photocurrent generation from light absorption by
TRANSCRIPT
Photocurrent Generation from Light Absorption by
Semiconducting Single Walled Carbon Nanotubes
by
Dominick J. Bindl
A dissertation submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
(Materials Science)
at the
UNIVERSITY OF WISCONSON—MADISON
2013
Date of final oral examination: 9/3/13 The dissertation is approved by the following members of the Final Oral Committee:
Michael S. Arnold, Assistant Professor, Material Science and Engineering Padma Gopalan, Associate Professor, Material Science and Engineering Paul Evans, Associate Professsor, Material Science and Engineering Zhianqiang Ma, Vilas Distinguished Achievement Professor, Electrical and Computer Engineering Thomas Kuech, Milton J. and A. Maude Shoemaker Professor, Chemical and Biological Engineering
i
Photocurrent Generation from Light Absorption by
Semiconducting Single Walled Carbon Nanotubes
By Dominick Bindl under the supervision of Professor Mike Arnold
at the University of Wisconsin Madison
Abstract
We demonstrate significant advances in the fundamental understanding of charge generation in
semiconducting single walled carbon nanotube (s-SWCNT) hybrid systems. By developing preparation
schemes based on the dispersion selectivity of poly(9,9 dioctylfluorenyl 2,7-diyl) and related copolymers,
we accessed solution-based populations of s-SWCNTs in purities high enough to study the intrinsic
photophysics of s-SWCNT light absorbers in cast films. Using these films we demonstrate that little-to-
no charge is generated in optically excited, films of polymer-wrapped s-SWCNTs. More importantly, we
demonstrate efficient charge generation via the dissociation of photogenerated excitons on s-SWCNTs at
type-II electronic heterojunctions between s-SWCNTs and charge accepting semiconductors, when
electronic offsets exceed the exciton binding energy. We demonstrate exciton dissociation via electron
transfer to C60 and photocurrent generation in quantum efficiencies exceeding 85%, and experimentally
identify a s-SWCNT diameter cutoff around 1.0nm above which the efficiency of photogenerated electron
transfer to C60 quickly falls off. We use the high efficiency of exciton dissociation at this interface and s-
SWCNT samples highly enriched in a single chiral species to measure photocurrent collection from
excitons optically excited into excitonic manifolds above the groundstate in equivalent efficiencies as
excitons directly excited into the groundstate. We extend our understanding of photocurrent generation in
s-SWCNT/C60 heterojunctions, in collaboration with scientists at the National Renewable Energy
Laboratory (NREL) and reveal the competition between ‘fast’ recombination processes intrinsic to the s-
SWCNT films with time constants of order 10ns and much slower recombination across the
heterointerface, with time constants of order 850 ns. We study the effect of residual PFO on photocurrent
ii
generation, and trace s-SWCNT film thickness trends in photocurrent generation efficiency back to
exciton diffusion and the percolation of individual s-SWCNTs within the film. We demonstrate
photovoltaic power conversion of near infrared light via s-SWCNT exciton dissociation variously
throughout the dissertation, and close with an outlook on the emergent field of s-SWCNT based
photovoltaics.
iii
Acknowledgements
I have been incredibly fortunate to enjoy the intellectual, fraternal, and emotional support of countless individuals and organizations throughout my thesis work; a number of whom I will mention here. I would like to thank Prof. Mike Arnold for his trust, his support, and the opportunities afforded by the research goals I pursued while in his group. I have benefitted greatly as his first graduate student and am aware of my fortune to have been under his tutelage. I have also benefitted tremendously by the research team Prof. Arnold has assembled in my time here. I am thankful to have worked alongside Nate Safron, Adam Brewer, Meng Yin Wu, Susmit Singha Roy, Bobby Jacobberger, Matt Shea, Amir Mashal, Jerry Brady, Changhao Wan, Dr. Feng Xu, and Dr. Yumin Ye. This research group has not only enriched my life at work but also provided encouragement, feedback, and useful suggestions. I have also had the privilege of sharing time in the lab with a number of promising and energetic undergraduate researchers. Fritz Prehn spent the better part of three years working alongside me, and I wish him the best in his studies at Colorado School of Mines. I also thank and wish the best to Rebeca Caban, Deanna Lanigan, Paul Dieterle, and Sohil Shah. I owe a large debt of gratitude to Dr. Jeffrey Blackburn and all his colleagues at NREL, specifically Kevin Mistry, Dr. Andrew Ferguson, Dr. Nikos Kopidakis, and Dr. Brian Larson. I greatly enjoyed my time at NREL and was only able to complete our collaborative project with the full support of this great team. Most importantly I would like to thank my wife, Jeannine. Words cannot describe what her constant presence has meant to me; nor can they weigh how it has enabled me.
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Contents Abstract .......................................................................................................................................................... i
Acknowledgements ...................................................................................................................................... iii
Contents ....................................................................................................................................................... iv
List of Figures ............................................................................................................................................... vi
1. Introduction .......................................................................................................................................... 1
1.1 Structure and relevant properties of SWCNTs .............................................................................. 2
1.1A. Structure ..................................................................................................................................... 2
1.1B. Diametric trends in bandgap and mobility .................................................................................. 3
1.1C. Optical transitions ........................................................................................................................ 4
1.1D. Excitons in s-SWCNT .................................................................................................................... 5
1.1E. Solution Processability and Sorting .............................................................................................. 6
1.2 Opportunities for s-SWCNTs in photodetectors and photovoltaics ................................................... 7
1.2A Opportunities in single junction organic photovoltaics ................................................................ 7
1.2B. Opportunities in multijunction photovoltaics ........................................................................... 10
1.2C. Opportunities in generation III photovoltaics ........................................................................... 11
1.2D. Opportunities in non-conventional photovoltaic architectures ................................................ 11
1.2E. Scope of this dissertation ........................................................................................................... 12
2. Free Charge Carrier Generation via Dissociation of Excitons79 ........................................................... 14
3. Quantifying Exciton Dissociation Efficiencies83 ................................................................................... 23
4. S-SWCNT / [60] PCBM Bulk Heterojunctions84 ................................................................................... 30
5. Diffusion of Excitons95 ......................................................................................................................... 36
6. Photocurrent from Above-Gap Excitonic Transitions110 ..................................................................... 47
7. Free Carrier Generation and Recombination in Polymer Wrapped Semiconducting Carbon Nanotube
Films and Heterojunctions .................................................................................................................. 57
8. Summary and Outlook ........................................................................................................................ 78
8.1 Enhancing the performance of planar heterojunctions ............................................................. 79
8.2 Enhancing the performance of bulk heterojunctions ................................................................. 81
8.3 Perspective ...................................................................................................................................... 81
References .................................................................................................................................................. 83
APPENDIX A: s-SWCNT Solution Preparation ............................................................................................ 101
General s-SWCNT Isolation and Dispersion .......................................................................................... 101
v
(7,5) s-SWCNT Isolation and Dispersion................................................................................................ 101
(6,5) s-SWCNT Isolation and Dispersion................................................................................................ 102
Appendix B: Supplmentary information for chapter 3 ............................................................................. 103
Characterization of film morphology ................................................................................................... 103
Thickness trends of external QE and film reflectance for mixed-SWCNT devices ................................ 103
Photovoltaic response of mixed-SWCNT device ................................................................................... 103
Device area independence.................................................................................................................... 104
Photovoltaic spectrum .......................................................................................................................... 104
Absorption Efficiency Calculation ......................................................................................................... 105
Integrated external QE/Jsc matching ..................................................................................................... 106
Optical cross-section of semi-SWCNTs ................................................................................................. 106
Estimation of absorption length, LA ...................................................................................................... 107
Preparation of mixed-SWCNTs ............................................................................................................. 109
XI. Device characterization.................................................................................................................... 109
Appendix C: Supplmentary information for chapter 5 ............................................................................. 110
Quantification of PFO Content .............................................................................................................. 110
Determining Absorption Efficiency ....................................................................................................... 111
Modeling Exciton Diffusion ................................................................................................................... 112
Appendix D: Supplmentary information for chapter 6 ............................................................................. 114
IQE of E11 and E11 + X transitions: .......................................................................................................... 114
IQE of E22 transition: .............................................................................................................................. 118
Appendix E: Supplmentary information for chapter 7.............................................................................. 121
vi
List of Figures
Figure 1.1 Number of papers published concerning carbon nanotubes over the past 10 years. Data extracted from
Web of Knowledge database. _____________________________________________________________________ 1
Figure 1.2 Chiral map schematically representing the circumferential vector (Ch) and chiral angle for the (9,3)
metallic SWCNT. Unit vectors a1 and a2 of the graphene lattice, and axes corresponding to Ch direction for zigzag
and armchair SWCNTs also provided. (n,m) chiralities corresponding to s-SWCNTs are in black, while metallic
SWCNTs are in red. _____________________________________________________________________________ 3
Figure 1.3 A. Diameter dependence of optical band gap in s-SWCNTs. Data taken from empirical measurements in
Weisman et al.2 B. Room temperature, peak mobility on s-SWCNTs, as measured in CVD grown s-SWCNT FETs by
McEuen et al.9 and as calculated by Goldsman et al.
11 _________________________________________________ 4
Figure 1.4 A. Optical absorption spectrum of a polymer-dispersed solution of (6,5) s-SWCNTs in >95% chiral purity.
Spectrally sharp features protruding from smooth “continuum” absorption identified according to optical
transitions B. Diameter dependence of Eii optical transitions.1,2
__________________________________________ 5
Figure 1.5 Exciton binding energy trends A. Ebi as a function of s-SWCNT diameter in vacuum, calculated according
to Capaz et al.4 B. Ebi as a function of s-SWCNT dielectric environment, calculated for the (7,5) s-SWCNT, which has
a diameter d=0.8 nm10
__________________________________________________________________________ 6
Figure 1.6 Typical JV characteristic of photovoltaic device demonstrating short circuit current density (JSC) open
circuit voltage (VOC) and fill factor (FF), the product of which yield the maximum power generation of the device.
The ratio of the maximum power to the incident power yields the power conversion efficiency ( P ). ___________ 8
Figure 1.7 Thin film absorptance (1 – transmittance) calculation for varying thickness (7,5)@PFO films. Plot
generated using absorption coefficient extracted from 30nm thick film on quartz. _________________________ 10
Figure 2.1 Photosensitive capacitor measurement circuit and energy band diagram. Photogenerated excitons on s-
SWCNTs are dissociated at interfaces with acceptors when ΔIP or ΔEA > EB. _______________________________ 15
Figure 2.2 A. Normalized optical absorptivity of PFO-wrapped s-SWCNTs in chloroform solution (dotted, red) and in
thin films (solid, blue). B. SEM micrograph of a thin film of 1:1 PFO:s-SWCNTs on ITO coated glass. ___________ 16
Figure 2.3 A. Magnitude of the exciton dissociation driven current responsivity for various 1:1 wt ratio PFO:s-
SWCNT/semiconductor heterojunctions measured using photoactive capacitor devices. Responses are offset but
not scaled. B. Responsivity of s-SWCNT/P3OT (black, solid) device compared with calculated, spectrally resolved
optical intensity in P3OT (blue, dotted) and in s-SWCNT (red, dashed) for a device stack of: glass / ITO (100nm) / s-
SWCNT (7nm) / P3OT (30 nm) / PVP (1900 nm) / Ag (50nm). ___________________________________________ 17
Figure 2.4 A. Bias dependent responsivities for s-SWCNTs interfaces with poly(thiophene) derivatives and fullerene-
derivatives. Arrow denotes direction of increasing bias (on Ag) from -5 V (solid, blue) to +5V (dotted, red) in 2.5 V
steps. Responsivity curves are offset but not scaled. __________________________________________________ 18
vii
Figure 3.1 A. Device architecture. B. Schematic depicting charge transfer at nanotube/C60 interface. C. Normalized
optical absorption spectra of mixed (dot-dash, blue) and semiconducting (solid, red) carbon nanotube solutions (top
curves, offset vertically by 1 A.U.) and resulting films (bottom curves). ___________________________________ 24
Figure 3.2 Comparison of characteristics of mixed-SWCNT (dot-dash, blue) and semi-SWCNT (solid, red) devices. A.
Typical dark current-voltage characteristics. B. Spectrally resolved short-circuit external QE for devices with
optimized thicknesses, and spectrally varying optical intensity at the s-SWCNT/C60 interface (grey, dashed)
predicted using optical transfer matrix simulations. __________________________________________________ 25
Figure 3.3 Diameter and thickness dependencies. A. External quantum efficiency (EQE) of semi-SWCNT/C60
heterojunction devices for increasing semi-SWCNT film thickness. Each spectrum is offset by 10% from the previous
spectrum, starting with the thinnest (blue curve) to the thickest film (red curve). B. 1-Reflectance data for the semi-
SWCNT device stacks shown in part A where Reflectance is the measured reflectance at ~normal incidence from
each device stack. The Ag cathode serves as a mirror in each device; therefore, Reflectance and 1-Reflectance are
measures of the irradiation that have and have not been absorbed by the device stack, fully considering optical
interference and film thickness. Data is not offset. The black, dashed curve is the measured 1-Reflectance for a
control device stack containing no SWCNTs. Absorption losses in the NIR in the control stack arise from the ITO and
red-shift as the nanotube thickness increases. Each 1-Reflectance curve was fit (see Supporting Information) to
determine the fraction of the absorption from the nanotubes (ηA) versus the fraction from the ITO. C. Internal QE
versus diameter and chirality compared with the expected energetic driving force for exciton dissociation at the
semi-SWCNT/C60 interface. D. Thickness dependence of internal QE for the (8, 6) nanotube in terms of the
absorption length, LA. Red line is a fit of the experimental data for a one-dimensional diffusion model with an
exciton diffusion length, LD=0.13 ± 0.4 LA. _________________________________________________________ 27
Figure 3.4 Spectrally resolved photoluminescence (PL) of semi-SWCNTs in solution (red, dashed curve), in a thin film
of NIR optical density ~ 0.02 (light blue, solid curve), and in the same thin film interfaced with C60 (gray, dotted
curve), in all cases the laser excitation is at 658 nm, in resonance with the E22 optical transitions of the (7, 5) and (7,
6) chiralities. In solution, the PL arises predominantly from the directly excited (7, 5) and (7, 6) chiralities,
confirming the isolation of the nanotubes. However, in thin film, the PL indirectly arises mostly from the non-
excited (8, 6), (8, 7), and (9, 7) chiralities, which have smaller band gaps, indicating coupling of the nanotubes in
thin film and efficient exciton energy transfer from the (7, 5) and (7, 6) chiralities. After the nanotubes in the thin
film are covered by thermally evaporated C60, their PL is nearly completely quenched, consistent with the
hypothesis of nearly perfect exciton dissociation and electron transfer from the photoexcited (7, 5) and (7, 6)
nanotubes to the C60 molecules. __________________________________________________________________ 28
Figure 4.1 Normalized optical absorption of PCBM, s-SWCNT and blended PCBM:s-SWCNT thin films in red
(dotted), grey (dot-dash) and blue (solid), respectively. B. Expected energy alignments in prepared device stack of
ITO / ca. 10 nm s-SWCNT:PCBM / 100 nm C60 / 10 nm BCP / Ag. Mid-gap conduction states in BCP illustrated as
dashed lines. _________________________________________________________________________________ 31
Figure 4.2 A Current density vs. voltage response of typical device in dark (dashed grey) and in response to 137 mW
cm-2
NIR irradiance (solid red). B. Intensity dependence of power conversion efficiency (ηP), fill factor (FF), open
circuit voltage (Voc) and current responsivity (R). C. Spectrally resolved zero-bias external QE. Contribution from
specific s-SWCNT E11 transitions are identified according to s-SWCNT chirality. ____________________________ 32
viii
Figure 4.3 A. TEM micrograph of blended PCBM:s-SWCNT film. Inset reveals individual s-SWCNT sidewalls,
measured as 9 ± 1 Å with example illustrations of relative orientation. B. Bias dependent photocurrent normalized
at -1. Photocurrent is defined as the difference between the measured current under irradiation and the measured
dark current. Arrow indicates direction of increasing NIR intensity (from 0.1 to 50 mW cm-2
). ________________ 33
Figure 5.1 A. Solution absorbance of 22%, 36% and 43% s-SWCNT solutions, normalized at λ = 1050 nm. B. Film
absorbance of films cast from 22%, 36% and 43% s-SWCNT solutions, normalized at λ = 1050 nm. C.
