EXCITON RECOMBINATION IN THE FULLERENE PHASE OF BULK
HETEROJUNCTION ORGANIC SOLAR CELLS
A DISSERTATION
SUBMITTED TO
THE DEPARTMENT OF APPLIED PHYSICS
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
George Frederick Burkhard
April 2011
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/hb980zz5771
2011 by George Frederick Burkhard. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Michael McGehee, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Ian Fisher, Co-Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Alberto Salleo
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
iii
iv
Abstract Finding alternatives to fossil fuel energy sources is necessary to stem global
warming, to provide economic and political independence, and to keep up with
increasing energy demand. Because of their low cost, flexibility, and because the
material resources needed to make them are abundant, organic polymer solar cells are
an attractive alternative to conventional solar technology. Organic solar technology
has been developing rapidly; however, with the best power conversion efficiencies at
~8%, much improvement is needed before it can be competitive with established solar
technologies.
Poly-3-hexylthiophene:[6,6]-phenyl-C61-butyric acid methyl ester
(P3HT:PCBM) solar cells are the most studied type of organic solar cell. Nevertheless,
their loss mechanisms are still not fully understood. In this work, we study excitonic
losses in the PCBM phase of the blend. We develop a way to accurately measure
internal quantum efficiencies (IQEs) and use this technique to characterize
P3HT:PCBM devices. We observe spectral dependence of the IQE and conclude that a
majority of excitons generated in the PCBM are lost to Auger recombination with
polarons that are trapped in that phase. We also provide evidence that this process may
happen in other materials and may be a critical factor in limiting exciton diffusion in
organic semiconductors.
v
Acknowledgments As with any scientific work, this thesis builds on the knowledge of countless
others. Although they are too numerous to mention in full, there are several
individuals who deserve special acknowledgment.
Perhaps more than anyone else, Shawn Scully developed my understanding of
the physics of polymer solar cells. He was the original owner of this project; I took
over working on P3HT:PCBM after more than a year of failed attempts to observe
singlet exciton fission in pentacene. Although the project has diverged since his time
here, my experience learning from him was invaluable.
Eric Hoke has been co-author on all of my papers and has been a valuable
source of conversation and brainstorming. He also wrote the vast majority of the
transfer matrix modeling software and put together the current version of the external
quantum efficiency measurement apparatus. Zach Beiley has also been invaluable in
his knowledge of traps and energetic disorder. He came up with the idea to add traps
to PCBM using F4TCNQ, which was a critical part of showing that excitons could
recombine with trapped polarons. I also undoubtedly owe various other ideas to lively
conversations with Craig Peters, Michael Rowell, and I-Kang Ding who have shared
my corner of our office for years and who have been invaluable for bouncing ideas off
of.
My advisor, Mike McGehee, has taught me much in my 5.5 years in his group.
Perhaps the most useful thing I’ve learned is the ability to structure scientific papers
and presentations to grab and hold the attention of an audience. He also has given me
vi
great insight into how to determine what questions are important to answer and,
importantly, which projects are feasible. At the same time he has given me the
freedom to determine my own research path and to spend some of my time doing what
I love most (making useful gadgets to improve the lab).
Elizabeth Schemm deserves special mention, not only for her endless
emotional support, but also for being the only person I trust to edit my papers.
The entire Stanford cycling team has not only kept me fit but provided the
necessary balance to my scientific life. They are not only my teammates, but many are
my close friends and I probably owe my sanity to them and my bikes. Similarly, I owe
my continued presence in grad school to Justin Brockman, Melissa Berry, Dave
Bernstein, and Matt Donovan. Without you I would certainly have quit sometime
during our first two years of classes.
Finally, to my mother and brother, Paula, and Phil; I owe everything to you,
and certainly could not be who I am today without your guidance.
vii
This work is dedicated to the memories of my father, George, and grandfather, George. My love of science began with their love of everything electrical and
mechanical and their desire to share that love with anyone.
viii
Table of Contents
1 Background ............................................................................................................ 1
1.1 The need for solar power ..................................................................................... 1
1.2 Organic solar ........................................................................................................ 3
1.3 Photovoltaic principles ......................................................................................... 4
1.3.1 Absorption ................................................................................................ 4
1.3.2 Charge generation ..................................................................................... 7
1.3.3 Charge collection .................................................................................... 10
1.3.4 Bulk heterojunction vs. bilayer architectures ......................................... 12
1.3.5 Recombination ........................................................................................ 13
1.4 Förster resonance energy transfer ...................................................................... 19
2 Characterization techniques .............................................................................. 20
2.1 Measuring Absorption, Reflection, Transmission, and Diffuse Scattering
Using an Integrating Sphere ............................................................................... 20
2.1.1 Experimental procedures ........................................................................ 21
2.2 External quantum efficiency .............................................................................. 25
2.3 Current density-voltage characterization ........................................................... 27
2.4 Transfer matrix optical model ............................................................................ 29
ix
3 Materials .............................................................................................................. 32
3.1 regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT) ...................................... 32
3.2 [6,6]-phenyl-C61-butyric acid methyl ester (PC60BM) ....................................... 32
3.3 [6,6]-phenyl-C71-butyric acid methyl ester (PC70BM) ....................................... 33
3.4 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ) .................. 33
4 Accounting for Interference, Scattering, and Electrode Absorption to
Make Accurate Internal Quantum Efficiency Measurements in
Organic and Other Thin Solar Cells ................................................................. 34
4.1 Introduction ........................................................................................................ 34
4.2 Current methods in the field .............................................................................. 36
4.3 Reducing error in the transfer matrix method .................................................... 38
4.4 Importance of using an integrating sphere for accurate measurements of
reflection-mode absorption ................................................................................ 41
4.5 Using active layer absorption to calculate internal quantum efficiency ............ 43
4.6 Common misconceptions ................................................................................... 46
4.7 Conclusion ......................................................................................................... 48
4.8 Device fabrication details .................................................................................. 48
5 Incomplete exciton harvesting from fullerenes in bulk heterojunction
solar cells .............................................................................................................. 50
5.1 Introduction ........................................................................................................ 50
x
5.2 Internal quantum efficiency in P3HT:PCBM solar cells ................................... 52
5.3 Physical origins of wavelength dependent internal quantum efficiency ........... 54
5.4 Modeling internal quantum efficiency ............................................................... 55
5.5 Implications of incomplete exciton harvesting .................................................. 56
5.6 Conclusion ......................................................................................................... 62
5.7 Device fabrication .............................................................................................. 62
5.8 Additional information regarding device modeling ........................................... 63
5.8.1 Calculating donor and acceptor contributions to active layer
absorption ............................................................................................... 63
5.8.2 Comparison of calculated total reflectance vs. experimentally
measured reflectance. ............................................................................. 66
6 Trap-Assisted Auger Recombination Between Excitons and Electron-
Polarons in Fullerenes Used for Solar Cells ..................................................... 68
6.1 Introduction ........................................................................................................ 68
6.2 Auger recombination in organic semiconductors .............................................. 69
6.3 Influence of electrical bias on external quantum efficiency .............................. 70
6.4 Inducing trap-assisted Auger recombination by creating deep level trap
states ................................................................................................................... 74
6.5 Further discussion .............................................................................................. 76
6.6 Implications for other cell chemistries ............................................................... 79
xi
6.7 Auger recombination with trapped charge may explain other
observations in the literature .............................................................................. 80
6.8 Auger recombination between excitons and free polarons in P3HT ................. 82
6.9 Conclusion ......................................................................................................... 84
6.10 Experimental details ........................................................................................... 84
6.11 Gaussian disorder model .................................................................................... 85
7 Conclusion ............................................................................................................ 87
7.1 Summary ............................................................................................................ 87
7.2 Future work ........................................................................................................ 87
8 Bibliography and References ............................................................................. 89
xii
List of Figures
Figure 1-1. Average world power consumption. Data beyond 2010 is
projected. .................................................................................................................. 2
Figure 1-2. Worldwide available renewable energy. ...................................................... 3
Figure 1-3. Absorption coefficient of GaAs as a function of photon energy.8 ............... 6
Figure 1-4. Absorption coefficient of poly-3-hexylthiophene. ...................................... 7
Figure 1-5. Electron and hole quasi-Fermi levels open up when a
semiconductor is illuminated. In this illustration generation is assumed to
be constant throughout the device. ........................................................................... 8
Figure 1-6. P-n junction under illumination with contacts held at potential V. ............. 8
Figure 1-7. Negative polaron in poly-para-phenylene. Its positive counterpart
is not shown, but has the same form except that instead of three non-
bonding electrons flanking the quinoidal section, it has only one electron,
resulting in a net positive charge. ............................................................................. 9
Figure 1-8. Energy diagram depicting charge generation in an organic
semiconductor solar cell. a) An exciton (bound electron-hole pair) is
formed after absorption in the donor. b) The electron is transferred to the
acceptor after the exciton diffuses to the heterojunction interface. The
LUMO-LUMO energy offset must be equal to or greater than the exciton
binding energy. ....................................................................................................... 10
Figure 1-9. Bulk heterojunction and bilayer organic solar cells under operating
conditions. a) The bulk heterojunction cell has no space charge build-up
xiii
and the electric field is approximately constant throughout the cell. b)
Bilayers necessarily have space charge build-up around the heterojunction,
which helps to cancel the applied field, reducing the charge collection
efficiency. ............................................................................................................... 13
Figure 2-1. Diagram of integrating sphere. .................................................................. 20
Figure 2-2. Characterizing the efficiency of the integrating sphere. ............................ 21
Figure 2-3. Measuring absorption of a device or film. ................................................. 22
Figure 2-4. Measuring direct transmission. .................................................................. 24
Figure 2-5. Measuring diffuse transmission. ................................................................ 25
Figure 2-6. Experimental setup for measuring external quantum efficiency. .............. 26
Figure 2-7. Typical J-V curve. Figures of merit are highlighted. ................................. 28
Figure 2-8. Total photocurrent generated by a cell as a function of active layer
thickness. ................................................................................................................ 29
Figure 2-9. Schematic of transmissions and reflections at each interface as
light passes through a film. ..................................................................................... 30
Figure 3-1. regioregular poly(3-hexylthiophene-2,5-diyl). .......................................... 32
Figure 3-2. [6,6]-phenyl-C61-butyric acid methyl ester. ............................................... 32
Figure 3-3. [6,6]-phenyl-C71-butyric acid methyl ester (PC60BM). ............................. 33
Figure 3-4. 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane .............................. 33
Figure 4-1. Parasitic absorption, active layer absorption, and total absorption
of a typical P3HT:PCBM cell (220 nm thick active layer) as calculated by
the transfer matrix optical model. ........................................................................... 37
xiv
Figure 4-2. Total absorptions for cells of varying thickness as calculated by the
transfer matrix method compared with experimentally measured values. ............. 38
Figure 4-3. Active layer absorption for optimized P3HT:PCBM solar cell
calculated using the method we propose with values of n and k as
measured by VASE for the active layer as well as values assuming n=2 at
all wavelengths. ...................................................................................................... 39
Figure 4-4. Absorption in a complete P3HT:PCBM cell as measured using a
traditional reflection-mode absorption measurement where only specular
reflection is detected and the same measurement made using an integrating
sphere. ..................................................................................................................... 43
Figure 4-5. Internal quantum efficiency of optimized (220 nm thick active
layer) P3HT:PCBM solar cell calculated using the method we describe to
generate active layer absorption spectrum. The IQE values below the
absorption onset (>650 nm) are less accurate because the assumption that
the active layer is responsible for a majority of the absorption is no longer
true (see Figure 4-1). .............................................................................................. 44
Figure 4-6. Total and active layer absorption of a P3HT:PCBM solar cell
optimized to 220 nm active layer thickness. .......................................................... 45
