Surface plasmon resonanceon conducting metal oxides

NC 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 then the response is multiplied by the number of electrons. All electrons act in phase in this model.

me∂2r∂t2

+ meΓ∂r∂t = eE0e– iωt

e

E = E0e-iωt

Dipole p = er0Polarization P = np = ner0P = (ε(ω) - 1)ε0Eχ(ω) = ε(ω) - 1

The plasmon frequency is the resonant frequency of the forced harmonic oscillator

The forcing term is the electric field of the incident light.

χ ω ∂2E∂t2

+ Γ∂E∂t = ne2

meε0E0e– iωt

χ ω =–ωp

2

ω2 + iωΓ ωp = ne2

meε0

ε ω = 1 –ωp

2

ω2 + Γ2 + iΓ ωp

2

ω ω2 + Γ2

For εm < 0 the p-polarized image chargeadds constructively to the incident field.

p polarizations polarization

+

+-

-

Ep = Ei(1 + rp) = 2Ei

rp = 1

-

+

εm < 0

For εm < 0 the s-polarized image chargeadds destructively to the incident field.

p polarizations polarization+

+

-

-

+

-

Es = Ei(1 + rs) = 0

rs = -1

εm < 0

SPR implementation

I

Flow Cell

Coupling of the light into the Au thin film requires a prism to provide wavevectormatching (Kretschmann configuration).

Reflected LightIncident Light

II

Incident Light Reflected Light

Flow Cell

SPR implementation

Molecules in solution exhibit changes in refractive index and give rise to a measurable SPR signal when binding occurs.

Plasmon bands for different indices of refraction

Angle-dependent absorption calculated for a thin Au film

Brockman et al.Ann. Rev. Phys. Chem. 2000

Self-Assembly of12-phosphododecanoic acidon a surface of In28Sn4O48

(10.12 Å x 10.12 Å x 28.00 Å)

Monolayer with carboxylate head groups

for functionalization

3 unit cells are shown

Reflectance FTIR spectra of 12-Phosphonododecanoic Acid on ITO

1.0

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce

(x10

-3)

31003000290028002700

Wavenumbers (cm-1)1.0

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce

(x10

-3)

1850180017501700165016001550

Wavenumbers (cm-1)

Deposited from DMSO:CH2 stretches 2858 (symmetric)2926 (asymmetric) cm-1

Deposited from 50/50 (v/v)

DMSO/18MΩ H2O :CH2 stretches2848 (symmetric)2922 (asymmetric) cm-1

C=O stretch at 1716 cm-1

Brewer, Brown and FranzenLangmuir 2002, 18, 6857

0.8

0.6

0.4

0.2

0.0

Ref

lect

ance

, Pow

er R

efle

ctiv

ity

1210864

Wavenumbers (x103) (cm-1)

7.6

13.8

9.7

experiment theory

ITO Plasmon Frequency vs. Sheet Resistance

60° incident anglep-polarization

Good Conductor

Poor Conductor

Brewer and Franzen, J. Alloys and Compounds (2002)

Evidence for plasmon shifts on ITO

The observed decrease in reflectivity is more was proposed to be a surface plasmon.

Poor ConductorTransparent

Good ConductorReflecting

Brewer and Franzen, U.S. Patent Application US2004/0113077 A1Brewer and Franzen JPC B 2002, 106, 12896

k+ = – k x2 – (ω/c)2εs

k– = k x2 – (ω/c)2εm

k–εs – k+εm = 0

The coupled fields inside (-) and outside (+) the solids are givenby:

where

The electric field of the surface plasmon (SP) represents a harmonic wave along the surface with a frequency w and awave vector kx, while perpendicular to the surface (z-direction)the fields are exponentially decaying. The boundary conditions require that:

E± x,z,t = E0±exp [i(k xx – ωt)]exp – k±z

The electric field at the interface

εm is the dielectric constant of the metalεs is the dielectric constant of the substrate

For the metal the dielectric constant is complexand can be derived from the index of refraction.

k sp = ωc

εm ω εs ω

εm ω + εs ω

The SPR Dispersion Relation

ε = ε′ + iε′′ , N = n + ikε = N2 = n2 – k2 + i2nkε′ = n2 – k2 , ε′′ = 2nk

Optical constants for ITO

N = n + ik

Dielectric constants for ITO

ε = ε′ + iε′′ε′ = n2 – k2

ε′′ = 2nk

ITO Dispersion Curve

k sp = ωc

εm ω εs ω

εm ω + εs ω

Instrumentation

GWC Modular Attachment for FT-SPRMany thanks to Steve Weibel and Thermo/Nicolet

2-D spectralComparison of ITO and Au

A. The dark swathrepresents the angle-dependent absorptiondue to ωsp. B. The feature at B isBelow the critical angle.We believe that this isωp.