Photoluminescence emission spectra of films cast from 22%, 36% and 43% s-SWCNT solutions in response to
excitation at λ = 653nm. ________________________________________________________________________ 38
Figure 5.2 Scanning electron micrographs of films cast from 43%, 36%, and 22% s-SWCNT solutions, left to right,
respectively. Image sizes and magnifications are equivalent, scalebars = 500 nm. __________________________ 41
Figure 5.3 Thickness-optimized external quantum efficiencies (EQE) achieved in ITO/PFO-wrapped s-SWCNT/ 120
nm C60/10 nm BCP/100 nm Ag thin film, planar bilayer heterojunction photodiodes. ________________________ 42
Figure 5.4 Thickness dependence of EQE measured at λ = 1195 nm for planar bilayer heterojunction photodiodes
constructed from films cast from A. 22% B. 36% and C. 43% s-SWCNT solutions. Black, dotted line represents best fit
to each dataset using measured absorption efficiencies and a 1-D exciton diffusion model for exciton diffusion,
schematically illustrated in D. Solid, purple line represents best fit to each dataset using measured absorption
efficiencies and exciton wicking model, schematically illustrated in E. ____________________________________ 43
Figure 6.1 A. Normalized absorbance of (7, 5) enriched s-SWCNT solutions (top, green) and thin films on quartz
(bottom, violet) cast from the above solutions. Solution absorbance spectra have been offset. B. Characteristic
external quantum efficiency (EQE) of photocurrent generation from ITO / active layer / 10 nm BCP / 100 nm Ag
devices. Active layers displayed are (7, 5) / 50 nm C60 (solid, blue), (7, 5) / 90 nm C60 (solid, red), 50 nm C60 (dashed,
blue), 90 nm C60 (dashed, red). ___________________________________________________________________ 49
Figure 6.2 A Measured 1 – Reflectance (i.e. ηA) for device stacks of ITO / active layer / 10 nm BCP / 100 nm Ag
devices. Active layers displayed are (7, 5) / 50 nm C60 (violet), and 50 nm C60 (green). B. C. and D. Display ∆ηA (solid
green); fits to ∆ηA (dashed blue); and measured EQE (solid red) for three devices. (E) Extracted IQE for optical
excitation at E11, E11 + X and E22 transitions, following treatment outlined in Supplementary Information. _______ 51
Figure 6.3 A. Current density versus voltage characteristics in the dark (green) and illumination under 100 mW cm-2
at λ = 1053 nm (violet) plotted on a linear and B. log-linear scale. C. Photovoltaic device parameters versus
irradiance. ___________________________________________________________________________________ 54
Figure 7.1 A. Absolute absorptance (1 – transmittance) of a neat PFO-wrapped s-SWCNT film (Red, s-SWCNT) and
a comparable film in a bilayer with 90 nm C60 (Blue, s-SWCNT/C60). B. Semi-log plot of the microwave
photoconductance transients acquired after exciting neat films and bilayers (Red and Blue, respectively) with an
absorbed photon flux of ~6 1011
photons cm-2
. C. Semi-log plot of the photoconductance transients for the neat s-
SWCNT film across a wide range of absorbed photon fluxes from ~1 1011
photons cm-2
(dark blue) to ~6 1013
photons cm-2
(light blue). D. Semi-log plot of the photoconductance transients for the s-SWCNT/C60 bilayer film
photoconductance transients across a wide range of absorbed photon fluxes from ~4 1010
photons cm-2
(dark red)
to ~5 1013
photons cm-2
(light red). ______________________________________________________________ 62
ix
Figure 7.2 A. Absorbed photon fluence dependence of the yield-mobility product () at end-of-pulse (EOP, peak)
for Neat and Bilayer films. Solid lines represent fits with Eq. 2 (see main text). B. Fluence dependence of the long-
lived (350ns) fractional contribution for bilayer films, indicating a strong enhancement of the long-lived signal
at low absorbed photon fluences. ________________________________________________________________ 65
Figure 7.3 A. Spectral dependence of end-of-pulse photoconductance (GEOP), normalized to the incident photon
fluence (I0), for neat PFO-wrapped s-SWCNTs (Neat, Red diamonds) and a PFO-wrapped s-SWCNT film in bilayers
with C60 (Bilayer, Blue circles) compared to the absolute absorptance (1 – Transmittance) for the same samples. B.
Near-Infrared spectral dependence of the yield-mobility product () at end-of-pulse for Neat and Bilayer films.
Vertical grey bars indicate wavelengths in resonance with the S1 transition of the s-SWCNT chirality indicated. __ 69
Figure 7.4 A. Photoluminescence emission of PFO-wrapped s-SWCNT films before (Red diamonds) and after (blue
circles) deposition of C60.. B. Fluence dependence of the calculated free carrier generation yield (ϕ ) for neat films
(Red diamonds) and bilayers with C60 (blue circles) ___________________________________________________ 74
1
1. Introduction
Carbon nanotubes (CNTs) demonstrate a wide range of interesting and exceptional properties.
Semiconducting, single walled carbon nanotubes (s-SWCNTs, see section 1.1) in particular, demonstrate
marked potential for various electronic and optical applications.1 Consequently, a great deal of research
effort has been devoted to understanding the precise nature of those properties and exploiting these
properties in various applications. The past ten years have witnessed an explosion of activity along these
lines, evidenced by the large volume of resulting literature (see Figure 1.1). This dissertation is focused
on enabling applications which seek to utilize s-SWCNTs to convert light energy into electrical energy,
including photovoltaic photodetectors and photovoltaic energy converters.
Figure 1.1 Number of papers published concerning carbon nanotubes over the past 10 years. Data extracted from Web of Knowledge database.
1992 1998 2004 2010
0
5,000
10,000
15,000
20,000
25,000
30,000
"carbon nanotube*" Web of Science
# p
ub
lic
ati
on
s
Year
2
1.1 Structure and relevant properties of SWCNTs
1.1A. Structure
SWCNTs can be structurally considered as a single sheet of sp2 hybridized carbon (graphene) rolled into
a seamless cylinder. The direction and magnitude of the circumferential vector with respect to the
underlying graphene lattice is known as the chiral vector and is quantified as:
21 amanCh Eq. 1.1
Where a1 and a2 are the lattice vectors of graphene (See Figure 1.2). According to this notation, a
SWCNT of any diameter and chiral angle (θ) can be uniquely identified according to its (n,m) indices and
further quantified according to the relations:
22
220 2cos;
mnmn
mnmnmn
ad
Eqs. 1.2 ; 1.3
Where a0 is the magnitude of graphene lattice vectors, a0 = |a1| = |a2|, and is defined by the graphene
C-C bond length as a0 = 3 aC-C = 0.249 nm.15 In addition to structural properties, electronic properties
can be predicted from SWCNT (n,m) chirality. For instance, consider the ratio 3
mn . If this ratio returns
an integer value, that particular (n,m) chirality corresponds to a metallic SWCNT while all
semiconducting carbon nanotubes will return non-integer values.15
3
1.1B. Diametric trends in bandgap and mobility
The electronic wavefunction in s-SWCNTs is confined about the circumference. Correspondingly, the
bandgap of s-SWCNTs scales inversely with diameter. Optical bandgaps of s-SWCNTs have been
measured to sweep from over 2 eV for diameters ca. 0.5 nm, to 1 eV for 1nm diameters, and approach
the 0 eV semi-metallic behavior of graphene as s-SWCNTs approach infinite diameter (Figure 1.3).2 Also
scaling with diameter is the free carrier mobility. Resulting from strong diameter dependence in the
electron and hole effective masses, it has been theorized and experimentally verified that low-field free
carrier mobilities increase from order 103 to 105 cm2V-1s-1 for s-SWCNTs of diameter 1nm to 10nm,
respectively.9,11
Figure 1.2 Chiral map schematically representing the circumferential vector (Ch) and chiral angle for the (9,3)
metallic SWCNT. Unit vectors a1 and a2 of the graphene lattice, and axes corresponding to Ch direction for zigzag
and armchair SWCNTs also provided. (n,m) chiralities corresponding to s-SWCNTs are in black, while metallic
SWCNTs are in red.
4
1.1C. Optical transitions
Circumferential quantum confinement renders s-SWCNTs 1-D semiconducting materials, introducing van
Hove singularities (vHs) into the density of states (DoS).16 Optical absorption exciting carriers across the
bandgap reflects this underlying electronic structure and produces spectral absorption coefficients
which are highly structured, with the spectral features corresponding to individual (n,m) s-SWCNTs. For
example, figure 1.4 shows the absorption of a s-SWCNT solution enriched to >95% in the (6,5) chirality.
All dominant spectral features depicted are attributed to the (6,5) species. It is clear that atop the broad
background absorption (absorption across the continuous DoS in the valence and conduction bands,
below the vHs) are sharp features corresponding to optical transitions across the first, and second
coordinate pair of vHs in the DoS, denoted E11 and E22 transitions, respectively. The E1,2 and E2,1
transitions strongly overlap one another, and are much lower probability transitions as they do not
conserve angular momentum.17 Also clear are sidebands to these distinct absorption features arising
from strong phonon-exciton coupling.17,18 Not pictured are higher energy transitions, such as the E33 and
E44 which are energetically in the UV for the (6,5) chirality.2
Figure 1.3 A. Diameter dependence of optical band gap in s-SWCNTs. Data taken from empirical measurements in
Weisman et al.2 B. Room temperature, peak mobility on s-SWCNTs, as measured in CVD grown s-SWCNT FETs
by McEuen et al.9 and as calculated by Goldsman et al.11
0.5 1.0 1.5 2.00.0
0.5
1.0
1.5
2.0
2.5
EG
, O
ptica
l (e
V)
s-SWCNT Diameter (nm)
1.0 2.0 3.0 4.0 5.0
103
104
105
Peak M
obili
ty (
cm
2V
-1s
-1)
s-SWCNT diameter (nm)
Goldsman et al.
McEuen et al.
A B
5
1.1D. Excitons in s-SWCNT
Like semiconducting polymers and small molecules, optical absorption by s-SWCNTs predominantly
results in excitons – which are bound electron-hole pairs with binding energies >> kBT. The binding
energies of excitons on s-SWCNTs depend strongly on both the diameter of the host s-SWCNT, and the
local dielectric immediately surrounding the s-SWCNT.4 More explicitly, ab initio and tight binding
calculations have proposed an inverse proportionality between the exciton binding energy (Ebi) and s-
SWCNT diameter, and a scaling relation between Ebi and the local dielectric environment of
(Fig. 1.5). It has also been shown that these calculations are in good agreement with binding energies
measured via two-photon spectroscopy measurements.4,19
The large aspect ratios of s-SWCNTs favorably influence the diffusivity and therefore diffusion lengths of
photogenerated excitons on s-SWCNTs. While excitons in most organic systems are described as Frenkel
excitons - residing largely on individual molecules - excitons on s-SWCNTs are more closely characterized
as Wannier-Mott type and are consequently greatly delocalized.20 Spectroscopic studies on isolated,
small diameter (ca. 0.8nm) s-SWCNTs reveal exciton sizes of order 2 – 3 nm with diffusion lengths up to
600nm.21,22
Figure 1.4 A. Optical absorption spectrum of a polymer-dispersed solution of (6,5) s-SWCNTs in
>95% chiral purity. Spectrally sharp features protruding from smooth “continuum” absorption
identified according to optical transitions. The dispersing polymer does not absorb in this spectral
range. B. Diameter dependence of Eii optical transitions.1,2
400 600 800 1000 12000.0
0.5
1.0
Ab
s.
(No
rma
lize
d)
Wavelength (nm)
E11
E22
E11 + XE12,21
E22 + X
0.5 1.0 1.5 2.00
1
2
3
4
5
E11
E22
E33
E44
En
erg
y (
eV
)
s-SWCNT Diameter (nm)
A B
6
1.1E. Solution Processability and Sorting
Knowledge concerning the processability of carbon nanotubes has greatly increased in the past ten
years, leading to tremendous advances in our ability to manipulate them in solution. Covalent sidewall
functionalization can induce great solubility in a variety of solvents, however this functionalization
disrupts the conjugated structure and therefore compromises many appealing properties including free
carrier mobility and all optical properties. 23,24 Dispersion of isolated SWCNTs and small bundles of
SWCNTs into aqueous and organic solvent systems has also been demonstrated via non-covalent surface
functionalization with surfactants,25,26 and polymers,27,28 including DNA.27,29 It has also been
demonstrated that solutions of pristine, isolated SWCNTs can be achieved in certain solvents, including
superacids such as chlorosulfonic acid,30,31 and more docile solvents like cyclohexylpyrrolidone.32
A number of these dispersion routes produce opportunities to sort s-SWCNTs from the heterogeneous
SWCNT dispersions. For instance, Dr. Ming Zheng and co-workers have developed a library of DNA
sequences with specificity toward certain s-SWCNT chiralities and have enabled, via ion exchange
chromatography, access to nearly monodisperse s-SWCNT samples.29,33 Unfortunately, the incredible
expense and poor scalability of DNA/ion exchange chromatography (IEX) have limited its applicability to
laboratory-scale production and make it highly unlikely to ever achieve gram-scale production.
Figure 1.5 Exciton binding energy trends A. Ebi as a function of s-SWCNT diameter in vacuum,
calculated according to Capaz et al.4 B. Ebi as a function of s-SWCNT dielectric environment,
calculated for the (7,5) s-SWCNT, which has a diameter d=0.8 nm10
0.6 0.8 1.0 1.20.4
0.6
0.8
1.0
Eb
i (e
V)
s-SWCNT diameter (nm)
1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
(7,5) s-SWCNT
Eb
i (e
V)
r
A B
7
An alternative route is available through the use of surfactant dispersed SWCNTs. It is now well
understood that the dispersion of SWCNTs into aqueous solutions containing surfactants such as sodium
cholate and sodium dodecyl sulphate results in surfactant decorated SWCNTs with buoyant densities
and surface chemistries which vary from chirality to chirality. By placing these dispersions in a density
gradient, or running them through a chromatography column loaded with Sephacryl gel, highly enriched
(>90%) s-SWCNT samples can be accessed in a more scalable manner than DNA/IEX enables.34-37
Alternatively, it has been shown that by dispersing small diameter SWCNTs in toluene solutions
containing certain semiconducting polymers, specifically poly(9,9 dioctylfluorene 2,7-diyl) (PFO) and
related copolymers, select chiralities of s-SWCNTs can be extracted in good yield with electronic type
purities > 99.9%. 17,27,38,39
1.2 Opportunities for s-SWCNTs in photodetectors and photovoltaics
The photophysical properties outlined above present many opportunities for photovoltaics and
photodetectors. Many of these opportunities exist within the constext of existing materials science
problems and research areas - for example in organic photovoltaics. These areas will be discussed
below. Additional opportunity exists in leveraging the unique photophysics of s-SWCNTs for non-
conventional devices and new architectures. While an exhaustive list of such possibilities is
exceptionally limited by this author’s creativity and intellect, a couple choice examples will be
highlighted.