Figure 4-7. Total and active layer absorption of a P3HT:PCBM solar cell with
a 45 nm active layer. ............................................................................................... 45
Figure 4-8. Electric field intensity for 450nm monochromatic light vs. position
in a real device and as calculated by measuring absorption in a film and
doubling the optical density. ................................................................................... 47
xv
Figure 4-9. Absorption spectrum of the active layer in a real device and as
calculated by measuring absorption in a film and doubling the optical
density. .................................................................................................................... 47
Figure 5-1. Experimentally measured EQE and absorption of a P3HT:PCBM
cell cast from 1,2-dichlorobenzene (solvent and thermally annealed). The
absorption in the active layer was extracted from the total absorption using
a transfer matrix optical model. The contributions of the P3HT and PCBM
to the active layer absorption were determined by multiplying the active
layer absorption by the ratio of each component’s imaginary index of
refraction to the total imaginary index of refraction of the blend. ......................... 53
Figure 5-2. Experimentally measured IQE curves of P3HT:PCBM cells cast
from 1,2-dichlorobenzene (solvent and thermally annealed), chlorobenzene
(as cast), and chloroform (as cast) as well as modeled IQE for the
dichlorobenzene cell. .............................................................................................. 53
Figure 5-3. IQE curves for devices of varying active layer thickness. These
devices were processed in the same manner as the high efficiency device
shown as the top curve in Figure 5-1. ..................................................................... 58
Figure 5-4. Exciton generation rate in the active layer vs. position in the device
for an optimized (220 nm active layer thickness) under AM1.5G
illumination. The left side of the plot (0 nm) represents the interface with
the PEDOT; the right boundary (220 nm) represents the boundary with the
reflective metal electrode. ...................................................................................... 61
Figure 5-5. Typical parasitic absorption in electrodes. ................................................ 65
xvi
Figure 5-6. Typical active layer absorption extracted using the techniques
outlined in this section. ........................................................................................... 66
Figure 5-7. Calculated and experimentally measured reflectance spectra. .................. 67
Figure 6-1. EQE with increasing reverse bias in P3HT:PC60BM cells. PCBM
exciton harvesting efficiency increases with no change in the P3HT parts
of the spectrum. ...................................................................................................... 71
Figure 6-2. EQE with increasing reverse bias in P3HT:PC70BM cells. The
exciton recovery with bias is more pronounced than with the cells
containing PC60BM. ............................................................................................... 71
Figure 6-3. Absorptions in each phase of the P3HT:PC60BM cell (220-nm-
thick active layer) as well as the total absorption and EQE at Jsc. .......................... 72
Figure 6-4. Modeled exciton harvesting and charge collection efficiencies in
P3HT:PC60BM as a function of applied bias calculated using the method
from section 5.8.1. .................................................................................................. 72
Figure 6-5. I-V curves of “standard” P3HT:PCBM cells and of cells with 0.1%
(F4-TCNQ/PCBM weight). Figures of merit: Jsc=7.82 mA/cm2, FF=0.65,
Voc=0.605V for cells treated with F4-TCNQ, Jsc=9.72 mA/cm2, FF=0.66,
Voc=0.635V for standard cells. ............................................................................... 75
Figure 6-6. EQE of P3HT:PCBM cells with F4-TCNQ additive at varying
reverse bias. No change in spectral shape is observed, indicating that
excitons are recombining with deep-level traps that are not affected by the
applied bias. ............................................................................................................ 76
xvii
Figure 6-7. Intensity dependence of EQE in P3HT:PC60BM cells. There is no
dependence on excitation intensity, indicating that bimolecular and higher-
order processes are not important at these intensities. ........................................... 78
Figure 6-8. Intensity dependence of EQE in cells made with PC70BM. The
small difference in intensity is due to the fact that the minimum chop
frequency we use at 1 sun to effectively measure a signal was 70 Hz,
whereas at 0 sun we could use a 16 Hz chop frequency (see figure 5). ................. 78
Figure 6-9. AC response of P3HT:PC70BM and P3HT:PC60BM cells vs
frequency. P3HT:PC60BM cells show no roll off at these frequencies. ................. 79
Figure 6-10. Photoluminescence (black dots) and current density (red curve)
vs. applied bias in P3HT-only diode. PL drops when current is injected,
indicating that excitons recombine with injected carriers. ..................................... 82
Figure 6-11. Photoluminescence (black dots) and current density (red curve)
vs. applied bias in P3HT:F4-TCNQ diode. Photoluminescence increases as
bias moves from 0 V to -5 V as the free holes created by the F4-TCNQ are
removed. PL drops at further reverse bias as charges are injected from the
electrodes. ............................................................................................................... 83
Figure 6-12. Gaussian disorder model of density of states. ......................................... 85
1
1 Background
1.1 The need for solar power
The energy needs of the world have been increasing steadily since the Industrial
Revolution, with the world’s average power consumption currently exceeding 16TW
(Figure 1-1).1 Until recently, all of this power was generated using non-renewable
resources such as coal, gas, oil, and to a smaller extent, nuclear, which are burned in
heat engines that convert chemical energy into electrical energy. These resources are
finite and cannot, by themselves, support the current power usage trend through the
next century. Furthermore, the combustion products created when these substances are
burned are dirty, polluting the environment with hydrocarbons, toxic compounds,
particulate matter, and greenhouse gases such as carbon dioxide. The ocean helps to
buffer the atmosphere at the expense of its ability to buffer its pH. Ocean acidification
has lead to extreme losses in coral (and other shelled animals) and along with them,
the ocean life that depend on reefs. With global temperatures rising due to global
warming and oilfields becoming harder to locate and drill, the world has recognized
the need for alternative, renewable sources of energy.
2
1960 1970 1980 1990 2000 2010 2020 2030 2040
5
10
15
20
25
Wor
ld P
ower
Con
sum
ptio
n (T
W)
Year
Figure 1-1. Average world power consumption. Data beyond 2010 is projected.
Figure 1-2 shows the amount of power available from each source of
renewable energy. Of the four major sources of renewable energy, only solar and wind
can supply enough power to meet future demand. With over one hundred times more
power available, solar power provides a much more feasible way of meeting that
demand, since extracting power becomes increasingly difficult as the fraction of
power used approaches the total amount available. Furthermore, solar power can be
extremely reliable; desert locations provide high levels of incident power and have
very few cloudy days.
3
Hydro Geothermal Wind Solar100
101
102
103
104
105
Avai
labl
e Po
wer (
TW)
Figure 1-2. Worldwide available renewable energy.
Because of these advantages, there has been much interest in developing solar
technology. Crystalline silicon based solar cells have been improving since the 1960s
and are currently performing near their theoretical maximum efficiency.2 They also
have become cheaper as the semiconductor industry has seen exponential growth.
However, although they are almost fully optimized, the cost of silicon based solar still
cannot compete with current fossil fuel technology.3 If environmental damage
continues to be left out of the fossil fuel pricing equation, silicon solar will not be able
to compete with it in the energy market.
1.2 Organic solar
Organic semiconductors, discovered in the 1980s, have been developing quickly
and have already been commercialized in various forms including organic light
emitting diodes, electronic ink, and flexible circuits.4 Similarly, organic solar cells
4
offer several advantages over their crystalline silicon counterparts that may allow solar
to be competitive with fossil fuels. Organic semiconductors are made either as
polymers or small molecules, and most can be processed from solution, essentially as
an electrically active paint. They are extremely absorptive so that films of only a few
hundred nanometers absorb all of the incident light. This means that very little
material is needed to make organic solar cells. Furthermore, films can be processed at
low temperatures on flexible substrates, allowing for high throughput roll-to-roll
coating in processes similar to what is used to print newspapers.5 Recently, solution
processable electrodes have been demonstrated that supersede their inorganic
counterparts.6 Together, these properties allow organic solar cells to be much cheaper
than their silicon counterparts. Despite these advantages, organic solar is still a young
technology and efficiencies are not yet high enough to compete with silicon, except in
some niche applications.
1.3 Photovoltaic principles
1.3.1 Absorption
Semiconductor solar cells are based on the photovoltaic effect. In
semiconductors, near-infrared to ultraviolet absorption is due to band-to-band
transitions in the material. When a photon is absorbed, its energy is transferred to an
electron in the material, which is promoted from the ground state to an excited state.
Because energy is conserved, the difference in energy between the initial and final
5
states must be equal to the energy of the photon. The overall probability (or rate) of
absorption can be given approximately by Fermi’s Golden Rule,
𝑃 ∝ 𝜌��𝜓𝑖��⃑� ∙ �̂��𝜓𝑓��2
(Eq. 1-1)
where ψi and ψf are the initial and final electronic states, �⃑� is the oscillator dipole
moment, �̂� is a unit vector in the direction of the electric field of the photon, and ρ is
the density of final states in the material. This basic principle explains the absorption
spectra of the semiconductors used to make solar cells.
The band structures in inorganic crystals, such as silicon and gallium arsenide,
arise from energy level splitting of the atomic orbitals that, when overlapped, make up
the σ bonds that hold the crystal together. When a photon is absorbed, an electron is
promoted from the valence band to the conduction band in a σ – σ* transition (where *
denotes the excited state). Because σ bonded atomic orbitals interact strongly (have
significant wavefunction overlap), energy bands in inorganic crystals are wide.7
Consequently, since absorption can occur between any occupied state and any
unoccupied state, the absorption bandwidth is large in inorganic crystals. In fact, most
inorganic materials begin absorbing at the band gap and absorb more strongly as the
photon energy increases. This is illustrated in Figure 1-3, which shows the absorption
coefficient of GaAs, a direct bandgap semiconductor, as a function of photon energy.
6
1 2 3 4 5103
104
105
106
107
Abso
rptio
n Co
eff.
α (c
m-1)
Energy (eV)
Figure 1-3. Absorption coefficient of GaAs as a function of photon energy.8
In contrast, the transitions that are responsible for absorption in organic
molecules are π – π* transitions. The wavefunctions that form π bonds overlap much
less than those in σ bonds; consequently, the bandwidths in organic molecule crystals
are narrower than in inorganics. Additionally, since interaction between molecules in
an organic crystal is through a relatively weak Van der Waals interaction, the
absorption characteristics of the bulk are primarily determined at the molecular level.
With few exceptions, the absorption in organic molecules is described almost entirely
by the molecular orbitals and is only weakly affected by intermolecular interactions.
This is illustrated in Figure 1-4, which shows the absorption coefficient of poly-3-
hexylthiophene, one of the most studied semiconducting polymers.
7
1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.0
0.5
1.0
1.5
2.0
Abso
rptio
n Co
eff.
α (x
105 c
m-1)
Energy (eV)
Figure 1-4. Absorption coefficient of poly-3-hexylthiophene.
1.3.2 Charge generation
Inorganic semiconductors are highly polarizable and therefore have large
dielectric constants (ε~12). Because of this, charges in inorganic semiconductors are
easily screened from each other so that the thermal energy (kT = 0.026 eV at room
temperature) is sufficient to separate an electron-hole pair formed by the absorption of
a photon. When an inorganic crystal is illuminated, electrons and holes are formed,
diffuse randomly through the bulk, and eventually recombine. Under illumination, a
dynamic equilibrium is reached such that there is a steady state population of electrons
in the conduction band and holes in the valence band. This is indicated using separate
electron and hole quasi-Fermi levels, as illustrated in Figure 1-5.
8
Figure 1-5. Electron and hole quasi-Fermi levels open up when a semiconductor is illuminated. In this illustration generation is assumed to be constant throughout the device.
The key functionality of a solar cell is that it has an interface that separates
electrons and holes so that they must travel through the external electronic circuit to
recombine. This implies that all solar cells must be diodes (devices where current can
flow only in one direction). In inorganic solar cells, this is accomplished using a p-n
junction (Figure 1-6). As the quasi-Fermi levels indicate, there is net negative charge
on the n side of the junction and net positive charge on the p side. These charges travel
through the external circuit to recombine, maintaining dynamic equilibrium.
Figure 1-6. P-n junction under illumination with contacts held at potential V.
Free charges in organic semiconductors are formed as polarons – distortions in
π conjugation where a pair of electrons that were participating in a π bond enter non-
bonding states, forcing a portion of the molecule into its quinoidal form (Figure 1-7).
Because the charges are in non-bonding orbitals, they do not exist in the π or π* bands,
EV
EC
Ener
gy
p n
qV
Ene
rgy
9
but rather in polaron energy levels that have slightly less energy. For the remainder of
this work, the terms, ‘electron’ and ‘hole’ may be used in the context of organics
semiconductors to mean ‘electron polaron’ and ‘hole polaron’. Although nuances
exist, the intended meaning is clear from context.
Figure 1-7. Negative polaron in poly-para-phenylene. Its positive counterpart is not shown, but has the same form except that instead of three non-bonding electrons flanking the quinoidal section, it has only one electron, resulting in a net positive charge.
Organic semiconductors have much smaller dielectric constants than
inorganics (ε~4). Consequently, electrons and holes are not screened as effectively and
the thermal energy at room temperatures is insufficient to separate photogenerated
electron-hole pairs. Instead they remain bound to each other as excitons. Excitons are
zero-charge quasiparticles composed of a correlated electron-hole pair. Because they
have zero charge, they are not affected by the presence of an electric field (unless the
field is strong enough to separate the charges, which is not applicable in most cases).
Organic solar cells therefore require a heterojunction to separate excitons into their
constituent charges. A heterojunction is a junction between two dissimilar materials,
which have different electron affinities and ionization potentials. The electron affinity
and ionization potential refer to the energies of the lowest unoccupied molecular
orbital (LUMO) and highest occupied molecular orbital (HOMO), respectively. When
two such materials are brought together, there is a difference in the chemical potentials
-
10
of these orbitals; it is more energetically favorable for the excited state electron to be
in one of the materials (the electron acceptor) and the hole to be in the other (the
electron donor). Therefore when an exciton in one of the materials diffuses to the
heterojunction interface, charge is transferred to the other material, splitting the
exciton into its constituent charges (Figure 1-8). It should be noted that although this
scheme looks similar to the case of the p-n junction, it is the chemical potential that
drives separation, not a built-in electric field.
Figure 1-8. Energy diagram depicting charge generation in an organic semiconductor solar cell. a) An exciton (bound electron-hole pair) is formed after absorption in the donor. b) The electron is transferred to the acceptor after the exciton diffuses to the heterojunction interface. The LUMO-LUMO energy offset must be equal to or greater than the exciton binding energy.
