Download EELS

Introduction to nanooptics
with fast electrons
M. Kociak
Laboratoire de Physique des Solides
Orsay, France
[email protected]
http://www.stem.lps.u-psud.fr
20 nm
What do we want to
• Surface plasmons
measure?
• Mix of charge density waves and photons
• frequency depends on shape and size
• and also depends on dielectric environment
• resonances: they dominate optical spectra of
NP
• standing waves at the surface of the NP: they
oscillate and concentrate EM energy at
nanoscale
Applications in sensing, therapy,
Need for more optical
spatial resolution
• All these excitations happen at very small
scale:
• Plasmons: λ<< 1 microns, modulations ~ 10
nm
• Quantum confinement: << 10s nm
• Alloying: << 100s nm
• Defects: down to 0.1 nm
Well below the diffraction limit!
•
•
•
•
Need for more
structural/chemical
spatial resolution
Plasmons: sub-10 nm morphological and chemical
details and crystallinity might influence their
properties
Exact quantum confined objects dimensions as well
as strain state influence the emission properties
Alloying content determines emission wavelength
Defect type determine properties (atom/point
defect/dislocation...)
Need to combine optics with sub-nm analytical techniqu
Working at the relevant size
λ0/2 λsp/2
λsp/2
100 nm
100 nm
1 nm
‣Optical signal down to the nanometer
‣Structure down to the atomic size
Roussow et al. Nanoletters (2011)
Boudarham et al. PRL (2010)
‣Spectral resolution down to the meV andMazzucco
et al. EPJAP (2011)
Zagonel et al. Nanoletters (2011)
‣On the same object
M. Kociak et al., CRASS (2014)
Nanooptics
Scattering/Luminescence
Absorption
Extinction
Observables: Extinction/absorption/scattering?
Quantum fields?
Lifetime measurements?
Non-linear optics?
‣All this @ nm
Electron Energy Loss Spectroscopy &
Cathodoluminescence
in a STEM
M. Kociak and O. Stéphan, Chem. Soc. Rev. (2014)
CL
hν
hν
e-
EELS
See the pionnering works of Batson, Acheche, Ugarte, Kohl, Howie, Zabala, Yamamoto, de
Abajo, etc...
‣ Probe size << 10 nm: A source (and detector) of light at the
nanometer scale?
Outline
Nanoplasmonics
Sphere: simple concepts
Electron Spectromicroscopy:
What are we mapping?
Applications of spectromicroscopy
Quantum emitters
Will not be tackled in this school
Nanoplasmonic with fast
electrons
F. J. García de Abajo,
Rev. Mod. Phys. 82, 209
(2010)
M. Kociak and O.
Stéphan, Chem. Soc.
Rev. 43, 3865 (2014).
C. Colliex, et al.,
Ultramicroscopy 162, A1
(2016).
Bridging optics with
electrons and
photons: the sphere
NB: for the sake of demonstration, we will
mainly stay in the quasistatic approximation,
but retardation can be taken into account!
Spheres momenta
-
Electric dipole
(response to a
plane wave for
a small NP)
+
+
-
+
We skip the magnetic (right) parts
Multipolar polarizabilities
For a dipole the resonant condition is
Which leads in the Drude model to a resonance energy:
Optical crosssections
extinction
scattering
a is the radius of the sphere
‣ Both quantities will have a resonance close to the SP
energy
EELS/CL geometry
v
R⊥
a
EELS and CL
probabilities
Garcia de Abajo, F. Phys. Rev. B 59, 3095–3107 (1999).
Kociak, M. & Stéphan, O. Chem. Soc. Rev. 43, 3865–3883 (2014
EELS depends on all modes
L, in the QS approximation, depends only on the dipole
uasi-exponential decay with e-beam to sphere distance
EELS and CL
probabilities
(small nanoparticles)
If a<<w/c
Garcia de Abajo, F. Phys. Rev. B 59, 3095–3107 (1999).
Kociak, M. & Stéphan, O. Chem. Soc. Rev. 43, 3865–3883 (2014).
EELS is proportional to the extinction cross-section
CL is proportional to the scattering cross-section
For small objects, prefer EELS!