1.2A Opportunities in single junction organic photovoltaics
The quest for low-cost solar derived electricity has motivated intense research into the development of
organic photovoltaic materials, including polymer-based materials systems which are compatible with
inexpensive manufacturing techniques, such as roll-to-roll processing.40 The enormous body of literature
8
resulting from this flurry of research yields considerable insight into the mechanisms of photocurrent
generation in organic systems, and chronicles the advancement of the 1 sun AM1.5G power conversion
efficiency (the power conversion efficiency of a photovoltaic device experiencing 100 mWcm-2 solar
irradiance through a standard 1.5 atmospheric airmasses) to values of 9 - 11% at the time I write this
dissertation.41 Organic photovoltaic devices function through a very different mechanism as compared
against more conventional inorganic photovoltaics, and thermodynamic consideration of these
differences reduces the maximum theoretical power conversion efficiency (PCE, or P ) from ca. 30% in
inorganic materials (the so called Shockley-Queisser limit, or SQ limit)42 to 20 – 24%.43 The factor of two
discrepancy between theoretically accessible PCE for organic photovoltaics and that which has been
achieved in the laboratory is largely attributed to low internal quantum efficiencies (IQE, the efficiency
of converting an absorbed photon into collected electron/hole pair) in forward bias as a result of
enhanced free carrier recombination, resulting in low fill factor (FF) and reduced open circuit voltage
(VOC ).44 These limitations can largely be related to low free carrier mobilities, which reduce the charge
extraction rate and enable the recombination of free carriers to suppress FF and VOC.
Figure 1.6 Typical JV characteristic of photovoltaic device demonstrating short circuit current density (JSC) open circuit
voltage (VOC) and fill factor (FF), the product of which yield the maximum power generation of the device. The ratio of the
maximum power to the incident power yields the power conversion efficiency (P ).
J(m
Acm
-2)
V (V)
0 0.2 0.4 0.6 1.00.8-0.1
-10
-5
-25
-15
-20
0
5
VOC
JSC
VOC JSCFF =
PMAX
9
The high intrinsic carrier mobilities on s-SWCNTs is an appealing antidote to this problem, and for this
reason carbon nanotubes have been extensively explored as charge-carrying additives to
polymer/fullerene blends.45-63 However, the vast majority of this work was conducted by adding
unsorted multi-wall CNTs or unsorted SWCNT, which contain, 33% metallic CNTs. Such metallic CNTs
have been shown to serve as recombination centers for free carriers and excitons.64 In order to use s-
SWCNTs in this application, they must be in purities high enough to minimize or eliminate the negative
effects of metallic CNTs.
More promising yet, are applications in single junction organic photovoltaics which replace
semiconducting polymers with s-SWCNTs. S-SWCNTs contain the same bandgap tunability and solution
processability that make organic polymers appealing for photovoltaics, yet have superior carrier
mobilities and large aspect ratios which will help to suppress recombination via rapid carrier extraction,
and offer exciton diffusion lengths which exceed those of polymers and small molecules by an order of
magnitude.65
Furthermore, s-SWCNTs are strong broadband absorbers. Figure 1.7 demonstrates the expected thin
film absorptance (1 – transmittance) of polymer-sorted (7,5) s-SWCNTs (enriched to >90% chiral purity)
for various s-SWCNT film thicknesses. The absorption coefficient used for this calculation was generated
from 30nm thick film of ca. 1:1 (7,5):PFO. Therefore, films of s-SWCNT in which the polymer used to sort
electronic type has been completely removed will be stronger absorbers yet, and will likely broaden
excitonic transitions (i.e. Eii transitions) further increasing the effective, broadband absorption strength.
However , despite the persistence of sorting polymer, > 99% absorptance of above-gap irradiance can be
achieved in films < 1 μm.
10
1.2B. Opportunities in multijunction photovoltaics
As demonstrated above, s-SWCNTs are strong broadband absorbers, yet have highly structured
absorption coefficients with exceptionally strong absorbance across Eii transitions. In addition to the
tunability of these transitions with s-SWCNT diameter, this structured absorbance offers unprecedented
precision in the spectral absorption of mono- or polychiral s-SWCNT films and is highly advantageous in
the design and fabrication of low-cost and solution-processed multijunction photovoltaics. Such
multijunction photovoltaics, or ‘tandem’ devices, offer one potential route to overcoming the SQ limit
and achieving high efficiencies.66 Tandem devices function by serially combining multiple photovoltaic
devices in a thin film stack to sum voltages and thus, improve the voltage output of the device. Minimal
current losses in tandem cells can be achieved by ensuring that each sub-cell generates an equivalent
photocurrent, which in turn requires that each sub-cell absorbs an equivalent photon flux (assuming all
sub-cells function in equivalent, high IQE). Additionally, the same challenges facing the single-junction
organic photovoltaic community – outlined above - face those interested in fabricating low-cost multi-
junction cells, namely low carrier mobilities.
Figure 1.7 Thin film absorptance (1 – transmittance) calculation for varying thickness
(7,5)@PFO films. Plot generated using absorption coefficient extracted from 30nm thick film on
quartz.
400 600 800 1000 1200 1400 16000.0
0.2
0.4
0.6
0.8
1.0
Absorp
tance
Wavelength (nm)
10 nm
100 nm
1000 nm
11
1.2C. Opportunities in generation III photovoltaics
In addition to tandem structures, photovoltaic devices which incorporate semiconducting materials
capable of generating multiple charges (or multiple excitons) from a single photon with greater than
twice the lowest energy exciton have been intensely studied.66-68 It has recently been demonstrated
that such a scheme can lead to external quantum efficiencies (EQE) greater than 100% in colloidal
quantum dot solar cells based on PbSe.67 Carrier multiplication (or multiple exciton formation) as a
process has been both theorized and measured to be greatly enhanced in quantum objects.66
Spectroscopic measurements have also confirmed multiple exciton formation in s-SWCNTs and further
suggest that the onset of multiple exciton formation approaches the theoretical limit of 2Eg.68 For these
reasons, opportunity exists to capture MEG in a photovoltaic device based on s-SWCNT light absorption
in much the same way as has been demonstrated in the colloidal quantum dot system. Such a route has
the potential to offer an alternative route to overcoming the SQ limit towards high efficiency, low cost
photovoltaics.
1.2D. Opportunities in unconventional photovoltaic architectures
The highly structured absorption spectrum of s-SWCNTs and other excitonic light absorbers also creates
opportunities in less-than-conventional photovoltaic applications. For instance, by using
semiconducting materials which absorb strongly in the near infrared (NIR) and UV, but weakly in the
visible, it has been experimentally demonstrated that visibly-transparent photovoltaic devices can be
fabricated with good color rendering indices.69-71 Such devices can be integrated into pre-existing
structures such as windows and electronic device screens. S-SWCNTs are promising materials for these
applications, for all the aforementioned reasons, specifically their highly structured, tunable, NIR
absorbance.
12
1.2E. Scope of this dissertation
Despite both the motivation initiated by these remarkable properties, and the flurry of research
surrounding the use of carbon nanotubes in light-conversion schemes, progress toward a light
harvesting system incorporating s-SWCNTs has been limited at best. Analysis of the factors preventing
the exploitation of s-SWCNTs in these roles reveals that overwhelmingly, research has been stymied by
extrinsic factors resulting from the heterogeneity of as-produced carbon nanotube materials, most
specifically a historical limitation in one’s ability to access samples of high purity, diameter-controlled s-
SWCNTs. By using the methods outlined above - specifically the procedure by which s-SWCNTs are
isolated and dispersed by PFO in toluene – we access samples of highly enriched s-SWCNTs to probe
intrinsic challenges to photocurrent generation from light absorption by these materials.
The greatest intrinsic challenge facing photocurrent generation from s-SWCNT absorption stems from
the strong exciton binding energy. Previously, exciton dissociation has been accomplished in individual
s-SWCNT field effect transistors and p-n junctions via a field-dissociation mechanism.72-75 In such
devices, dissociation occurs in strong fields arising from band bending near metal-nanotube Schottky
contacts or due to split gate biasing. While individual s-SWCNT devices have invaluably aided in
understanding nanotube photophysics, the absolute absorbance of a single nanotube is insufficient for
large-area photovoltaic and photodetector applications. In contrast, large area films of many nanotubes
with an optical density ~ 1 are needed to more realistically implement s-SWCNTs as the optically
absorptive components of photosensitive devices.
The organic photovoltaic community (both small molecule and polymeric) have successfully addressed
this challenge by the formation of donor/acceptor complexes. Donor/acceptor pairs are selected
semiconductor materials pairs which together, form a type-II electronic heterojunctions whereby
ionization potential/electron affinity offsets are greater than the binding energy of photogenerated
13
excitons on light absorbing components. Such heterojunction interfaces efficiently drive hole/electron
transfer and the subsequent dissociation of excitons.65,76,77
The first such demonstration of s-SWCNT exciton dissociation at heterojunction interfaces was made by
M. S. Arnold et al.78 This work reported on the utilization of SWCNTs, nonselectively dispersed by
semiconducting polymers, to collect photogenerated excitons from the SWCNT component in
photodetector devices. Despite the electronic heterogeneity of the SWCNT films used, external quantum
efficiencies (incident photon to collected electron efficiencies) of up to 1% were demonstrated. By
inserting a Sub-Pthalocyanine buffer layer between the polymer-wrapped SWCNT film and C60 film,
evidence for photocurrent generation via electron transfer to C60 was demonstrated.
14
2. Free Charge Carrier Generation via Dissociation of Excitons79
To extend this work and provide a framework for better understanding photocurrent generation via
SWCNT light absorption, we developed a novel photosensitive capacitor measurement technique which
sensitively measures charge transfer away from optically excited s-SWCNTs to complementary, charge-
accepting semiconductors. Because this technique measures the build-up of separated charge rather
than a photoconductivity, it is advantageously insensitive to photo-thermally induced changes in
conductivity that have plagued previous thin film measurements. Additionally, we have implemented
post-synthetically sorted s-SWCNTs in our studies rather than mixed as-produced nanotubes in order to
more clearly characterize the conditions necessary to achieve exciton dissociation from semiconducting
tubes without exciton quenching effects of metallic tubes.
We have specifically examined exciton dissociation and charge transfer at s-SWCNT heterojunction
interfaces with archetypical polymeric photovoltaic materials including fullerenes, poly(thiophene)s,
poly(phenylene vinylene)s, and poly(fluorene)s. These polymeric photovoltaic materials can be easily
incorporated into device stacks with s-SWCNTs via solution-processing or vacuum thermal evaporation.
Additionally, the energy levels of these materials have been well-characterized in literature which
facilitated the prediction of which materials
15
To measure exciton dissociation using the
photoactive capacitors schematically presented
in Figure 2.1, a time-modulated exciton
population is generated on the s-SWCNTs using
a spectrally-resolved time-modulated light-
source. In the absence of a driving force for
dissociation, excitons photogenerated on s-
SWCNTs recombine without separation and a
charge build-up on the capacitor is not detected. In contrast, electron or hole transfer from the
photoexcited s-SWCNTs to the donor or acceptor materials will induce a build-up of charge in the
capacitor. In this case, charge evolution can be quantified by either measuring the transient
photovoltage on the capacitor or by characterizing the transient charging and discharging current in
response to the pulsed illumination.
High quality s-SWCNTs were prepared by using the HiPCO/PFO/toluene system, as described in
Appendix A. To fabricate the photosensitive capacitors, planar thin films of s-SWCNTs (~ 7 nm) were cast
onto the transparent anode (indium-tin oxide, ITO) via a doctorblading technique. A scanning electron
micrograph demonstrates a doctor bladed film of PFO wrapped s-SWCNT (Fig. 2.2B) with a 1:1 weight
ratio PFO:s-SWCNT. The s-SWCNT remain well isolated, as determined from the persistence of sharp E11
and E22 absorption peaks in the films (Fig. 2.2A).
Following the deposition of the s-SWCNTs, thin films of the polymeric photovoltaic materials were
deposited on top of the s-SWCNTs by either vacuum thermal evaporation or by spin-casting from
solution to form the planar heterojunctions. Poly(vinylpyrrolidone) (PVP) dielectric films (2.0 ± 0.5 um)
were then spun-cast atop the heterojunctions from a methanol solution and 50 nm Ag was evaporated
Figure 2.1 Photosensitive capacitor measurement circuit
and energy band diagram. Photogenerated excitons on s-
SWCNTs are dissociated at interfaces with acceptors
when ΔIP or ΔEA > EB.
16
for the cathode. Two subsets of active interfaces were fabricated, one which was annealed at 130 °C
both before and after dielectric deposition, and one which was not annealed at all. S-SWCNT exciton
dissociation and charge transfer are expected when ΔEA > EB or ΔIP > EB, in which ΔEA is the difference
between the electron affinity (EA) of the s-SWCNT and the possible electron acceptor and ΔIP is the
difference between the ionization potential (IP) of the s-SWCNT and the possible hole acceptor. After
their dissociation, the free electronic carriers are able to diffuse away from the interface due to a non-
equilibrium concentration gradient, resulting in a charge build-up on the capacitor. The work function
offset between the anode and cathode also adds a drift component to the transport, which can be
modulated with application of an external bias.
The measured zero-bias, spectrally-resolved charging-current photoresponsivity of nanotube / annealed
polymer and unannealed fullerene material pairs are shown in Fig. 2.3A. Annealing was observed to
improve the photoresponsivity of polymer devices but not fullerene devices.
Figure 2.2 Normalized optical absorptivity of PFO-wrapped s-SWCNTs in chloroform solution (dotted, red) and in thin
films (solid, blue). (B) SEM micrograph of a thin film of 1:1 PFO:s-SWCNTs on ITO coated glass.
17
The heterojunctions consisting of s-SWCNTs and fullerene-derivatives and s-SWCNTs and
poly(thiophene)-derivatives demonstrated the largest photoresponsivity (Fig. 2.3A). In the NIR, the
measured photoresponse matches the s-SWCNT thin film absorption spectrum (modulated by
microcavity effects) indicating that the photoresponsivity arises from excitons originally generated on
the s-SWCNTs rather than excitons on the other materials -- none of which have significant absorptivity
in the NIR. In comparison with the fullerene derivatives and poly(thiophene) derivatives, zero or weak
photoresponsivity in the NIR was observed for s-SWCNT thin films interfaced with polycarbonate, PFO,
or a control without a donor or acceptor (referred to as PVP); and a small photoresponse was observed
for the s-SWCNT / poly(2-methoxy-5-(3’,7’dimethyloctyloxy)-1,4-phenylenevinylene) (MDMO-PPV)
sample.
In addition to a signal in the NIR, a photoreponsivity was also observed in response to excitation of the
s-SWCNTs at their E22 and E11 + X phonon sideband transitions, from 500-800 nm and 800-900 nm,
Figure 2.3 A. Magnitude of the exciton dissociation driven current responsivity for various 1:1 wt ratio PFO:s-
SWCNT/semiconductor heterojunctions measured using photoactive capacitor devices. Responses are offset but not scaled. B.
Responsivity of s-SWCNT/P3OT (black, solid) device compared with calculated, spectrally resolved optical intensity in P3OT
(blue, dotted) and in s-SWCNT (red, dashed) for a device stack of: glass / ITO (100nm) / s-SWCNT (7nm) / P3OT (30 nm) / PVP
(1900 nm) / Ag (50nm).
18
respectively, and in response to optical
excitation of the polymeric semiconductor
materials in the visible spectrum. The E22 +
X phonon sideband transitions were not
resolved due to spectral congestion.
An external bias was utilized to determine
the polarity of charge transfer for the
devices in which s-SWCNT exciton
dissociation was observed. From the
energy diagram in Fig. 2.1, it is expected
that a positive bias applied to the Ag should
enhance (inhibit) electron (hole) extraction from the s-SWCNTs resulting in a larger (smaller)
photocurrent transient due to the drift component of free carrier transport. The measured effect of the
external bias on the responsivity was small (<10% of the overall signal), however, by measuring the
direction of the change in responsivity with bias, the charge transfer polarity could be determined.
Qualitatively, the measured photoresponsivity of the s-SWCNT/C60 and s-SWCNT/[C61]-PCBM
photosensitive capacitors increased with the application of a positive bias to the Ag, indicating electron
transfer from photoexcited s-SWCNTs to the fullerenes (Fig. 4). In contrast, the measured
photoresponsivity of s-SWCNT/P3HT and s-SWCNT/P3OT photoactive capacitors decreased with the
application of a positive bias to the Ag, indicating hole transfer from the s-SWCNTs to the
poly(thiophene) derivatives.