1.3.3 Charge collection
Once electrons and holes are separated, they must move through the active layer
and be collected at the electrodes in order to be used to perform work in the external
circuit. Charges migrate via two different mechanisms, drift and diffusion. Drift is the
movement of the charge due to an electric field and is characterized by the relation,
𝑣 = 𝜇𝐸
(Eq. 1-2)
Donor Acceptor
HOMOs
LUMOs
Ener
gy
EVacuum
Donor Acceptor
HOMOs
LUMOsEn
ergy
EVacuum
a) b)
11
where v is the average drift velocity, µ is the charge carrier mobility, and E is the
electric field intensity. The drift current is the net movement of an ensemble of such
charges:
𝐽Drift = 𝑞𝜇𝜌(𝑥)𝐸(𝑥)
(Eq. 1-3)
where J is the current density, q is the elementary charge, and ρ is the charge carrier
density. Generally, electrons and holes have different mobilities and have different
carrier densities at a particular location in the device, so the electron and hole currents
must be calculated separately. Diffusion is the random thermal motion of charges. It is
an entropic force, so that charges spread from areas of high concentration (low
entropy) to areas of low concentration. Diffusive current is characterized by
𝐽Diffusion = 𝑞𝐷𝑑𝜌(𝑥)𝑑𝑥
(Eq. 1-4)
where D is the diffusivity. The total current is the sum of the drift and diffusive
currents for each carrier type.
In an inorganic solar cell, the built-in electric field is created by co-depletion at
the p-n junction; there is no electric field outside of the depletion region. Therefore,
once charges are separated at the junction, they migrate toward their respective
electrodes by diffusion only (see Figure 1-6). This is in contrast to an organic solar
cell, where both the donor and acceptor materials are normally intrinsic and there is no
depletion region formed where the materials contact each other. Thus, drift is a strong
factor in extracting charge carriers in organic solar cells.
12
1.3.4 Bulk heterojunction vs. bilayer architectures
Because the semiconductors used in organic photovoltaics are intrinsic,
organic solar cells are majority carrier devices; the density of photogenerated charge
carriers is large compared to the density of intrinsic carriers, so that the band structure
of the device can vary greatly with illumination intensity. In a bilayer organic solar
cell, all of the photogenerated charges are created at the planar interface between the
donor and acceptor materials, and each type of charge carrier is driven to its respective
extracting electrode by the applied electric field. However, the carriers also experience
a force in the opposite direction caused by their electrostatic attraction to their partner
charges. As illumination intensity increases, the generation rate increases and the
electric field at the junction diminishes as space charge builds up. At sufficiently high
illumination intensity, enough charges are generated so that the field from the space
charge completely cancels the applied field. Photocurrent may still increase with
illumination because of diffusion, but the electric field at the heterojunction may even
point in the wrong direction given sufficiently large generation rates.
The bulk heterojunction architecture alleviates this problem by blending the
donor and acceptor into a single interpenetrating network of phases. When light is
absorbed, excitons diffuse to an interface, splitting into electrons and holes. Electrons
are still confined to the acceptor and holes to the donor; however, because the
respective phases are distributed throughout the film, there is no buildup on any one
particular charge carrier in a given location. On average, the field due to the
photogenerated charges cancels, and the net field is that imposed by the electrodes.
13
Figure 1-9 illustrates the key differences between the bulk heterojunction and bilayer
architectures.
Figure 1-9. Bulk heterojunction and bilayer organic solar cells under operating conditions. a) The bulk heterojunction cell has no space charge build-up and the electric field is approximately constant throughout the cell. b) Bilayers necessarily have space charge build-up around the heterojunction, which helps to cancel the applied field, reducing the charge collection efficiency.
1.3.5 Recombination
All charges that are not extracted at the electrodes recombine somewhere within
the device. There are several types of recombination, which exhibit different kinetic
properties depending on the particular materials and geometries used. The following is
an overview of the types of recombination most relevant to the cells explored in this
work.
Donor HOMO
Donor LUMO
Acceptor HOMO
Acceptor LUMO
Donor Acceptor
a) b)
Electrodes
14
1.3.5.1 Geminate recombination
After an exciton is split at the donor/acceptor interface, the constituent charges
(known as the geminate pair) form a charge transfer state.9 The charge transfer state
represents a state that has character somewhere between a bound exciton and a pair of
completely separated charges. In the charge transfer state, the electron resides in the
acceptor and the hole in the donor. They are still coulombically bound, although much
weaker than in the case of an exciton. The charges may escape each other’s influence
through diffusive motion, using energy from the thermal bath in combination with
energy from the applied electric field. It has also been suggested that excess kinetic
energy from the original excitonic state may aid in charge separation.10 However, it is
also possible that the charge transfer state may recombine via back-transfer to a lower
lying triplet exciton state or direct internal conversion to the ground state. This
recombination of the original electron-hole pair after charge transfer occurs is termed
geminate recombination, after the Latin term Gemini, referring to the twin electron
and hole that came from the parent exciton.
Because both particles that recombine during the geminate recombination
process start off bound to each other, the rate of geminate recombination is not
dependent on diffusion of either particle and is a one-body (monomolecular) process –
in this case, the single body is the charge transfer state. The rate of charge-pairs lost to
geminate recombination can therefore be written as
𝑑𝑁𝑑𝑡
= −𝛼𝑁
(Eq. 1-5)
15
where 𝑑𝑁𝑑𝑡
is the number of charge transfer states lost to geminate recombination per
unit time, N is the charge transfer state density, and α is the geminate recombination
rate constant.
An important aspect of monomolecular processes is that their rates depend
only on the population of particles in question. This implies that a constant fraction, α,
of particles will be lost to geminate recombination, irrespective of their population
density. The experimental implication is that geminate recombination and other
monomolecular processes are independent of generation rate, and therefore, the loss in
quantum efficiency due to such processes will not depend on illumination intensity.
1.3.5.2 Bimolecular recombination
Once the charge transfer state is split into free charges, the electron and hole
polarons are able to move about the bulk. As an electron (hole) moves through the
device there is some chance it will encounter a hole (electron). When the two
oppositely charged polarons meet, they may form an exciton (or charge transfer state,
if the particles are in different materials) and recombine. Because this process requires
diffusion to bring the two charges together, it depends on both the electron and hole
concentrations. Bimolecular recombination then takes the form of Equation 1-6.
𝑑𝑁𝑑𝑡
= −𝛽𝑛𝑝
(Eq. 1-6)
Here, β is the bimolecular recombination constant and n and p are the electron and
hole concentrations, respectively. Thus, the rate of bimolecular recombination is
16
dependent on the illumination intensity because both n and p are proportional to the
generation rate.
1.3.5.3 Shockley-Reed-Hall (trap-assisted) recombination
Shockley-Reed-Hall (SRH) recombination is a trap-assisted form of charge
carrier recombination. If there are a significant number of mid-gap energetic traps,
they can act as recombination centers for charge carriers. As carriers diffuse through
the device, there is a chance that either an electron or hole will fall into the trap. Once
in the trap, the particle is immobile, and will remain trapped until a charge carrier of
the opposite sign diffuses to it and recombines. SRH recombination is a two step
process, and each step is monomolecular since the trap density is a property of the
material and does not depend on illumination intensity. This is made more clear by
examining the functional form that characterizes SRH recombination,11
𝑑𝑁𝑑𝑡
= −𝐶𝑛𝐶𝑝𝑁𝑡𝑛𝑝 − 𝑛1𝑝1
𝐶𝑛(𝑛 + 𝑛1) + 𝐶𝑝(𝑝 + 𝑝1)
(Eq. 1-7)
where Cn and Cp are the capture coefficients of electrons and holes, respectively, Nt is
the density of electron traps, n and p are the electron density in the conduction band
and the hole density in valence band, and
𝑝1 = 𝑁𝑣𝑒𝐸𝑣/𝑘𝑇
(Eq. 1-8)
𝑛1 = 𝑁𝑐𝑒−𝐸𝑐/𝑘𝑇
(Eq. 1-9)
17
are, respectively, the intrinsic (thermally generated) hole and electron populations, so
that p1n1=ni2. The organic solar cells of interest to this work are not doped, so that the
photogenerated carriers greatly outnumber the intrinsic carriers (𝑛,𝑝 ≫ 𝑛1,𝑝1). The
rate of SRH recombination then simplifies to,
𝑑𝑁𝑑𝑡
≈ −𝑁𝑡𝑛𝑝𝑛 + 𝑝
(Eq. 1-10)
and since in a bulk heterojunction electrons and holes are generated together and there
is no space charge. Then n ≈ p ≡ q, so that
𝑑𝑁𝑑𝑡
≈ −𝑁𝑡𝑞
(Eq. 1-11)
where q refers to the general charge carrier density. From this simplified form, it is
easy to see that SRH recombination displays monomolecular behavior in bulk
heterojunction solar cells and thus the fraction of charges lost to SRH recombination is
constant with illumination.
1.3.5.4 Auger recombination
Auger recombination is the recombination of an electron-hole pair with a third
charge carrier (an electron or hole). The electron-hole pair recombines, transferring its
energy to the third carrier, which moves up higher into its band before thermalizing
back to the band edge, dissipating the energy of the original pair as heat (phonons). In
18
inorganic solar cells this is a three-body process, since the electron-hole pair is made
up of free carriers. The Auger recombination rate is given by
𝑑𝑁𝑑𝑡
= −𝛾𝑛2𝑝
(Eq. 1-12)
where γ is a constant and we have assumed that the electron-hole pair recombines with
an electron. For recombination with a hole, n2p would be replaced with p2n. Because
this is a three-body process, it is only relevant at very high illumination intensities in
intrinsic (non-doped) materials.
In organics, however, the electron-hole pair is bound as a neutral exciton and
the energy is transferred between the exciton and hole via Förster resonant energy
transfer.12 Consequently, Auger recombination in organics is bimolecular,
𝑑𝑁𝑑𝑡
= −𝛾𝑋𝑝
(Eq. 1-13)
where X is the density of excitons and we have assumed recombination with free
holes. Thus, Auger recombination in organics should be much more important under
normal operating conditions (1 sun illumination). Despite this, it has received little
attention in the literature and was only recently demonstrated experimentally.13
19
1.4 Förster resonance energy transfer
Förster resonance energy transfer (FRET) is the transfer of energy from an excited
state oscillator (energy donor) to another oscillator (energy acceptor). In this case,
energy is transferred via the near-field electromagnetic interaction; the oscillators
behave effectively as dipoles, and because energy is conserved, the receptor must have
states available such that the gain in energy of the receptor is equal to the energy loss
of the donor. The rate of energy transfer is given by the Förster equation,
𝑘Forster ∝1𝑟6𝜅2
𝑛4�𝐹𝐷(𝜆)𝜀𝐴(𝜆)𝜆4𝑑𝜆
(Eq. 1-14)
where n is the index of refraction of the medium, FD(λ) and εA(λ) are the emission and
absorption spectra of the donor and acceptor dipoles, respectively, r is the distance
between the two oscillators, and κ is the orientation factor that describes the angle
between the two dipoles. The integral over the donor and acceptor absorption and
emission spectra represents a way to evaluate the overlap between the number of
occupied states in the donor and the number of available states in the acceptor with a
given energy. This equation is usually valid, except in some cases where far-field
absorption is forbidden due to symmetry considerations as opposed to a dearth of
available states. Even though the acceptor absorbs weakly in such instances, the rate of
FRET may be higher than Eq. 1-14 suggests because FRET is a near-field interaction.
20
2 Characterization techniques
2.1 Measuring Absorption, Reflection, Transmission, and Diffuse Scattering Using an Integrating Sphere
Figure 2-1. Diagram of integrating sphere.
Blended organic thin films used for the active layers of organic solar cells are
not optically ideal. Their surfaces have some roughness and the films themselves
scatter light. Thus, measuring the absorption of a device is not as simple as measuring
the spectral reflection from the surface. To capture scattered light, we measure
absorption using an integrating sphere. An integrating sphere is a hollow sphere whose
innards are coated with a very reflective coating (usually barium sulfate) that
efficiently scatters light in all directions. In our sphere, there is a detector port that
houses a silicon photodiode and a baffle that blocks the diode from any direct source
of light. This baffle is very important because the sphere’s coating is far from perfect;
Internal Baffle
Photodiode
21
there is an efficiency associated with the scattered light that reaches the detector. If all
the light that reaches the detector is scattered light, then comparisons between
different situations can be easily made. However, if the light at the detector is a
mixture of direct and diffuse light, then the situation is much more complicated.
2.1.1 Experimental procedures
Figure 2-2. Characterizing the efficiency of the integrating sphere.
The first steps in making a measurement using the sphere are to characterize
the light source, the photodiode’s external quantum efficiency, and the sphere’s
scattering efficiency. This is easily done by measuring a spectrum with no sample.
22
2.1.1.1 Absorption
Figure 2-3. Measuring absorption of a device or film.
When measuring absorption of a sample, it does not matter if the sample is
reflective or transmissive. The sphere captures all light that is not absorbed in the film
and scatters it until it is picked up by the photodiode. Of course this scattered light can
also be reabsorbed by the sample, so it is important that the sample be much smaller
than the sphere itself and preferably much smaller than the detector, since these are the
two surfaces competing to absorb the light. As long as the sample is small, secondary
absorption is small and can be neglected.
When measuring total absorption, we put the sample inside the sphere at a
slight angle. The small tilt from normal incidence is important because there is
significant specular reflection from the air/substrate interface. If the sample is placed
at normal incidence, this specular reflection will leave the sphere through the entrance
Sample
Spectral Reflection Transmission
23
port and this loss of light will mistakenly be attributed to absorption by the sample.
