Simulating EELS spectra of isolated and coupled metallic ...

Simulating EELS spectra of isolated and
coupled metallic nanoparticles in
the discrete dipole approximation
Stéphane-Olivier Guillaume & Luc Henrard
18-20 June 2012
Uppsala, Sweden

Outline
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Localized Plasmon Resonance
Optical vs EELS experiments
The Discrete Dipole Approximation
Results on gold nanorods
– Isolated
– Size effect
– Substrate effect
– Coupled dimer

Localized Plasmon Resonance
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Metallic nanoparticles exhibit resonances when
excited by an external electric field
These resonances are called LPR and correspond to
collective oscillations of conduction electrons
Their properties depend on the size, geometry &
environment of the particle
For a sphere with r

Localized Plasmon Resonance
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At the resonance frequencies
– Intense electric field around the particle
– Very high absorption and scattering
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Can be used for
– Surface Enhanced Raman Spectroscopy
– Phototherapy
– Photovoltaic
– Sensing

Localized Plasmon Resonance
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Coupling effects for close particles
– Described in terms of hybridization of individual
modes
– Bright modes have
a non-zero net
dipole moment
– Dark modes have a
vanishing net dipole
moment

Localized Plasmon Resonance
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Interests of coupled nanoparticles
– More intense E-field in the gap compared to
isolated particles
– Tuning of the resonances spectral positions with the
size of the gap

Optical vs EELS experiments
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Optical experiments
– Global excitation
– Usually used to measure extinction spectra
– But light interacts with bright modes only
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EELS
– Local excitation
– Allows to probe bright and dark modes
– Peak intensities will vary with the impact parameter

The Discrete Dipole Approximation
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Powerfull method to compute scattering and
absorption properties of particles with arbitray
shapes
● First proposed by Purcell & Pennypacker in 1973
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Particles are described as a cubic
lattice of interacting dipoles

The Discrete Dipole Approximation
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Having solved for the dipoles, it is possible to
compute measurable quantities
– Extinction
– Loss probability

The Discrete Dipole Approximation
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It is possible to take a semi-infinite substrate into
account with the Method of Images
The system to solve is
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Image dipoles will depend on the orientation of the
interface

The Discrete Dipole Approximation
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A big number of dipoles is need for
– Large particles
– Particles with fine details
– Coupled particles
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Becomes ressources demanding for theses cases
DDEELS : homemade code written by N. Geuquet
http://perso.fundp.ac.be/~geuquetn/ddeels.php

Results : isolated gold nanorods
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Geometry
a=10nm
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d=1nm ⇒ 4000 dipoles
L=400nm
1,81 eV
2,41 eV
1,81 eV
x50
E
k
k
E
2,30 eV
2,41 eV

Results : isolated gold nanorods
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2 peaks in optics : 1,81 eV and 2,41 eV
1 additionnal peak in EELS : 2,30 eV
Identify the signature of the modes given by the z
component of the E-field
Longitudinal
1 st dark mode
Transverse
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Good agreement with experimental results

Results : isolated gold nanorods
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Size effect at constant aspect ratio
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L=200nm
a=50nm
Same modes
but redshifted
– 0,39 eV
– 0,10 eV
– 0,00 eV
1,42 eV
2,20 eV
2,41 eV

Results : isolated gold nanorods
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Increased aspect ratio
L=80nm
a=10nm
Same modes
but redshifted
– 0,57 eV
– 0,34 eV
– 0,00 eV
1,24 eV
1,96 eV
2,41 eV

Results : isolated gold nanorods
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Substrate effect
● εsub =2,25
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Same modes
but redshifted
1,63 eV
– 0,18 eV
– 0,16 eV
– 0,07 eV
2,14 eV
2,35 eV

Results : coupled gold nanorods
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2 identical gold nanorods
Transverse coupling
● Longitudinal coupling
g=5nm
g=5nm

Results : coupled gold nanorods
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Longitudinal coupling
E
k k E
x50
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2 additionnal peaks in EELS

Results : coupled gold nanorods
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Modes signature
Bright modes
Dark modes
1,66 eV 1,90 eV
2,41 eV
2,29 eV

Results : coupled gold nanorods
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Transverse coupling
E
k
k
E
x25
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3 additionnal peaks in EELS

Results : coupled gold nanorods
● Modes signature
1,96 eV
1,54 eV
2,41 eV
2,17 eV
2,35 eV

Results : coupled gold nanorods
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Gap size effects
Longitudinal coupling
Transverse coupling

Conclusions & perspectives
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We are able to simulate extinction and EELS spectra
of metallic nanoparticles
Some interesting effects
– Size
– Substrate
– Coupling
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We are developping a code for multiparticle systems
to overcome DDA limitation

Acknowledgement
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Luc Henrard
Nicolas Geuquet
Computer ressources
– iSCF
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Financial support
– F.R.I.A.
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BTS Team

Thank you for your attention !
Any questions