The driving force for exciton dissociation and the polarity of charge transfer can be predicted by
comparing the energy levels of the s-SWCNTs with the energy levels of the polymeric semiconductor
Figure 2.4 Bias dependent responsivities for s-SWCNTs interfaces
with poly(thiophene) derivatives and fullerene-derivatives. Arrow
denotes direction of increasing bias (on Ag) from -5 V (solid, blue)
to +5V (dotted, red) in 2.5 V steps. Responsivity curves are offset
but not scaled.
19
materials, also considering the exciton binding energy. We use the work function calculations of Barone
et al.80 and the exciton binding scaling relationship of Perebeinos et al.10 with a relative permittivity εr =
4.0 to estimate the energetics of the s-SWCNTs. Accordingly, EB, EA, and IP for the (8,6) (7,6) (7,5) (8,7)
and (9, 7) chiralities of s-SWCNTs range from 0.2-0.26 eV, 3.79-3.93 eV, and 5.04-5.12 eV, respectively.
Therefore, complementary materials with an EA > 4 eV or IP < 4.9 eV should be capable of inducing s-
SWCNT exciton dissociation and electron or hole transfer, respectively, for s-SWCNTs in this diameter
range. Louie et al 3 have calculated an EA for C60 of 4.05 eV suggesting a ΔEA ~ EB (Table 2.1). Literature
values for the IP of the poly(thiophene) derivatives vary from 4.7-5.0 eV suggesting a ΔIP ~ EB. These
offsets are thus approximately sufficient for exciton dissociation and are consistent with our
observations of electron transfer from the SWCNT to the fullerenes and hole transfer to the
poly(thiophene) derivatives.
Table 1 Comparison of measured photoresponsivity averaged over the range 900 – 1400 nm with
expected energy offsets.
Material Averaged NIR
Photoresponsivity
[µA W-1]
Carrier Extracted
from SWCNT
Ionization
Potential
[eV]
Electron
Affinity
[eV]
s-SWCNT - - 3.7 – 4.1 4.9 – 5.3
C603 58 ± 27 e
- 6.2 4.0
[C61]-PCBM5 93 ± 45 e
- 6.1 3.8
P3HT6-8
12 ± 3 h+ 4.7 2.1
rr P3HT6 5 ± 2 h
+ 5.0 2.2
P3OT12
11 ± 6 h+
5.0 2.2
MDMO-PPV13
3 ± 2 - 5.3 2.8
PVP < 1 - n/a n/a
Polycarbonate < 1 - n/a n/a
PFO14
< 1 - 5.8 2.2
20
Weak exciton dissociation at the s-SWCNT/MDMO-PPV interface sheds light onto the maximum IP
energy level allowable to extract photoexcited holes. An IP = 5.3 eV is expected for MDMO-PPV, which
is 0.3-0.5 eV more electronegative than P3HT or P3OT. Accordingly, exciton dissociation and hole
transfer from the s-SWCNT to the PPV-derivatives should be inhibited by an energy barrier of up to 0.2
eV in addition to EB. The IP of PFO is even deeper (5.8 eV), further inhibiting exciton dissociation and
charge transfer which is consistent with our results. The wide band gap of poly(carbonate) and
poly(vinylpyrrolidone) result in larger energy barriers at the heterojunction interface, inhibiting s-SWCNT
exciton dissociation and electron or hole transfer, which is consistent with our measured results.
It is important to note that despite the predictive power of the IP/EA comparisons, the measurement of
such energy levels is nontrivial and accompanied by a measurement uncertainty of up to 0.4 eV81.
Furthermore, quantitative comparison of charge transfer efficiency at the interface between s-SWCNTs
and semiconductors is affected by several higher order factors. For example, the IP/EA levels of
polymeric electronic materials are highly morphology dependent6 and will likely be perturbed due to
electronic and steric interactions with the s-SWCNTs, as well as surface dipoles and local disruptions in
molecular packing. Variation in free carrier extraction efficiency will also have a secondary effect on the
measured photoresponsivity and is affected by morphology and crystallinity, which is variable from
material to material. For instance, these secondary factors may account for the small difference in the
observed photoresponsivity among the different poly(thiophene) derivatives. Nonetheless, while some
deviation from the predicted energy offsets is expected, our results are well described by the predicted
energy offsets to first order.
The strong exciton dissociation photocurrent measured at the s-SWCNT/C60 interface observed here
agrees with previous measurements of exciton dissociation at SWCNT/C60 interfaces in photodetector
devices fabricated by Arnold and Zimmerman et al78. Our results also extend beyond that of Arnold and
21
Zimmerman et al and show that the fullerene derivative [C61]-PCBM and poly(thiophene) derivatives
are potential electron and hole acceptors, respectively, that can be paired with s-SWCNTs to achieve the
dissociation and separation of photogenerated charges in s-SWCNTs, as well. In particular, these new
findings are important because whereas C60 is not solution-processable, [C61]-PCBM and the
poly(thiophene) derivatives can be dissolved at relatively high concentrations in solvents such as
chlorobenzene. As a result, it should be possible to fabricate blended heterojunction devices for
photovoltaic and photodetector applications that will overcome the expected inter-tube exciton
diffusion bottleneck in s-SWCNT thin films.
Previous measurements using terahertz spectroscopy82 have suggested that free carriers are generated
with > 10% efficiency in neat s-SWCNT films even without the implementation of a type-II
heterojunction. In contrast with this terahertz spectroscopy work, we do not observe a photoresponse
in the absence of a type-II heterojunction. This absence of a response suggests that if photogenerated
excitons are dissociated in the bare s-SWCNTs films, the lifetime of resulting free carriers is sufficiently
short that these charges rapidly recombine prior to their spatial separation.
Exciton dissociation and interfacial charge transfer from semiconducting single walled carbon nanotubes
(s-SWCNTs) to a variety of polymeric photovoltaic materials have been studied using a photoactive
capacitor measurement technique. We have shown that photogenerated excitons on s-SWCNTs in thin
films are dissociated at interfaces with C60, [C61]-PCBM, P3OT, regioregular and regiorandom P3HT.
Photocurrent bias dependencies reveal that fullerene and poly(thiophene) derivatives serve as electron
accepting and hole accepting materials to s-SWCNTs, respectively. In contrast, insufficient band offsets
for dissociation and charge transfer result when s-SWCNTs are paired with wider gap materials such as
MDMO-PPV, PVP, polycarbonate and PFO. Beyond the polymeric photovoltaic materials characterized
22
here, it is further anticipated that a host of other materials exist with the appropriate energetics to
dissociate excitons on s-SWCNTs.
23
3. Quantifying Exciton Dissociation Efficiencies83
The photocapacitor technique described above is an excellent method for monitoring the generation of
charge in a photoactive system and comparing the relative efficiency of that charge generation process
across donor/acceptor systems. However, the ultimate efficiency of a photovoltaic system is limited by
the absolute quantum efficiency of charge generation following photon absorption (internal quantum
efficiency, or IQE). For this reason, quantification of the IQE of s-SWCNT photovoltaic systems is critical
for the development of devices based on the same.
In order to measure the absolute IQE of photocurrent generation, we chose to focus on the
heterojunction interface between s-SWCNT and C60. By employing this planar interface in a thin-film
photovoltaic architecture, we were able to measure the absorption efficiency (ηA), the incident-photon-
to-collected-electron photocurrent generation efficiency (i.e. external quantum efficiency, or EQE) and
extract the ratio, which is defined as the IQE. That is:
EQE = ηA ·IQE
The heterojunction devices consisted of thin films of PFO-wrapped nanotubes and C60 molecules
between an indium tin oxide (ITO) anode and a Ag cathode. First, s-SWCNT thin films of tunable optical
density were deposited onto ITO coated glass via “doctor-blading”. Next, a 120 nm thick film of C60 was
thermally evaporated (Pvac < 1 μTorr) on top of the nanotube films with the threefold role of (1)
extracting photoexcited electrons from the nanotubes, (2) preventing the nanotubes from directly
bridging the anode and cathode and (3) modulating the microcavity effects to achieve NIR constructive
interference ~1200 nm in the nanotube films. Representative electron micrographs of the nanotube
films prior to the C60 deposition are shown in Fig. 2.1. The nanotubes are predominantly randomly
aligned in plane with the ITO substrate. While the minor roughness of the nanotube films results in a
24
small degree of interpenetration between the nanotube and C60 layers, no additional effort was made to
blend these materials together via annealing or mixing. We therefore refer to the heterointerfaces as
planar. Following deposition of the C60, a 10 nm exciton blocking layer of bathocuproine (BCP) and a 100
nm Ag cathode were thermally evaporated to complete the device stacks.
Optical absorption spectra of the semi-SWCNTs and mixed-SWCNTs in solution and in thin films are
compared in Fig. 3.1C. The spectral congestion in the NIR of the mixed-SWCNT solutions and films
evidences their significantly greater diameter-polydispersity, whereas only the (7, 5), (7, 6), (8, 6), (8, 7),
and (9, 7) chiralities are apparent in the semi-SWCNT samples. Absorption from metallic SWCNTs (~ 500
nm) was immeasurable in the semi-SWCNTs but is apparent in the mixed-SWCNTs. The full-width at
half-maximum of the E11 band gap optical transitions of the semi-SWCNTs in chloroform was 23 ± 2 meV
but heterogeneously broadened to 36 ± 4 meV in film without spectral-shift.
Typical dark current-voltage characteristics of the semi-SWCNT/C60 and mixed-SWCNT/C60
heterojunction devices are compared in Fig. 3.2. The semi-SWCNT/C60 heterojunctions are highly
Figure 3.1 A. Device architecture. B. Schematic depicting charge transfer at nanotube/C60 interface. C. Normalized optical
absorption spectra of mixed (dot-dash, blue) and semiconducting (solid, red) carbon nanotube solutions (top curves, offset vertically
by 1 A.U.) and resulting films (bottom curves).
25
rectifying with an ON/OFF current ratio of ~ 103 at
±1 V, as expected for a type-II heterojunction in
which band offsets create barriers for electron
and hole transport across the heterojunction
interface. The forward bias characteristics follow
the ideal diode equation with a thermal current
density Jth = 8.5 ± 10.7 μA cm-2 (with the smallest
Jth=0.4 μA cm-2), diode ideality factor of n = 2.3 ±
0.8, and a series resistance Rs = 5.1 ± 3.9 Ω cm2.
In contrast, the mixed-SWCNT/C60 heterojunction
devices are poorly rectifying. One explanation for
the poor rectification is that the expected
substantial fraction (~1/3) of metallic nanotubes
in the mixed-SWCNT films renders these devices
similar to metal/C60/metal stacks in which both
the metallic nanotubes (work function ~ 4.5 eV)
and the Ag (work function ~ 4.2 eV) make n-type contacts to the C60. Another factor that may influence
the rectification of the mixed-SWCNT devices is the presence of small bundles. While the semi-SWCNTs
prepared in toluene are expected to be completely isolated, the wrapping of small bundles by PFO is
seemingly more favorable in chlorobenzene (as evaluated by centrifugation sedimentation-based
investigations). The small bundles will be more rigid than isolated nanotubes and therefore increase the
film roughness, potentially also affecting rectification by adding shunt pathways, although the
substantial C60 layer will help to minimize the small roughness variations. Nonetheless, the excellent
rectification that we have achieved here using semi-SWCNTs without significant polymer dilution
Figure 3.2 Comparison of characteristics of mixed-SWCNT
(dot-dash, blue) and semi-SWCNT (solid, red) devices. A.
Typical dark current-voltage characteristics. B. Spectrally
resolved short-circuit external QE for devices with
optimized thicknesses, and spectrally varying optical
intensity at the s-SWCNT/C60 interface (grey, dashed)
predicted using optical transfer matrix simulations.
26
demonstrates the excellent quality of the semi-SWCNT materials and their potential for enhanced
applications in photovoltaic and photodetector devices.
In response to optical illumination, both the semi-SWCNT/C60 and mixed-SWCNT/C60 devices showed a
photovoltaic effect arising from the spontaneous dissociation and separation of photogenerated
electron-hole pairs at the nanotube/C60 interface. We have previously shown that this photoresponse is
not present or insignificant in films of semi-SWCNTs, alone, due to the EB > 0.2 eV.78,79 The zero-bias EQE
(electron-hole pairs collected at the contacts per incident photons in short-circuit conditions) varied as a
function of nanotube film thickness. The EQE of the thickness-optimized semi-SWCNTs and mixed-
SWCNT devices are compared in Fig. 3.2B. The semi-SWCNT devices exhibited a strong photoresponse
throughout the NIR at the optical band gaps of the five present chiralities, with a peak EQE of 12.9 ±
1.3% for the (8, 6) semi-SWCNT at 1205 nm (Fig. 6B). Photoresponse was also observed from C60
absorption at λ < 500 nm. The E22 optical transitions (600-800 nm) of the semi-SWCNTs were largely
suppressed by deconstructive interference effects in the layered stacks. By reducing the thickness of
the C60 acceptor layer, the deconstructive interference in the s-SWCNT film could be blue-shifted and
the photoresponsivity due to E22 absorption could be restored (data not shown).
In contrast, the mixed-SWCNT devices showed significantly weaker EQE < 2.5% in the NIR (Fig. 3.2B).
We postulate that the substantially weaker QE is the result of spurious metallic-SWCNTs in the mixed-
SWCNT thin films, which rapidly quench optically generated excitons and also serve as free carrier
recombination sites. These processes are expected to both decrease the exciton lifetime in the films
and reduce the exciton diffusion length. The larger peak short-circuit external QE of the mixed-SWCNT-
C60 devices presented, here, compared with that previously achieved by Arnold and Zimmerman et al.
(~2% versus ~1%, respectively) can be potentially be attributed to differences in the chemical
composition of the polymer wrapper, polymer:nanotube mass ratio, or charge collection efficiency.78
27
While EQE is an important parameter that affects device performance, IQE is a more useful parameter
for understanding the behavior of excitons in semi-SWCNT/C60 heterojunctions because it ignores
efficiency losses due to photons that are never absorbed. The internal QE can be related to the external
QE by the thin film absorption efficiency, ηA, according to EQE = IQE · ηA. In our case, we have
specifically determined ηA by measuring the spectrally resolved reflectance from the devices stacks (Fig.
3.3B). We have used this data to determine the diameter dependent internal QE and the thickness
Figure 3.3 Diameter and thickness dependencies. A. External quantum efficiency (EQE) of semi-SWCNT/C60 heterojunction
devices for increasing semi-SWCNT film thickness. Each spectrum is offset by 10% from the previous spectrum, starting with the
thinnest (blue curve) to the thickest film (red curve). B. 1-Reflectance data for the semi-SWCNT device stacks shown in part A
where Reflectance is the measured reflectance at ~normal incidence from each device stack. The Ag cathode serves as a mirror in
each device; therefore, Reflectance and 1-Reflectance are measures of the irradiation that have and have not been absorbed by the
device stack, fully considering optical interference and film thickness. Data is not offset. The black, dashed curve is the measured
1-Reflectance for a control device stack containing no SWCNTs. Absorption losses in the NIR in the control stack arise from the
ITO and red-shift as the nanotube thickness increases. Each 1-Reflectance curve was fit (see Supporting Information) to determine
the fraction of the absorption from the nanotubes (ηA) versus the fraction from the ITO. C. Internal QE versus diameter and
chirality compared with the expected energetic driving force for exciton dissociation at the semi-SWCNT/C60 interface. D.
Thickness dependence of internal QE for the (8, 6) nanotube in terms of the absorption length, LA. Red line is a fit of the
experimental data for a one-dimensional diffusion model with an exciton diffusion length, LD=0.13 ± 0.4 LA.
28
dependent QE, which can be related to the efficiencies of exciton dissociation and diffusion,
respectively.
For the thickness-optimized semi-SWCNT device shown in Fig. 3.3, the IQE approaches 100% for the (7,
5), (7, 6), (8, 6) nanotubes of diameter < 1.0 nm but decreases < 40% for the larger diameter (8, 7), and
(9, 7) nanotubes (Fig. 7C). We have corroborated the high QE for diameters < 1.0 nm via investigations
of photoluminescence quenching. Specifically, in Fig. 3.4, we show that the NIR band gap
photoluminescence from a thin film of semi-SWCNTs is nearly completely quenched by C60, indicating
almost perfect exciton dissociation and electron transfer from photoexcited nanotubes to C60 molecules.
