ELECTRONICS &PHOTONICS DEPARTMENT · PDF fileELECTRONICS &PHOTONICS DEPARTMENT Definitions of...
Transcript of ELECTRONICS &PHOTONICS DEPARTMENT · PDF fileELECTRONICS &PHOTONICS DEPARTMENT Definitions of...
ELECTRONICS & PHOTONICS DEPARTMENT
Institute of High Performance ComputingInstitute of High Performance Computing
Koh Wee Shing
December 2009
Koh Wee Shing
24 Oct 2013
ELECTRONICS & PHOTONICS DEPARTMENT
� 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
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ELECTRONICS & PHOTONICS DEPARTMENT
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
ELECTRONICS & PHOTONICS DEPARTMENT
� 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)
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Optical AbsorptionPolaron Generation
& Carrier dissocation
-
Carrier Transport
- - -
ELECTRONICS & PHOTONICS DEPARTMENT
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)
ELECTRONICS & PHOTONICS DEPARTMENT
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)
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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
ELECTRONICS & PHOTONICS DEPARTMENT
Polaron Generation & Carrier Recombination
� 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)
ELECTRONICS & PHOTONICS DEPARTMENT
Polaron Generation & Carrier Recombination
� 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
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[ ][ ]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]
ELECTRONICS & PHOTONICS DEPARTMENT
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
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� 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
ELECTRONICS & PHOTONICS DEPARTMENT
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])
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*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]
ELECTRONICS & PHOTONICS DEPARTMENT
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]
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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)
ELECTRONICS & PHOTONICS DEPARTMENT
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
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Control
POPV
ELECTRONICS & PHOTONICS DEPARTMENT
POPV Device: J-V Characteristics
Control (T=300K)
POPV (T=300K)
� % enhancement in Jsc isapprox % ↑ in opticalabsorption
� ↓ temperature → ↑Voc isconsistent withexperimental behaviorsmall molecule OPV
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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]
ELECTRONICS & PHOTONICS DEPARTMENT
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.
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