Optics/EELS
Courtesy L. Henrard, FUNDP, Namur,
Belgium
E
‣Dipoles couple to light and electrons
‣other multipoles couple only (QS approximation) to electrons
Yamamoto seminal paper
N. Yamamoto, K. Araya, and
F. García de Abajo, Phys.
Rev. B 64, (2001).
Note in EELS the pionnering
works of Batson, Echenique,
Ferrell, Ritchie, Ugarte, etc…
‣First 2D maps of plasmonic excitations in the visible range
‣Clearly showed that metalic particles do emit CL!
‣Very low S/R
‣Luminescence only: no dark modes
Comparison EELS/CL
T
EELS
CL
50nm
50nm
S
50nm
Losquin et al., Nano Letters
(2015)
‣CL probes only the radiative modes, EELS all modes
‣CL & EELS resonance energies and spatial distributions are
similar
A bit of electron
• We need to use an Electron Microscope
(EM)spectromicroscopy
•
•
•
Images are performed by Scanning the
probe and the signals are recorded in
serial mode; these are Scanning Electron
Microscopes
Two main different EMs: Scanning
Electron Transmission Microscopes
(STEM) or Scanning Electron
Microscopes (SEM)
Roughly, the former operate at voltages >
60 keV and are costly and complicated,
the later operate at < 30 keV and are
Fast electrons and
matter interaction
SEM
Electrons:
-Secondary
-Backscattered
-Auger
Incident electrons
Photons:
-IR, visible
-X
Cathodoluminescence
Induced current
EELS
Inelastically
transmitted electrons
Diffracted/scattered
electrons:
BF
-Collective excitations
-Individual excitations
Elastically
Scattered/Diffracted
electrons
EDX/EDS
EBIC
HR
Diffraction
(HA)ADF
Holography
For using most of these signals at the same time, one needs a localized probe
Imaging
Electron
Detectors
There are no lens to form an
image! The magnification is
given by the scanning coils.
Serial recording
Electron
Probe
As many pixels as desired!
Dedicated STEM
diagram
BF
Detectors
HADF
MADF
Collector Aperture
Projector Lens
Specimen
Objective Lens
Scanning coils
Real Objective Aperture
Selected Area Aperture
Condenser Lens
Virtual Objective Aperture
Electron gun
EELS
From the outside
Detectors
Nion
UltraSTEM
100kV
Projectors
Sample Stage
Sample Exchange
and Storage
Aberration Corrector
Condenser
Gun
Loads of cables!
Field
CdSe Platelets,
courtesy B. Dubertret
Mind the atomic (0,1 nm) resolution
fast electrons probes can be made much smaller than the
typical visible light wavelength
EELS: Principle
electron
Ek , k
k

cible=solide

k’
q//
Ekf , k’
qE
q
k
q
k’
Scintillator
d
How to measure E?
E-E
E
transferred
momemtum q
Energy Loss E
CCD camera
B
In all theoretical treatments here, an infinite angle of collection will be assumed
Electron Energy Loss Spectroscopy...
PhononsPlasmons
IR
Absorption edges
RX
UV
visible
Intensity (counts) x 10 6
2.5
Low-Losses
Core Losses
CK
2.0
1.5
1.0
MnL2,3
0.5
x106
x50
0
100
200
300
400
Energy Loss (eV)
‣A lot of spectroscopic informations
500
600
700
EELS limitations
•
This sounds pretty easy... why hasn’t it be done before?
•
The major issue was to get a high spectral resolution and a high spatial resolution
together
•
Typical energy resolution were at best 350 meV, but more routinely in the 1 eV range!
This is due to fundamental and/or technological reasons
•
High voltage and spectrometers were noisy (stringent requirements on electronics!)
•
One solution is to monochromatize the beam
•
This induces very large drop of brightness
•
And thus spatial resolution is lost!
•
Now, higher brightness guns are available, monochromation is a mature technology,
and this begins to be possible.
•
Also, numerical treatment to increase spectral deconvolution are now available
•
Much less noisy and faster detectors (CCD) are available
How get rid off the ZL?
Multi acquisition
High Dynamics
Better signal to noise ratio
Better energy resolution
•PSF deconvolution
Better energy resolution
Better signal to background
ratio
Monochromators
down to 10 meV
now
The best for CL-SI
• One wants the highest collection angle (high
NAc)
• The biggest field of view
• The highest spectral resolution (low NA , small
s
entry slit D)
These are incompatible requests!