To better understand the diameter-dependence of the IQE, we have determined the energetic driving
force for exciton dissociation by estimating the expected conduction band offset, ΔE, which should exist
at the nanotube/C60 heterointerface. For these calculations, we have used a C60 lowest unoccupied
molecular orbital (LUMO) energy of 4.05 eV3, the chirality-dependent nanotube work-function
calculations of Barone et al.80, and the chirality-dependent EB calculations of Capez et al.4, assuming that
Figure 3.4 Spectrally resolved photoluminescence (PL) of semi-SWCNTs in solution (red, dashed curve), in a thin film of
NIR optical density ~ 0.02 (light blue, solid curve), and in the same thin film interfaced with C60 (gray, dotted curve), in all
cases the laser excitation is at 658 nm, in resonance with the E22 optical transitions of the (7, 5) and (7, 6) chiralities. In
solution, the PL arises predominantly from the directly excited (7, 5) and (7, 6) chiralities, confirming the isolation of the
nanotubes. However, in thin film, the PL indirectly arises mostly from the non-excited (8, 6), (8, 7), and (9, 7) chiralities,
which have smaller band gaps, indicating coupling of the nanotubes in thin film and efficient exciton energy transfer from the
(7, 5) and (7, 6) chiralities. After the nanotubes in the thin film are covered by thermally evaporated C60, their PL is nearly
completely quenched, consistent with the hypothesis of nearly perfect exciton dissociation and electron transfer from the
photoexcited (7, 5) and (7, 6) nanotubes to the C60 molecules.
29
EG,E = EG,O + EB, where EG,E and EG,O are the electrical and optical band gaps of the semi-SWCNTs,
respectively, and using a relative permittivity εr = 5. The predicted chirality-dependent ΔE is compared
with the internal QE in Fig. 3.3. The expected ΔE is positive (denoting a favorable driving force for
dissociation) for the (7, 5), (7, 6), (8, 6) / C60 heterojunctions but negative for the (8, 7), and (9, 7) / C60
heterojunctions, closely matching the trend evidenced by the experimentally measured internal QE.
More accurate experimental measurements of the electron affinity and LUMO levels of the materials
would be needed to draw a more complete picture of the chirality-dependent exciton dissociation
efficiency; however, in general, the magnitude of ΔE should decrease with increasing nanotube
diameter as the electron affinity of the nanotubes approaches the work-function of graphite (~ 4.5 eV).
In summary, we have shown that photogenerated electron-hole pairs can be efficiently harvested using
electronic-type-sorted, chirality-controlled semiconducting carbon nanotubes. We have demonstrated
peak EQE > 12 % in the NIR, which is an order of magnitude better than what has been previously
achieved. We show that exciton migration in the semiconducting carbon thin films is diffusion-limited
with an effective diffusion length of LD = 0.13 LA and that for films < LD and for nanotube diameters < 1.0
nm, the IQE for exciton dissociation and charge collection approaches 100%.
30
4. S-SWCNT / [60] PCBM Bulk Heterojunctions84
Poor agreement between the absorption length and the exciton diffusion length (LD = 0.13 LA) has thus
far limited both the photovoltaic power conversion efficiency (ηP) and external QE due to s-SWCNT
absorption in the NIR to 0.6% and 12.9%, respectively83. Poor agreement between the exciton diffusion
and absorption lengths has historically been observed in polymer and small molecule organic
photovoltaics85 but overcome through the formation of blended heterojunctions with precise control
over phase separation and thus, domain sizes.86,87 Here, we work to overcome diffusion limitations in s-
SWCNT films through formation of a blended heterojunction between s-SWCNT and the C60 derivative
[6,6]-phenyl-C61-butyric acid methyl ester (PCBM).
S-SWCNT and PFO concentrations in solution were calculated from absorption measurements using the
optical cross section estimates of Tsyboulski et al.88 and Islam et al.89 for s-SWNT E22 absorption at λ =
600 – 800 nm, and reference solutions of PFO at λ = 400 nm. For device fabrication, PCBM was added to
result in a chlorobenzene solution of x:5:4 PCBM:PFO:s-SWCNTs by weight, where x was varied from 5 to
20. The photocurrent response was not observed to be a strong function of x in this range and we
focused on a 10:5:4 ratio, here. Active films were deposited atop solvent- and UV-ozone-cleaned ITO
coated glass in a nitrogen environment. Fig. 4.1A demonstrates absorption of films. Strong absorption
in the range of λ = 1000 – 1400 nm corresponds to the E11 band gaps of the five s-SWCNT chiralities
present.17 Devices were completed through vacuum thermal evaporation of 100 nm C60 as a hole
blocking layer, 10 nm bathocuproine (BCP) as an exciton blocking layer, and a 100 nm Ag cathode.
Expected energy alignments are illustrated in Fig. 4.1B for the (7, 5) chirality and PCBM/C60, with lowest
unoccupied molecular orbital (LUMO) energies of 3.74 eV and 4.05 eV, respectively.
31
Completed devices demonstrated a strong
photovoltaic effect in response to NIR and
visible irradiance. To selectively study the role of
the s-SWCNTs as light absorbers (as opposed to
the PFO and the PCBM, which absorb in the
visible), we characterized the current-voltage
characteristics of the resulting diodes under NIR
irradiation (1000 < λ < 1365 nm). A strong
photovoltaic effect was observed (Fig. 4.2A)
over a large range of irradiances (Fig. 4.2B) with
peak ηP = 1.36% at 52 mW cm-2, and a
corresponding fill factor (FF), open circuit
voltage (Voc) and current responsivity (R) of 0.41, 0.4 V, and 0.083 A W-1, respectively (Fig. 4.2B).
In order to characterize the contribution to R from the various materials present, we spectrally resolved
the zero-bias external QE (Fig. 10c). High EQE was observed for λ < 600 nm due to the C60, PCBM, and
PFO components and for 900 < λ < 1400 nm due to the s-SWCNTs. Limited responsivity was observed
for 600 < λ < 900 nm due to destructive interference in the active layer through this spectral range. The
peak EQE in the NIR at λ = 1205 nm was 18.3% arising from the (8, 6) s-SWCNT. The average device-to-
device EQE at λ = 1205 nm was 15.1 ± 1.8% respectively.
The observed EQE in these devices is substantially greater than the EQE achieved in our previous work
with planar s-SWCNT/C60 heterojunction devices. Moving from a thickness-optimized planar
heterojunction to a thickness-optimized blended heterojunction nearly doubled the NIR (1000 < λ <
Figure 4.1 A. Normalized optical absorption of PCBM, s-
SWCNT and blended PCBM:s-SWCNT thin films in red
(dotted), grey (dot-dash) and blue (solid), respectively. B.
Expected energy alignments in prepared device stack of ITO
/ ca. 10 nm s-SWCNT:PCBM / 100 nm C60 / 10 nm BCP /
Ag. Mid-gap conduction states in BCP illustrated as dashed
lines.
32
1365 nm) R from 0.047 to 0.088 A W-1 (at 15 mW cm-2). This increase is accounted for not only by an
improvement of peak EQE from 12 to 18% at λ = 1205 nm due to the (8, 6) chirality, but also by an
enhanced relative contribution to R from the larger band gap (7, 5) and (7, 6) chiralities. Increased
contribution from these chiralities increased the EQE from 6.0 to 16.4% and 9.5 to 18.2% at λ = 1060 nm
and λ = 1150 nm, respectively. Moving from a planar to a blended heterojunction also increased Voc
towards saturation; for example, at a NIR irradiance of 15 mW cm-2, the Voc increased from 0.25 to 0.34
V. These enhancements combined to increase ηP from 0.6 to 1.4% over this spectral range.
The increased efficiency indicates an enhanced harvesting of s-SWCNT excitons at the bulk interfaces of
the s-SWCNT/PCBM blends with respect to planar s-SWCNT/C60 heterojunctions. In planar SWCNT films
in which most of the tubes predominantly lie with their long-axis perpendicular to the direction of
charge collection, the s-SWCNT excitons must diffuse from tube to tube to the C60 interface before they
can be dissociated and harvested as free charges. However, the exciton diffusion length, LD, in this case
is limited by several factors including the PFO wrapper, which disrupts the tube-tube coupling, diameter
polydispersity which traps excitons on small band gap nanotubes, and the short exciton lifetime ~ 100
Figure 4.2 A Current density vs. voltage response of typical device in dark (dashed grey) and in response to 137 mW cm-2
NIR irradiance (solid red). B. Intensity dependence of power conversion efficiency (ηP), fill factor (FF), open circuit voltage
(Voc) and current responsivity (R). C. Spectrally resolved zero-bias external QE. Contribution from specific s-SWCNT E11
transitions are identified according to s-SWCNT chirality.
33
ps90. The superior performance of
blended heterojunction devices relative
to planar devices indicates that the
exciton harvesting efficiency has been
substantially increased, overcoming the
exciton migration problems to a
significant extent.
We have utilized transmission electron
microscopy to better understand the s-
SWCNT/PCBM blend morphology and
bulk interfaces that exist between these
two materials. TEM analysis (Fig. 4.3a)
reveals an ultrafine dispersion of PFO-
wrapped s-SWCNTs isolated from one-
another and surrounded by PCBM with
average domains of PCBM, LP, < 5 nm.
The fine morphology was observed to
persist through annealing at moderate temperatures (T < 150 °C) and demonstrates that there is indeed
an ultrahigh interfacial area between the s-SWCNTs and the PCBM, promoting rapid and uniform exciton
dissociation through the bulk of the active layer.
The morphology of the blends also suggests that even further enhancement of efficiency will be possible
with future optimization of the phase separation. By reducing LP < LD in our films, we have moved from
an exciton dissociation-limited regime to a charge recombination/collection-limited regime in which a
Figure 4.3 A. TEM micrograph of blended PCBM:s-SWCNT film. Inset
reveals individual s-SWCNT sidewalls, measured as 9 ± 1 Å with
example illustrations of relative orientation. B. Bias dependent
photocurrent normalized at -1. Photocurrent is defined as the difference
between the measured current under irradiation and the measured dark
current. Arrow indicates direction of increasing NIR intensity (from 0.1
to 50 mW cm-2).
34
fraction of photogenerated charges recombine before they are collected and in which the series
resistance is increased. We observe the effects of recombination and higher series resistance in our
devices as a voltage-dependent responsivity in reverse-bias and as a low fill factor (Fig. 4.3B). These
effects are especially noticeable with increased film thickness. For example, by increasing the active film
thickness from 10 to 30 nm, zero-bias EQE at 1210 nm and peak FF fall from 18.3 to 5.3%, and 41% to
26%, respectively, while series resistance increases from 6 to 30 Ωcm2. With increased thickness, the
shape of the photocurrent contour is also observed to be a strong function of illumination intensity near
the operating point in forward bias. This is specifically indicative of a recombination mechanism
described through bimolecular kinetics; namely i) free carrier recombination via non-geminate charge
transfer excitons or ii) exciton quenching with free carriers via an Auger process91. Both of these
recombination mechanisms stand to be greatly reduced via control of the blend morphology, further
optimizing the pathways for current collection in each of the two phases. The series resistance of
polymer photovoltaic systems is also known to increase with decreasing phase separation and has been
attributed to reduced charge transport mobility with smaller PCBM domains.86 The same is likely true in
the s-SWCNT/PCBM blends. The series resistance may be additionally increased because the s-SWCNTs
in the blends are mostly “lying-down” in-plane and somewhat decoupled from one-another by residual
PFO wrapper and the PCBM. The lying-down morphology exists because of surface-tension effects
during solvent evaporation and because the s-SWCNTs are significantly longer (100’s of nm) than the
blended film thickness ca. 10 nm. Thus, the high intra-tube charge transport mobility of the s-SWCNTs is
not exploited. Overall, the LP < 5 nm increases both recombination losses and series resistance, causing
a net reduction in performance for blended film thicknesses > ca. 10 nm.
In polymer/fullerene systems, the morphology is thought to be optimized with domain sizes of order 2LD
92. At this size, the excitons can still be harvested but the percolation pathways for charge collection
will be maximized. Unlike in polymers, however, the LD for s-SWCNTs is highly anisotropic with an
35
expected LD > 100 nm along the length of a single s-SWCNT93 and a measured LD of 3-5 nm in the
transverse direction (hopping between polymer-wrapped s-SWCNTs. This anisotropy suggests that the
ideal structure for s-SWCNTs in blended photovoltaic devices would be in the form of an interconnected
network of long-bundles that are ~ 6-10 nm in diameter – not as individualized and well-isolated s-
SWCNTs. The voids between the interconnected network of long bundles would ideally be filled with an
electron accepting species such as PCBM that would form a second network for electron collection.
While LP can be controlled in many polymer systems via annealing, the invariance of the SWCNT/PCBM
blend morphology with temperature indicates that alternative approaches will be required for tuning
phase separation in the SWCNT/PCBM materials system such as engineering SWCNT bundle formation in
solution prior to film-casting. The charge collection efficiency will furthermore be improved by
increasing the out-of-plane orientation of the s-SWCNTs in order to better exploit their exceptional
transport properties.
In conclusion, photovoltaic devices have been demonstrated with peak NIR ηP = 1.4% and external QE =
18.3%. These devices, based on a bulk electronic heterojunction between post-synthetically sorted s-
SWCNTs and PCBM, are a significant improvement over planar s-SWCNT/C60 devices. These gains are
achieved by overcoming the exciton diffusion limitations inherent in s-SWCNT planar films by forming a
blended heterojunction with PCBM. The blended SWCNT devices demonstrated here significantly
outperform state-of-art polymer-based photovoltaic and photodetector devices94 beyond 1000 nm,
enhancing EQE by an order of magnitude in this spectral range. This improvement originates from
enhanced absorptivity in the NIR by the s-SWCNTs. Further improvement is expected with optimization
of charge collection via controlled nanotube bundling.
36
5. Diffusion of Excitons95
As discussed above, it is clear that by forming a highly disordered interface between s-SWCNT and [60]
PCBM, exciton dissociation can occur in bulk, blended films. Such a device architecture sidesteps the
challenges associated with exciton management (i.e. intentionally routing excitons photogenerated in
bulk s-SWCNT films through engineered pathways to interfaces at which they can be dissociated and
collected). However, understanding how excitons move in s-SWCNT films is critically important to
photovoltaics implementing s-SWCNTs in planar or bulk geometries. An additional motivation for a study
of exciton diffusion pathways in s-SWCNT films is the apparent discrepancy between diffusion lengths
measured spectroscopically as 200 – 600nm21,96,97, and our own solid-state measurements which place
the diffusion length around 3nm.
We understood this discrepancy in diffusion length partly by determining that the s-SWCNT film
morphology consisted of s-SWCNTs overwhelmingly “lying-down” on the ITO, requiring that exciton
migration to the C60 interface occur through the slower process of tube-tube exciton hopping.
Developing a complete understanding of the mechanisms of exciton migration in our polydisperse films
and identifying extrinsic factors which influence this migration will be critical to realizing the full
potential of s-SWCNTs as photoabsorbers.
In the case that exciton hopping from tube to tube dominates exciton migration, increasing the
electronic coupling between s-SWCNTs should enhance exciton migration. In our films, the coupling
between s-SWCNTs is modulated by the coexistence of poly(9,9 dioctylfluorene 2,7-diyl) (PFO), which
we use for its selective affinity for small diameter s-SWCNTs in toluene and toluene-like solvents.27,39,98
While these polymers are critical for obtaining samples of s-SWCNTs with low concentrations of metallic
species and aggregates, the quantity of residual polymer present in cast films influences inter-tube
37
coupling and therefore inter-tube exciton migration. Here, we examine the effects of excess PFO on the
extraction of excitons and charges from s-SWCNT films. Specifically, we have created s-SWCNT films
with varying amounts of PFO and have employed spectrally resolved photoluminescence and thickness-
dependent measurements of photocurrent evolution as tools to characterize the migration of excitons.
