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ELECTRONICS & PHOTONICS DEPARTMENT

Institute of High Performance ComputingInstitute of High Performance Computing

Koh Wee Shing

December 2009

Koh Wee Shing

24 Oct 2013


� Definitions of Measures of Solar Cells

� Overview of Processes in an Organic BHJ Solar Cell

� Device Model:� Optical� Polaron Generation & Carrier Recombination

Outline

� Polaron Generation & Carrier Recombination� Charge Transport

� Validation & Calibration of Simulation Model with Experiment

� Plasmonic OPV device

� Summary

� Acknowledgements

2


Definitions of Measures of Solar Cells

� Isc = short circuit current

� Voc = open circuit voltage

� Imp = max power point current

� Vmp = max power point voltagevoltage

� Fill factor, FF =

� Efficiency =

3

ocsc

mpmp

VI

VI

in

ocsc

P

FFVI


� Basic Processes� Optical Illumination & Absorption (in whole structure)

� Polaron Generation & Carrier Recombination (in P3HT:PCBM only)

� Carrier Transport ( in P3HT:PCBM only)

Review of Physics of Organic Solar Cells

+

-

+

-

+ + +

- - -

Other OPV device model

� 1D electronic model from University of Groningen, The Netherlands developed by Koster et al (PRB 72,085205, 2005) for BHJ solar cells� Constant optical generation in active layer assumed

� 2D optoelectronic model from University of Bath, UK by J. Williams et al (Nanotechnology 19, 424011,2008)� Only single wavelength illumination demonstrated

� 3D optoelectronic model by Koh et al� Reduced recombination factor (IEEE Journal of PV, 1, 84, 2011)� Non-germinate recombination due to traps (SPIE Photonic West OPTO Symposium 2013)

4

Optical AbsorptionPolaron Generation

& Carrier dissocation

-

Carrier Transport

- - -


Optical

� Solve the Frequency-Domain Maxwell Equations:

optopt

optropt

HjE

EjH

0

0

2

2

πνµ

επνε

−=×∇

=×∇

typermittivi relative

frequency

vector fieldelectric

vector fieldmagnetic where

=−=

=

=

=

21 εεε

ν

j

E

H

r

opt

opt

5

� Spectral absorbed energy density in the photoactive layer (P3HT:PCBM) at each position (x, y, z) [1]:

2

02

1),,,( optEczyxQ αηεν =

index refractive of part real

index refractive of partimaginary

light incoming of wavelength

tcoefficien absorption

light of speed where

=

=

=

==

=

η

κ

λ

λ

πκα

2

c

1) J. Williams et al, Nanotechnology, 19, 424011 (2008)


Polaron Generation & Carrier Recombination

Excitons

(e---h)

Polaron

Pairs

(e---h+)

Free

carriers

(e- & h+)

Ground

state

dissociation

recombination

Exciton

diffusion

decay

to

hν

� Generation of polarons at each frequency ν and position (x, y, z)

6

state

202),,,( optEhh

QzyxG

επε

νν ==

� Integrate the frequency dependent G over the AM1.5G solar spectrum

∫=GAM

tot dSzyxGzyxG5.1

)(),,,(),,( ννν

spectrum solar AM1.5Gthe ofdensity spectral)( where =νS



� At steady state and at each position (x, y, z) in the active layer (P3HT:PCBM), the net free carriers generated [2] is

RXkGXk fd +−=

� From Osnager & Braun’s germinate theory,

constant rate ionrecombinat rbimolecula carrier

constant ratedecay polaron

constant rate ndissocatio polaron

ionconcentrat polaron where

=

=

=

=

R

k

k

X

f

d

distance separation h) & e (bound polaron mean where =a

7

( )b

bJe

aETak

Tk

E

db

b

2

22

4

3),,( 1

3−

−=

−

π

γ

( )

holes)( electrons ofmobility

factor Langevin

order first of function Bessel

constant Boltzmann

energy binding polaron

torsemiconducorganic in fieldelectric tic electrosta

etemperatur

distance separation h) & e (bound polaron mean where

n

pn

=

=+=

=

=

=

==

=

=

=

)(

0

1

22

0

3

0

2

8

4

p

r

br

b

r

b

εε

q

J

Tkεπε

Eqb

k

a

qE

E

T

a

µ

µµγ

επε

[2] L. J. A. Koster et al, PRB, 72, 085205 (2005)



� The decay rate constant kf can also be derived from Osnager and Braun’s model with the following relation to kd:

df kP

Pk

−=

1

( ) ( )

separation h-e withpolarons of ndissocatio ofy probabilit

ondissociati polaron ofy probabilit average where

==

== ∫∞

0

,,,

d rk

p

drarfETrpP

8

[ ][ ]iitfp

iitfn

pnnpR

pnpnR

−=

−=

γ

γ

� The recombination rate of free carriers to polarons Rn,p can be described bythe using a trap model which will enable us to account for the dark currentgenerated due to traps [4]:

material disordered a is polymer the as r for ondistributi Gaussianf

separation h-e withpolarons of ndissocatio ofy probabilit

==

=+

=

2

2

2

3

4a

r

fd

era

rkk

p

π

ionconcentratcarrier intrinsic

ionconcentrat ole)electron(h free

ionconcentrat ole)electron(h trapped where

=

=

=

)(pn

)(pn

)(pn

ii

ff

tt

3) J. A. Barker et al, PRB, 67, 075205 (2003)

