High-Resolution
Surface Plasmon Imaging
Andreas Trügler, Ulrich Hohenester, Bernhard Schaffer, and Ferdinand Hofer
http://physik.uni-graz.at/~atr,
http://www.felmi-zfe.tugraz.at
1.70 eV
W. Barnes et al., Surface plasmon subwavelength optics, Nature 424, 824 (2003).
H. Atwater, The promise of plasmonics, Scientific American 296(4), 56 (2007).
„Flat light“
Particle plasmons
Meta materials
Agenda:
Theoretical background and how to map a plasmon
Simulation technique
Comparison between experiment and theory
The promise of plasmonics...
Theoretical background and
how to map a plasmon
No!
Because the wavelength of light is (much) larger
than the nanoparticle
but:
What about other microscopy techniques?
EELS
Electron Energy Loss Spectroscopy
EFTEM
Energy Filtered Transmission Electron Microscopy
F. J. García de Abajo :
Optical excitations in electron microscopy,
arXiv:0903.1669v1 (2009)
Can one „directly see“ surface plasmons?
Electron beam excites surface plasmon
(evanescent source of radiation)
Surface plasmon
acts back on electron
Raster scanning of electron beam
probes dielectric environment of MNP
~ 100 keV electrons
( approx. 70 % of c )
Electron interaction
Maxwell‘s equations:
4-vector notation,
.
Solution by Green’s functions:
Structure of equations we want to solve:
Green function equation:
Liénard-Wiechert potentials
Maxwell‘s equations:
4-vector notation,
.
Solution by Green’s functions:
Structure of equations we want to solve:
Solution for an arbitrary charge distribution:
Liénard-Wiechert potentials
Solution for a relativistic moving charge:
Charge distribution of an electron moving along r(t):
Liénard-Wiechert potentials
Solution for a relativistic moving charge:
Charge distribution of an electron moving along r(t):
Liénard-Wiechert potentials
Solution for a relativistic moving charge:
Charge distribution of an electron moving along r(t):
Liénard-Wiechert potentials
Solution for a relativistic moving charge:
Charge distribution of an electron moving along r(t):
Liénard-Wiechert potentials
Solution for a relativistic moving charge:
Charge distribution of an electron moving along r(t):
Final potentials:
Liénard-Wiechert potentials
Energy loss of the fast electron:
Fourier transform
Energy loss can be related to the work against the induced electric field!
Process reminiscent of a self energy.
Probe of the electrost. potential of the SP!
U. Hohenester, H. Ditlbacher, and J. R. Krenn:
On the interpretation of electron energy loss spectra of plasmonic NPs
(to be published)
~ 100 keV electrons
Electron energy loss
Energy loss of the fast electron:
Fourier transform
Energy loss can be related to the work against the induced electric field!
Loss probability:
The problem reduces to solving the electric field induced by the electron:
Electron energy loss
Fourier transform:
Time domain:
Electron beam interacts with a SP oscillating in time.
Frequency domain:
The SP oscillation becomes frozen, and interacts with a
periodically modulated charge distribution of the
electron beam.
(Interaction along the whole trajectory!)
Change of the reference frame
Electric Green tensor:
The electromagnetic response of a structured material is fully captured in its electric
Green tensor.
Green tensor - link to simulation
Simulation technique…
Mie theory
Analytic results for spherical particles to test the simulation.
Boundary Element Method (BEM)
Approximate surface of scatterer by small surface elements. Works for
scatterers which have a homogeneous dielectric function. Up to a few 1000
surface elements.
Simulation of particle plasmons
1. Discretization of particle surface
Using standard triangulation techniques of Matlab®
with typically a few thousand surface elements
Simulation of particle plasmons
2. Excitation of nanoparticle
( illumination, molecule, electron beam ... )
Oscillating dipole
emetal(w), eb
Inside and outside the metallic nanoparticle Maxwell‘s equation are the usual wave equations!
The only non – trivial contribution comes from the boundaries.
