what are surface plasmons? - north carolina state university
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What are surface plasmons?
NC State UniversityNC State University
A plasmon is a collective oscillation of the conduction electrons
The free electron optical response uses the Drude-Lorentz-Sommerfeld model. The influence of external forces is considered for one electron alone and thenThe influence of external forces is considered for one electron alone and then the response is multiplied by the number of electrons. All electrons act in phase in this model.
me2rt2 + me
rt = eE0e– it
e
Electron motion
Force + Friction = Driving term
Dipole p = er
Force + Friction = Driving term
E = E0e-it
Dipole p = er0Polarization P = np = ner0Polarization driven by
l i fi ld P ( ) Ean electric field P = ()0ESuscepticility () = () - 1
Electric vector
The plasmon frequency is the t f f f i ti llresonant frequency of frictionally
damped electron motionpThe forcing term is the electric field of the incident light.
2E E ne2 E
t2 + Et = ne
me0E0e– it
2
E = E0e-it
=–p
2
2 + i p = ne2
me0
= 1 –p
2
2 + 2 + i p
2
2 + 2
Real part Imaginary part
Dielectric constants for a f l t d tfree electron conductor
Imaginary partOut-of-phaseAbsorptionAbsorption
Real partReal partIn-phaseDispersion
Surface selection rules
For c < 0 the p-polarized image chargeadds const cti el to the incident fieldadds constructively to the incident field.
p polarization +p polarizations polarization
++
+- -
+
rp = 1
- c < 0
Ep = Ei(1 + rp) = Ei(1 – cos2)
For c < 0 the s-polarized image chargedd d t ti l t th i id t fi ldadds destructively to the incident field.
p polarizationp polarizations polarization+
-
- +
-rs = -1
+ m < 0
Es = Ei(1 + rs) = 0
Kretschmann configuration
IRE > s
p polarization+ +
p polarizations polarization
- -IREcs
Thin film on a prism
Attenuated total reflection ( > c )
Condition for surface plasmon resonance
p polarizations polarizationrS = -1
rp = 1 IRE
s polarization +rS = -1 +
- c-
s
Evanescent Wave in Medium
Dispersion relations from Dispersion relations from DrudeDrude
ncz = – c2
c + s, nsz = – s
2
s + c, nx =
cs
s + cc s s c s c
Plasmon Dispersion Curve for ITOPlasmon Dispersion Curve for ITOωp = 17700 cm-1 Γ = 500 cm -1
k sp = c
c s
c + s
Surface Plasmon Resonance on Gold
The intensity of the reflected light is reduced at a specific incident l d i h di f langle producing a sharp dip-a surface plasmon resonance
The surface plasmon resonance is related to the material adsorbed onto the thin metal filmadsorbed onto the thin metal film
Visible electromagnetic radiation
p = ne2
m
1/2
Plasma frequencyn is charge carrier density
me0
http://www.gwctechnologies.com/images/spreffect.gifn is charge carrier densityme is effective mass
SPR BiosensorReflected LightIncident Light
I
Flow Cell
Coupling of the light into the Au thin filmrequires a prism to provide wavevectorq p pmatching (Kretschmann configuration).
SPR implementation
II
Incident Light Reflected Light
Flow Cell
Molecules in solution induce changes in refractive index and give rise to a gmeasurable SPR signal when binding occurs.
For c = - 2s the plasmon can be excitedtl t i ld h t f thresonantly to yield an enhancement of the
local fieldp polarizationp polarization+
?+-
?
