universitat estiu2011 j_ferre

Numerical Modeling of Photonic Nanostructures (and Organic

Solar Cells)Josep Ferré i Borrull, Mohammad Mahbubur Rahman, Pedro

Granero, Josep Pallarès, Lluis F. Marsal

[email protected]

Universitat Rovira i Virgili

N a n o e l e c t r o n I c and P h o t o n I c S y s t e m s

Universitat d’Estiu URV. July 2011.

Universitat d’Estiu URV. July 2011.

Numerical Modeling

OUTLINE

• Introduction to Photonic Nanostructures

– Photonic Crystals/Photonic Quasicrystals/Random Nanostructures

• Photonic Properties of Quasi-random Nanostructures

– The Quasi-Random Structure

– Numerical Methods

– Results

• Light Trapping in Nanostructured Organic Solar Cells

– Scattering by subwavelength-sized nanostructuring

– Simulation of light absorption by finite-element

– Simulation of exciton diffusion

• Conclusion

3Universitat d’Estiu URV. July 2011.

Introduction to Photonic Nanostructures

Photonic Crystals (More Properly: Photonic Band Gap Materials)


5

Photonic Crystals

ε(r)

r

a

Band gap

Band gap

0 k2π/aπ/a-2π/a -π/a

ω

-G

G

allowed

allowed

ckk )(

Dispersion relation for 1D photonic crystal

h


Photonic Crystals: The Band Structure

TMTM

TETE

E

H

E

H

NormalizedNormalizedFrequency!!!Frequency!!!ωωa/2πc=a/a/2πc=a/λλ

NormalizedNormalizedFrequency!!!Frequency!!!ωωa/2πc=a/a/2πc=a/λλ


7


Photonic QuasicrystalsOrdered structures, but not periodic:


8


Random Photonic NanostructuresRandom Lasers


9

OUTLINE







– Results





• Conclusion

10

Photonic Properties of Quasi-random Nanostructures

Nanoporous Anodic Alumina: a quasi-random strucuture

Photonic Properties??? (e.g. photonic band gap)


11


Numerical Method

Source Detector

PML

Computational Domain

FDTD

L

Variables:Pore (scatterer radius): r Domain Length: L


12



Finite-Differnce Time-Domain Method (FDTD)Finite-Differnce Time-Domain Method (FDTD)

Discretization of Maxwell Equations in Space and TimeDiscretization of Maxwell Equations in Space and Time

z

E

t

H

z

H

t

E

xy

yx

1

1

Ex z, t Ex kz,nt Exn k H y z, t H y kz,nt H y

n k

t

kEkE

t

En

x

n

xx

2

1

2

1

1

13



Finite-Differnce Time-Domain Method (FDTD)Finite-Differnce Time-Domain Method (FDTD)

Discretization of Maxwell Equations in Space and TimeDiscretization of Maxwell Equations in Space and Time

Exn1/2 k Exn 1/2 k 1

tx

H yn k 1/2 H y

n k 1/2

H yn1 k 1/2 H y

n k 1/2 1

tx

Exn1/2 k 1 Exn1/2 k

HH

00

HH

11

HH

22

HH

33

HH

44

EE1/21/2 EE3/23/2 EE5/25/2 EE7/27/2 EE9/29/2

Important Aspect! Boundary Conditions at the Important Aspect! Boundary Conditions at the Limits of The Computational SpaceLimits of The Computational Space

14



a average interpore distance

Averaging over N randomly chosen domains

L = 12·a

L = 16·a

L = 20·a


Results: quasi-random structure on Si, r/a=0.35TE PolarizationDomain Length

M K M0.0

0.2

0.4

0.6

0.8

wavevector

Nor

m.

Fre

q.

a/2

c

TE Polarization



Results: quasi-random structure on Si, r/a=0.35TM PolarizationDomain Length

M K M0.0

0.2

0.4

0.6

0.8

wavevector

Nor

m.

Fre

q.

a/2

c

TM Polarization



Results: quasi-random structure on Si, L=19aScatterer radius

TE Polarization TM Polarization



Decreasing trend of the transmittance with :Simulation of a fully random structure

TE Polarization TM Polarization



Quasi-random crystals with metallic components.