ITO Angle Dip in Air: Dependence on Angle

14 0

12 0

10 0

8 0

6 0

4 0

2 0

10 00 09 00 080 00700 06 000500 0

W aven um ber ( c m -1)

'4 0 d eg ' '4 5 d eg ' '5 0 d eg ' '5 5 d eg ' '6 0 d eg ' '6 5 d eg ' '7 0 d eg '

Bu lk P las m o nS urfa ce P las m o n

Ind iu m T in O xide _B K7 _air

Rhodes, Maria, Weibel and Franzen et al. Manuscript in preparation

ωsp in Kretschman configuration ωp plasmon

ωsp =ωp2

ITO Angle Dip in Air:Single wavenumber representation

Crissy Rhodes, Steve Weibel, Jon-Paul Maria

From Chaney et al. App. Surf. Sci. 2003, 218, 258

HR-ELS confirmation of surface plasmon and band gap

The primary plasmonis the surface plasmonexcited by electrons.

The agreement withoptical measurementsis good. Optically wemeasure 0.8 eV.

The band gap is also reasonable. OpticallyWe measure 3.5 eV.

10 20 30 40 50-5000

0

5000

10000

15000

20000

25000

30000

35000

In

tens

ity [a

rb. u

nits

]

Energy Loss [eV]

Silicon SiO2 ITO

AB C

Bulk or Volume Plasmon (VEELS)

Crissy Rhodes, Donavon Leonard, Gerd Duscher

Comparison ofWater and 1% EtOHA large change is observed.The difference for a 1% EtOH solution compared to pure water is shown in the lower panel.

The minimum response in wavenumbers is 4410 cm-1 in the top panel and 4690 cm-1 in the bottom panel. In gold the shift is 70 cm-1 for this solvent comparison.

H2O – 1% EtOHH2O – H2O

Generalization of the method• SPR on metal oxide thin films is a general phenomenon• sp-type include the transparent conducting oxides• d-type are compatible with semi-conductors and are

extremely robust conducting substrates0.8

0.6

0.4

0.2

0.0

Ref

lect

ance

1210864

Wavenumbers (x103) (cm-1)

Increasing Angle

IrO2

Brewer, Franzen and Maria. Chem Phys. 2005, 205, 313

Steve Weibel (GWC Technologies)NIH, NSF, ARO, Applied Biosystems Inc.

Cell Delivery ProjectDr. Alex TkachenkoJoseph RyanChiamaka AgbassiYanli LiuEric Kaufman

Viral NanotechnologyProf. Steve LommelDr. Richard GuentherLina Loo

Acknowledgements

SPR and NanosensorsProf. Jean-Paul MariaProf. Gerd DuscherDr. Simon LappiDr. Marta Cerruti (poster)Crissy Rhodes (poster)Selina MosesMark LosegoDonavon Leonared

DehaloperoxidaseDr. Vesna SerranoJennifer BelyeaMichael DavisLauren GilveyZach Nicholson

RNA NanotechnologyProf. Bruce EatonProf. Dan FeldheimDr. Richard GuentherShowyi JuMagda Dolska

1.0

0.8

0.6

0.4

0.2

0.0f(e)

(Num

ber o

f Ele

ctro

ns)

-8 -7 -6 -5 -4 -3 -2 -1

Energy (eV)

IncreasingSn Content

)(11)( ee fe

ef −−+= β

Band gap and charge carrier density of ITO

4

3

2

1

n (e

lect

rons

/cm

3 ) (x1

021)

121086420

Number of Sn Atoms

Band gap ConductionValence

Charge carrier densityIn28Sn4O48 (three unit cells)

Determination of reduced mass by energy calculation in reciprocal space

A primitive cubic cell was usedfor calculation of conduction bandenergies along various k vectors

Calculated me ωp∆ (Γ → X) 0.31 11,430 cm-1

Σ(Γ → M) 0.42 9,880 cm-1

Λ (Γ → R) 0.54 8,670 cm-1

E k = Eo + h2k2

2me

ωp = ne2

meε0

Brewer and Franzen JPC B. 2002, 106, 12986Alloys and Compounds, 2002, 338, 73