-m = -2s
Local field Ep = gEi
g = – 0
+ 20m + 2s
m - s
Absorption and dispersion in conductorsAbsorption and dispersion in conductors
Franzen, S. “Surface Plasmon Polaritons and Plasma Absorption in Indium Tin Oxide Compared to Silver and Gold” J. Phys. Chem. C 2008, 112, 6027-6032
Biosensing using surface plasmonsKnown methods:Fluorescence quenching (molecular beacon)Surface plasmon resonance (SPR)
Kretschman configurationNanoparticle plasmon resonanceNanoparticle plasmon resonanceThermographic detection
Proposed methods:Surface enhanced Raman effectSurface enhanced fluorescenceSurface enhanced infrared
Fluorescence quenching b lby plasmons
Example: Quenching to Ru(bipy)32+
N
NNN
RuN
NN SH
Molecular beacon approachGlomm, Franzen et al. JPC B 2005, 109, 804
Tsourkas et al. Anal. Chem. 2003, 75, 3697
Plasmon ThermographyPlasmon ThermographyExcite surface plasmons and detect heating byh i bl kb d di ti W T4change in blackbody radiation: W = T4
US patent application US2004/0180369A1p pp
Laser-Induced Temperature Jumpp pElectrochemistry and Thermography
Thermographic array imager Anodic current for an ITO electrode
off
ssDNA/gold nanoparticleson
ssDNA/ITO
Lowe, Franzen, Feldheim JACS 2003. 125. 14258
Dynamic Range and Limit of Detection of Gold Particles Dropcast Onto Nylon Substrates
ABI White NylonCoherent Antares Laser @ 532 nm
p y
10@
Laser power: 1 W, beam diameter 2 mm
1T [K
] T
B k d
0.33 attomoles/cm2 of particles
0.1
Background
0.1 1 10 100# of Gold Particles on Surface [amols]
Are gold and silversilver the only SPR substrates?g y
Fixed charge carrier density: ~1023 electrons/cm3
Limited electrochemical range: Gold is oxidized above 0.8 V
Thiol surface chemistry
Conducting metal oxides offer possibilities not present on gold–No quenching of fluorescence–Stable electrochemistry over a wide range–Processible surfaceProcessible surface–Many surface chemistries possible
There are hundreds of mixed metal oxide substrates possible.
Indium Tin Oxide (ITO)Composition: 90% Indium Oxide and 10% Tin Oxide
Commercial 1700Å thick 8-12 /□
Band Gap 3.7 eV
St t Bi b it bi t l t tStructure: Bixbyite cubic crystal structure
Tunability: C t i f f ifi ti
Type: sp type conductor
Customize surfaces for specific reactionsResistivity changes:
Thickness changeAlteration of annealling onditions
Common Uses:Heat ShieldsFlat Panel Displays
Alteration of annealling onditionsDoping change
Crystal orientation changes: Deposition temperatureDeposition temperature Change in annealling conditions
Experimental and Calculated Reflectance of ITOThree Phase Fresnel Model (air/ITO/glass)
60º, p-polarization
0.8
0 6Ref
lect
ivity
ipp
ipp
p errerr
r 22312
22312
1
0.6
0.4nc
e, P
ower
R7.6 square
9.7
pp e2312
Rp = rp2
0.2
0.0Ref
lect
an
12108643 1
13.8
Wavenumbers (x103) (cm-1)
In 2002, Brewer and Franzen predicted that ITO would have a surface plasmon
1. Alloys and Compounds, 2002, 338, 73-792. J. Phys. Chem. B. 2002, 106, 12986-12992
Tunable Parameters• Thickness:• Thickness:
- deposition time
• Carrier Concentration:- First Annealing Process: 5%H2/95%N2 (Forming gas)- Second Annealing Process: Varies the Partial Pressure of Oxygen 7x10-7mTorr to 50mTorr
• Mobility:- Sputtering gas Argon: 6mTorr to 20mTorrSputtering gas, Argon: 6mTorr to 20mTorr
• Composition:p- Sn:In ratio 0 – 10%
Fourier-Transform SPR
Steve Weibel, GWC Technologies, Inc.1. Rhodes C.; Franzen, S.; Maria, J-P.; Losego, M.; Leonard, D.N.; Laughlin, B. ; Duscher G.; Weibel, S.;“Surface Plasmon Resonance in Conducting Metal Oxides” J Appl Phys 2006 100 Art No 054905Surface Plasmon Resonance in Conducting Metal Oxides J. Appl. Phys. 2006, 100, Art. No. 054905