Simulation of particle plasmons
3. Add surface charges and currents
such that BC of Maxwell‘s equations are fulfilled
Oscillating dipole
Boundary Element Method approach (BEM )
Garcia de Abajo & Howie, PRB 65, 115418 (2002); Hohenester & Krenn, PRB 72, 195429 (2005).
Simulation of particle plasmons
Results and comparison
between experiment and theory
Incident high energy electrons
60-300 kV
X-rays
Auger electrons
Secondary
electrons
Thin specimen
10-200 nm
Elastically scattered
electrons
Inelastically scattered
electrons
TEM, HREM, ED
EELS, EFTEM
Ferdinand Hofer and Bernhard Schaffer,
Austrian Centre for Electron Microscopy and Nanoanalysis (FELMI) , TU Graz
Transmission electron microscopy
Gold particles (low-loss)
ZLP – zero loss peak
(energy resolution: FWHM)
HAADF
plasmon peaks
ZLP: Measures energy distribution of primary electron beam, defines resolution
Monochromated STEM-EELS
Experiment
Theory
J. Nelayah, M. Kociak , O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard , D. Taverna, I. Pastoriza-Santos,
L. M. Liz-Marzán, and C. Colliex, Mapping surface plasmons on a single metallic nanoparticle, Nature Phys. 3, 348 (2007).
Surface plasmon mapping with EELS
Narrow slit (0.3 eV) combined with monochromator gives an energy resolution of ~0.4 eV.
This allows EFTEM imaging close to the zero-loss peak, showing SP modes of Au nanoparticles.
Image size:
Energy range:
Slit width:
Energy steps:
Energy resolution:
Acq. time:
512 x 512 px
-1 to 4.5 eV
0.3 eV
0.1 eV
~400 meV
17 min
1.0 1.6 2.4
eV eV eV
Schaffer et al., Micron (2008), DOI:10.1016/j.micron.2008.07.004
Low-loss mapping by EFTEM
Monochromated EFTEM
Image size:
Energy range:
Energy Res.:
Acq. time:
512 x 512 px
-1 to 4 eV
450 meV
15 min
Monochromated STEM EELS
Image size:
Energy range:
Energy Res.:
Acq. time:
@1.0 eV
@ 1.0 eV
@1.8 eV
@ 1.8 eV
64 x 64 px
-2 to 8 eV
220 meV
54 min
EELS and EFTEM results
Comparison with Simulation
1
2
3
@ 1.08 eV
@ 1.85 eV
@ 2.29 eV
B. Schaffer, U. Hohenester, A. Trügler, and F. Hofer
Phys. Rev. B 79, 041401(R) (2009)
EELS and EFTEM results
Comparison with Simulation
1.08 eV
1.85 eV
2.29 eV
(0.80 eV)
(1.50 eV)
(2.33 eV)
1
2
3
@ 1.08 eV
@ 1.85 eV
@ 2.29 eV
B. Schaffer, U. Hohenester, A. Trügler, and F. Hofer
Phys. Rev. B 79, 041401(R) (2009)
EELS and EFTEM results
Comparison with Simulation
1.08 eV
1.85 eV
2.29 eV
(0.80 eV)
(1.50 eV)
(2.33 eV)
EELS and EFTEM results
Theoretical description
Liénard-Wiechert potentials
Electromagnetic Green tensor
link to simulation
Simulation
Discretize particle surface
boundary element method
Results
Very nice agreement with EELS & EFTEM measurements
Direct observation of surface plasmons with unmatched spatial resolution!
Summary
Theoretical Nanoscience (KFU)
Ulrich Hohenester
Hajreta Softic
Jürgen Waxenegger
Nanooptics (KFU)
Joachim Krenn
Alfred Leitner
Harald Ditlbacher
Daniel Koller
Andreas Hohenau
Franz Aussenegg
FELMI (TU Graz)
Ferdinand Hofer
Bernhard Schaffer
Thank you for your
attention!