Placing the sample at a small angle ensures that the reflected light gets scattered
around the sphere and is properly accounted for. The small angle does not affect the
reflection intensity in any appreciable way.
We quantify all of the light that is not absorbed by the sample by dividing the
spectrum taken with the sample in place with the original calibration spectrum. The
efficiencies of the sphere, photodiode, and the light source are present in both terms
and cancel out, leaving only the difference in intensity caused by the presence of the
sample.
Intensity = 𝜂system ∗ source spectrum ∗ sample
𝜂system ∗ source spectrum
(Eq. 2-1)
Note: This is the total light not absorbed by the sample, i.e. the transmission plus
reflection of the film, as well as the reflection from the air/substrate interface. To
make an accurate measurement of absorption in the film only, one must normalize by
the total light available to the film (by dividing by the source spectrum the
transmission coefficient of the glass).
24
2.1.1.2 Separating diffuse scattering from direct transmission/reflection
Figure 2-4. Measuring direct transmission.
To quantify diffuse versus direct transmission or reflection, a measurement
without the integrating sphere is necessary. If the detector is placed far from the
sample, then most of the scattered light escapes without striking the detector; this
effectively measures the directly transmitted (or reflected) light.
The integrating sphere captures all light not absorbed in the sample. One need
only subtract the direct spectrum from the total spectrum to obtain the total scattered
light.
Sample
25
Figure 2-5. Measuring diffuse transmission.
Sometimes it is necessary to know only about the forward-scattered light (eg.
when calculating how much light will pass through a hazy transparent electrode). In
this case, we place the sample on the entrance port of the sphere. Only the direct and
diffuse transmitted light will enter the sphere, and the direct part can be subtracted as
before.
2.2 External quantum efficiency
External quantum efficiency (EQE) is the ratio of charges extracted from a solar
cell to the number of photons incident on the cell in a particular wavelength range. If
there is no recombination in the cell, the EQE spectrum is the same as the absorption
spectrum of the active layer. If there is recombination occurring in the cell, the EQE is
reduced. Depending on the type of recombination, different areas of the EQE spectrum
Sample
26
may be affected in different ways, so this measurement provides insight into the
processes occurring within the cell.
Figure 2-6. Experimental setup for measuring external quantum efficiency.
A diagram depicting the experimental apparatus used to measure EQE is shown
in Figure 2-6. Monochromatic light is created by sending white light (from a tungsten
or arc source) through a monochromator. Order sorting filters are used to reject second
and higher-order diffraction. The light is then focused on the cell to be measured and
simultaneously sampled by a reference detector using a beamsplitter. This second
detector is monitored in real time, which allows us to take any fluctuations in the lamp
intensity into account. A bias light is shone on the solar cell at the same time as the
monochromatic probe. The bias light ensures that the total generation rate, and hence
the charge carrier and exciton concentrations, are the same as they would be under
normal operating conditions. To extract the response of the cell to the monochromatic
Ref Signal
Transimpedance Amp and Lock-in
Mono-chromator
with sorting filter(s)
Photodiode
Optical Chopper
Lamp
White light bias lamp
(for monitoringchanges in lamp
intensity)
Monochromatic light intensity <1mW/cm2
27
light, an optical chopper is used to modulate the monochromatic light and a lock-in
amplifier is used to monitor the AC response of the solar cell caused by the
modulation of the monochromatic light. The monochromator is scanned through the
wavelength range of interest and the response is recorded from the lock-in, creating a
response spectrum. This response spectrum can be turned into a quantum efficiency
spectrum by normalizing it by the response spectrum of a calibration photodiode with
known quantum efficiency.
2.3 Current density-voltage characterization
Current density-voltage (J-V) curves provide the most basic information about
solar cell performance. The cell is placed under operating conditions (AM 1.5G solar
illumination for all cells investigated in this work) and the current through the cell is
measured as a function of voltage using an off-the-shelf power source/meter. The
measured current is normalized by the active area of the cell, yielding the current
density. As illustrated in Figure 2-7, the J-V curve provides the figures of merit for the
cell, which include the open-circuit voltage (VOC), the short-circuit current (JSC), the
power at the maximum power point (PMax), and the fill factor (FF). The fill factor is
the ratio of PMax to VOC*JSC, and provides a measure of the rectification quality of the
diode. The efficiency of the cell is simply the power at the maximum power point
divided by the total light-power incident on the cell.
28
-0.5 0.0 0.5 1.0-20
-15
-10
-5
0
5
10
J (m
A/cm
2 )
Applied Bias (V)
VOC
JSC
PMAX
FF=PMAX/(VOC*JSC)
Figure 2-7. Typical J-V curve. Figures of merit are highlighted.
29
2.4 Transfer matrix optical model
Figure 2-8. Total photocurrent generated by a cell as a function of active layer thickness.
Because solar cells are made up of a stack of materials, the amount of light
absorbed in each layer is coupled to the light absorbed or reflected in every other
layer. This implies that the active layer absorption in a solar cell is not experimentally
accessible in any direct way. Furthermore, since the thickness of the layers in an
organic solar cell is smaller than a wavelength of light, optical interference dominates
the absorption properties of the film (Figure 2-8). Therefore, to determine active layer
absorption, a theoretical model is needed. We use the method of transfer matrices14 to
0 200 400 600 800 100002468
10121416
J max
(mA/
cm2 )
active layer thickness (nm)A
30
calculate the reflection and transmission coefficients at each interface in the stack as
well as the attenuation of the electric field as the light wave passes through each layer.
Figure 2-9. Schematic of transmissions and reflections at each interface as light passes through a film.
Figure 2-9 illustrates a plane wave being transmitted and reflected at each
interface as it passes from air, through a film, and back into air. E+ represents the
forward propagating wave and E- represents the reverse propagating waves. rij and tij
are the Fresnel transmission and reflection coefficients and are given by
𝑟𝑖𝑗 =𝑛�𝑖 − 𝑛�𝑗𝑛�𝑖 + 𝑛�𝑗
(Eq. 2-2)
𝑡𝑖𝑗 =2𝑛�𝑖
𝑛�𝑖 + 𝑛�𝑗
(Eq. 2-3)
where 𝑛�𝑖 is the complex index of refraction, n+ik, of the ith layer. The reflection and
transmission properties are described by an interface matrix and the attenuation in the
layer is described by a layer matrix.
Layer 1 Layer 2 Layer 3
E0+
E0-
r12
r23
t12
t23
Ef+
31
𝐼𝑖𝑗 =1𝑡𝑖𝑗�
1 𝑟𝑖𝑗𝑟𝑖𝑗 1 �
(Eq. 2-4)
𝐿𝑖 = �𝑒−𝑖𝜉𝑖𝑑𝑖 0
0 𝑒−𝑖𝜉𝑖𝑑𝑖�
(Eq. 2-5)
where 𝜉𝑖 = 2𝜋𝜆𝑛�𝑖. The total system is described by the scattering matrix,
𝑆 = �𝑆11 𝑆12𝑆21 𝑆22
� = 𝐼12𝐿2𝐼23 …𝐿𝑚𝐼𝑚𝑛
(Eq. 2-6)
and the final waves are calculated from the initial waves
�𝐸0+
𝐸0−� = 𝑆 �
𝐸𝑓+
𝐸𝑓−�
(Eq. 2-7)
This yields the electric field intensity everywhere in the device. The amount of energy
absorbed at a particular location in the device is given by
𝑄𝑖 =12𝑐𝜀0𝛼𝑖𝑛𝑖|𝐸𝑖(𝑥)|2
(Eq. 2-8)
where c and ε0 are the speed of light in the vacuum and the permittivity of free space,
and αi and ni are the absorption coefficient and refractive index of the ith layer. These
equations can be used to calculate the absorption of light of all wavelengths of interest
as a function of position in the device, allowing one to calculate the total absorption in
any layer.
32
3 Materials
The structures and HOMO/LUMO energies for all materials used in this work follow.
3.1 regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT)
Figure 3-1. regioregular poly(3-hexylthiophene-2,5-diyl).
3.2 [6,6]-phenyl-C61-butyric acid methyl ester (PC60BM)
Figure 3-2. [6,6]-phenyl-C61-butyric acid methyl ester.
O
O
LUMO energy: -3.5 eV
HOMO energy: -5.2 eV
LUMO energy: -4.4 eV
HOMO energy: -6.0 eV
33
3.3 [6,6]-phenyl-C71-butyric acid methyl ester (PC70BM)
Figure 3-3. [6,6]-phenyl-C71-butyric acid methyl ester (PC60BM).
3.4 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ)
Figure 3-4. 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane
O
O
F F
FF
CN
CNNC
NC
HOMO energy: -4.4 eV
LUMO energy: -6.0 eV
HOMO energy: ~-7 eV
LUMO energy: -5.2 eV
34
4 Accounting for Interference, Scattering, and Electrode Absorption to Make Accurate Internal Quantum Efficiency Measurements in Organic and Other Thin Solar Cells
4.1 Introduction
In solar cells, internal quantum efficiency (IQE) is the ratio of the number of
charge carriers extracted from the cell to the number of photons absorbed in the active
layer. Because IQE measurements normalize the current generation efficiency by the
light absorption efficiency, they separate electronic properties from optical properties
and provide useful information about the electrical properties of cells that external
quantum efficiency measurements alone cannot. The magnitude of the IQE is
inversely related to the amount of recombination that is occurring in the cell, while the
spectral shape of the curve can provide information about the efficiency of harvesting
excitons in the cell or about the spatial dependence of charge recombination.15,16
Effects like multiple exciton generation17-19 and singlet exciton fission,20 as well as
bias-dependent photoconductivity,21 can lead to interesting spectral shapes and be
detected by measuring IQEs greater than 100%. Despite its usefulness as a
characterization tool, IQE is rarely reported. When IQE is reported, absorption is
frequently not measured in actual devices; this can lead to errors since reflective
electrodes induce strong interference effects that substantially affect absorption. When
absorption is measured in actual devices, parasitic absorptions are almost never taken
into account. We hope that by demonstrating a straightforward method of measuring
35
IQE, such measurements will become standard and the community may benefit from a
better understanding of how the best performing cells work.
Organic photovoltaics (OPVs) and other ultra-thin solar cells19,22-24 are made as
a stack of materials including an active semiconducting layer, electrodes, and – in
some cases – modifier layers such as charge blocking layers and optical spacers.25-28
The active layer is responsible for all charge generation in the cell. Typically 5-10% of
the incident light is absorbed in the electrodes. In many solar cells, the IQE should not
vary with wavelength. Since parasitic absorption does vary with wavelength, one must
account for it to observe the correct spectral shape.16 Consequently in the general case,
it is critically important to take this parasitic absorption into account when calculating
internal quantum efficiency.
Determining the active layer’s contribution to the total absorption can be a
challenge, as it generally requires optical modeling to relate the experimentally
measurable total absorption to the absorptions in each layer. The absorptions of each
layer cannot independently be measured because, due to interference effects, the
optical density of the stack is not simply the sum of the optical densities of each layer.
The most accurate commonly used model uses a transfer matrix formalism to calculate
the interference of coherent reflected and transmitted waves at each interface in the
stack.14,29 This calculation requires knowledge of the wavelength-dependent complex
index of refraction of each material. The imaginary part, k, is related to the extinction
coefficient and is responsible for absorption in a medium. The real part, n, determines
the wavelength of light of a given energy in a material and is important for calculating
where areas of constructive and destructive interference occur. Typically the optical
36
constants are measured using variable angle spectroscopic ellipsometry (VASE).30-34
The data produced by this technique when measuring anisotropic organic materials are
difficult to interpret and require complicated modeling not available to many research
groups. Moreover, in blended donor-acceptor films, the optical properties depend
strongly on morphology and therefore on processing conditions. Thus films of
different thicknesses, cast from different solvents, or dried for different amounts of
time have different optical constants.35,36 In such composite materials, morphology is
also a function of depth due to vertical phase segregation.36,37 In these cases the optical
constants are spatially dependent and the data gathered by these methods are
approximations themselves. It is not always feasible to use VASE to measure n and k
for each film, so a simpler method of determining active layer absorption is desirable.
In this section we show that for typical OPVs, precise knowledge of the real
part of the complex index of refraction of the active layer is not required for making
measurements of the active layer absorption necessary for calculating IQE. We have
investigated several methods to calculate the active layer absorption using published
values of the optical constants.30-34 We propose a method that minimizes error by
using an optical model to calculate the parasitic absorption (the absorption by the
layers that do not contribute to photocurrent) and subtracting this from the
experimentally measured total absorption.
4.2 Current methods in the field
The transfer matrix method can be used to model active layer absorption,
accounting for optical interference effects as well as parasitic absorption. This method
37
calculates the reflection and transmission at each interface as well as attenuation in
each layer.14,29 Figure 4-1 shows the absorption in each layer as well as the total
absorption for a typical poly-3-hexylthiophene:[6,6]-phenyl-C61-butyric acid methyl
ester (P3HT:PCBM) cell as calculated by this method. The optical model is limited in
accuracy, however, in that it does not account for diffuse scattering and the spatially-
dependent optical constants of the blend layer. The error associated with these
approximations can be observed by comparing the total device absorption predicted by
the model to the experimentally measured absorption spectrum (Figure 4-2);
substantial differences exist at all device thicknesses.