(STEM)-CL
optimization
Collecting and propagating optics
Electron Photon
beam
beam
O1
I2
I1
D
O2
NAc
NAs
Spectrometer entrance
Max. slit width for a given FOV (without loss of
intensity)
D=FOV*NAs/NAc~FOV*NAs~10*FOV
around
1
nm
resolution
for
10
µm
FOV
Edwards, P. R. & Martin, R. W. Semicond. Sci. Technol. 26, 064005 (2011).
Kociak, M. & Stéphan, O. Chem. Soc. Rev. 43, 3865–3883 (2014).
(STEM)-CL
optimization
Collecting and propagating optics
Electron Photon
beam
beam
O1
I2
I1
D
O2
NAc
NAs
Spectrometer entrance
There’re workarounds (see Edwards, P. R. & Martin, R. W. Semicond. Sci.
Technol. 26, 064005 (2011); Kociak, M. & Stéphan, O. Chem. Soc. Rev. 43, 3865–3883
(2014).)
But in any case:
•The collection optics must move indepent of the sample
•The alignment has to be better than a few microns
A (small) room with a view
upper Obj. Pole Piece
CL mirror
Sample holder
2 mm
lower Obj. Pole Piece
Credit: F. Houdellier
Spectral Imaging with electrons
EELS CCD camera
EELS spectrometer
40 X 40 pixels
Total SI acquisition
time: < 80s
30 pA, 100 keV
EELS scintillator
EELS aperture
HAADF
c
CL Spectrometer
Sample
Jeanguillaume, C. & Colliex, C
Ultramicroscopy (1989)
N. Yamamoto, K. Araya, and F.
García de Abajo, Phys. Rev. B
64, (2001).
J. Nelayah, et al., Nat Phys 3,
348 (2007).
CL Mirror
Objective lens
CL PM
Scan coils
64 X 64 pixels,
Total SI acquisition
time: < 4s
3 nA, 100 keV
Electron gun tip
ΔE=300 meV
0.6<E<2000 eV
40-100 keV
ca 1 nm spatial resolution
Silver nanoprism, 200 nm long thickness 30 nm
M. Kociak, unpublished (2014)
coll. F. Schmidt, F. Hofer, J. Krenn, Graz Univ
Kociak, M. & Stéphan, O.
Mapping plasmons at the
nanometer scale in an
electron microscope.
Chem. Soc. Rev. 43,
3865–3883 (2014).
Nanometer scale mapping of optical properties of
silver nanoprisms
A
‣Surface plasmons mapping?
C
B
D
Energy map of the „tip“ mode
CL-SPIM
‣Surface
plasmon
mapping?
EELS, CL in practice:
summary
• A fast electrons probe (less than a nm) can be
formed and monitored in a Scanning
(Transmission) Electron Microscope
• EELS spectrometer and CL detectors are
obviously needed to collect the relevant particles
• Recent technological breakthrough have made
relevant EELS and CL signals quantifiable
• Spectral Imaging is required, but difficult to
analyze
What are we
mapping???
Surface plasmon for an infinite cylinde
+ + +
- -
m=2
m=1
+
+
+
+
+
+ + +
m=0
Kociak & Stéphan, Rev. Chem. Soc. (2014)
kd
-
Surface plasmon for
an infinite cylinder
k is the in-plane wave
vector
d is the cylinder diameter
The lowest branch is
symmetric in charge
One directly see the effect of the
symmetry on the energy
Surface plasmon for a nano-resonato
m=0
d
+
+
+
+
-
+
+
+
+
+
-
-
-
+
-
+
2d/L
+
+
3d/L
kd
Kociak & Stéphan, Rev. Chem. Soc. (2014)
L
The link to the eigencharge
Kociak & Stéphan, Rev. Chem. Soc. (2014)
Eigencharges
Eigenpotentia
Eigenfield
EELS
CL
EELS (exp.)
