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