300 400 500 600 700 8000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Abso
rptio
n
Wavelength (nm)
Parasitic Abs. Active Abs. Total Abs.
Figure 4-1. Parasitic absorption, active layer absorption, and total absorption of a typical P3HT:PCBM cell (220 nm thick active layer) as calculated by the transfer matrix optical model.
38
300 400 500 600 700 800
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Abso
rptio
n
Wavelegnth (nm)
48 nm Experiment 105 nm Experiment 234 nm Experiment 48 nm Model 105 nm Model 234 nm Model
Figure 4-2. Total absorptions for cells of varying thickness as calculated by the transfer matrix method compared with experimentally measured values.
4.3 Reducing error in the transfer matrix method
The most accurate method of isolating active layer absorption that we have
investigated uses the transfer matrix optical model to calculate the absorptions in the
various layers in the stack but only makes use of the solutions for the absorptions in
the electrodes. Rather than using the model to predict the absorption in the active
layer, we make use of the experimentally measured total absorption, which consists
mainly of active layer absorption. From this, we subtract the parasitic absorptions
calculated by the model. Because the experimentally measured total absorption is
highly accurate, errors in the resulting active layer absorption are only as small as the
errors in the parasitic absorptions. For example, even if the error in the parasitic
absorption were as high as 10%, in a typical cell where the total parasitic absorption
comprises 10% of the total absorption at most wavelengths, the error in the active
39
layer absorption would only be 1%. Typical errors are smaller than this, as we show
below, so the method is generally very accurate. This robustness provides some added
flexibility in that we can loosen the requirements on the accuracy of the optical
constants of the blend, which are notoriously difficult to measure. In fact we can make
reasonable predictions of active layer absorption by estimating n and measuring k for
the blend. Figure 4-3 shows the active layer absorption using values of n determined
by VASE as well as the absorption calculated using a constant value of n=2. Both
curves were generated using the method that combines the modeled parasitic
absorption with the experimentally measured total absorption.
300 400 500 600 700 800
0.0
0.2
0.4
0.6
0.8
1.0
Abso
rptio
n
Wavelength (nm)
True n n = 2
Figure 4-3. Active layer absorption for optimized P3HT:PCBM solar cell calculated using the method we propose with values of n and k as measured by VASE for the active layer as well as values assuming n=2 at all wavelengths.
The absorption spectrum calculated using the approximation that n=2 is in
close agreement with the spectrum generated using the more accurate values of n
measured by VASE. There is less than 1% discrepancy at wavelengths where the
40
active layer absorbs strongly, which are the wavelengths of interest for IQE
measurements. The values of the optical constants for the electrode layers are easily
found in the literature30-34, and so one can produce very good IQE spectra without
having to resort to any special methods of measuring n in the active layer.
Because our method of calculating active layer absorption allows us to
estimate the real part of the index of refraction of the active layer, the only optical
constant we need to measure is the imaginary part, k. The imaginary part of the index
of refraction is related to the absorption coefficient by
𝑘 = 𝜆𝛼4𝜋
(Eq. 4-1)
where λ is the wavelength of light and α the absorption coefficient. α can be
determined from measurements of the transmission or optical density (OD) of a film
and its thickness, which can be measured using profilometry. α is related to the optical
density (OD) and the transmitted intensity by
𝛼 =(OD) ln(10)
𝑥
(Eq. 4-2)
𝐼𝐼0
= 𝑒−𝛼𝑥
(Eq. 4-3)
41
where 𝐼𝐼0
is the fraction of light that remains after passing through the film and 𝑥 is the
film thickness. Equation 4-2 is useful for many off-the-shelf absorption spectrometers
that output optical density. Equation 4-3 is more appropriate in configurations that
output transmission such as the one used in this work. To be clear, equation 4-3
describes the decay of the intensity of a wave as it passes through an absorbing film. It
does not represent the total position-dependent intensity in a device under solar
illumination, which includes interference with waves transmitted and reflected at each
interface in the device. Because this equation does not describe reflection at the
interfaces, it does not take coupling efficiency into account. Thus it is important to
take into account the reflection/transmission at the air/substrate (glass) interface using
the Fresnel equations. Without knowing, a priori, the value of the real part of the
index of refraction of the film, it is impossible to know exactly how much light is
coupled into the film and how much is reflected at the film-substrate interface.
However, reflection at this interface is small (approximately 2%) so it can be
estimated by assuming n=2 (for organics) without much loss of accuracy.
4.4 Importance of using an integrating sphere for accurate measurements of reflection-mode absorption
We measure the total absorption using a reflection-mode measurement inside
of an integrating sphere. The use of the integrating sphere greatly enhances the
accuracy of the measurement, since a significant amount of light is diffusely reflected
or scattered into waveguide modes in the glass substrate. Figure 4-4 shows an
absorption measurement taken with the sample inside of an integrating sphere, in
42
contrast to a more traditional reflection measurement where only the spectral
reflection is measured. The strongly scattered light escapes the device in all directions
and is captured by the integrating sphere. In other reflection mode configurations this
light would be lost and would mistakenly be attributed to absorption by the device.
This is especially important for the short wavelengths where Rayleigh scattering is
more efficient, so an error in absorption at these wavelengths can significantly affect
the shape of the IQE curve. While the integrating sphere is not necessary for
wavelengths where the cell absorbs strongly, it is necessary to obtain the correct
spectral shape across the whole absorption spectrum. The integrating sphere is quite
easy to use for this type of measurement, since all that is required is to compare the
intensity of light in the sphere with and without the sample present. The scattering
efficiency of the sphere does not need to be characterized, since it is a factor present in
both measurements and is accounted for when the two intensities are divided.
However, it is important for the sample to be much smaller than the sphere itself so
that it does not present a large area for secondary absorption of light.
43
300 400 500 600 700 8000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Refle
ctan
ce
Wavelength (nm)
w/o Sphere w/Sphere
Figure 4-4. Absorption in a complete P3HT:PCBM cell as measured using a traditional reflection-mode absorption measurement where only specular reflection is detected and the same measurement made using an integrating sphere.
4.5 Using active layer absorption to calculate internal quantum efficiency
Figure 4-5 shows an IQE curve generated for a P3HT:PCBM cell using the
method we describe. The external quantum efficiency was measured using standard
techniques. We only show IQE for wavelengths where the active layer absorbs; the
calculated IQE values are less accurate for absorption below the bandgap, since the
active layer absorption is close to zero and this term appears in the denominator. For
practical purposes, the IQE is only relevant at wavelengths where the active layer
absorbs significantly. We have shown that in this system, the IQE spectrum is not flat
due to differences in the efficiencies at which P3HT and PCBM excitons are
harvested. However, in systems where harvesting is equally efficient in both materials,
this method produces flat IQE curves as expected.16 These observations would not
44
have been possible without taking parasitic absorptions into account using the method
we propose.
300 400 500 600 700 8000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0In
tern
al Q
uant
um E
fficie
ncy
Wavelength (nm)
IQE
Figure 4-5. Internal quantum efficiency of optimized (220 nm thick active layer) P3HT:PCBM solar cell calculated using the method we describe to generate active layer absorption spectrum. The IQE values below the absorption onset (>650 nm) are less accurate because the assumption that the active layer is responsible for a majority of the absorption is no longer true (see Figure 4-1).
There are many instances in the literature where absorption by the electrodes is
ignored under the assumption that the absorption in the electrodes is insignificant
compared to that of the active layer. To illustrate how important it is to subtract the
electrode absorption, we compare the active layer absorption of a typical P3HT:PCBM
cell as determined by the method we propose to the measured total absorption (Figure
4-6). Not only is the active layer absorption significantly smaller than the total
absorption, but the shape is moderately different. This data is for a cell with a strongly
absorbing, 220-nm-thick active layer. For thinner active layers, the difference in shape
45
is even more dramatic (Figure 4-7) since more light is available to be absorbed by the
electrodes in devices with weakly absorbing active layers.
300 400 500 600 700 8000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Abso
rptio
n
Wavelength (nm)
Active Abs. Total Abs.
Figure 4-6. Total and active layer absorption of a P3HT:PCBM solar cell optimized to 220 nm active layer thickness.
300 400 500 600 700 800-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Abso
rptio
n
Wavelength (nm)
Active Layer Total
Figure 4-7. Total and active layer absorption of a P3HT:PCBM solar cell with a 45 nm active layer.
46
4.6 Common misconceptions
A strategy often used when reporting IQE in the literature is to measure the
absorption of the active layer alone on a glass substrate in transmission mode. The
optical density is then doubled to take into account two optical passes caused by the
reflective metal electrode. Although this is very convenient in that it allows one to use
an off-the-shelf spectrometer in transmission mode, it does not take into account
interference effects, most importantly the area of low electromagnetic field intensity
close to the metal electrode where absorption is necessarily weak. It also ignores
parasitic absorption, albeit in a different way than results from attributing 100% of the
total absorption to the active layer; rather than counting parasitic absorption toward
the active layer absorption, it treats the electrodes as if they are lossless in that the
active layer sees the full solar spectrum. Figure 4-8 shows the intensity of 450 nm
light in a device configuration as well as in a film configuration when the optical
density is doubled. Both interference and parasitic absorption occur in the device but
not in the film. Because of this, the shape of the absorption spectrum calculated by
doubling the optical density of a film can differ significantly from the absorption
spectrum in the active layer of a real device. This effect becomes more pronounced in
thinner films where interference effects are even more important. Figure 4-9 shows the
absorption spectrum calculated by doubling the optical density of a film versus the
true active layer absorption.
47
0 50 100 150 200 2500.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Inte
nsity
(I/I0
)
Position in active layer (nm)
Intensity in device Intensity in film (2 passes)
Figure 4-8. Electric field intensity for 450nm monochromatic light vs. position in a real device and as calculated by measuring absorption in a film and doubling the optical density.
300 400 500 600 700 800
0.0
0.2
0.4
0.6
0.8
1.0
Abso
rptio
n
Wavelength (nm)
Film absorption Device absorption
Figure 4-9. Absorption spectrum of the active layer in a real device and as calculated by measuring absorption in a film and doubling the optical density.
48
4.7 Conclusion
Internal quantum efficiency measurements provide detailed information about
the electronic properties of solar cells, including insight into things like recombination
and morphology-dependent properties. We have described a method to easily measure
internal quantum efficiency that takes into account parasitic absorptions in the
electrodes and/or other non-active layers in the stack. Our method is relatively
insensitive to modeling error, allowing some of the optical constants used in the model
to be relatively imprecise; an educated guess is sufficient in most cases. Since this
method eliminates the need for precise measurements of the active layer’s complex
index of refraction using a time consuming technique, we hope that more OPV
publications will include measurements of internal quantum efficiency. This method
will also be useful for all-nanocrystal solar cells and other thin film technologies.
4.8 Device fabrication details
P3HT:PCBM devices were made with the structure, indium tin oxide
(ITO)/PEDOT:PSS/P3HT:PCBM/Ca/Al with the following thicknesses (in nm):
110/35/220/7/200. ITO substrates were purchased from Sorizon Technologies;
PEDOT:PSS from Baytron; P3HT from Rieke; PCBM from NanoC; and metals from
K. J. Lesker. Substrates were cleaned in an ultrasonic bath with Extran 300, rinsed in
deionized water and then cleaned in acetone and isopropanol followed by 20 minutes
of UV-ozone treatment. PEDOT:PSS was spin-coated and the substrates were
annealed at 140˚ C for 10 minutes. They were then transferred to a nitrogen glovebox,
49
where they remained for the duration of the fabrication process as well as for all
characterizations performed. P3HT:PCBM (1:1 ratio by weight) was cast from 1,2-
dichlorobenzene and was allowed to slow-dry overnight. The films were then
thermally annealed at 110° C for 10 minutes. Calcium and aluminum metal electrodes
were deposited in a thermal evaporator. All devices had power conversion efficiencies
greater than 4%.
50
5 Incomplete exciton harvesting from fullerenes in bulk heterojunction solar cells
5.1 Introduction
In this section we investigate the internal quantum efficiencies (IQEs) of high
efficiency poly-3-hexylthiophene:[6,6]-phenyl-C61-butyric acid methyl ester
(P3HT:PCBM) solar cells and find them to be lower at wavelengths where the PCBM
absorbs. We find that because the exciton diffusion length in PCBM is too small,
excitons generated in PCBM decay before reaching the donor-acceptor interface. This
result has implications for most state of the art organic solar cells, since all of the most
efficient devices use fullerenes as electron acceptors.
Since their inception, organic photovoltaics (OPVs) have steadily improved in
performance. OPVs generate power through three major processes: exciton generation
(absorption), exciton harvesting (the process of excitons migrating to the
donor/acceptor interface and being split into their constituent charges), and charge
transport.29,30 A typical device consists of a charge-generating active layer sandwiched
between hole-extracting and electron-extracting electrodes. The active layer consists
of an electron donating material in contact with an electron accepting material.
Excitons, bound electron-hole pairs, are generated when light is absorbed in one of the
materials. If an exciton is sufficiently close to the donor/acceptor interface, the exciton
is split into its constituent charges, leaving an electron in the acceptor and a hole in the
donor.
