Taming light with plasmons – theory and experiments

Aliaksandr Rahachou, ITN, LiU Kristofer Tvingstedt, IFM, LiU 2006.10.19, Hjo

OUTLINE

• 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

INTRODUCTION TO PLASMONICS

p-polarization: E-field is parallel to the plane of incidence y z=0 E z H y E E x q 1 x q 2 z e 1 e 2 s-polarization: E-field is perpendicular to the plane of incidence (German senkrecht = perpedicular) H z H z=0 E y H x q 1 e 1 y x e 2 q 2 z

p-polarized incident radiation will create polarization charges the interface. We will show that these charges give rise to a surface plasmon modes at Boundary condition: (a) transverse component of E is conserved, (b) normal component of D is conserved y z=0 E 1z x H 1y E 1 E 1x E 2z H 2y E 2 E 2x e 1 e 2 z 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

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

s-polarized incident radiation does not charges at the interface. It thus can not create polarization excite surface plasmon modes y z=0 H 1z x E 1y H 1 H 1x H 2z E 2y H 2 H 2x e 1 e 2 z Boundary condition (note that E-field has a transverse component only): transverse component of E is conserved, compare with p-polarization: no polarization charges are created case of p-polarization only  no surface plasmon modes are excited!

In what follows we shall consider the

More detailed theory Let us check whether p-polarized incident radiation can excite a surface mode dielectric e 1 E 1z y z=0 z metall e 2 x H 1y E 1 E 1x

e i

(

k x x

 

t

) z ~

e ik z z

; components of E-, H-fields: E = (E x , 0, E z ); H = (0, H y , 0)

k z

intensity  

i



z

we are looking for a localized surface mode, decaying into both materials Thus, the solution can be written as

solution for a surface plasmon mode: dielectric e 1 E 1z y z=0 H 1y E 1 E 1x x z metall e 2 Let us see whether this solution satisfies Maxwell equation and the boundary conditions: condition imposed on k-vector +

let us find k:

k x

substitute

k x



k k

1

z

 

k

2

z

    1

k

2 

k

1 2

x

  1

k

2 

k

2 2

x

e e

r

1

r

1 e 

r

e 2

r

2   2

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 

k x

 

c

e e

r

1

r

1 e 

r

e 2

r

2

k

k x



k

e e

r

1

r

1  e

r

e 2

r

2 Ideal case: e r1 and e r2 are real (no imaginary components = no losses) Dielectric: e r1 >0 Metal: e r2 < 0, | e r2 | >> e r1 k x is real resonant width = 0  lifetime =  k

k x



k

e

r

e 1

r

1 e 

r

e 2

r

2

Realistic case: e

r

2  e '

r

2  e r1 is real, and e r2

i

e

r

'' 2 is complex, imaginary part describes losses in metal

k x



k

  

k x

' e e

r

1

r

1 e 

r

e 2

r

2 

ik x

'' 

k

e e

r

1

r

1    e '

r

e 2

r

' 2  

i

e

i

e

r

'' 2

r

'' 2   resonant width (gives rise to losses)

k x

''  1 2

k

e

r

3 1 / 2 e e

r r

'' 2 2   2 k Dielectric functions of Ag, Al e

r

' e

r

'' e e

r r

'' 2 2   2

metall e 2 dielectric e 1 z surface plasmon length scales: propagation length

OPTICAL EXCITATION OF PLASMONS

dielectric e 1 is it possible to excite a plasmon mode by shining light directly on a dielectric/metal interface?

metall e 2

k x k x

 

c

e e

r

1

r

1 e 

r

e 2

r

2

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!

METHODS OF PLASMON EXCITATION

q 1 prism coupling gap metal Otto geometry q 1 prism metal Kretschmann-Raether geometry

k x

'

G x



k x

  Grating  2 

G x k x

'

d k x

   0 2 

d

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 nm Depth: ~48 nm Rougness ~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

ESTIMATING THE POSITION OF A PLASMON PEAK 35x10 6 APF03:PCBM 1:4-Al dispersion relation 30 25 20

k x



k

e e

r

1

r

1 e 

r

e 2

r

2 Dielectric function of APFO3:PCBM 1:4 in direction normal to the surface 15 15

k

'

x x

 

k

 

G x

2  20 25 30 k x , m -1 35

k

40 45x10 6 450x10 -9 400 350 300 d = 277 nm 250 200 150 300 400 500  0 600  nm 700 800 900

NUMERICAL RESULTS (Green’s function method) ~120nm

Flat surface…

TE (P)-polarized light E y H z E x Air

APFO3:PCBM 1:4

Al Air

Flat surface and experiment once again...

THEORETICAL RESULTS (Ideal sinosoidal surface) ~120nm TE (P)-polarized light E y H z E x Air

APFO3:PCBM 1:4

Al Air 46nm 277nm

THEORETICAL RESULTS (Sinusoidal surface)

Smooth surface variation Realistic surface ~120nm Roughness ~ 6x4nm TE (P)-polarized light E y H z E x Air

APFO3:PCBM 1:4

Al Air 46nm 277nm

Realistic surface 25nm

Absoptance peaks ?

~250 nm thick polymer

CONCLUSIONS

• 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!

THANK YOU

!

Acknowledgements

• •

Nils-Christer Persson

for optical characterization of the materials

Chalmers

for materials