Transcript Plasmonics in optoelectronic devices

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
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
Hy
z
Ey
Ex
q1
z=0
y
H
x
e1
e2
Hx
q1
z=0
y
q2
z
x
e1
e2
q2
p-polarized incident radiation will
create polarization charges at
the interface. We will show that
these charges give rise to a
surface plasmon modes
Boundary condition:
(a) transverse component of E is conserved,
(b) normal component of D is conserved
E1z
E1
z=0
y
z
H1y
x
E1x
E2z
H2y
E2
E2x
e1
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
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 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
z=0
y
z
E1y
x
H1x
H2z
E2y
H2
H2x
e1
e2
compare with p-polarization:
no polarization charges are created 
no surface plasmon modes are excited!
In what follows we shall consider the
case of p-polarization only
More detailed theory
Let us check whether p-polarized incident radiation can excite a surface mode
dielectric e1
ik z z
E1z
~e
E1
z=0
y
H1y
E1x
x
z
intensity
~ ei ( k x xt )
wave propagating
in x-direction
we are looking for a localized
surface mode, decaying into
both materials
z
metall e2
components of E-, H-fields:
; k z  i z
E = (Ex, 0, Ez); H = (0, Hy, 0)
Thus, the solution can be written as
solution for a surface plasmon mode:
dielectric e1
E1z
E1
z=0
y
H1y
E1x
x
z
metall e2
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
let us find k:
substitute
kx  k
kx
n1k 2  k12x
k2 z  
n1k 2  k 22 x
2
?
k
e r1e r 2
e r1  e r 2
The surface plasmon mode always
lies beyond the light line, that is it
has greater momentum than a free
photon of the same frequency 

kx 
k1z  


c
e r1e r 2
e r1  e r 2
k
kx  k
e r1e r 2
e r1  e r 2
Ideal case: er1 and er2 are real (no imaginary components = no losses)
Dielectric: er1 >0
Metal: er2 < 0, |er2| >> er1
kx is real
resonant width = 0 
lifetime = 
k
kx  k
e r1e r 2
e r1  e r 2
Realistic case: er1 is real, and er2 is complex,
e r 2  e r' 2  ie r''2
kx  k
e r1e r 2
k
e r1  e r 2

imaginary part describes losses in metal

e r1 e r' 2  ie r'' 2
e r1  e r' 2  ie r'' 2

resonant width (gives rise to losses)

k x''
   k x'  ik x''
1 3 / 2 e r'' 2
 ke r1
2
2
e'
 
r2
k
Dielectric functions of Ag, Al
e r'
e r''
e r'' 2
e 
' 2
r2
surface plasmon length scales:
metall e2
propagation length
dielectric e1
z
OPTICAL EXCITATION OF PLASMONS
dielectric e1
is it possible to excite a plasmon
mode by shining light directly on a
dielectric/metal interface?
metall e2
kx

The surface plasmon mode always
lie beyond the light line, that is it has
greater momentum than a free
photon of the same frequency .
kx 

c
e r1e r 2
e r1  e r 2
k
This makes a direct excitation of a
surface plasmon mode impossible!
METHODS OF PLASMON EXCITATION
q1
prism
coupling gap
metal
q1
prism
Otto geometry
metal
Kretschmann-Raether
geometry
Grating
k x'  k x  Gx
2
Gx  
d
kx  0
k x'  
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
APF03:PCBM 1:4-Al
dispersion relation
6
Dielectric function of
APFO3:PCBM 1:4 in
direction normal to the
surface
n/c, m
-1
30
25
e r1e r 2
e r1  e r 2
kx  k
20
15
20
k  k  Gx
'
x
Gx  
2
d
25
30
kx, m
35
40
45x10
6
450x10
-1
normal incidence
2
kx  0 k  
d
'
x
where d is a period of grating
(sinusoidal, tiranglar or step-like)
-9
400
d=2kx
15
350
300
d = 277 nm
250
200
0
150
300
400
500
600
 nm
700
800
900
NUMERICAL RESULTS (Green’s function method)
~120nm
Flat surface…
TE (P)-polarized light
Ey
Hz
Ex
Air
APFO3:PCBM
1:4
Al
Air
Flat surface and experiment once again...
THEORETICAL RESULTS (Ideal sinosoidal surface)
~120nm
TE (P)-polarized light
Ey
277nm
Hz
Ex
Air
APFO3:PCBM
1:4
Al
46nm
Air
THEORETICAL RESULTS (Sinusoidal surface)
Realistic surface
Roughness ~ 6x4nm
~120nm
Smooth surface variation
TE (P)-polarized light
Ey
277nm
Hz
Ex
Air
APFO3:PCBM
1:4
Al
46nm
Air
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