51
Today’s best OPVs are made with active layers using a bulk heterojunction
structure obtained by blending a polymer donor with a fullerene acceptor.38-40 In bulk
heterojunction solar cells, the donor and acceptor are naturally nanostructured due to
phase segregation of the polymer and fullerene. The morphology of the nanostructure
is somewhat tunable through thermal and solvent annealing. Annealing typically
increases the size of the domains in the blend, which increases the distance excitons
need to travel to dissociate at the heterojunction interface. The increase in domain size
also affects charge carrier mobilities and therefore the recombination mechanisms in
the devices.41
Optimized devices have power conversion efficiencies of 5-6%;39,40,42 pushing
these efficiencies higher requires detailed analysis of the losses in these devices. A
fraction of the excitons in most pure materials decay radiatively, so exciton harvesting
is usually evaluated by observing photoluminescence quenching. In C60 fullerene
systems like poly-3-hexylthiophene:[6,6]-phenyl-C61-butyric acid methyl ester
(P3HT:PCBM), the PCBM emission is extremely weak and its emission spectrum
overlaps that of the polymer, so this technique can only effectively probe exciton
quenching in the polymer phase. Most analyses assume the overall exciton harvesting
efficiency to be very close to 100%.43-45 However, we find that the exciton harvesting
in the fullerene phase is less than 50% efficient. While absorption in the fullerene is
weak compared to the polymer, recovering this loss would increase the photocurrent
by 7-8%.
52
5.2 Internal quantum efficiency in P3HT:PCBM solar cells
External quantum efficiency (EQE), the ratio of charges extracted from a
device to the number of incident photons, is an important benchmark of solar cell
performance. Figure 5-1 shows the EQE and absorption of a typical high performance
(power conversion efficiency >4%) P3HT:PCBM solar cell used in this study and is
consistent with EQE spectra of high efficiency cells published in the literature.39,41,46
Internal quantum efficiency (IQE), the ratio of charges extracted from a device to the
number of photons absorbed by the active layer, provides a useful way to isolate
electronic loss mechanisms from light coupling and parasitic absorption losses in a
solar cell. The top curve in Figure 5-2 shows a typical IQE spectrum for the same high
efficiency P3HT:PCBM devices. We found that the IQE curves were far from flat; the
IQE ranges from 50-75%, with lower IQE at shorter wavelengths. Because more of the
short-wavelength absorption occurs in the PCBM, the low IQE in this region suggests
that not all excitons generated in the PCBM are harvested.
53
Figure 5-1. Experimentally measured EQE and absorption of a P3HT:PCBM cell cast from 1,2-dichlorobenzene (solvent and thermally annealed). The absorption in the active layer was extracted from the total absorption using a transfer matrix optical model. The contributions of the P3HT and PCBM to the active layer absorption were determined by multiplying the active layer absorption by the ratio of each component’s imaginary index of refraction to the total imaginary index of refraction of the blend.
Figure 5-2. Experimentally measured IQE curves of P3HT:PCBM cells cast from 1,2-dichlorobenzene (solvent and thermally annealed), chlorobenzene (as cast), and chloroform (as cast) as well as modeled IQE for the dichlorobenzene cell.
54
5.3 Physical origins of wavelength dependent internal quantum efficiency
The IQE can be factored into three distinct parts: exciton diffusion, charge
transfer, and charge collection.
𝜂IQE = 𝜂ED × 𝜂CT × 𝜂CC
(Eq. 5-1)
Each of these terms can have wavelength dependence. Exciton diffusion and charge
transfer are processes that involve excitons in either the donor or the acceptor phase
and therefore might have different efficiencies depending on the properties of the
phase in question. Such differences would result in wavelength dependence of the
exciton diffusion and charge transfer efficiencies since the absorption contribution and
thus the exciton generation contribution of each of the phases changes with
wavelength. Effects that generate multiple excitons from a single photon could also
result in wavelength dependent exciton diffusion and charge transfer efficiencies,
however these effects have not been observed in polymer-fullerene blend systems.
Charge collection encompasses all of the transport processes involved in moving
electrons and holes to their respective electrodes and includes geminate and
bimolecular recombination. The charge collection process begins after excitons are
split at the heterojunction interface and is therefore insensitive to the exciton’s origin;
the charge collection process always begins with an electron in the acceptor and a hole
in the donor. The charge collection efficiency, however, can vary with position in the
device due to differences in distances the charges need to travel to be extracted,
variations in morphology, or interactions with electrodes. Optical interference effects
55
cause exciton generation profiles for different wavelengths of light to have maxima at
different locations in the device. When combined, these two effects can lead to
wavelength dependence of the charge collection efficiency. However, in a device
where the exciton diffusion and charge transfer efficiencies are equal in both
materials, and the charge transport efficiency does not change much throughout its
thickness, the IQE should be independent of excitation wavelength.
5.4 Modeling internal quantum efficiency
To allow for different exciton diffusion and charge efficiencies for the donor
and acceptor materials, we modeled the IQE with the equation
IQE =𝜂CC(𝑥)�𝜂D ∗ 𝐴𝑏𝑠D(𝜆) + 𝜂A ∗ 𝐴𝑏𝑠A(𝜆)�
𝐴𝑏𝑠D(𝜆) + 𝐴𝑏𝑠A(𝜆)
(Eq. 5-2)
where AbsD and AbsA are the contributions to the absorption spectrum and ηD and ηA
are the exciton harvesting efficiencies (𝜂ED ∙ 𝜂CC) of the donor and acceptor,
respectively. Note that the numerator corresponds to the external quantum efficiency
and the denominator corresponds to the total absorption in the active layer. AbsD and
AbsA were determined by measuring the total reflectance of the device and deriving
from this the absorption of the active layer using a transfer matrix optical model.14,29
The absorption due to either component in the blend was then calculated by
multiplying the active layer absorption by the ratio of the k value (the imaginary part
56
of the complex index of refraction) in question to the total k at the wavelength of
interest
𝐴𝑏𝑠P3HT = 𝐴𝑏𝑠Active Layer ×𝑘P3HT
𝑘P3HT + 𝑘PCBM
(Eq. 5-3)
The top curves in Figure 5-2 show the fit between the modeled and
experimental IQEs. Figure 5-1 shows the experimentally measured EQE and
absorption data used to generate the IQE curve. The best fit of equation 5-2 to the IQE
curve in Figure 5-2 is obtained by taking ηCC=79 +1/-4%, ηD=95 +5/-2%, and ηA=41
+5/-1%. These are standard errors and represent the extreme values the fit parameters
could take at the 50% confidence level assuming a normal distribution of error. The fit
value for exciton harvesting in the donor, ηD=95%, is consistent with
photoluminescence measurements, which show 95% quenching of the emissive
excitons.
5.5 Implications of incomplete exciton harvesting
The observation that only 41% of excitons in PCBM are harvested indicates
that either the diffusion length is smaller than the PCBM domain size or that there is
some other excitation decay pathway. If the former is true, then by reducing the
domain size we should be able to recover all of the excitons lost in the PCBM.
Modeling the system with ηA=ηD=95% suggests that if all of the PCBM excitons were
harvested, we would see an increase in the photocurrent of 7-8%.
57
To probe the dependence of exciton harvesting on domain size, we created
blends cast from lower boiling point solvents (chloroform and chlorobenzene) without
annealing to ensure that the domains were as small as possible. As seen in the two
lower curves in Figure 5-2, the IQEs of these devices are independent of wavelength,
indicating that both the PCBM and P3HT have high exciton harvesting efficiencies. Of
course the IQE is also low, indicating that while shrinking the domains improved
exciton harvesting, it dramatically decreased the charge transport efficiency, making
the device less efficient overall.
We considered several possible explanations for the wavelength dependence of
the IQE spectra in devices with larger domains/higher efficiencies. We considered the
possibility that the wavelength dependence could be due to position dependent
variations in ηCC coupled with the optical interference effects. This might cause light
of different wavelengths to be absorbed in regions of the device with different charge
collection efficiencies. If this were the case, we would expect to see IQE minima at
different wavelengths for devices of different thicknesses. However, we observed that
the IQE minimum always occurs in the blue end of the spectrum (Figure 5-3). This
implies that charge collection in these devices has negligible dependence on excitation
wavelength. We also considered the possibility that singlet excitons generated in the
PCBM might be lost via mechanisms other than internal conversion, such as energy
transfer to polarons47-49 or intersystem crossing to the triplet state.50 It is possible that
triplets have lower charge separation efficiency due to their lower energy; however,
the fact that we were able to recover these excitons by making the PCBM domains
smaller points to exciton diffusion rather than charge separation as the reason for the
58
reduced IQE. Additionally, the IQE curves are independent of excitation intensity up
to one sun (data not shown), which discounts energy transfer to polarons since this
recombination pathway depends on the carrier density.
Figure 5-3. IQE curves for devices of varying active layer thickness. These devices were processed in the same manner as the high efficiency device shown as the top curve in Figure 5-1.
The exciton diffusion lengths in PCBM have not yet been thoroughly studied,
however Cook et al. have performed measurements that suggest a value as small as 5
nm.51 We have not measured the exciton diffusion length because most methods for
doing so detect photoluminescence quenching and PCBM is a very weak emitter.
Furthermore any technique that analyzed thin films of pure PCBM might not reveal
the exciton diffusion length for PCBM in a bulk heterojunction due to differences in
morphology. PCBM domain sizes vary, and are typically 10-100 nm after annealing
59
for 5 minutes at 100˚ C,52 and up to tens of microns after annealing at higher
temperatures for longer periods of time.53 It is therefore not surprising that the
domains might be significantly larger than the exciton diffusion length.
Incomplete exciton harvesting from fullerenes might help explain some effects
seen by others. Moulé et al. observed a “reduced generation zone” (RGZ) in the active
layer near the poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS)
interface.54 Several studies have shown vertical phase segregation of the active
layer,38,55 where larger fullerene domains lie near this interface. This could be due to
the more polar nature of PCBM compared with P3HT,36,37,56,57 or because PCBM is
more soluble than the polymer in the casting solvent, which evaporates from the top
surface first. These studies used multiple characterization techniques including
ellipsometry, near-edge x-ray absorption fine structure spectroscopy, dynamic
secondary ion mass spectroscopy, and energy compatibility arguments. Our data is
consistent with the hypothesis that the observed RGZ is due to excitonic losses in the
fullerene due to the larger domain size near the active layer/PEDOT boundary. Having
less polymer at this interface would also weaken absorption in this area, reducing
generation; however this would not explain the wavelength dependence of the IQE we
observe. Figure 5-3 shows IQE curves for devices made in the same manner as the
high efficiency cells but with active layers of varying thickness. We observed that
while all of the cells had similar IQEs at longer wavelengths, thinner cells generally
had higher IQEs at shorter wavelengths than thicker cells. This is consistent with a
vertical phase segregation model where the largest PCBM domains appear close to the
PEDOT interface. TEM tomography has suggested that vertical phase segregation
60
occurs with the opposite orientation (PCBM accumulating near the metal electrode).58
A thorough discussion of this issue is beyond the scope of this work, however we note
that TEM methods can only differentiate PCBM from crystalline P3HT. Thus, the
TEM data could be interpreted to mean that there is more polymer at the PEDOT
interface or that the P3HT is more crystalline in this region. While the general effect
of vertical phase segregation would be that thicker films will show a larger fraction of
oversized PCBM domains, this effect might be especially important for the thick films
used to make high efficiency solar cells. Optical interference modeling, shown in
Figure 5-4, confirms that for these cells (optimized to 220 nm active layer thickness),
the highest excitation rates occur near this interface. It should be noted that solvent
and thermal annealing of the blend results in larger PCBM domains throughout the
film, so we would predict poorer exciton harvesting in the PCBM phase regardless of
vertical phase segregation.
61
Figure 5-4. Exciton generation rate in the active layer vs. position in the device for an optimized (220 nm active layer thickness) under AM1.5G illumination. The left side of the plot (0 nm) represents the interface with the PEDOT; the right boundary (220 nm) represents the boundary with the reflective metal electrode.
Park et al. published work on a 6.1% efficient cell using poly[N-900-hepta-
decanyl-2,7-carbazole-alt-5,5-(40,70-di-2-thienyl-20,10,30-benzothiadiazole)
(PCDTBT) as a donor material that does not require long periods of solvent or thermal
annealing to achieve good device performance40 and does not suffer from an exciton
harvesting problem in the fullerene, as evidenced by their flat, near-100% IQE. Their
high, flat IQE shows that the exciton harvesting problem is not an insurmountable one,
and that better design rules are enough to make higher efficiency organic solar cells.
Their device uses a very thin (80 nm) active layer. Because charge carriers have less
distance to travel, mobility requirements are less stringent and annealing is not
required to make high efficiency devices. Because they do not anneal their films, the
donor and acceptor are probably more intimately mixed. If this is true, it might explain
62
why their exciton harvesting efficiency is very close to 100% for both the polymer and
the fullerene.
5.6 Conclusion
We used IQE measurements as a tool to investigate exciton harvesting
efficiencies in P3HT:PCBM bulk heterojunction solar cells and found that in the best
performing cells with high electron and hole mobilities, there is incomplete harvesting
of excitons in the fullerene phase. The exciton diffusion length in the fullerene is
generally shorter than the domain size, and approximately 60% of excitons generated
in the fullerene phase decay before being harvested. Our findings have implications
for most bulk heterojunction solar cells since the vast majority use PCBM as an
electron acceptor. Novel geometries that use strongly absorbing, thin active layers may
bypass this issue by using blends with smaller domains, as having high charge carrier
mobilities is less important in a thinner device. It may also be possible to solve this
problem in more standard devices using novel nanostructures or new acceptors.