2. Rhodes, C.L. ; Cerruti, M. ; Efremenko, A. ; Losego, M. ; Aspnes, D.E. ; Maria, J.-P.; Franzen, S. “Dependence of Plasmon Polaritons on the Thickness of Indium Tin Oxide Thin Films” J. Appl. Phys. 2008, 103, Art. No. 093108
Sputteringp g
ITO Process ITO SputterS t
Process ParametersSputter Pressure (Ar)System Sputter Pressure (Ar)
Power Input
Power Type (RF vs DC)Power Type (RF vs DC)
Substrate Distance
Substrate Temperaturep
Time/Thickness
O2/Ar Plasma
Sputteringp g
POWERON
Cathode
Argon
Ar
---–- Target (ITO)
ArAr
Ar Ar+
Ar+
Ar+
Ar+
Ar
Substrate
Sputteringp g
POWERON
Argon---–-
In
O
Sn
O
In
OOITO Film
ITO Angle Dip in Air:Single wavenumber representation
40 42 44 46 48 50
Angle Range: 42°-53°Surface Plasmon Resonance on ITOSurface Plasmon Resonance on ITO
Calculated
Angle Range: 42°-53°Surface Plasmon Resonance on ITOSurface Plasmon Resonance on ITO
Experimental
SurfaceSPR
CapacitiveCPR SPR_ +CPR
+
_
In‐planeOrthogonal
Optical Resonances Observed in Thin Films ElectronVolts(eV)
Capcitive plasmon resonance:(CPR)
i thi fil100
80ce (a
.u.)
1.21.11.00.90.80.70.6 Electron Volts (eV)
160nm• appears in thinner films• narrow appearance • weak angle dependence• near IR range
80
60
40
20R R
efle
ctan
c
• near-IR range
ElectronVolts (eV)
20
0 SP
R
1000090008000700060005000
Wavenumber (cm-1)
Surface Plasmon Polariton100
80ce (a
.u.)
1.21.11.00.90.80.70.6Electron Volts (eV)
Surface Plasmon Polariton (SPP)
• optimum film thickness 160 nm• strong angle dependence
80
60
40
20R R
efle
ctan
c
30nm
• mid-IR range20
0 SP
R
1000090008000700060005000
Wavenumber (cm-1)
The planar limit of LSPR as a limiting case of an oblate spheroid
+ + + + + +
- - - - - -Sphere Oblate ellipsoid Planar limit
The planar limit of LSPR as a collection of nanoparticles+ + + + + + +
- - - - - - -
Controlled Atmosphere AnnealingAnnealing
Controlled Atmosphere Annealing
XRD of ITO FilmsB f d Aft A li g
In-situ
Before and After Annealing
tens
ity
ITO Aft A l
Gas Inlet(N2 & H2)
s tuTransfer
In
ITO As Deposited
ITO After Anneal
Process ParametersTemperature
10 20 30 40 50 60 70 802 (�)
Temperature
Time
AtmospherepLosego, S.; Efremenko, A.; Rhodes, C.; Cerruti, M.; Franzen, S.; Maria, J.-P. “Conductive Oxide Thin Films: Model Systems for Understanding and Controlling Surface Plasmon Resonance” J. Appl. Phys. 2009, 106, 024903
Plasma frequency is inversely l t d ith i ti itcorrelated with resistivity
Change in Film Conductivity Shift in plasma frequency
5 10-4
g ywith Annealing Atmosphere
p q yMeasured using FT-SPR
3 10-4
4 10-4
*c
m)
2 1/2
2 10-4
3 10
esis
tivity
(p = ne2
me0
1/2
0 100
1 10-4
18 16 14 12 10 8
Re
10-18 10-16 10-14 10-12 10-10 10-8
~Oxygen Partial Pressure of Annealing Atmosphere (Torr)
CarrierConcentration
1.21.11.00.90.80.70.6 Electron Volts (eV)
1.21.11.00.90.80.70.6Electron Volts (eV)
ConcentrationSeries:
1 Oxygen fills
pO2
0.01mTorr A Theory pO2
0.01mTorr E22
1. Oxygen fills vacancies
2. Sn and O trap e-3. n decreases
pO 10-4mTorr B 4
4. ωp also decreases5. SPP shifts into the
mid-IR
pO2 10 mTorr B Theory pO2 10-4mTorr F
p = ne2
0pO2 10-5mTorr C Theory pO
2
10- 5 mTorr G
Theory pO2 10-7mTorr H
2
-5
Carrier Concentrations cm-3:A. 3.948x1020
B 5 659x1020 pO2 10-7mTorr D
Theory pO2 10 mTorr H
B. 5.659x1020
C. 7.136x1020
D. 1.120x1021
Experimental Theoretical
1098765 Wavenumber (x103
cm-1)
pO2 10 mTorr D
1098765 Wavenumber (x103
cm-1)
AFM Measurement of Grain SizeAr+ 10 mTorr Ar+ 20 mTorr
Grain Size:100 nm
Mobility:
Grain Size:< 40 nm
Mobility:ob ty35 cm2/Vs
ob ty7 cm2/Vs
60
80
100
ce (a
.u.)