4) N. C. Giebink et al, PRB 82, 155305 (2010)

[3]


Device Model: Charge Transport

� Drift diffusion equations

� Poisson equation

( )q

fppfp

fnnfn

peDVepJ

neDVenJ

∇+∇−=

∇+∇−=

µ

µ

E

Pp

Tk

ENn

HOMOcathodef

B

gap

LUMOcathodef

=

−=

,

, exp

Boundary Conditions

� At hole-ohmic PEDOT:PSS

9

� Continuity equation

( )tftf

r

ppnnq

V −−+=∇εε 0

2

state)(steady 01

state)(steady 01

=−+∇=

=−+∇=

pdp

ndn

RXkJqdt

dp

RXkJqdt

dn

q

EVV

gap

acathode −=

0

exp,

,

=

−=

=

anode

B

gap

HOMOanodef

LUMOanodef

V

Tk

EPp

Nn

� At electron-ohmic Ca


Validation and Calibration of Simulation

Model with Experiment

0.0 0.2 0.4 0.6 0.8 1.0-6

-3

0

3

(J [m

A/c

m2])

10

*Simulated J-V curves (symbols)*Experimental J-V curves courtesy of IMRE (solid line)

0.0 0.2 0.4 0.6 0.8 1.0

-1.0 -0.5 0.0 0.5 1.00

1

2

log

10(J

[m

A/c

m

Va [V]


Simulation ParametersParameter Symbol Simulation Value Remarks

Bandgap Egap1.1eV LUMO (PCBM=-4eV) [5],

HOMO (P3HT)=-5.1eV [6]

E-h pair separation a 1.15nm Related to kd [from Ref 7]

Electron mobility µn0.7 x10-4 cm2/Vs Experimental Measurement=~10-4 cm2/Vs

Hole mobility µp0.7 x10-4 cm2/Vs Experimental Measurement=~10-4 cm2/Vs

Decay rate kf3x104 Constrained Fitting Parameter

E-h pair separation a 1.15nm Related to k [from Ref 7]

11

E-h pair separation a 1.15nm Related to kd [from Ref 7]

P3HT:PCBM relative permittivity εr3.4 Average Value of P3HT & PCBM

Characteristic temperature of

trapped electrons (holes)Tt,A

(Tt,D)

1200K Unique fitting parameter for dark current

Density of states of free

electrons (holes)NLUMO

(PHOMO)

4.2x1022 cm-3 Constrained Fitting Parameter related to

Tt,A (Tt,D)

Density of states of trapped

electrons (holes)HA (HD) 2x1013cm-3 Constrained Fitting Parameter related to

Tt,A (Tt,D)

Series Resistance Rs1.8Ω Experimental measurement is ~1-2Ω

5) M. D. Irwin et al, PNAS, 105, 2783-2787 (2007)

6) M. C. Scharber et al, Advanced Materials, 18, 789-794 (2006)

7) W. S. Koh et al, IEEE J. Photovoltaics, 1, 84-92 (2011)


Plasmonic OPV (POPV) Device:

Optical & Polaron Generation

� Structure with 200nm (long axis) by 40nm (short axis) Agnanoellipsoid in PEDOT:PSS @ 1% coverage is illuminated byAM1.5G spectrum

Absorption Rate Generation of Polarons

12

Control

POPV


POPV Device: Carrier TransportElectron Conc

13

Potential


POPV Device: J-V Characteristics

Control (T=300K)

POPV (T=300K)

� % enhancement in Jsc isapprox % ↑ in opticalabsorption

� ↓ temperature → ↑Voc isconsistent withexperimental behaviorsmall molecule OPV

14

Device

Characteristic

Control Cell

(Experiment)

Control Cell

(T=300K)

POPV Cell

(T=300K)

POPV Cell

(T=250K)

Voc (V) 0.55 0.55 0.55 0.64

Jsc (mA/cm2) 9.61 9.61 9.76 10

Efficiency (%) 3.6 3.76 3.82 4.6

Fill Factor 0.68 0.71 0.71 0.72

POPV (T=300K)

POPV (T=250K)

small molecule OPVdevice by Giebink et al.[4]


Summary

� Developed a full 3D optoelectronic model for organic bulk-heterojunction solar cell

� Validated our model with experiment for a control structure

� Illustrate and predict both optical and electrical characteristics of a3D Plasmonic OPV device3D Plasmonic OPV device

� Open up possibilities to design and simulate nanostructureenhanced organic bulk-heterojunction solar cells.

� Device physics is applicable for both polymer and small molecule-based organic bulk-heterojunction solar cells.

15


Thank You for your Attention

Any Questions?

16

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