Ψ( r ) = exp( −iφ( 

x, 

y) 

) 


Electrons as particles or waves 

Ψ( r ) 

r 

p = 

r 

mv 

λ = 

h 

p 

E 

= T 

= 

e - 0 

In free space the energy is completely kinetic 

2 

p 

2m 

λ = 

h 

2meV 0 

p = 2mT 

= 2meV 

V 0 is the accelerating potential 

Ψ 

r 

u 

r 

( r ) = exp( − iu ⋅ r ) 

= 

2π 

λ 

r 

r 


Electrons inside a crystal 

Inside the crystal the electrons 

have also a potential energy 

E 

T 

= eV0 

= eV0 

r 

= T − eV (r ) 

r 

+ eV (r ) 

λ before = 

h 

2meV 0 

λ 

inside 

= 

h 

( V ( r ) + ) 

2me 

V 0 

V (r r ) 

Crystal 


Phase shift 

Ψ 

r 

( r ) = exp( − iu ⋅ r ) = exp( − iφ 

) 

r 2π 

u = 

λ 

r 

r 

⎛ 

⎞ 

⎛ 

⎞ 

⎜ 

2π 

2π 

⎟ 

2π 

r 

= ⎜ 

V ( r ) 

⎟ 

π 

dφ 

= − dz 

1+ 

−1 

dz = V dz 

⎝ λinside λbefore 

⎠ λbefore 

⎝ V0 

⎠ λbeforeV0 

φ 

t 

( r ) + K 

2πmeλ 

, ∫ = 

cell ∫ dz 

2 

h 

( x y) = V ( x, 

y, 

z) dz σN 

V ( x, 

y, 

z) 

Ψ 

0 

unit cell 

( ) 

( x, y) = exp − iσN 

V ( x y) 

cell proj 

, 

t 

The phase of the exit wave function 

is a map of the projected potential 


Weak phase object 

for electrons 

Ψ 

2 

( ) = 1− 

iσN 

V ( x, 

y) − ( σN 

V ( x, 

)) + K 

( x y) = exp − iσN 

V ( x, 

y) 

, y 

cell 

proj 

cell 

proj 

cell 

proj 

Direct space 

Ψ 

( x, y) = 1 − iσN 

V ( x y) 

cell proj 

, 

Direct beam 

Scattered beams 

Ψ 

2 

( x, 

y) = 1 

Fourier (reciprocal) 

Space 

Diffraction 

~ r r λt 

ψ 

i r 

Ω 

( u) = δ ( u) − F( u) 


Zernike’s microscope 

e - 

back focal plane 

image plane 

object plane 

Lens 

phase changing plate 

Ψ 

π 

2 

2 

( x, 

y) = exp( ± i ) − iσN 

V ( x, 

y) = 1± 

2σN 

V ( x y) 

im cell proj 

cell proj 

, 

By defocusing the ojective lens in TEM we produce a phase shift in the 

direct beam so that we have a visible contrast. HREM images are taken 

always out of focus!!!! 

2 


Sample 

Image formation 

e - 

Objective 

Lens 

Back Focal 

Plane 

resolution 

Image 

Plane 


Bright Field 

On Olivine 


Bright Field 

On Diamond 


Dark Field 

On a Silicon Film 


High resolution 

On uvarovite 

Ca 3 

(Al 0.4 

Cr 0.6 

) 2 

(SiO 4 

) 3 


Defocus 

-77nm -115nm -154nm 

2 celle 

50 Å 

Forsterite 

Thickness 

100 Å 

200 Å 

300 Å 


4. Probe techniques 


X-ray Microanalysis 

• Microanalysis on a nanometric scale 

(FEG) 

• Problems with light elements 

• X maps (STEM) 


STEM imaging 

2 A 

High angle anular 

dark field detector 

Coherent scattering at low angle 

Incoherent Rutherford scattering at high angle Pure Z contrast with 

atomic resolution 


EELS Electron Energy Loss Spectroscopy 

Ionization edges: chemical 

analysis on light elements 


5. Examples 


Olivine planar defects along [001] 