60
80
100
ce (a
.u.)
0
20
40
60
Ref
lect
anc
0
20
40
60
Ref
lect
anc
05000 6000 7000 8000 9000 10000
Wavenumber (cm-1)
05000 6000 7000 8000 9000 10000
Wavenumber (cm-1)
Hall Effect Measurements
1.5 1021
m-3
)
40
Carrier Concentration Mobility
1 1021
ntra
tion
(cm
20
25
30
35
(cm
2 /V*s
)1.5x Change
5 1020
rrie
r Con
ce
5
10
15
20
Mob
ility
(
5x Change
06 8 10 12 14 16 18 20 22C
a
Sputter Pressure (mTorr)
06 8 10 12 14 16 18 20 22
Sputter Pressure (mTorr)
Although sputter pressure affects the carrier concentration, it has a much larger impact
on mobility of the charge carriers
M bilit S i
1.21.11.00.90.80.70.6 Electron Volts (eV)
6mTorr A
1.21.11.00.90.80.70.6Electron Volts (eV)
Theory 6mTorr E
Mobility Series:
1. Peaks around 9 mTorr Th9 mTorr
1. Decreases going away from maxima
2. Damping constant
9mTorr B Theory 9mTorr F
increases3. Peaks broaden
12mTorr C Theory 12mTorr G
15mTorr D Theory em
e
Mobilities cm2/Vs:A. 23.7 B. 30.0C 21 2
15mTorr D y15mTorr H
C. 21.2D. 9.385
Experimental Theoretical
1098765 Wavenumber (x10 3cm-1)
1098765 Wavenumber (x103
cm-1)
Hybrid plasmons
50 nm50 nmNano AuAu
80 nm80 nm 80 nm ITO
80 nm ITO ITOITO
1. Franzen. S; Rhodes C.; Cerruti, M.; Efremenko, A.Y.; Gerber, R.W.; Losego, M.; Maria, J.-P.; Aspnes D.; “Equivalences between Gold and Indium Tin Oxide as Plasmonic Materials” Opt. Lett., 2009, 34, 2867-2869
2. Gerber, R.W.; Leonard, D.N.; Franzen. S; “Conductive thin film multilayers of gold on glass formed by self-assembly of multiple size gold nanoparticles” Thin Solid Films, 2009, 517, 6303-6308
Multilayer composite films12 nm and 2.6 nm particles
Indium tin oxide (ITO)Intermediate thickness: no CPR or SPR
80 nm ITO
Perpendicular polarizations
CPR
Rp/R
sR
30 nm
ITO
Parallel polarization
160 NR
nmITO
SPR
Indium tin oxide (ITO)Intermediate thickness: no CPR or SPR
80 nm ITO
Quench SPR, Activate CPR
5050 nmACPR Au
Rp/R
s
CPR
80 nm R
ITO
Activate SPR, Quench CPR
50 nmNano Au
NRNano Au
80 nm ITOSPR
Comparison of Hybrid and Thickness
Pl i lifi tiPlasmonic amplification:What is possible for a Raman process?p p
Surface-enhanced resonance RamanSpectroscopy (SERS) and hemeSpectroscopy (SERS) and heme
• Observation of large Raman signals for molecules associatedith bl t l ti l l il d ld Fi t b dwith noble metals, particularly silver and gold. First observed
in 1974 for pyridine on rough silver electrode.
• Electromagnetic and chemical mechanisms. The chemicalmechanism could be resonant Raman.
