Basics and applications of low-loss EELS

Basics and Applications 

of Low-loss EELS 

W. Sigle, B. Ögüt, N. Talebi, C. T. Koch, L. Gu, M. Rohm, P. A. van Aken 

Max Planck Institute for Intelligent Systems, Stuttgart 

R. Vogelgesang 

Max Planck Institute for Solid State Research, Stuttgart 

1 

MPI for Intelligent Systems

Outline 

I. Dielectric formulation 

II. 

III. 

IV. 

Low-loss mechanisms in bulk and finite media 

Instrumentation and methods 

Applications 

2 


The energy-loss process 

+ 

+ 

+ 

- 

- 

- 

Electron probes 

z-component 

of electric field 

Path 

3 

Energy loss: 

 

Path 

 

E ( r, 

t) 

dt 

v – electron velocity 

t - time 


The dielectric function 

Polarizability 

Absorption 

Dielectric function 

 

( 2 

) 

1( 

) 

i 

( ) 

describes the response of a 

material to an applied field 

 


Dielectric formulation of energy loss 

S( 

E) 

Single 

scattering 

distribution 

 

2 I0 t 

b 

Im( 1/ ( 

E)) 

2 

ln1 

( ) 

a m v 

qE 

0 

0 

Normalization and 

sample thickness 

Energy loss 

function 

2 

 

 

 

Angular scattering 

distribution 

m o – Electron rest mass 

a o – Bohr radius ≈ 0.0529 nm 

b – Collection angle 

q E ≈ DE/2E o 

The EELS spectrum contains the full information about the 

dielectric function, including optical properties of the material. 

5 


The energy-loss function 

Im( 

1 

) 

 

 

 

2 

1 

2 

 

2 

2 

Maxima: 

2 small, 1 close to zero Plasmon (collective excitation) 

2 small, 1 close to 1 Im(-1/)= 2 Interband transition 

(single-electron excitation) 

6 



Example: Al 

3 

2 

1 

0 

Eps1 

Eps2 

ELF 

-1 

-2 

5 7 9 11 13 15 17 19 

Energy (eV) 

7 


4 


Volume plasmon 

Example: Ag 

dsp interband transitions 

(+ plasmon) 

Surface plasmon 3 

2 

1 

Eps1 

Eps2 

-Im(1/Eps) 

-Im(1/(Eps+1)) 

0 

-1 

1 3 5 7 9 

Energy (eV) 

is closely connected with the electronic structure of a material 


How to obtain the complex (E) 

Input: 

Refractive index 

= 

x 

S( 

E) 

 

2 I 

t 

a m 

0 

b 

Im( 1/ ( 

E)) 

ln1 

( 

qE 

0 2 

) 

2 

0 

v 

 

 

 

9 

Courtesy : M. Stöger-Pollach 


Calculation of electron scattering from 

Specimen 

 

Momentum transfer q 

(scattering angle) 

Image plane 

g 

Energy loss 

DE = ħ ∙ ω 

ω-q maps: Raising the specimen 

above eucentric position in image 

mode with spot illumination 

ω-q maps: Dispersion of excitations, e.g. 

plasmon modes and Cerenkov losses 

10 



E. Kröger, Z. Physik 216, 115 (1968)) 

Volume loss + Cerenkov 

Surface plasmons 

Guided-light modes 

11 


Energy loss (eV) 


Electron loss versus scattering angle in Ag 

(perpendicular transmission through thin film) 

Thickness 

Bulk 

0 

50 nm 100 nm 

10 

(Max=6·10 6 ) (Max=6·10 6 ) (Max=30) 

0 100 

µrad 

SP coupling 

0 100 

µrad 

No SP coupling 

0 100 

µrad 

12 

Relativistic calculation (after E. Kröger, Z. Physik 216, 115 (1968)) 


Outline 


II. 

III. 

IV. 