5.7 Device fabrication
Substrates were cleaned and PEDOT:PSS was deposited as described in §4.8.
P3HT:PCBM (1:1 ratio by weight) was cast from 1,2-dichlorobenzene, chlorobenzene,
or chloroform. The devices cast from dichlorobenzene were allowed to slow-dry
overnight and were thermally annealed at 110° C for 10 minutes. Calcium and
aluminum metal electrodes were deposited in a thermal evaporator.
63
IQE was calculated using an external quantum efficiency (EQE) measurement
as well as a reflection-mode absorption measurement, described in §0 and §2.1
respectively. Parasitic absorption in the ITO, PEDOT, and metals was calculated using
a transfer matrix formalism14,29 to evaluate the coherent superposition of light waves at
each interface, which is described in §2.4. The active layer absorption was then
calculated by subtracting the modeled parasitic absorption from the experimentally
measured total absorption. Indices of refraction for the various materials were either
taken from literature30 or measured using a combination of spectroscopic ellipsometry
and absorption/reflection measurements.
5.8 Additional information regarding device modeling
5.8.1 Calculating donor and acceptor contributions to active layer absorption
AbsD and AbsA were generated from experimental data by the following
method: The absorption of the complete device was measured in reflection mode
inside of an integrating sphere to capture all of the light that was not absorbed,
including scattered light. Using the experimental values for the real and imaginary
parts of the complex index of refraction (n and k as a function of wavelength), we
calculated the total absorption in each part of the device with an optical model using a
transfer matrix formalism. From this, the parasitic absorption (absorption in the parts
of the device that are not part of the active layer) was separated from the total
absorption. In the wavelength range where the active layer absorbs, this is a small
correction to the total absorption. To minimize any error due to disagreement between
64
the modeled and experimental absorption values, the absorption in the active layer was
generated by subtracting the calculated parasitic absorption from the experimental
total absorption. Since the parasitic absorption values are small, any error is
minimized. This yields the total absorption in the active layer, Abstot = AbsD + AbsA.
To obtain the absorption due to each part of the blend, AbsD and AbsA, we make use of
the fact that the total imaginary part of the complex index of refraction of the blend is
approximately the weighted sum of the imaginary indices of the blend’s components,
𝑘tot = 𝑘P3HT × 0.5 + 𝑘PCBM × 0.5
(Eq. 5-4)
where here each component is weighted by 0.5 because the blend is composed of 50%
of each component.
It is important to note that the P3HT contribution to the total index of
refraction is very sensitive to the way the blend is processed for morphological
reasons; crystallization of the P3HT varies depending on drying/annealing conditions
and is also influenced by the presence of PCBM. The PCBM contribution, on the other
hand, is relatively insensitive to these parameters. Therefore, to extract the
contributions from each component, we subtracted the experimentally measured
PCBM k spectrum from the spectrum of the entire blend. This gives us the
contribution of each component of the blend to the total absorption.
We can tell how strongly each component is absorbing at a particular
wavelength in the actual device by taking the active layer absorption we determined
earlier and multiplying by the ratio of the k value in question to the total k (at the
wavelength of interest), e.g.
65
𝐴𝑏𝑠P3HT = 𝐴𝑏𝑠Active Layer ×𝑘P3HT
𝑘P3HT + 𝑘PCBM
(Eq. 5-5)
Figure 5-5. Typical parasitic absorption in electrodes.
66
Figure 5-6. Typical active layer absorption extracted using the techniques outlined in this section.
5.8.2 Comparison of calculated total reflectance vs. experimentally measured reflectance.
Most disagreement between modeled and actual device absorption happens near
the P3HT bandgap, where the film morphology has a large impact on the absorption.
This disagreement would be much reduced if one measured n and k values for every
device modeled. However, this is not practical, as these values are difficult to measure
for blends of organic semiconductors. In our case, because we subtract the parasitic
losses from the experimental total absorption, the error is minimized. Note that
agreement is very good at lower wavelengths where the PCBM is absorbing.
67
Figure 5-7. Calculated and experimentally measured reflectance spectra.
68
6 Trap-Assisted Auger Recombination Between Excitons and Electron-Polarons in Fullerenes Used for Solar Cells
6.1 Introduction
As we have shown in §5, under short-circuit conditions, approximately half of the
excitons generated in the fullerene phase of poly-3-hexylthiophene:[6,6]-phenyl-C61-
butyric acid methyl ester (P3HT:PCBM) solar cells recombine before they can be
harvested.16 Shrinking the domain size or applying a reverse bias fixes this problem.
Here we will show that the reason for the low harvesting efficiency is that the excitons
are recombining with deeply trapped electrons via an Auger-type process. Applying a
large reverse bias lowers the quasi-Fermi level, decreasing the population of trapped
electrons and effectively increasing the exciton diffusion length.
Much work has been done investigating the role of energetic traps on charge
carrier mobility and exciton diffusion, focusing mostly on the relatively shallow traps
that affect charge and exciton transport.59-63 We show that energetic traps can also play
a significant role in exciton recombination; exciton diffusion length is limited by
Auger recombination with deeply trapped electrons in the PCBM. Because the
electrons are deeply trapped, they do not affect charge transport, and thus have not
received much attention in the literature. They do, however, affect exciton
recombination and therefore have impact on overall device efficiency.
69
6.2 Auger recombination in organic semiconductors
Auger recombination is a carrier-mediated recombination process where an
electron and hole recombine, transferring their energy to another charge carrier (an
electron or hole). For a short duration of time, that carrier is ‘hot’; however it
thermalizes on a picosecond timescale to the band edge, dissipating the energy of the
original pair.64-66 Although Auger recombination is only relevant at high carrier
densities in inorganic solar cells, Auger recombination can occur more easily in
organic solar cells via Förster energy transfer between excitons and polarons.13
Because the exciton is a bound electron-hole pair and acts as a single particle, Auger
recombination between excitons and polarons is a two-body process. Additionally,
Förster energy transfer requires overlap of the exciton’s emission spectrum and the
polaron’s absorption spectrum. In most semiconducting polymers, this is naturally the
case.67,68
Because the electron mobility in PCBM is high (ca. 3×10-3 cm2/Vs),69 the
steady-state electron density is low and Auger recombination between excitons and
free polarons does not appear to take place. In the remainder of this chapter, we
investigate the process of Auger recombination between excitons and trapped
polarons in the PCBM phase of P3HT:PCBM solar cells. Because only trapped
electrons are relevant for exciton recombination in these devices, and because the trap
density is independent of the generation rate, the rate of Auger recombination depends
only on the exciton density and is essentially a monomolecular process.
70
6.3 Influence of electrical bias on external quantum efficiency
We measure external quantum efficiency (EQE) spectra under different lighting
conditions and with different applied biases, and observe that the spectral shape is
dependent on the applied bias. As the applied bias becomes more negative, the EQE
improves only in the short-wavelength end of the spectrum. We observed the same
behavior when PCBM exciton harvesting was enhanced by shrinking the domain
sizes, making them smaller than the exciton diffusion length (see §5).16 The EQE
enhancement with bias therefore appears to be due to a similar recovery of lost PCBM
excitons.
Figure 6-1 and Figure 6-2 show EQE spectra of P3HT:PCBM cells, made with
PC60BM and PC70BM, at increasing reverse bias. For both types of fullerene, the EQE
increases much more under reverse bias at wavelengths below 500 nm, which is where
the fullerenes absorb strongly, suggesting that the increase in EQE arises from
something that happens in the fullerene phase. Figure 6-3 shows the contributions to
the total absorption of each phase as well as the EQE at short-circuit (Jsc). The EQE is
proportional to the sum of the absorptions in each phase weighted by the exciton
harvesting efficiency in each phase. As shown in our previous work, all of the P3HT
excitons and only about half of the PCBM excitons are harvested at Jsc.16 Figure 6-4
shows the modeled efficiencies at -1V, -4V, and -8V.
71
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
EQE
Wavelength (nm)
-1V -4V -8V
Figure 6-1. EQE with increasing reverse bias in P3HT:PC60BM cells. PCBM exciton harvesting efficiency increases with no change in the P3HT parts of the spectrum.
300 400 500 600 700 800-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
EQE
Wavelength (nm)
0V -8V
Figure 6-2. EQE with increasing reverse bias in P3HT:PC70BM cells. The exciton recovery with bias is more pronounced than with the cells containing PC60BM.
72
Figure 6-3. Absorptions in each phase of the P3HT:PC60BM cell (220-nm-thick active layer) as well as the total absorption and EQE at Jsc.
-8 -6 -4 -2 0
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
Excit
on H
arve
stin
g or
Cha
rge-
Colle
ctio
n Ef
ficie
ncy
(Fra
ctio
n)
Vapplied
PCBM P3HT Charge Collection
Figure 6-4. Modeled exciton harvesting and charge collection efficiencies in P3HT:PC60BM as a function of applied bias calculated using the method from section 5.8.1.
73
Any recombination process that occurs after charge transfer at the
donor/acceptor interface would result in a change in the magnitude of the EQE
spectrum, but not a change in the shape, because the geminate pair thermalizes on a
picosecond timescale following charge transfer.65,66 Charges generated from blue
photons absorbed in PCBM are the same as charges generated from red photons
absorbed in P3HT. Although generation of charges from different wavelengths of light
may occur at different positions in the device due to interference effects, we observe
no dependence of this effect on device thickness. We therefore attribute this spectral
change to an imbalance of exciton recombination, where excitons in the fullerene
phase recombine at a much higher rate than excitons in the polymer phase. Excitonic
effects that might cause a change in spectral shape with bias include direct free-carrier
generation, photoconductivity70, Auger recombination with free electrons in PCBM,
and trap assisted Auger-type recombination between excitons and trapped electron-
polarons in PCBM.64,71
It has been suggested that a significant number of polarons recombine
monomolecularly in annealed P3HT:PCBM films due to trapping, and that they may
even be extracted by applying a bias.72 A monomolecular process that would be
consistent with the apparent loss of PCBM excitons is trap-assisted Auger
recombination between the PCBM excitons and trapped electrons.71 CELIV
measurements of electron and hole transport in P3HT:PCBM films suggest that
electrons are more strongly trapped than holes.73 Furthermore, Lenes et. al. have
shown, using a Gaussian disorder analysis74 of the densities of states, that PCBM
variants made with C70 have wider trap distributions than those made with C60.75
74
Using the same analysis and assuming that all states deeper than σ2/kT below the band
energy represent immobile (trapped) carriers, we calculate a trap density of
approximately 7×1018 cm-3 in PCBM.76,77 This represents one trap every 5 nm, which
is on the order of the exciton diffusion length in most organic materials and is
consistent with diffusion length measurements made on PCBM.51
The number of occupied traps is dependent on the quasi-Fermi levels in the
device. Changing the applied bias shifts the quasi-Fermi levels, changing the density
of exciton recombination centers and hence, the recombination rate. Although light
intensity also shifts the quasi-Fermi levels, the steady-state population of
photogenerated charges is only approximately 1015 cm-3 at 1 sun at reverse bias,
assuming charge carrier mobilities of 10-4 cm2/Vs. This is much smaller than the total
number of trapped charges, 7×1018 cm-3. Hence, we would expect little dependence of
EQE on illumination intensity but strong dependence on applied bias.
6.4 Inducing trap-assisted Auger recombination by creating deep level trap states
All of the aforementioned data taken from “standard” P3HT:PCBM cells
points to trap-assisted Auger recombination as the cause of the exciton loss in the
fullerene phase. To further investigate this possibility, we added deep electron traps to
the blend by including a small amount (0.1% of the total weight of PCBM) of 2,3,5,6-
tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ). F4-TCNQ is an electron
acceptor with an energy level approximately mid-gap in the fullerene and within the
thermal energy (kT) of the P3HT HOMO. Consequently any F4-TCNQ molecules near
75
PCBM molecules act as deep level electron traps. Any molecules near P3HT can also
accept electrons act as mild hole dopants. The F4-TCNQ is present in a sufficiently
small quantity that the morphology of the cell should not be affected appreciably, and
the hole dopant concentration is small enough that, aside from the photocurrent, it only
mildly affects the figures of merit: 20% reduction in Jsc, 5% reduction in Voc, 1%
reduction in FF (Figure 6-5). The electrical effects are probably due to the space
charge and increased dark current caused by the hole doping of P3HT, possibly along
with Shockley Reed Hall recombination between electrons and holes in the F4-TCNQ.
-1.0 -0.5 0.0 0.5 1.0
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
with
F4-
TCNQ
Applied Bias (V)
with F4-TCNQ Standard
Figure 6-5. I-V curves of “standard” P3HT:PCBM cells and of cells with 0.1% (F4-TCNQ/PCBM weight). Figures of merit: Jsc=7.82 mA/cm2, FF=0.65, Voc=0.605V for cells treated with F4-TCNQ, Jsc=9.72 mA/cm2, FF=0.66, Voc=0.635V for standard cells.