In order to study exciton migration in films of s-SWCNTs with varying amounts of PFO, films were cast
from three different s-SWCNT solutions, which were taken after the second, third and fourth pelleting
iterations during the removal of excess PFO (see Appendix A). Solution absorbance was measured to
quantify PFO content and chirality distributions (Fig. 5.1A). The (7, 5), (7, 6), (8, 6), (8, 7), and (9, 7) s-
SWCNTs were present in abundances of 23, 28, 29, 19, 2%, respectively, (determined from fit E11 full-
width-half-maximum-amplitude products, assuming optical cross section chirality family dependences
directly proportional to exciton oscillator strength family dependences calculated by Ando99. Relative
chirality abundance remained constant among the three samples studied by extracting solutions 1, 2,
and 3 from the same master-batch during processing. The PFO concentration in each solution was
determined by analyzing the PFO spectral weight at 390 nm, having subtracting off broad background
absorption and expected absorption arising from the E33 and E44 optical transitions of the s-SWCNTs in
their pre-determined abundance. A measured PFO solution optical cross-section of 1.69 x 105 cm2/g,
(assumed to remain constant whether free in solution or wrapping a s-SWCNT) was used to quantify PFO
concentrations in solution. S-SWCNT concentrations were determined by using the E11 optical cross-
section of Hertel and coworkers of 1.02 x107 cm2/mol C with a width of 44 meV for the (6,5) chirality, 100
and the exciton oscillator strength family dependences of Ando.99 The change in s-SWCNT optical cross-
section from the work of Hertel and coworkers to ours due to changes in the external dielectric constant
is expected to be minor (<10%) and was thus ignored.99 In particular, the s-SWCNTs were estimated to
represent 22%, 36%, and 43% of the solute by weight, for solutions 1, 2, and 3, respectively. Solutions
containing roughly 43% by weight s-SWCNTs are consistently the lowest PFO:s-SWCNT ratio we can
38
achieve using our approaches. It is unclear from our analysis whether successive removal of PFO from
solution is due to desorption of PFO from the s-SWCNT surface, or whether PFO-wrapped s-SWCNT
hybrids exist in this PFO:s-SWCNT ratio inherently.
The line-width of the E11 optical transitions in solution was fairly narrow, independent of the relative
concentration of PFO. For example, the linewidth of the (7, 5) chirality in absorption was 23 meV in
solution. However, this line-width increased to 42, 53, and 54 meV in films cast from solutions 1, 2, and
3, respectively (Fig. 5.1B). This increased broadening with increased removal of PFO suggests an
increase in heterogeneity of the dielectric landscape and increased tube-tube coupling. The ratio of PFO
peak absorbance at 390 nm to integrated absorbance across the E22 s-SWCNT transitions from 600 - 780
reduced significantly from solution to film. However, this change was consistent whether samples were
drop-cast or doctorbladed, suggesting that PFO is not appreciably rinsed off during doctor-blading.
We characterized tube-tube coupling further using photoluminescence (PL) spectroscopy. We optically
excited samples using a diode laser at λ = 653 nm, in-tune with the E22 transitions of the (7, 5) and (7, 6)
chiralities. The emission spectra of solutions 1-3 were nearly identical (Fig. 5.1C), with emission
Figure 5.1 A. Solution absorbance of 22%, 36% and 43% s-SWCNT solutions, normalized at λ = 1050 nm. B. Film
absorbance of films cast from 22%, 36% and 43% s-SWCNT solutions, normalized at λ = 1050 nm. C. Photoluminescence
emission spectra of films cast from 22%, 36% and 43% s-SWCNT solutions in response to excitation at λ = 653nm.
39
primarily arising from the (7, 5) and (7, 6) chiralities at λ = 1048 and 1142 nm, respectively. Some minor
emission is observed from the (8, 6) and (8, 7) chiralities at λ = 1204 and 1288 nm, respectively, due to
weak excitation of E22 + phonon sidebands of these larger diameter tubes.17 The solution PL spectra are
consistent with that of highly isolated, poorly coupled s-SWCNTs with emission emanating from the
same chiralities which are optically excited. In contrast, the strongest PL emission arises from the (8, 7)
chirality in all films measured; indicating energy transfer from optically excited (7, 5) and (7, 6) chiralities
to the smaller bandgap chiralities, consistent with observations made elsewhere.101-104 The magnitude of
observed energy transfer increases with decreasing PFO concentration, indicating stronger tube-tube
coupling and faster energy transfer, as is anticipated.
Insights into the rates of intertube energy transfer in films are provided by the shape of the PL emission
spectra. The fact that the majority of emission arises from the smaller bandgap s-SWCNTs suggests that
the hopping rate from larger to smaller bandgap s-SWCNTs is faster than the non-radiative exciton
decay rate in PFO-wrapped s-SWCNT films, which has been measured elsewhere to be on the order of
0.1 ps-1.96,105,106 However, the persistence of emission from the (7, 5) and (7, 6) species suggests that this
hopping rate is only marginally faster than 0.1 ps-1, which prevents rapid and complete transfer of
excitons to smaller bandgap chiralities and consequently, prevents complete quenching of emission for
large bandgap species. Therefore, we estimate a characteristic intertube transfer rate in the range 0.1 –
1 ps-1, in good agreement with ultrafast energy transfer measurements on comparable, solid-state
samples made from the PFO/HiPco system, as well as DNA-wrapped CNTs.106,107
The emission line-width in film was similar to that in absorbance and there was a negligible Stokes’ shift,
within resolution of our PL spectrometer (slit-width of 22 nm resolution). The similar emission and
absorption linewidths and lack of red-shift suggest minimal pooling of excitons in low-energy ‘traps’
resulting from heterogeneity or defects, as is seen in s-SWCNT samples with covalent sidewall
40
modification.108 While this picture does not imply that low energy traps do not exist, it does imply that
excitons are capable of moving through such traps, if they exist.
In brief, the absorbance and PL spectroscopy suggest a picture of exciton transport along s-SWCNTs,
through the spread of excitonic states resulting from film heterogeneity, with some degree of exciton
hopping from large to small bandgap s-SWCNTs. In such a picture, long-range (100’s of nm) exciton
transport will only be possible along the long-axis of a s-SWCNT, and exploiting this long-range exciton
transport in energy harvesting devices will be highly dependent on film morphology.
To determine film morphologies, we imaged films cast from the solutions 1-3 using scanning-electron
microscopy (SEM). Representative micrographs are compared in Figure 5.2. A morphology which is
relatively consistent for all film compositions is observed to consist of ‘fibers’ with varying diameters of
order 10 nm lying-down predominantly in-plane with the substrate. These fibers are presumed to be
composed of multiple s-SWCNTs and PFO chains. This ‘fiber’ interpretation is substantiated by instances
where individual fibers in the films are observed to ‘branch-off’ larger fibers. We hypothesize that
individual s-SWCNTs remain well-isolated by PFO within each fiber. The individual s-SWCNTs are
certainly well-isolated from one-another in solution prior to film-casting, as evidenced by the strong
selectivity of the PFO for near-armchair nanotubes and the narrow spectral-linewidth and lack of energy
transfer in solution. The s-SWCNTs can be pelleted out of solution and then easily re-dispersed back into
solution and we have been unable to remove PFO to increase the s-SWCNT concentration beyond 43%,
furthermore implying that the PFO is tightly bound. The fact that film morphology is consistent across
such a large range of compositions also implies that excess PFO is incorporated into the fibers,
surrounding individual s-SWCNTs, filling interstices among the s-SWCNTs, and potentially also wrapping
the fiber, itself.
41
In order to further characterize exciton migration in the films prepared from solutions 1-3, we fabricated
bilayer heterojunction diodes with films of s-SWCNTs and C60, as previously described, and monitored
zero-bias photocurrent generation as a function of wavelength and s-SWCNT film thickness.83 External
quantum efficiency (EQE, number of electron-hole pairs collected as photocurrent per incident photon)
provides a quantitative measure of exciton flux at the s-SWCNT/C60 interface; therefore, monitoring the
thickness dependence of this quantity offers a method for tracking exciton migration to the interface.
EQE spectra measured at zero-bias conditions from the s-SWCNTs from solutions 1-3 are compared in
Fig. 5.3. A photocurrent is observed in response to the excitation of all chiralities present at their E11
transitions from λ = 1000 – 1400 nm. Response at the E22 transitions in the visible spectrum is largely
suppressed by destructive optical interference in the s-SWCNT containing film for this particular device-
stack.65,83 Peak EQE at λ = 1195 nm (corresponding to the (8, 6) chirality) increases from 15.5% to 16.9%
to 23.0% when the s-SWCNT content of the film increases from 22%, to 36%, and 43%, respectively. The
average EQE from λ = 1000 – 1350 nm increases even more dramatically, from 6.0% to 8.1% to 11.0%,
respectively, because not only is the peak EQE increasing but the spectral line-width is increasing as well,
mirroring the increase in absorbance line-width.
Figure 5.2 Scanning electron micrographs of films cast from 43%, 36%, and 22% s-SWCNT solutions, left to right, respectively.
Image sizes and magnifications are equivalent, scalebars = 500 nm.
42
The EQE at λ = 1195 nm in resonance with the
E11 optical bandgap of the (8, 6) chirality is
plotted vs. s-SWCNT film thickness in Fig. 5.4 A-
C. In each case, the EQE starts at 0% for a film
thickness of 0 nm. The EQE initially linearly
increases with film thickness but then goes
through a maximum somewhere in the range of
5 – 15 nm before abruptly falling off with
increasing thickness. In the thin limit, EQE tracks
linearly with increases in light absorption and
thus, film thickness. However, with increasing
film thickness, the efficiency by which photogenerated excitons are able to migrate to the C60
heterointerface decreases. The maximum in each EQE curve corresponds to the situation in which
further increase in film thickness and optical density are outweighed by a larger decrease in the fraction
of excitons that are able to migrate to the heterointerface. Interestingly, the EQE vs. s-SWCNT thickness
curve becomes increasingly sharp with decreasing PFO concentration. To better understand these
profiles and decouple exciton transport phenomena from changes in exciton generation, we have
measured the absorption efficiency of each device via normal-incidence reflectance measurements, and
modeled exciton transport (ηED) to the C60 interface.
Assuming perfect charge transfer at the C60 interface and perfect charge collection through both
material phases, i.e. ηct = ηcc = 100%, the product of the absorption efficiency with that of exciton
diffusion efficiency, ηED, will yield EQE, that is: ηEQE = ηct ηcc ηA ηED = ηA ηED..77 The thickness-dependence
of ηED will depend on the mechanism for diffusion. We have considered two mechanisms in separate
models. First, if s-SWCNTs are lying perfectly in-plane, the only mechanism for transport to the C60
Figure 5.3 Thickness-optimized external quantum
efficiencies (EQE) achieved in ITO/PFO-wrapped s-SWCNT/
120 nm C60/10 nm BCP/100 nm Ag thin film, planar bilayer
heterojunction photodiodes.
43
interface will be intertube hoping. From our PL measurements it is clear that such motion does occur,
and more complete removal of PFO increases the rate of intertube hopping relative to the
recombination rate. For this case, we consider that ηED will vary with s-SWCNT film thickness according
to a one-dimensional diffusion model. 65,109 This model (depicted in Fig. 5.4D) is referred to as the 1-D
diffusion model and has one free parameter, LD , the diffusion-length.
A second model was developed to consider intratube exciton transport along individual s-SWCNTs and
fibers, directly to the s-SWCNT / C60 heterointerface. This mode of transport is possible if the s-SWCNTs
have some component of their long-axis penetrating out-of-plane, extending from the heterointerface
Figure 5.4 Thickness dependence of EQE measured at λ = 1195 nm for planar bilayer heterojunction photodiodes
constructed from films cast from A. 22% B. 36% and C. 43% s-SWCNT solutions. Black, dotted line represents best fit to
each dataset using measured absorption efficiencies and a 1-D exciton diffusion model for exciton diffusion, schematically
illustrated in D. Solid, purple line represents best fit to each dataset using measured absorption efficiencies and exciton
wicking model, schematically illustrated in E.
44
into the s-SWCNT film. In this model, we ignore intertube exciton transport, and assume the efficiency
of exciton transport to the active interface is perfect up to a characteristic length, physically
representing the average ‘penetration depth’ of the 1-D pathway into the network film. Excitons
generated beyond this characteristic depth have zero probability of reaching the active interface due to
a lack of direct pathways. This model (depicted in Fig. 5.4E) is referred to as an exciton-wicking model
and has one free parameter, LP , the penetration-depth. We assume that exciton generation is spatially
uniform throughout the s-SWCNT films in both models, with a generation rate determined by the
experimental measurement of ηA, as described above.
Both the 1-D diffusion and the exciton wicking models have been fit to each of the three EQE-thickness
curves in Fig. 5.4. The extracted LD are 4.2, 6.5, and 8.0 nm for 22, 36 and 43% s-SWCNT films,
respectively. The extracted LP are 4.1, 6.9, and 6.7 nm, respectively. In all cases, the exciton wicking
model qualitatively provides the better fit of the two models and is able to reproduce the sharp maxima
of the EQE vs. s-SWCNT thickness curves that are especially apparent in the 43% s-SWCNT films. With
this said, both fits are plausible in consideration of the assumptions made. The difference in
‘penetration depth’ from 22 to 36% s-SWCNTs is substantial and represents a real, physical difference.
However, going from 36 to 43% s-SWCNTs, the change in penetration depth is within experimental
error. Considering the roughly equivalent LP and LD for 36 and 43% films, the enhancement of EQE in the
latter case is completely compensated by increases in the near-infrared optical density achieved by
decreasing PFO content, therefore improving the absorption efficiency.
A more complete picture emerges when this description of exciton transport is taken into account along
with the insights gained from the PL spectra and the electron micrographs of the ‘fiber’ morphology.
The full body of data here presents a story whereby intertube energy transfer is enhanced with removal
of PFO, but likely remains on the ps-1 time scale. This timescale limits the number of ‘hops’ an exciton
45
can undergo during its lifetime to only several. Since the observed fibers seemingly contain 10’s of s-
SWCNTs, photogenerated excitons are unlikely to ever leave the fiber in which they were generated.
Thus, the residual polymer, even when minimized in the 43% s-SWCNT films, still limits intertube exciton
migration, and only the excitons generated on the surfaces of fibers immediately located at the
heterointerface can contribute to the photocurrent via intertube transfer. Longer-range, out-of-plane
motion of the excitons to the heterointerface is theoretically possible via intratube or intrafiber diffusion
but depends on the orientation of the fibers relative to the active interface. Here, the limited out-of-
plane orientation of the fibers relative to the active interface is limiting.
In reality, it is likely that both the intra- and intertube diffusion mechanisms play important roles in
enabling the migration of excitons to the heterointerface of bilayer devices. For example, an exciton
generated deep in a s-SWCNT film might first rapidly diffuse along the length of a fiber until the fiber
reaches the film surface. But, there, the exciton will still need to migrate radially through the fiber via
intertube diffusion, to reach the fiber exterior and contact with the electron accepting C60. Thus, it may
not be possible to take full advantage of a long LP, if LD < the fiber diameter. In our case, the fiber
diameter is on the order of 10 nm, which is > LD. Therefore, it is likely that the fit LP is underrepresenting
the actual penetration depth of the fibers into the films and is also reflecting the short LD.
By decreasing the residual polymer in s-SWCNT films, we have increased the photocurrent responsivity
of s-SWCNT components in s-SWCNT/C60 heterojunction diodes significantly beyond the previous state-
of-the-art 83 to a peak EQE of 23% at λ = 1195 nm. By reducing the PFO content of cast films, energy is
more efficiently transferred from large to small bandgap s-SWCNTs. However, the relatively slow rate of
intertube energy transfer is still a primary restriction, limiting the efficiency by which excitons are
transported to the s-SWCNT/C60 heterojunction where they dissociate into free carriers. Our data
suggest that intertube diffusion is limited to short length scales, no greater than 4.2, 6.5, and 8.0 nm for
46
16, 28 and 30% s-SWCNT films, respectively. Intratube diffusion along the length of individual s-SWCNTs
or along fibers of s-SWCNTs may also facilitate exciton transport to the heterointerface, but intratube
diffusion is limited by the orientation of fibers - which are overwhelmingly lying-down - in addition to
the slow escape of excitons from the fibers via intertube diffusion.