Au – Drude-Lorentz Model

Good fit between λ=500nm-1000nm

Vial et al., PRB 71, 085416 (2005)

No scale invariance


500 600 700 800 900 1000Wavelength (nm)

-50

-40

-30

-20

-10

0

real

( )

1

2

3

4

5

imag

( )


Quasi-random crystals with metallic components.

Triangular Lattice.X Direction

Quasi-random.r/a=0.05


21

OUTLINE







– Results





• Conclusion

Light Trapping in Nanostructured Organic Solar Cells

Planar Heterojunction


Organic Solar Cells: Morphologies

Ex

h+

e-

h+

Ex

e-

h+e-

?

Ex

h+

e-

Bulk Heterojunction

Nanostructured Heterojunction

Donor Acceptor



Diffraction: a possible way for light trapping

Incident Light Wavelength:

Diffracted Light

pn

sin

Period: p

p



Diffraction: a possible way for light trapping

Incident Light Wavelength:

Trapped Light

Period: p

p < >90º



Nanostructuring Organic Solar Cells with Templates: Nanoporous Anodic Alumina

500nm

2µm



Nanostructuring Organic Solar Cells with Templates: Nanoporous Anodic Alumina

1 µm



Numerical Modeling: COMSOL®

• RF Module: Maxwell Equations

• Time-dependent and stationary

• Possibility of evaluating absorption as a function of position

• Connection with drift-diffusion and Poisson equations

• 1-D Periodicity (period 2) • P3HT and PCBM optical constants n and k.• Width: 4m



-Taking into account the exciton diffusion length (~10nm)

- Four different size ranges:i) 1.25nm 12.5 nm

ii) 20nm 100 nm

iii) 125nm 250 nm

iii) 400nm 2 m

Unit Cell

2a

10n

m2

0nm

10n

m



3W/m;rQ Total Dissipated Power

W ;3HTP

dVrQQ

W i

iTotal QQ



Reference Cells

Bilayer – Planar Heterojunction

PHTotal

PH QQ ,

Effective Medium:n, k: average of P3HT

and PCBM

20n

m2

0nm

10n

m2

0nm

10n

m



Absorption Results. Features much smaller than wavelength.

PHQQ / nmrQ 450;

100nm

1m

Effective

Medium

a=1.25nm a=12.5nm



Absorption Results. Features smaller than wavelength.

PHQQ /



Absorption Results. Feature size the order of wavelength.

PHQQ / nmrQ 450;

100nm

1m

a=200nm a=250nma=125nm



Absorption Results. Features bigger than wavelength.

PHQQ / nmrQ 450;

100nm

1m

a=400nm a=2mBilayer



Absorption Results

€

QTotal /QTotalPH



Exciton Diffusion.

Ex

ExEx

Ex

How much absorbed light contributes to current? IPCEExcitons reaching the D/A interface vs incident photons

hh



Exciton Diffusion. Planar Heterojunction (Reference)

Exciton Concentration (inc=540nm)

40nm

100n

m



Exciton Diffusion. Smallest features (a=12.5nm)


40nm

100n

m



Exciton Diffusion. Wavelength-order features (a=250 nm)


40nm

200n

m

40

Conclusion

• Photonic Quasi-Random Nanostructures: photonic band

gap other possible photonic properties (resonant

cavities, 3D structures).

• Absorption in Nanostructured Organic Solar Cells: light

trapping for wavelength-order nanostructuring sizes.

• Exciton Diffusion in Organic Solar Cells: favored by the

smallest nanostructuring sizes.


41

Acknowledgments

Seniors:

Pilar Formentín

Students:

Abel Santos

Collaboration with:

• Enric Garcia-Caurel

École Polytechnique Paris

• Sabine Portal

Universitat de Barcelona

• Mar Sánchez

• Ignacio Moreno

Universidad Miguel Hernández


universitat estiu2011 j_ferre

Technology

outline universitat

virgili universitat

x direction quasirandom

address universitat

time h

morphologies h

organic solar cells

diffracted light period