D. Rossouw et al., Nano letters (2011)
Simulations using MNPBEM (Hohenster et al
EELS is a spatially resolved extinction
Poles @ plasmons energy
Spatial
variations of
the plasmon
eigenpotential
A. Losquin et al., Nano Lett. 15, 1229 (2015)
A. Losquin & M. Kociak, ACS Photonics (2016)
‣EELS maps plasmons, and behaves spectrally as extinction
CL is a spatially
resolved scattering
Poles @ plasmons energy
Spatial
variations of
the plasmon
eigenpotential
‣CL also maps the plasmon, but a slight energy shift is expected (same
for scattering) due to difference between imaginary part and square
EMLDOS for dissipative sytems
The EMLDOS has an eigenmode decomposition even for
plasmonic, dissipative modes!
(Drude)
‣One can show that the EELS is a very good approximation of the EMLD
‣EMLDOS is a very concise description of optical excitations
‣The EELS is a map of the plasmons “eigenfunction” (with some marks...
‣The STEM-EELS is a decent plasmonic counterpart of the STM for
electronic wavefunctions
‣Mind the ressemblance with the expressions
in the symmetric cases!
45
Comparing EELS and the zEMLDOS
F. García de Abajo and M. Kociak, Phys. Rev. Lett. 100, (2008)
A.Losquin & M. Kociak, ACS Photonics (2015)
A. Hörl, A. Trügler, and U. Hohenester, ACS Photonics 150911083805002 (2015).
‣Close to the EMLDOS for flat particles (but not quantitative)
Applications
• This is just a partial view on applications
• Difficult to be updated, as the field is
growing fast. A possible review is here:
• Colliex et al., Ultramicroscopy (2016)
• As a rule of thumb: EELS/CL are
interesting everywhere structure and
spectral properties are entangled
Impressive output!
For a review
Nelayah et al. Nature Physics (2007)
Kociak, M. et al. Seeing and measuring in colours:
Vesseur et al. Nano Letters (2007)
Electron microscopy and spectroscopies applied to nano
Rossouw et al. Nano Letters (2011)
optics.
Gu et al. PRB (2010)
Comptes Rendus Physique 15, 158–175 (2014).
Present directions
• Understanding e-plasmon-light
interaction
• Understanding plasmon physics
• Investigating new plasmonic materials
3D plasmonics
S. M. Collins,
ACS
Photonics 2,
1628 (2015).
Make it quantitative
Bosman, M. et al. Surface Plasmon Damping Quantified with an Electron Nanoprobe.
Sci. Rep. 3, (2013).
‣quantitative «high spectral resolution» spectral imaging
Direction/Polarization resolved
CL
T. Coenen, et al. , Nano Lett. (2011).
‣More difficult for small objects
N. Yamamoto, et al., Optics Lett. (2011).
Understanding
plasmons
physics
F. P. Schmidt, H.
Ditlbacher, F. Hofer, J. R.
Krenn, and U.
Hohenester, Nano Lett.
140709125708007
(2014).
Understanding plasmon physics
Losquin, A. et al. Experimental evidence of nanometer-scale
confinement of plasmonic eigenmodes responsible for hot spots
in random metallic films. Phys. Rev. B 88, 115427 (2013).
‣SP modes in random films unveiled
Quantum coupling
Scholl, J. A., García-Etxarri, A., Koh, A. L. & Dionne, J. A. Observation of Quantum
Tunneling between Two Plasmonic Nanoparticles. Nano Lett. 13, 564–569 (2013).
‣Quantum tunneling plasmons
New materials
J. Martin et al., High-Resolution Imaging and Spectroscopy of
Multipolar Plasmonic Resonances in Aluminum Nanoantennas,
Nano Letters (2014)
‣Characterizing new and arbitrary plasmonic
systems
Other non tackled subjects
J. K. Hyun et al., Appl. Phys. Lett. 93, (2008).
Cha et al. PRB (2010)
and see
F. de Abajo et al., Phys. Rev.
Lett. 91, (2003).
‣Also good at mapping «photons» -guided modes, Bloch
waves, etc...
Conclusions
• Spectromicroscopies based on EELS and CL
allows to measure plasmons properties in
nanoparticles, and to correlate them with the
structure
• EELS (resp. CL) are a very good counterpart of
extinction (resp. scattering) at the nanometer scale
• They are especially important in cases where
spatial resolution matters, or when spatial and
spectral features are entangled