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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

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Taming light with plasmons theory and experiments

Taming light with plasmons –theory and experiments

Aliaksandr Rahachou, ITN, LiU

Kristofer Tvingstedt, IFM, LiU

2006.10.19, Hjo


Outline
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

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

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

Ez

Hz

E

H

Hy

Ey

Ex

Hx

q1

q1

e1

e1

z=0

z=0

y

y

e2

e2

x

x

q2

q2

z

z


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

(b) normal component of D is conserved

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

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

E1z

E1

H1y

e1

E1x

z=0

E2

E2z

y

e2

x

H2y

E2x

z


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


compare with p-polarization: two material.

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

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

transverse component of E is conserved,

H1z

H1

E1y

e1

H1x

z=0

H2

H2z

y

e2

x

E2y

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

H2x

z


intensity two material.

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

wave propagating in x-direction

z

Thus, the solution can be written as

More detailed theory

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

dielectric e1

E1z

E1

H1y

E1x

z=0

y

x

z

metall e2

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


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

condition imposed on k-vector

+

solution for a surface plasmon mode:

dielectric e1

E1z

E1

H1y

E1x

z=0

y

x

z

metall e2


substitute and the boundary conditions:

kx

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

light cone  = c k

w

k

What is the wavelength of the surface plasmon ?

let us find k:


Ideal case: and the boundary conditions:r1 and r2 are real (no imaginary components = no losses)

Dielectric: r1 >0

kx is real

Metal: r2 < 0, |r2| >> r1

resonant width = 0 lifetime = 

k


Realistic case: and the boundary conditions:r1 is real, and r2 is complex,

imaginary part describes losses in metal

resonant width (gives rise to losses)

k

Dielectric functions of Ag, Al


surface plasmon length scales: and the boundary conditions:

metall e2

decay into metal

propagation length

decay intodielectric

dielectric e1

z


dielectric and the boundary conditions: e1

kx

metall e2

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!

light cone  = c k

w

k

OPTICAL EXCITATION OF PLASMONS

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


prism and the boundary conditions:

prism

Grating

q1

q1

coupling gap

metal

metal

Kretschmann-Raether

geometry

Otto geometry

METHODS OF PLASMON EXCITATION



Introduction
Introduction and the boundary conditions:

  • 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

1 and the boundary conditions:

2

3

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


Grating manufacturing1
Grating Manufacturing and the boundary conditions:

Grating is metallized by thermal evaporation of ~90 nm Al


Grating characterization
Grating Characterization and the boundary conditions:

Period: 277 nm

Depth: ~48 nm

Rougness ~5 nm


Samples
Samples and the boundary conditions:

*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
Grating mirror reflectance and the boundary conditions:

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

*Polarized reflection

*Air metal SP


Sample reflectance
Sample reflectance and the boundary conditions:

New absorption peaks!

SP?

Waveguide?


Initial results photocurrent from inverted cells
Initial results: and the boundary conditions:Photocurrent from inverted cells


Clean grating mirror

Al-air plasmonic peak and the boundary conditions:

CLEAN GRATING MIRROR


Estimating the position of a plasmon peak

normal incidence and the boundary conditions:

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

ESTIMATING THE POSITION OF A PLASMON PEAK

APF03:PCBM 1:4-Al dispersion relation

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


Numerical results green s function method

TE (P)-polarized light and the boundary conditions:

Ey

Hz

Ex

NUMERICAL RESULTS (Green’s function method)

~120nm

Flat surface…

APFO3:PCBM

1:4

Al

Air

Air


Flat surface and experiment once again
Flat surface and experiment once again... and the boundary conditions:


Theoretical results ideal sinosoidal surface

~120nm and the boundary conditions:

TE (P)-polarized light

Ey

277nm

Hz

APFO3:PCBM

1:4

Ex

Air

Al

Air

46nm

THEORETICAL RESULTS (Ideal sinosoidal surface)


Theoretical results sinusoidal surface
THEORETICAL RESULTS (Sinusoidal surface) and the boundary conditions:


Realistic surface

Roughness ~ 6x4nm and the boundary conditions:

~120nm

Smooth surface variation

TE (P)-polarized light

Ey

277nm

Hz

APFO3:PCBM

1:4

Ex

Air

Al

Air

46nm

Realistic surface


Realistic surface1

25 and the boundary conditions:nm

Realistic surface


Absoptance peaks

~250 nm thick and the boundary conditions:

polymer

Absoptance peaks

?


Conclusions
CONCLUSIONS and the boundary conditions:

  • 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!

THANKYOU!


Acknowledgements
Acknowledgements and the boundary conditions:

  • Nils-Christer Persson for optical characterization of the materials

  • Chalmers for materials


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