Applications 

13 


Valence electron energy losses 

Bulk 

Interband transition 


Phonon scattering 

Finite media 

Surface plasmon 

Interface plasmon 

Transition radiation 

Cerenkov radiation 

Guided-light modes 

DE< 0.2 eV 

Bremsstrahlung 

Exciton 

14 

http://northbeggar.wordpress.com/2009/10/04/exciton/ 

http://www.j-schoenen.de/abc-manual/a/Strahlung.html 

Battacharya et al. , J. Non-Cryst. Sol. (2012) 

http://www.kph.uni-mainz.de/243.php MPI for Intelligent Systems

Cerenkov losses 

q C 

vt 

ct/ 1/2 

vt 

ct/ 1/2 

 

c 

 

 

c 

 

15 


Cerenkov loss 

Volume 

Interband transition 

Cerenkov radiation 

(if b 2 >1) 

q 

Si , 100 keV 

P 

Volume 

plasmon 

DE 

Simulation (after Kröger 1968) 


efractive index n 

Cerenkov loss 

acceleration voltage (kV) 

A lower acceleration voltage allows higher n materials 

to be probed without Cerenkov losses. 

17 


Outline 


II. 

III. 

IV. 



Applications 

18 


Instrumentation 

SESAM 

200 kV FEG, HV stability: 2∙10 -7 (rms) 

Electrostatic Ω-type monochromator 

Extremely stable support frame 

with hanging column 

2 HAADF detectors 

(STEM, EFSTEM) 

MANDOLINE energy filter 

Filter current stability: 2∙10 -8 (rms) 

Plan film camera 

with imaging plates, 

SSCCD, TV-CCD 

Koch et al., Microscopy and Microanalysis 12 (2006) 506 

19 


Data acquisition 

Specimen 

STEM 

Energy-filtered 

imaging 

EFTEM 

20 


EFTEM versus STEM 

EFTEM 

STEM 

Image sampling + – 

Spectral sampling – + 

Electron dose high low 

…..STEM and EFTEM are complementary 

21 


EFTEM versus STEM 

Surface plasmon detection with electrons 

STEM– 

EELS 

J. Nelayah et al., Nature Physics 3 (2007) 348. 

ω = 0.9 eV 

ω = 1.5 eV 

ω = 2.0 eV 

EFTEM 

100 nm 

100 nm 100 nm 100 nm 

J. Nelayah et al., Proc.14th EMC (2008) 243. 

J. Nelayah et al., Optics Letters 34 (2009) 1003. 

STEM and EFTEM give qualitatively same results …. 

22 


Electron monochromator 

Emitter Assembly 

Gun Lens 

High dispersion 

Piezo driven multi slit 

Straight beam path (MC off) 

Dispersion-free (no rainbow 

illumination) 

MC 

Slit Selector 

Dispersive 

Plane (Slit) 

23 


Energy resolution 

VG 

VG 

Tails of zero-loss peak are markedly reduced 

by use of monochromator 

24 


Delocalization (nm) 

How local is the excitation 

Electron probe size (STEM): 

0.1 nm 

BUT: Coulomb excitation is long-range 

1–20 nm (depending on energy loss) 

nach Egerton 

Small energy transfer 

= small momentum transfer 

20 

15 

10 

(after Egerton) 

5 

Large uncertainty of excitation position 

0 

1 10 100 1000 


25 


Outline 


II. 

III. 

IV. 



Applications 

26 


DOS 

Interband transitions 

Core loss 


E F 

E g 

E 

Joint density of states 

27 


3.3eV 


Minimizing Cerenkov effects 

Thick 

0 50 100 (μrad) 

Thin 

0 50 100 (μrad) 

(eV) 

0 

Cerenkov 

losses 

3.3 eV 

Gap clearly 

resolved 

5 

10 

Thick 

Thin 

15 

Thin specimen reduce Cerenkov contributions 

28 

Gu et al, Phys. Rev. B 75 (2007) 195214 


Counts (10 3 ) 


bandgap (eV) 

Apparent bandgap onset (eV) 

20 

15 

10 

Apparent band gap onset in GaN 

Raw 1.7 t/λ 

4 

4 

1.5 t/λ 

Nominal value 

0.8 t/λ 

3 

3 

5 

0 

1 

2 

0.6 t/λ 

0.4 t/λ 

0.3 t/λ 

3 4 


5 

2 

2 

1 

1 

0 0.5 1.0 1.5 2.0 

0 0,5 1 1,5 2 

Relative thickness (t/λ) 

thickness (t/λ) 

