Taming light with plasmons –Taming light with plasmons –theory and experimentstheory and experiments

Aliaksandr Rahachou, ITN, LiU Aliaksandr Rahachou, ITN, LiU Kristofer Tvingstedt, IFM, LiUKristofer Tvingstedt, IFM, LiU

2006.10.19, Hjo

OUTLINEOUTLINE

• Introduction to plasmonics

• Optical excitation of plasmons

• Plasmons in organic solar cells

• Experimental results for APFO3:PCBM on Al gratings

• Theoretical results for APFO3:PCBM on Al gratings

p-polarization: E-field is parallel to the plane of incidence

s-polarization: E-field is perpendicular to the plane of incidence (German senkrecht = perpedicular)

x

z

y

1

Hx

2

z=01

2

Ey

H

Hz

x

z

y

1

Ex

Ez

2

z=0 1

2

Hy

E

INTRODUCTION TO PLASMONICSINTRODUCTION TO PLASMONICS

x

z

y

z=0 1

2

E1x

E1z

H1y

E1

p-polarized incident radiation will create polarization charges at the interface. We will show that these charges give rise to a surface plasmon modes

E2x

E2z

H2y

E2

creation of the polarization charges

if one of the materials is metal, the electrons will respond to this polarization. This will give rise to surface plasmon modes

Boundary condition:(a) transverse component of E is conserved,

(b) normal component of D is conserved

Polarization charges are created at the interface between two material.

The electrons in metal will respond to this polarization giving rise to surface plasmon modes

x

z

y

z=0 1

2

H1x

H1z

E1y

H1

s-polarized incident radiation does not create polarization charges at the interface. It thus can not excite surface plasmon modes

H2x

H2z

E2y

H2

no polarization charges are created no surface plasmon modes are excited!In what follows we shall consider the case of p-polarization only

Boundary condition(note that E-field has a transverse component only):

transverse component of E is conserved,

compare with p-polarization:

More detailed theory

Let us check whether p-polarized incident radiation can excite a surface mode

x

z

y

z=0

dielectric1

metall 2

E1x

E1z

H1y

E1

)(~ txxkie

wave propagating in x-direction

intensity

z

zzzzik ike ;~

we are looking for a localized surface mode, decaying into both materials

components of E-, H-fields: E = (Ex, 0, Ez); H = (0, Hy, 0)

Thus, the solution can be written as

x

z

y

z=0

dielectric1

metall 2

E1x

E1z

H1y

E1

solution for a surface plasmon mode:

Let us see whether this solution satisfies Maxwell equation and the boundary conditions:

+condition imposed on k-vector

What is the wavelength of the surface plasmon ?k

2

let us find k: 2

22

12

21

211

xz

xz

kknk

kknk

substitute

21

21

rr

rrx kk

k

kx

21

21

rr

rrx ck

lig

ht co

ne =

c

k

The surface plasmon mode always lies beyond the light line, that is it has greater momentum than a free photon of the same frequency

Ideal case: r1 and r2 are real (no imaginary components = no losses)

Dielectric: r1 >0

Metal: r2 < 0, |r2| >> r1

k

resonant width = 0 lifetime =

21

21

rr

rrx kk

kx is real

21

21

rr

rrx kk

Realistic case: r1 is real, and r2 is complex, ''2

'22 rrr i imaginary part describes losses in metal

'''

''2

'21

''2

'21

21

21

xx

rrr

rrr

rr

rrx

ikk

i

ikkk

k

resonant width (gives rise to losses)

2'2

''22/3

1''

2

1

r

rrx kk

Dielectric functions of Ag, Al

''r

'r 2'

2

''2

r

r

surface plasmon length scales:

dielectric1

metall 2

z

decay into metal

decay into

dielectric propagation length

dielectric1

metall 2

is it possible to excite a plasmon mode by shining light directly on a dielectric/metal interface?

k

kx

21

21

rr

rrx ck

lig

ht co

ne =

c

k

The surface plasmon mode always lie beyond the light line, that is it has greater momentum than a free photon of the same frequency .