76
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
EQE
Wavelength (nm)
0V -1V -2V -4V -6V -8V
Figure 6-6. EQE of P3HT:PCBM cells with F4-TCNQ additive at varying reverse bias. No change in spectral shape is observed, indicating that excitons are recombining with deep-level traps that are not affected by the applied bias.
Because the F4-TCNQ traps reside deep within the PCBM bandgap, a
moderate applied bias should not be able to depopulate them. Figure 6-6 shows EQE
curves at increasing reverse bias for devices with F4-TCNQ added. Unlike the
standard devices shown in Figure 6-1, the spectral shape of the EQE no longer
changes with bias. There is an overall increase in the EQE with bias because the bias
helps to extract charges that would otherwise recombine; however we no longer
observe any excitonic effects. These data strongly suggest that there are many trapped
charges in PCBM and that they can cause excitons created in that phase to recombine.
6.5 Further discussion
An alternate explanation is that excitons generated in the PCBM might be
recombining with free polarons that are also present in that phase. In this case the
77
PCBM EQE would increase with bias because those polarons are swept out faster,
lowering the steady-state electron density in that phase and lowering the rate of Auger
recombination. Because exciton recombination is suppressed, excitons can diffuse to
an interface with P3HT and the exciton harvesting efficiency is improved. Because
this recombination pathway depends on the density of both excitons and free polarons,
it is a bimolecular process and should depend on illumination intensity. We performed
experiments on standard cells (ITO/PEDOT:PSS/P3HT:PCBM/Ca/Al, with
thicknesses 110 nm, 35 nm, 220 nm, 7 nm, 200 nm) containing both the PC60BM and
PC70BM varieties of PCBM. We varied illumination intensity and observed no change
in the EQE (Figure 6-7 and Figure 6-8). This indicates that the process is not
bimolecular and thus does not involve free charges. The small change in EQE in
Figure 6-8 is due to the slower frequency response of devices made with PC70BM.
Because we use an optical chopper to measure EQE with light bias, the choice of
chopping frequency can affect the measured EQE value if the device responds much
more slowly than light is modulated. Devices made with PC70BM show extremely
slow photocurrent response with roll-off beginning at 16 Hz, which is slower than the
lowest frequency we could use with 1 sun light bias (70 Hz). The frequency response
of cells made with PC70BM is shown in Figure 6-9.
78
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
EQE
Wavelength (nm)
0 Sun 0.1 Sun 0.5 Sun 1 Sun
Figure 6-7. Intensity dependence of EQE in P3HT:PC60BM cells. There is no dependence on excitation intensity, indicating that bimolecular and higher-order processes are not important at these intensities.
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
EQE
Wavelength (nm)
1 Sun, 0V 0V
Figure 6-8. Intensity dependence of EQE in cells made with PC70BM. The small difference in intensity is due to the fact that the minimum chop frequency we use at 1 sun to effectively measure a signal was 70 Hz, whereas at 0 sun we could use a 16 Hz chop frequency (see figure 5).
79
10 100
52
54
56
58
60
62
64
66
68
70
P3HT:PC70BM P3HT:PC60BM
Resp
onse
(arb
.)
Frequency (Hz)
Figure 6-9. AC response of P3HT:PC70BM and P3HT:PC60BM cells vs frequency. P3HT:PC60BM cells show no roll off at these frequencies.
6.6 Implications for other cell chemistries
It should be noted that we only see trap-assisted Auger recombination in
P3HT:PCBM cells. We have also measured EQE as a function of applied bias in cells
made from poly[N-9''-hepta-decanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl-2',1',3'-
benzothiadiazole)] (PCDTBT):PCBM and poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-
phenylene vinylene] (MEH-PPV):PCBM but saw no spectral dependence on bias,
which is consistent with our previous observations that the exciton harvesting in the
fullerene is dependent on domain size.16 P3HT is unique among high-efficiency
photovoltaic polymers in that it forms large crystals that do not contain fullerenes.
Cells made with P3HT and fullerenes optimize near a 1:1 ratio and can be thick
enough to absorb almost all of the light (>200 nm). In contrast, most polymers are
amorphous, optimize at 1:4 ratio with PCBM because of intercalation78-80, and result
80
in active layers that are only effective in thin layers, presumably because of
comparatively low charge carrier mobilities.40,81 Making high efficiency P3HT:PCBM
cells requires long periods of solvent and/or thermal annealing41, resulting in domain
sizes that are much larger than in other cells. PCBM excitons in these cells must
therefore diffuse farther than they would in devices with other cell chemistries. There
is also strong evidence for vertical phase segregation in optimized P3HT:PCBM cells,
indicating that there are large concentrations of fullerene near the transparent substrate
and also near the metal electrode.36,37,82 It is possible that those areas have larger
PCBM domains than in the rest of the bulk and are the areas where PCBM excitons
are not being efficiently quenched. As we have previously shown, shrinking the
domain size in P3HT:PCBM cells results in 100% exciton harvesting efficiency in the
fullerene phase, so this explains why we only see this effect in P3HT:PCBM cells.16
6.7 Auger recombination with trapped charge may explain other observations in the literature
Auger recombination of excitons with trapped polarons may be important in
other materials systems. Huang, et al.’s work on photoconductivity in pentacene/C60
cells attributes a similar spectral dependence to photoconductivity in the PCBM phase
only.70 They also observe spectral changes in their EQE curves that depend on applied
bias. Photoconductivity occurs either when charges in a device change the injection
barrier at non-ohmic contacts, leading to an increase in dark current under illumination
– or when charges fill traps in the bulk, changing the mobility under illumination. In
both cases the injected (dark) current is greater under illumination than it is when there
81
are no photogenerated carriers. Thus, the current under illumination is not simply the
sum of the dark current and the photocurrent. However, because this effect only
requires charges to be present in the material in question, it should not matter if those
charges were generated from excitons created in the donor or the acceptor material.
Thus there should be no spectral dependence to a photoconductive effect since
exciting the donor (or acceptor) creates charges in both the donor and acceptor.
One other possibility is that there is direct free carrier generation in the PCBM
or that the excitons are only weakly bound in this material and the applied field is
strong enough to split some fraction of the excitons, generating free charges. There
have been studies using optical characterization techniques to probe free carrier
generation in C60;83,84 however the number of long-lived carriers generated is quite
small (1% after ~10 ns at typical operating conditions)84 so this cannot explain the
50% increase in harvesting efficiency with bias that we observe. Additionally, the
currently accepted theories would not agree with such an increase: the change in
energy required to separate excitons (0.3-0.6 eV) is provided almost entirely by the
chemical potential offset at the heterojunction and by thermal energy. The additional
energy gained by the applied field is negligible in comparison and would not be
expected to efficiently separate excitons in a single phase. Furthermore, given the high
density of electrons in the fullerene phase, holes generated in this way would likely
recombine with electrons before they could be pulled into the polymer phase.
82
6.8 Auger recombination between excitons and free polarons in P3HT
To demonstrate that Auger recombination with polarons can occur in other
materials, we fabricated diodes made with the same structure as the solar cells
mentioned above, but with neat P3HT central layers rather than P3HT:PCBM blends.
We also fabricated the same diodes with the F4-TCNQ additive to dope the P3HT
with free holes. To directly observe exciton quenching by charge carriers, we
monitored photoluminescence from these diodes as a function of applied bias. The
excitons were generated by pumping the diode with the 514 nm laser line from an
argon ion laser (Spectra Physics). Fluorescence was monitored using a
monochromator/spectrograph (Acton).
Figure 6-10. Photoluminescence (black dots) and current density (red curve) vs. applied bias in P3HT-only diode. PL drops when current is injected, indicating that excitons recombine with injected carriers.
-20 -15 -10 -5 0 5-80
-60
-40
-20
0
20
VApplied
J (m
A/c
m2 )
-20 -15 -10 -5 0 55
5.4
5.8
6.2
6.6
7x 105
Pho
tolu
min
esce
nce
(cou
nts)
83
Figure 6-11. Photoluminescence (black dots) and current density (red curve) vs. applied bias in P3HT:F4-TCNQ diode. Photoluminescence increases as bias moves from 0 V to -5 V as the free holes created by the F4-TCNQ are removed. PL drops at further reverse bias as charges are injected from the electrodes.
Figure 6-10 shows photoluminescence intensity and current density in a P3HT-
only diode as a function of applied bias. Figure 6-11 shows the same information for a
P3HT diode doped with F4-TCNQ. In both cases, whenever the injected carrier
density increases, photoluminescence drops, indicating that excitons are recombining
with the injected carriers. In the case of the diode doped with F4-TCNQ,
photoluminescence first increases as the bias becomes negative. This is because,
although an appreciable number of charges is not being injected, the bias serves to
lower the quasi-Fermi level, clearing the device of the holes that were added by the
F4-TCNQ dopant. This reduces exciton recombination and increases
photoluminescence efficiency. The observation that the photoluminescence efficiency,
-10 -8 -6 -4 -2 0 2-10
0
10
20
30
40
50
60
VApplied
J (m
A/c
m2 )
-10 -8 -6 -4 -2 0 23.2
3.4
3.6
3.8
4
4.2
4.4
4.6x 105
Pho
tolu
min
esce
nce
(cou
nts)
84
and hence the exciton lifetime, are altered by the presence of charge carriers serves as
evidence for Auger recombination between excitons and polarons in organic materials.
6.9 Conclusion
We have observed Auger recombination between excitons and trapped electrons
only in the PCBM phase of P3HT:PCBM solar cells. However, since we have
demonstrated that the presence of charge carriers shortens the exciton lifetime (and by
association, the diffusion length) in other materials, it does hold general implications.
If polymer cells are to be a viable source of energy in the future, they will need to
optimize at large film thicknesses to ensure that all of the incident light is absorbed.
Therefore they may require similarly large PCBM domains to maintain efficient
carrier extraction. If the trap density in the fullerene phase can be reduced, perhaps by
increasing material purity or by better controlling film morphology, device
performance will be improved. Furthermore, the exciton diffusion lengths in other
materials may be limited by Auger recombination with charges present in those
materials because of doping from contaminants, morphological effects, or injected
dark current. By addressing these issues, internal quantum efficiencies in current state
of the art devices may be improved.
6.10 Experimental details
Standard devices had power conversion efficiencies greater than 4% and were
made with the same structure and methodology outlined in §4.8. Devices made with
F4-TCNQ were made using the same procedure except that 0.002% additional F4-
85
TCNQ solute was added to the stock P3HT:PCBM solution and allowed to stir
overnight before spin casting.
External quantum efficiency spectra were taken according to the method
described in §0. Exciton harvesting efficiencies were modeled by calculating internal
quantum efficiency contributions from each component of the active layer, as
described in §5.8.1.85
6.11 Gaussian disorder model
To estimate the number of occupied traps, we assume a Gaussian distribution of
states around the band edge. We assume that all states within σ2/kT of the band are
accessible to conduction, i.e. carriers in those states are mobile.86 Carriers below this
level are considered immobile. To calculate the total number of trapped carriers we
simply integrate the number of states up to σ2/kT from the band energy.
Figure 6-12. Gaussian disorder model of density of states.
LUMO
HOMO
Energy
Density of States
86
The Gaussian parameters (total number of states and standard deviation) are taken
from the literature.75 The number of trapped carriers is then calculated via
𝑁 =𝑁0
𝜎√2𝜋� 𝑒
−𝐸22𝜎2�
−𝜎2/𝑘𝑇
−∞𝑑𝐸
(Eq. 6-1)
where N0 is the total number of states in the band (which is equal to the number of
molecules in the film, since each contributes one state), and σ is the width of the
Gaussian distribution.
87
7 Conclusion
7.1 Summary
Fullerene molecules are the only electron acceptors that have successfully been
used to make high efficiency (>5%) organic solar cells. By developing a method to
accurately measure internal quantum efficiency, we have discovered an important loss
mechanism for excitons in fullerenes used as acceptors in bulk heterojunction solar
cells. We have shown that excitons are able to recombine with polarons and that by
removing the charges with an applied bias, we are able to recover those excitons. We
can also recover them by making the domains smaller, indicating that this is an exciton
diffusion problem. We have reproduced the problem by purposefully adding charges
through adding deep level traps that cannot be removed with a bias, by doping a diode
with free carriers, or by injecting charges from the electrodes. Photoluminescence
measurements provide direct measurement of the emissive portion of the exciton
population and these results support our theory.
7.2 Future work
The exciton diffusion length in organic molecule films has always been shorter
than theory predicts: experiments have shown typical exciton diffusion lengths to be
approximately 5 nm47,87,88, while theory predicts upwards of 200 nm.89 Our work
suggests that the exciton diffusion length is limited by Auger recombination with
trapped charges that are intrinsic to the materials. If excitons’ diffusion lengths are
88
limited by recombination with intrinsic charges, chemists might choose to focus their
efforts on creating materials that are ‘cleaner’. Such efforts could lead to organic solar
cells with much higher efficiencies, both due to increased exciton harvesting and also
due to enhanced charge transport properties. By allowing for larger domain sizes,
charge carrier mobility will likely be enhanced. Additionally, having larger domains
decreases the heterojunction surface area, reducing bimolecular recombination of both
photogenerated charges and injected ‘dark’ charges, increasing quantum efficiency
and boosting open circuit voltage by reducing dark current.
89
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