Influence of Cerenkov signal is negligible for thin specimens 

Band gap reliable at thickness t/l < 0.5 

29 

Gu et al., Phys. Rev. B 75 (2007) 195214 



Critical points 

3.3 eV 

4.3 eV 

GaN 

Al 45 Ga 55 N 

3.3 eV 

6.9 eV 

8.0 eV 

9.1 eV 

11.1 eV 

Acquisition time: 1 min 

0 2 4 6 8 10 1 2 14 


Detection of band gap and critical points 

30 


Gu et al, J. Phys. Conf. Ser. 126 (2008) 012005 



Removal of zero-loss peak 

Rafferty et al., Phys. Rev. B 58 (1998) 10326–10337 

31 

M. Stöger-Pollach, Micron 39 (2008) 1092 



2D mapping of band gaps 

EFTEM series 

Energy-loss range 

Energy slit width 

Monochromator slit 

0 – 20 eV 

0.2 eV 

0.2 eV 

x 

y 

E 1 

E 2 

E i 

E 

32 



2D mapping of band gaps 

Al 45 Ga 55 N 

GaN 

Image size 64 x 64 pixel 

Pixel size 6 nm x 6 nm 

Determination of the band gap values 

from the 3D EFTEM images stack. 

33 



Dark-field techniques 

Star-shaped filter-entrance aperture 

aperture 

q 

q 

Suppression of collection of Cerenkov 

losses while permitting high-angle 

indirect band gap transitions. 

DE 

34 




Shift of angle-limiting 

aperture away from 

the optical axis 

35 



counts x 10^4 


200 

GaN 

180 

160 

BF 

12 mrad 

140 

120 

100 

80 

60 

40 

20 

0 

-0 5 10 15 20 25 30 35 

eV 

0 5 10 15 20 25 30 35 


Spectra demonstrate validity of the DF 

collection. Main spectroscopic features 

remain intact even if a large transverse 

momentum transfer is involved. 

36 

Gu et al., Ultramicroscopy 109 (2009) 1164 




Advantages: 

Suppression of Cerenkov losses 

GaN 

DF 

BF 

Detection of indirect band gaps 

1 5 10 15 


Improved spatial resolution: < 5 nm 

Disadvantage: 

Low signal intensity Noise 

Silicon 

1 2 3 4 5 6 


37 


Gu et al., Ultramicroscopy 109 (2009) 1164 



Charge oscillations 

Free-electron density 

- + - + - + - + 

E P 

 

 

 

2 

ne 

m 

0 

0 

e – electron charge 

o – vacuum 

permittivity 

38 



Plasmon peak mapping 

Si 3 N 4 

SiC 

BN, C 

SiBCN precursor ceramic 

Zeiss 912 Omega 

Best precision achieved recently on Zeiss SESAM: 3–5 meV 

39 

W. Sigle et al., Ultramicroscopy 96 (2003) 565 



1. Plasmon energy is characteristic for a particular phase 

in a material. 

2. In alloys plasmon energy shifts with alloy composition 

3. Presence of hydrogen can change plasmon energy 

4. Plasmon energy can vary with elastic strain (change of 

unit cell volume) 

40 



Plasmon peak map 

Plasmon energy variation across 

Al 45 Ga 55 N/GaN interface 

Variation much more gradual than Al 

concentration (blue) or band-gap variation 

But: Good correspondence to strain 

variation 

Strain map 

Plasmon energy scales with strain! 