600 - 700 °C 

Bright field 

HREM 

a 

c 


Hematite formation 

600 - 700 °C 

(Mg 0.84 

Fe 2+ 0.16 ) 2 SiO 4 + 0.08O 2 0.16Fe3+ 2 O 3 + 0.84Mg 2 SiO 4 + 0.16SiO 2 

Hematite Forsterite Amorphous silica 

• Hematite stable up to 1130 °C 


Elongated precipitates 800 - 900 °C 


Globular precipitates 800 - 900 °C 


800 - 900 °C 


800 - 900 °C 

Olivine [210] 

Amorphous SiO 2 

Hematite [301] 


800 - 900 °C 


800 - 900 °C 

SAED 

FFT 

[010] OL 

= [010] HE 


Olivine and hematite grow coherently by conserving the hexagonal close 

packing of O atoms 

Topotactic relationship: 

(100) OL 

//(001) HE 

(001) OL 

//(100) HE 

a OL 

//c HE 

b OL 

//b HE 


Olivine 

Hematite 

a=4.814Å 

b=10.40 Å 

c=6.086 Å 

Olivine (Orto) 

Hematite(Hex) 

a=4.984 Å 

c=14.33 Å 

Supercell (Orto) 

c s 

=3a OL 

~c HE 

=14.4 Å 

c s 

=b OL 

~2b HE 

=10.4 Å 

c s 

=3c OL 

~4*sin(60°)a HE 

//(010) HE 

=17.4 Å 

(010) 

(0-10) 


A) 30 OL + 5 HE1 supercells 

B) 15 OL + 5 HE2 + 15 OL supercells 

Thickness = 350 Å 

Defocus = -115nm 

C) 20 OL + 5 HE1 + 5 HE2 supercells 

Thickness = 306 Å 

Defocus = -120nm 


Pyroxene formation 

1000-1300 °C 

Mg 2 

SiO 4 

+ SiO 2 

2Mg SiO 3 

Forsterite Amorphous silica Pyroxene 

• Pyroxene forms at 1040 °C 


Disordered Enstatite (Clino-Proto) 

1000-1300 °C 

HREM 

SAED 

Strong streaking is evident 


Ordered regions 1000-1300 °C 

A) Clino enstatite tilted 

B) Proto enstatite tilted 

FFT 

[010] 


Grain boundaries with olivine 

1000-1300 °C 

FFT 

• None topotactic relationship 

between pyroxene and olivine 

[010] EN 

[112] OL 

Pyroxene has never been observed 

inside the olivine matrix but always at 

the grain boundaries 


1100 - 1300 °C 

SAED 

[010] Olivine 

SAED 

? 


SAED simulations 

1100 - 1300 °C 

+ 

[010] Olivine 

[211] Magnetite 


Simulation 

SAED 

1100 - 1300 °C 

Zone axes: 

Olivine [010] 

Magnetite [211] 

Topotactic relation (100)Ol // (111)MT ; (001)Ol //(110)MT 


Ba-Cu-C-O System 

Aragonite – like structure 

CuO 

(Courtesy of A. Migliori) 


Witherite γ−BaCO 3 

(Courtesy of A. Migliori) 

Ba(CuO x 

) 1/2 

(CO 3 

) 1/2 


Ti 2 P: a structure ordered on a nanoscale 

Literature: 

• hexagonal a = 11.5 Å , c = 3.45 Å 

• Laue symmetry 6/mmm 

• Distorted Fe 2 

P model (hypothesis) 

Fe 

P 

b 

c 

a 

[001] 

[100] 

Mauro Gemmi Scuola GNM 2004 Otranto 14-18 Giugno 2004 

b


[001] [100] 

• Superstructure x3 a and b: a = 19.93 Å c = 3.45 Å 

• Disorder on the a b plane 



[001] 

[100] 

Structure solved with electron 

diffraction data 


HREM in [100] 

The structure is disordered on a very small scale 


HREM in [100] 

Symmetry of the superstructure must be reduced ! 


3 P vacancies 

Space Group P-6 

Simulations in [100] 


Simulations in [001] 

a) a) P-6 model 

b) b) P-62m model

Microscopia elettronica in trasmissione di nanostrutture

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