This makes a direct excitation of a surface plasmon mode impossible!

OPTICAL EXCITATION OF PLASMONSOPTICAL EXCITATION OF PLASMONS

metal

coupling gap

prism

Otto geometry

metal

prism

Kretschmann-Raethergeometry

Grating

dG

Gkk

x

xxx

2

'

dkx

2'

0xk

METHODS OF PLASMON EXCITATIONMETHODS OF PLASMON EXCITATION

Observation of plasmon enhanced absorbtion in

Apfo3/PCBM

Introduction

• Prescence of periodic metal gratings in a dielectric environment triggers surface plasmons and creates an intense optical near field

• An absorbing layer on top of the grating should therefore be exposed to a strong field

• Plasmons are traveling along the interface (not perpendicular as the impinging light)

• Introducing Surface plasmons in solar cells may hence increase the absorption

Grating manufacturing

• Optical diffraction gratings are replicated via PDMS replica molding

• The PDMS replica is subsequently imprinted in a photocureable resin.

• Very high replication throughput

1

2

3

Grating Manufacturing

Grating is metallized by thermal evaporation of ~90 nm Al

Grating Characterization

Period: 277 nmDepth: ~48 nmRougness ~5 nm

Samples

*Metal gratings coated with ~150 nm Apfo3/PCBM 1:4 mixture

*Planar mirror reference samples manufactured

*Reflectance measured in integrating sphere (all angels collected)

Grating mirror reflectance

Different orientation/polarization shows very different reflectance in the UV region.

*Polarized reflection

*Air metal SP

Sample reflectance

New absorption peaks!SP?Waveguide?

Initial results: Photocurrent from inverted cells

CLEAN GRATING MIRROR

Al-air plasmonic peak

35x106

30

25

20

15

n/c

, m

-1

45x106

403530252015

kx, m-1

ESTIMATING THE POSITION OF A PLASMON PEAKESTIMATING THE POSITION OF A PLASMON PEAK

APF03:PCBM 1:4-Al dispersion relation

dG

Gkk

x

xx

2

'

dkx

2' 0xk

normal incidence

where d is a period of grating (sinusoidal, tiranglar or step-like)

Dielectric function of APFO3:PCBM 1:4 in direction normal to the surface

450x10-9

400

350

300

250

200

150

d=

2k

x

900800700600500400300

nm

d = 277 nm

0

21

21

rr

rrx kk

NUMERICAL RESULTS (Green’s function method)NUMERICAL RESULTS (Green’s function method)

AlAPFO3:PCBM1:4Air Air

~120nm

TE (P)-polarized light

Hz

Ey

Ex

Flat surface…

Flat surface and experiment once again...Flat surface and experiment once again...

THEORETICAL RESULTS (Ideal sinosoidal surface)THEORETICAL RESULTS (Ideal sinosoidal surface)

AlAPFO3:PCBM

1:4Air Air

~120nm

TE (P)-polarized light

Hz

Ey

Ex

46nm

277nm

THEORETICAL RESULTS (Sinusoidal surface)THEORETICAL RESULTS (Sinusoidal surface)

Realistic surfaceRealistic surface

AlAPFO3:PCBM

1:4Air Air

~120nm

TE (P)-polarized light

Hz

Ey

Ex

46nm

277nm

Roughness ~ 6x4nm

Smooth surface variation

Realistic surfaceRealistic surface

25nm

Absoptance peaksAbsoptance peaks

~250 nm thickpolymer

?

CONCLUSIONSCONCLUSIONS

• We demonstrated both experimentally and theretically enchanced absorptance of light in APFO3:PCBM 1:4 solar-cells with Al gratings

• Easy manufacturing with soft lithography.• The theoretical and experimental data agree very

well!

THANKTHANK YOUYOU!!

Acknowledgements

• Nils-Christer Persson for optical characterization of the

materials • Chalmers for materials