41 

L. Gu et al., J. Appl. Phys. 107 (2010) 013501 



Interface 

Surfaces 

B 

b 

A 

Energy loss depends on impact parameter 

3 

2.5 

2 

1.5 

1 

0.5 

0 

0 2 

(A. Howie) 

42 


CCD counts 


CCD counts 

4000 

3500 

Al 

Sp3.pict 

1000 

Sp2.pict 

3000 

800 

2500 

2000 

1500 

1000 

500 

Al 2 O 3 

Al 

600 

400 

200 

0 

-5 0 5 10 15 20 25 30 

Energy Loss (eV) 

0 

-0 5 10 15 

Energy Loss (eV) 


+ interface plasmon 

43 


Interface plasmon (solid/solid) 

hole 

Al 

EFTEM series across 

interface plasmon peak 

Al 2 O 3 

E 

Surface 

P 

 

E 

Bulk 

P 

/ 2 

Interface Bulk 

E P 

E / 1 

P 

44 


Interface plasmon (solid/liquid) 

EFTEM images recorded at 590 C 

Liquid Al 

Solid Si 


45 Palanisamy et al., Phys. Rev. B 85 (2012) 195305 



A 

B 

A 

Properties of B cannot be easily meaured if B-layer is thin. 

Volume plasmon regime: > 5 nm 

Band-gap regime: > 20 nm 

For thinner layer comparison with theory is necessary 

See, e.g. Moreau et al., Phys. Rev. B 56 (1997) 6774 

46 



Electrons located near the specimen 

surface can be collectively excited. 

E 


Surface 

P 

 

E 

Bulk 

P 

/ 

2 

Barnes et al., Nature 424 (2003) 824 

47 



low-energy mode 

Thin film 

high-energy mode 

48 


Surface plasmon (Ag nanorod) 

Resonances with different mode number can be excited 

49 O. Nicoletti et. al., Optics Express 19 (2011) 15371. 


Surface plasmon (Au nanorod) 

Au nanorod 

Visibility of longitudinal modes up to l = 5 and a transverse mode 

50 I. Alber et. al., ACS Nano (2011) online 


Surface plasmon (Au nanorod) 

Two rods with 8 nm gap 

Transverse 

mode not 

excited 

in gap 

Bonding and antibonding modes 

51 

I. Alber et. al., ACS Nano (2011) online 


Surface plasmon (Ag triangle) 

Comparison EFTEM vs. FDTD 

Incoherent 

integration of 

response 

field during one cycle 

This mimics the electron momentum transfer which 

is mostly perpendicular to the electron beam 

52 

L. Gu et al., Phys. Rev. B 83 (2011) 195433 



Plasmon dispersion 

53 




SPP propagation and losses 

3. Radiative losses 

1. Reflection 

„Fabry-Pérot“ 

2. Transmission „Whispering gallery 

mode“ 

Propagating 

polariton 

Mode energies depend on geometry (size, shape, thickness) and wavelength 

54 




Are the excitations coherent even though 

the excitation is much more local than the resonance 

Au nanoplatelets 

Our model of interference of transmitted and reflected SPs strongly supports this view 

55 


Surface plasmon (holes in Ag film) 

In confined systems surface plasmon resonances exist 

These lead to local field enhancement which are visible by EELS/EFTEM 

2.8 2.2 2.4 1.4 1.0 1.2 0.8 1.8 2.6 2.0 1.6 eV 

0.6 eV 

Electromagnetic fields of holes interact („couple“) 

56 W.Sigle et al., Optics Letters 34 (2009) 2150, Ultramicroscopy 119 (2010) 1094 


Energy (eV) 

Surface plasmon (slit in Ag film) 

Double Slits 

EFTEM 

Simulations 

min 

max 

57 B. Ögüt et. al. ACS Nano 5 (2011) 6701. 


Surface plasmon (slit in Ag film) 

Hybridization Scheme 

Nanoslits in a Ag film 

Effects of electromagnetic 

coupling on a slit system 

An example of Babinet 

complementarity 

58 B. Ögüt et. al. ACS Nano 5 (2011) 6701. 


Summary 

Valence-loss electron spectroscopy 

• Contains information about 

Electronic structure (optical properties (), band gaps) 

Electron density (phase separation) 

Elastic strain 

Electromagnetic fields („Plasmonics“) 

• Often has high signal intensity 

59 


Acknowledgements 

The European Union for financial support under 

the Framework 6 program under a contract for an 

Integrated Infrastructure Initiative. 

Reference 026019 (ESTEEM). 

ESTEEM homepage: http://esteem.ua.ac.be/ 

60 


Website: www.is.mpg.de/StEM 

61

Basics and applications of low-loss EELS

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