Looking forward, the rates of intertube energy transfer in fibers and films of PFO-wrapped SWCNTs will
likely not approach those possible in neat films of s-SWCNTs, free of polymer. For this reason, utilizing
PFO-wrapped s-SWCNTs in high efficiency photovoltaics and photodetectors will require novel schemes
for orienting the PFO / s-SWCNT hybrids while controlling their formation into fibers. Creating
nanostructured or blended heterojunctions between PFO / s-SWCNT hybrids and electron acceptors like
C60 is another possible route for overcoming the exciton diffusion limitation. Alternatively, the complete
removal of PFO through a more sophisticated method than that demonstrated here will likely restore
the ultrafast energy transfer seen elsewhere among bare nantoubes and potentially result in longer
intertube diffusion lengths and increased efficiency, even using planar bilayer heterojunction
architectures.
47
6. Photocurrent from Above-Gap Excitonic Transitions110
To date, the highest reported external quantum efficiency (EQE) for a s-SWCNT photoabsorber in a
photovoltaic device has been 22% at 1205 nm using a five chirality mixture of the (7, 5), (7, 6), (8, 6), (8,
7), and (9, 7) s-SWCNTs with E11 bandgap absorption ranging from 1050 to 1330 nm (0.93 to 1.18 eV).
This chiral distribution is non-optimal, however, because the small-bandgap (8, 7) and (9, 7) s-SWCNTs
have insufficient energetic offsets with C60 83, can potentially trap both excitons and free carriers95,111,112,
and reduce the optical density of the other larger-bandgap species in the s-SWCNT films, limiting
performance. In addition to decreasing performance, the s-SWCNT polydispersity present in these
devices and the resulting spectral congestion also make it difficult to analyze the efficiency of
photocurrent generation for above-bandgap ‘hot’ s-SWCNT absorption. The optical absorption
spectrum of a semiconducting nanotube is defined by strong absorption at not only its E11 bandgap
transition, but at higher order, ‘hot’ inter-band transitions (e.g. E22 and E33) and at transitions arising
from phonon-exciton coupling. The successful exploitation of s-SWCNTs in broadband single and multi-
junction devices will require an efficient means for harvesting energy and charges from these ‘hot’
excitons. However, the mechanisms by which ‘hot’ excitons relax and the efficiency of photocurrent
collection before and/or after relaxation are both poorly understood.
To overcome these challenges, we have fabricated highly monochiral (7, 5) s-SWCNT / C60 bilayer
photovoltaic devices. We show that employing highly monochiral s-SWCNTs increases efficiency by
minimizing the spurious, large-diameter / small-bandgap s-SWCNTs. The use of highly monochiral (7, 5)
s-SWCNTs also reduces spectral congestion, thereby making it possible to quantify the efficiency of
photocurrent generation at both bandgap and ‘hot’ transitions, for the first time. The devices
demonstrate peak external quantum efficiency (EQE) of 34% at 1055 nm. The high EQE allows us to
drive the diodes to relatively high current densities at photon fluxes comparable to terrestrial solar
48
applications. This, furthermore, provides a new opportunity to gauge trion, charge-exciton, and charge-
charge recombination relaxation pathways in s-SWCNT-based photovoltaic devices. Understanding
recombination losses due to trions is particularly important because recent work has shown that the
concurrent presence of free carriers and photogenerated excitons on a s-SWCNT results in the
formation of stable charged excitons, or trions.21,113-116 Trions will form at high irradiance and in device
operation would problematically drift in response to the build-in field away from the active
heterointerface where bound charges dissociate, thereby decreasing efficiency.
Highly monochiral (7, 5) s-SWCNTs were prepared for this study as described elsewhere27 and in
Appendix A. The enriched (7, 5) solutions contained a chiral distribution consistent with other reports
and determined by solution absorbance, Fig. 1A.27,113 Specifically, the tight diametric distribution of the
CoMoCAT SG65 growth process couples with the strong selectivity of the PFO/toluene system toward (7,
5), (7, 6), (8, 6), (8, 7), and (9, 7) chiralities, yielding solutions highly enriched in the (7, 5) chirality. Using
E11 oscillator strength chirality dependences predicted by Ando99 with fits of the absorption spectra, the
(7, 5) species was found to represent > 86% of the s-SWCNTs present. Minority s-SWCNTs were
observed to include (6, 5), (7, 6), (8, 6), (8, 7), and (9, 7) chiralities, none of which were found in
abundance > 5%. Additionally, insignificant absorbance was observed from metallic carbon nanotube
M11 transitions, which would appear as sharp peaks from 400 – 600 nm for carbon nanotubes in this
diameter range.35 Excess PFO has largely been removed from the solutions, as inferred from comparison
of s-SWCNT spectral features to PFO absorbance at 390 nm.95 Given the high monochirality of these
solutions, it is possible to attribute several distinct absorbance features to the (7, 5) chirality, including
both E11 and E22 absorbance at 1050 and 655 nm, respectively, and also a feature at 900 nm referred to
as the E11 + X sideband17,18 and attributed to a superposition of phonon sidebands of the bright singlet
(directly excited via E11 absorbance) and K-momentum dark singlet excitonic states.18,117,118
49
Despite noticeable broadening, these pronounced spectral features persist upon film deposition (Fig.
6.1A).
The measured EQE spectra of device stacks fabricated using 50 and 90 nm of C60, with and without s-
SWCNTs are compared in Fig. 6.1B. The E11, E11 + X, and E22 transitions strongly manifest in the EQE
spectra of the s-SWCNT/C60 device stacks (solid lines). The relative amplitude of each transition is
modulated by optical interference effects, largely determined by the overall C60 thickness. A
constructive interference node is spatially commensurate with the s-SWCNT film in the visible spectrum
when the C60 thickness is 50 nm, maximizing the E22 EQE. This constructive interference node shifts to
the near-infrared when the C60 thickness increases to 90 nm, maximizing the E11 and E11 + X EQE,
whereas a destructive interference node simultaneously minimizes the E22 EQE. The peak E11 EQE for a
~7 nm s-SWCNT / 90 nm C60 device stack is 34% whereas the peak E22 EQE for a ~7 nm s-SWCNT / 50 nm
Figure 6.1 A. Normalized absorbance of (7, 5) enriched s-SWCNT solutions (top, green) and thin films on quartz (bottom,
violet) cast from the above solutions. Solution absorbance spectra have been offset. B. Characteristic external quantum
efficiency (EQE) of photocurrent generation from ITO / active layer / 10 nm BCP / 100 nm Ag devices. Active layers
displayed are (7, 5) / 50 nm C60 (solid, blue), (7, 5) / 90 nm C60 (solid, red), 50 nm C60 (dashed, blue), 90 nm C60 (dashed,
red).
50
C60 device stack is 17%. Peak E22 EQE < the peak E11 EQE because of the smaller E22 absorption cross-
section.
In contrast, photocurrent generation in control device stacks without s-SWCNTs is limited to the C60
response < 700 nm. The spectral shape of the C60 response is similar with and without s-SWCNTs;
however, the magnitude of the response is smaller in the absence of the s-SWCNT/C60 heterointerface
which efficiently drives C60 exciton dissociation. In devices without s-SWCNTs, C60 photocurrent
responsivity likely arises from the dissociation of C60 excitons at the ITO interface. The C60/ITO interface
in the s-SWCNT-less devices is roughly the same distance from the Ag cathode as the s-SWCNT/C60
interface in s-SWCNT-based devices. We therefore expect that the optical interference profile will be
spectrally and spatially similar in devices with and without s-SWCNTs, resulting in comparable C60 EQE
spectra shape, consistent with experimental observation.
The EQE measured at each of the different s-SWCNT transitions can be related to the IQE if the
absorption efficiency, ηA, of each transition is known, according to the relationship IQE = EQE / ηA. The
IQE is equivalent to the absorbed-photon to collected-electron conversion efficiency and, considering
exciton diffusion and charge collection, is a lower-bound for the efficiency by which excitons relax and
dissociate into separated charge carriers. We have determined ηA with full consideration of internal
optical interference by measuring the optical Reflectance of the device stacks at normal-incidence.
Representative datasets of 1 – Reflectance, which quantifies total absorption by the device stack (ηA) in
the case of insignificant transmission by the cathode and negligible scattering65, are plotted in Figure
6.2A for device stacks with and without s-SWCNTs. 1- Reflectance spectra, henceforth referred to as ηA,
for the devices without s-SWCNTs are characterized by visible absorption arising from the C60 film and
near-infrared absorption due to free carrier losses in the ITO. These spectral features are again present
in ηA spectra of devices with s-SWCNTs, with the addition of absorption features of the s-SWCNTs.
51
The difference between the measured ηA spectra for control device stacks without s-SWCNTs and the
measured ηA spectra for device stacks with s-SWCNTs is defined as ∆ηA and provides a first
approximation of the fraction of incident photons captured by the (7, 5) s-SWCNT component of the
device stacks, ηA_cnt. The ∆ηA spectra for three devices are plotted against measured EQE on the same y-
axis in Figures 6.2B-D. Visual comparison of ∆ηA with measured EQE for these three devices is revealing:
the E11, E11 + X, and E22 spectral features are present in both the ∆ηA and the EQE with similar
magnitude. This qualitative observation alone indicates that excitons generated via these three
Figure 6.2 A Measured 1 – Reflectance (i.e. ηA) for device stacks of ITO / active layer / 10 nm BCP / 100 nm Ag devices.
Active layers displayed are (7, 5) / 50 nm C60 (violet), and 50 nm C60 (green). B. C. and D. Display ∆ηA (solid green); fits to
∆ηA (dashed blue); and measured EQE (solid red) for three devices. (E) Extracted IQE for optical excitation at E11, E11 + X
and E22 transitions, following treatment outlined in Supplementary Information.
52
photophysical mechanisms ultimately generate charge with comparable yields and further that the IQE
for each of these transitions is nearly unity.
To more precisely quantify ηA_cnt and therefore the IQE for these three transitions, fitting of ∆ηA is
necessary. Small sample-to-sample variations in ITO-free carrier losses, C60 film thickness, deviation
from normal incidence during reflectance measurement, perturbation of the optical interference profile
within the C60 and ITO films due to the added presence of the s-SWCNT film, and the addition of two
new interfaces within the device stack – all weakly perturb the background of the ηA curves, making ∆ηA
an insufficient quantification of ηA_cnt. However, because all these perturbations are spectrally broad, it
is straightforward to pick out the absorptive contribution of the much sharper E11, E11 + X, and E22
resonances by fitting. Details of the fitting procedure, as well as a device-by-device deconstruction of
∆ηA into ηA_cnt and background contributions (ηA_bg) are presented in the supporting information.
Overall, the ∆ηA fits are excellent (Figures 6.2B-D) and allow us to quantify the IQE as 85 ± 5%, 84 ± 14%
and 84 ±7% in response to E11, E11 + X, and E22 excitation, respectively. The high IQE resulting from E11
excitation is in good agreement with our previous report of 79 ± 16% for the (7,5) chirality from studies
on more heterogeneous films containing residual PFO and s-SWCNT samples synthesized via different
techniques.83
In addition to high IQE at the E11 exciton ground-state transition, we observe high IQE in response to E22
excitation. In fact, we measure efficiencies for E11 and E22 excitation which are nearly identical. If the
‘hot’ E22 excitons first relax to the E11 level and are then dissociated via electron transfer to C60, then the
IQE data tell us that this relaxation is nearly perfect. It is also possible that excitons generated at the E22
transition directly dissociate via ‘hot’ electron transfer to C60 or that the E22 excitons spontaneously
dissociate into free charge carriers within the s-SWCNTs followed by electron transfer to C60. However,
both calculation and experiment have suggested that the spontaneous dissociation of E22 excitons into
53
free charged carriers is a low probability event as compared against relaxation into the E11 level.79,119
More likely, our data support transient absorption spectroscopy measurements which show that
relaxation into E11 is ultrafast118,120 and efficient17. Direct comparison of these studies with ours is
complicated by the likelihood that the kinetics and energetics of photogenerated exciton relaxation may
be substantially perturbed in film versus solution, due to differences in polarizability and the diode’s
built-in electric field; therefore, more detailed studies are needed to determine the exact relaxation
pathway in devices. However, whatever the exciton relaxation kinetics or mechanism, the ultimate
result is that the IQE for photocurrent generation in response to E22 excitation is high.
The IQE for the E11 + X transition is also high. As previously mentioned, this transition has been ascribed
to a phonon-assisted absorption of the bright singlet and phonon assisted absorption of the K-
momentum dark exciton which itself lies roughly 25 meV above the bright, ground-state exciton.18 Our
measurements cannot determine whether the K-momentum dark exciton is itself efficiently dissociated,
or if the K-momentum exciton is efficiently transferred back to the bright groundstate where it is
dissociated. However, we can say that the net result is dissociation and charge generation with near
unity efficiency.
The high IQE for these three, fundamentally distinct photophysical absorption mechanisms is important
because it shows that free charge carriers can be efficiently generated from photons throughout the
visible and near-infrared spectra using s-SWCNTs as photoabsorbers in conjunction with C60 acceptors.
However, these IQE were measured at a relatively low-irradiance (< 10 μW cm-2) at which interactions
among free charge carriers and excitons are minimized. We next characterized the performance of the
s-SWCNT devices at substantially larger irradiance in order to assess trion, charge-exciton, and charge-
charge recombination losses. The illumination of a prototypical 15% single-junction inorganic solar cell
at an irradiance of one sun (~100 mW cm-2) will drive a short-circuit current density (Jsc) of 20 – 40 mA
54
cm-2, depending on the bandgap. We drove our (7, 5)/C60 heterostructures to a similar Jsc using a
monochromatic laser at 1053 nm.
The current-voltage (J-V) characteristics of a (7, 5)/C60 heterojunction with 90 nm of C60 are compared in
the dark and in response to 100 mW cm-2 irradiance at λ = 1053 nm in Figs. 6.3A and B. In the dark, the
heterojunction is highly rectifying with reasonably low series resistances (of order 0.5 Ω-cm2), consistent
with previous work on more heterogeneous s-SWCNT/C60 heterojunctions.83 Under illumination, a
photovoltaic effect is observed with a corresponding monochromatic power conversion efficiency (ηP),
open circuit voltage (VOC), fill factor (FF) and current responsivity (R) of 7.1%, 492 mV, 62% and 0.23
A/W, respectively (Fig. 6.3C). This particular device demonstrated an EQE of 24% at low power (< 10 μW
cm-2) at 1053 nm, which predicts R of 0.20 and agrees with the measured R to within 8% calibration
error. In J-V measurements, the measured R deviated by less than 7% over the range of 0.1 – 100 mW
cm-2. The reasonably high FF and VOC and, more importantly, the invariance of R with intensity suggest
that if trions are being formed, the ultimate effect on device performance is minimal. Losses due to
trion drift would likely result in a strongly deteriorating R with increasing irradiance as the rate of trion
formation will increase with increasing free carrier and exciton densities.
Figure 6.3 A. Current density versus voltage characteristics in the dark (green) and illumination under 100 mW cm-2 at λ =
1053 nm (violet) plotted on a linear and B. log-linear scale. C. Photovoltaic device parameters versus irradiance.
55
We extracted a diode ideality factor (n) of 1.4 and a saturation current density (JS) of 1.2 x10-8 A cm-2 by
fitting J-V curves of this device to a Shockley diode equation. Under the assumptions of low series
resistance, open circuit operation, and photocurrent (Jph) >> JS , we can predict VOC by simplification of
the generalized Shockley diode equation121 as,
. (1)
This relationship predicts a VOC = 508 mV, in good agreement with our measurement of 492 mV. It
should be noted that the device architecture we present does not make use of recent advances in
electron/hole selective contacts, or explore molecular coupling between s-SWCNTs and the acceptor to
further suppress JS and thereby enhance VOC.121-123 It may be possible to additionally suppress JS and
increase VOC by increasing s-SWCNTs length, decreasing recombination sites by passivating defects at the
open ends and side-walls, and further eliminating electronic disorder that arises from the PFO and the
remaining chiral impurities in film.