• Enhancement factors have increased from 106 to 1015
throughout a year period.
A resonance Raman spectrum is obtained by a laser light scatteringobtained by a laser light scattering
experiment
DetectorLens
S t hSample
Lens
Laser Spectrograph
Inelastic light scattering produces a frequency shift. There is exchange of energy between the vibrations of the molecule and the incident photonof the molecule and the incident photon.
Resonance Raman is a two photon process
Incident photonfrom a laser.
Scattered photonhas an energy shift
h
has an energy shift.
The difference isThe difference isbecause the moleculeis left in an excitedvibrational state.
Raman scatteringgRaman scattering is
i l ti li htan inelastic lightscattering process.In the resonantpicture it involves evolution in the excited state so itexcited state so italso depends on theFC factor and thet iti di ltransition dipole moment. On the left a sum-over-statespicture is shown.
An optimistic view of enhancement
+Z
First enhancement
SecondE0
+ ++
Second enhancementr
0
Ya
YX
g = – 0m - s
- - -
g = + 20m + 2s – 0 -
Static approximation >> a
g = 0
+ 20m + 2s
m s
Enhancements as large as 1015 !
Local fieldI = ½ e g2 E 2
I id t i t it
I = ½ e0 g2 E02
Scattered intensityIncident intensityI = ½ e0 E0
2
Scattered intensityI = ½ e0 g2 g2 E0
2
O ll h t th ht t b 4Overall enhancement thought to be g4
Two questions about g4 enhancement:
1 Is this correct?1. Is this correct?- Experimental SERS increases as |E|2, not |E|4
- Conservation of energy must be satisfied
2. How big is g?
- g is can be calculated directly using Drude model
- There must be a bandwidth to the SERS effect- There must be a bandwidth to the SERS effect
First enhancement Second enhancementA BZ+ ++
d
Zz
r- +
d
yr
+ -YX
a yx
E
Static approximation
E0 - - -
Planar image approx.a >> d >> a a >> d
Surface Enhancement on NPs• Local Field Treated by Clausius‐Mosotti Relation
( ) 1g() = 3() – 1() + 2 (sphere)
g() = 2() – 1() + 1 (cylinder)
( ) i h h f f li d fi ld
( )
g() = () – 1() (plane)
• g() is the enhancement factor for an applied field• Implicitly spheres are treated most often in SERS lit tliterature
Generalized Clausius‐Mosotti• The Clausius‐Mosotti relation connects the molecular polarizability with the dielectric function
•N0
= () – 1 () + 1/ – 1
• The parameter is the depolarization factor • The range is 0 < < 1• The enhancement factor for absorption enters as the square, which is the intensity of radiation.
g2() = 12() – 21() + 1 + 2
2()
2 12() + 2 1/ – 1 1() + 2
2() + 1/ – 1 2 1( ) 1( ) 2( )
Bandwidth for SERS limits effectFirst and second enhancement cannot both beAt the peak of the gain curveAt the peak of the gain curve.
Maximum enhancement• Note that this function is realistic in that it does not blow up when the resonance condition is met.blow up when the resonance condition is met.
• The maximum enhancement factor for absorption is:2
g2() p
2
• In addition, we find that there is a connection between the magnitude of the enhancement and the b d id h i b h d i bandwidth given by the damping .
• For a sphere = 1/3.
Concrete examples, Au and Ag
Conclusion• Surface plasmon resonance on free electron conductors is possibleconductors is possible
• Hybrid plasmons that cut across different conducting materials are possible
• Agreement of the free electron theory is very good• Application of these insights to the local field factor for Surface Enhanced Raman spectroscopy leads to a SERS bandwidth
• The SERS bandwidth limits the SERS effect to realistic• The SERS bandwidth limits the SERS effect to realistic values, orders of magnitude less than 1015
Acknowledgements
• Josh Guske Bill G b• Bill Gerber
• Dr. Crissy Rhodes• Dr. Marta Cerruti
•Dr. Jan Genzer Funding: would be nice
• Dr. Jon Paul Maria• Dr. Mark Losego
Dr Donovan Leonard• Dr. Donovan Leonard
•Dr. Daniel Fischer
• Dr. Stephen Weibel