Overall, our results point the way for the use of semiconducting carbon nanotubes and combinations of
them for efficiently harvesting light over a broad spectrum. We have shown that s-SWCNT absorption at
E11, E11 + X, and E22 spectral features all result in efficient charge generation. We therefore expect that
absorption at other excitonic transitions of s-SWCNTs (for example the E33 transitions in the ultraviolet)
can be exploited for efficient charge generation as well. High-efficiency broadband photovoltaics may
extend from these findings in any of the following device designs: (1) in single-junction photovoltaic cells
exhibiting broadband absorbance by a combination of Eii, Eii+phonon, and off-resonance optical
transitions arising from single or combinations of different (n, m) chiralities and bandgaps of s-SWCNTs,
possibly supplemented by absorbance from the acceptor; (2) in multi-junction devices that combine
cells each based on different (n, m) chiralities and bandgaps of s-SWCNTs; or (3) in multi-junction
S
SCOC
J
J
q
nkTV ln
56
devices that combine near-infrared s-SWCNT cells with visible organic or inorganic cells. Alternatively,
(4) monochiral s-SWCNT films of order of 10 nm in thickness could be coupled with efficient photon
down-conversion schemes which efficiently pump broadband excitation onto highly absorptive spectral
regions124, likely the s-SWCNT E11 region. The latter could be a novel strategy for fabricating ultrathin,
modestly performing photovoltaic devices.
In summary, we have reported on the use of highly enriched (7, 5) s-SWCNT thin films to elucidate the
internal quantum efficiency (IQE) for exciton dissociation and subsequent charge collection in response
to optical excitation of the s-SWCNT’s near-infrared E11 and E11 + X and visible E22 resonances as 85 ± 5%,
84 ± 14%, and 84 ±7%, respectively. These data indicate that the generation and separation of charge
from ‘hot’ excitons proceeds with nearly perfect efficiency either via relaxation to the E11 level followed
by electron transfer to C60 or via direct transfer of a ‘hot’ electron to C60. The (7, 5) / C60 bilayer
heterojunctions demonstrated a peak EQE of 34%, which is the highest reported EQE for a carbon
nanotube photoabsorber-based photovoltaic device. Current-voltage measurements in response to
optical excitation at λ = 1053 nm demonstrated photocurrent responsivities which were largely invariant
over the irradiance range 0.1 – 100 mW cm-2, suggesting limited losses due to trion (charged-exciton)
drift. These results point the way towards exploiting s-SWCNTs for efficiently harvesting light over a
broad spectrum, in bilayered or blended single-junction photovoltaic cells in which the solar spectrum is
captured by a combination of Eii, Eii+phonon, and off-resonance absorption arising from s-SWCNTs of
different chiralities; multi-junction devices that combine cells each based on different (n, m) chiralities of
s-SWCNTs; multi-junction devices that combine near-infrared s-SWCNT cells with visible organic or
inorganic cells; or even ultrathin s-SWCNT cells coupled with efficient photon down-conversion
schemes.
57
7. Free Carrier Generation and Recombination in Polymer Wrapped
Semiconducting Carbon Nanotube Films and Heterojunctions
Single-walled carbon nanotubes are a unique class of materials characterized by high charge
mobility and large aspect ratios. These properties have motivated research into their
incorporation into organic photovoltaics as transparent anode/cathode materials,45,48,79,125-130
electron acceptors for semiconducting polymer-based active layers46,52,79,131
, and high mobility
charge shuttling conduits in polymer-fullerene active layers.132
In addition to these roles, which
capitalize primarily upon high charge mobility, it has recently been proposed and demonstrated
that electronic-type sorted, small diameter semiconducting single walled carbon nanotubes (s-
SWCNTs) have the potential to serve as active, photon-absorbing electron donors in high
efficiency organic photovoltaics. Along with other groups, we have demonstrated that
photogenerated excitons on small diameter s-SWCNTs can be efficiently dissociated at type-II
heterojunctions with C60-based fullerenes and that the resulting free carriers can be efficiently
collected as photocurrent in thin-film photovoltaic devices.78,79,111,133,134
Photocurrent internal
quantum efficiency (IQE) measurements exceeding 85% in optimized s-SWCNT/C60 bilayer
heterojunctions indicate the dissociation of photogenerated excitons and the collection of
resulting free carriers with efficiencies approaching unity.83,110
We have exploited this high
charge generation yield at the s-SWCNT/C60 heterointerface to demonstrate a bilayer solar cell
with a 1% power conversion efficiency, in which most of the response is driven by absorption
from an ultrathin s-SWCNT layer < 5 nm in thickness.135
The high IQE of these 1% solar cells suggests substantial efficiency improvements can be
attained. These efficiency gains require (a) thicker films of s-SWCNTs in order to collect more
light, (b) the development of thin film morphologies which maintain a high photocurrent IQE
58
while increasing film thickness, and (c) a better understanding of free carrier generation and
recombination in these materials and devices, which ultimately impact the desired (optimum)
morphology. The latter (c) has not yet been extensively characterized and is the focus of our
studies here.
A number of recent spectroscopic studies have observed evidence for photogenerated charges in
SWCNTs coupled within aggregates,136
or networks,82
as well as in SWCNTs isolated on
substrates,115
in solution,115
137
or within a polymer matrix,138
all in the absence of an energetic
driving force for exciton dissociation. However, device-level photoresponsivity measurements,
performed at significantly lower fluences than pump-probe spectroscopic studies, indicate weak
or no spontaneous photocurrent generation at these low photon fluxes. For instance, Soavi et al
measured spectrally resolved and broadband photocurrent generation from continuous excitation
of a thin film of highly enriched (6, 5) s-SWCNTs in the planar structure ITO/(6, 5)-SWCNT/Al,
but do not quantify the quantum efficiency.139
However, they utilize related samples in a pump-
probe technique to estimate that 1 – 2% of photoexcitations result in the generation of long-lived
free carriers. Importantly, device-level studies suggest that a critical requirement for efficient
photocurrent generation in response to natural (unconcentrated) solar irradiance is an energetic
offset, e.g. at a s-SWCNT-C60 (donor-acceptor) heterointerface.79,83
These device studies, along
with the short-lived nature of photoconductivity transients in the absence of interfacial photo-
induced charge transfer,64,82,138
indicate that carrier recombination kinetics may also be critical to
device performance since they place additional constraints on the timescale for extraction of
photogenerated free charge carriers.
Here, we employ time-resolved microwave photoconductivity (TRMC) to probe the generation
yield and recombination kinetics of free charge carriers generated in optically excited thin films
59
of polymer wrapped semiconducting nanotubes with and without an overlying electron accepting
C60 layer. TRMC enables the direct measurement of the free carrier population by monitoring its
microwave absorption. The magnitude of the change in microwave photoconductance (ΔG)
following photoexcitation is proportional to the photogenerated free carrier generation yield ()
and the sum of the high-frequency free carrier mobilities (Σμ). More explicitly,
Ae FIqtG 0)( (1)
where β =2.2 and represents the ratio between the long and short axis of the microwave wave-
guide, qe the elementary charge, I0 the incident photon flux, and FA the fractional light
absorption. The change in microwave photoconductance at times immediately following the
photoexcitation pulse (denoted end-of-pulse, EOP), ΔGEOP, provides an estimate of the free
carrier generation yield (if mobility can be reliably estimated), whereas monitoring the time
evolution of ΔG(t) is a direct probe of free carrier loss processes, such as recombination and/or
trapping (if mobility remains unchanged).140
In the case where carrier loss processes occur on
timescales significantly shorter than the response time of the system (determined by the ~ 3–5 ns
width of the Gaussian laser pulse) the value of ΔGEOP enables an estimate of the lower limit for
.
Below we describe the photogeneration and recombination of free carriers in polymer-wrapped
s-SWCNT films and thin-film bilayers with C60, probed using TRMC. We show that rapid carrier
recombination is intrinsic to the s-SWCNT film, whereas the interface with C60 results in spatial
carrier separation that reduces the recombination rate. The spectral dependence of the
photoconductance in the SWCNT/C60 bilayer indicates that the driving force for electron transfer
to C60 from the larger diameter nanotubes is significantly reduced. By combining
photoluminescence quenching and TRMC measurements we provide estimates for the high-
60
frequency (9 GHz) hole mobility in s-SWCNTs and the intrinsic yield for free carrier
photogeneration in neat s-SWCNT films. This final observation confirms previous experimental
studies for neat s-SWCNT films, and we discuss possible mechanisms behind the phenomenon.
Thin film samples were prepared using the same methods established in our previous work on
polymer-wrapped s-SWCNT photovoltaic devices.95
Device quality solutions of s-SWCNTs
were prepared by dispersing 1 mg mL-1
raw HiPco® single walled carbon nanotubes (Unidym)
with 2–4 mg mL-1
poly(9,9-dioctylfluorene-2,7-diyl) (PFO, American Dye Source) in 100 mL
toluene using a horn tip ultrasonicator for 1 hour, utilizing a water bath to cool the solution. The
resulting suspension was then centrifuged for 15 minutes at 50,000 g over an 11 cm pathlength in
a swing-bucket rotor, the supernatant collected and the pellet discarded. The supernatant was
then filtered through a 5 µm syringe filter. The resulting dilute solution was concentrated while
simultaneously removing excess PFO by pelleting the s-SWCNTs out of solution at 50,000 g in
11 cm long fluoropolymer centrifuge tubes in a 30° fixed angle rotor held at a temperature of 4
°C over a period of time approaching 90 hours for high extraction yields. The pellet was then
redispersed and dissolved in fresh tetrahydrofuran (THF) by heating on a hotplate set to 90 °C
for iterative pelleting, or redispersed into chlorobenzene to yield a stable solution. The resulting
solutions consisted of primarily the (7, 5), (7, 6), (8, 6), (8, 7), and (9, 7) chiralities of
semiconducting nanotubes – typical of the HiPco PFO/toluene system – wrapped by tunable
amounts of PFO, with minimal quantities of metallic nanotubes, amorphous carbon, aggregates,
or residual catalyst. The solutions utilized here had negligible amounts of free solution-phase
PFO (i.e. not adsorbed to the s-SWCNT surface) and the total mass of PFO present was roughly
equivalent to the total s-SWCNT mass (i.e. the total PFO:s-SWCNT weight ratio was roughly
1:1).95
61
Thin films of s-SWCNTs were deposited on quartz substrates by doctorblade casting on a
hotplate with a surface temperature of 100 °C in a dry argon glovebox. Droplets (5–20 μL) of s-
SWCNT containing solution were placed at one end of the heated substrate and immediately
drawn across the substrate using a doctorblade (casting knife) with a substrate clearance between
0.1 and 0.25 mm. Films of increasing thickness were built up by iterative casting. Quartz
substrates were cleaned in a typical solvent degreasing process involving acetone, and
isopropanol; following solvent baths, the substrates were cleaned with oxygen plasma for 10
minutes. In bilayer samples, a 90 nm film of C60 was deposited on top of the s-SWCNTs via
thermal evaporation with a background pressure < 1 10-6
torr.
TRMC measurements were conducted by using an instrument described in detail elsewhere.138
Briefly, samples were placed in an X-band microwave wave-guide and photoexcited with ca. 4
ns light pulses of tunable wavelength emanating from a Nd:YAG pumped optical paramagnetic
oscillator (OPO) attenuated with various combinations of neutral density filters. Time dependent
changes in the microwave probe power were measured with a calibrated Schottky barrier diode.
The transient behavior of the changes in microwave power were tracked with an oscilloscope
with sub-ns resolution. While these types of measurements frequently employ a partially-
transparent metal iris to create a resonant microwave cavity to enhance signal at the expense of
inferior time response, the signal here was sufficiently strong so as to forego the iris and
therefore maintain the full temporal resolution afforded by the ns scale optical pump.
62
Figure 1A displays typical absorptance spectra of thin film samples used in this study. Neat PFO
wrapped s-SWCNT films display absorption features of the s-SWCNTs at their optical band gap
transitions in the NIR (S1 transitions, 900–1400 nm) and higher order S2 and S3 optical transitions
in the visible (600–800 nm) and UV (300–450 nm), respectively. Additional absorption in the
UV is attributed to absorption by residual PFO, with an absorption peak at 350 nm. Relatively
thin films of s-SWCNTs were employed, with thicknesses of approximately 6 nm, to ensure that
Figure 7.1 A. Absolute absorptance (1 – transmittance) of a neat PFO-wrapped s-SWCNT film (Red, s-SWCNT) and a
comparable film in a bilayer with 90 nm C60 (Blue, s-SWCNT/C60). B. Semi-log plot of the microwave photoconductance
transients acquired after exciting neat films and bilayers (Red and Blue, respectively) with an absorbed photon flux of ~6
1011 photons cm-2. C. Semi-log plot of the photoconductance transients for the neat s-SWCNT film across a wide range of
absorbed photon fluxes from ~1 1011 photons cm-2 (dark blue) to ~6 1013 photons cm-2 (light blue). D. Semi-log plot of
the photoconductance transients for the s-SWCNT/C60 bilayer film photoconductance transients across a wide range of
absorbed photon fluxes from ~4 1010 photons cm-2 (dark red) to ~5 1013 photons cm-2 (light red).
63
a large fraction of absorption occurred within one exciton diffusion length of the s-SWCNT/C60
interface.83
Therefore, the absolute absorbance of these films remained low, and only ~10% of
the incident photon flux is captured for s-SWCNT bandgap excitation. The absorptance spectra
of bilayer films contained all the s-SWCNT absorbance signatures present in the neat films, with
additional broad absorbance due to the C60 component in the visible region. The s-SWCNT
optical transitions are red-shifted by an average of 6 meV in bilayer films, potentially due to an
increased dielectric environment with the presence of C60.
ΔG(t) transients following photoexcitation of the PFO wrapped s-SWCNT films, both with and
without an overcoating layer of C60, are compared in Figure 1B at a fixed incident excitation
fluence of ca. 5 1013
photons cm-2
at λ = 1205 nm. In both cases, ΔG(t) increases immediately
following photoexcitation. The non-zero ΔG(t) implies that free carriers are photogenerated in
the s-SWCNT films, regardless of the presence of the C60 layer. In the PFO wrapped s-SWCNT
film without C60, the ΔG(t) signal nearly completely decays to pre-excitation, background levels
within the first 10 ns, similar to measurements made when exciting larger diameter SWCNT
samples containing the statistical ratio of s- and m-SWCNTs.64,138
However, in the PFO wrapped
s-SWCNT film overcoated by C60, different behavior is observed. While a part of the initial
ΔG(t) signal is similarly ‘short-lived’ and decays quickly within the first 10 ns, another
component of ΔG(t) persists for 100’s of ns, with a decay rate of (850 ns)-1
through the range 100
ns < t < 400 ns. The increase of ΔG for the bilayer sample indicates an enhanced yield of free
carriers due to interfacial exciton dissociation,79,83
and the long-lived decay suggests an
inhibition of carrier recombination due to separation across the SWCNT-C60 interface.
In general, the magnitude of ΔG(t), both at short and long times, increases with increasing
excitation fluence (Fig. 1C, 1D). In the neat PFO wrapped s-SWCNT films, the free carriers
64
remain short-lived for all fluences (Fig. 1C). However, in bilayers with C60, the relative fraction
of long- versus short-lived photoconductance components decreases with increasing fluence
(Fig. 1D). In order to analyze fluence dependencies in more detail, we compare the yield-
mobility product (), extracted as ΔG(t)/[qeI0FA] per eq. 1, at times both directly following
photoexcitation (denoted end-of-pulse, EOP) as well as at long times for the bilayer sample
(averaged from 300–400 ns, nominally referred to as 350 ns signal). Assuming μ remains
constant, provides a measure of the photogenerated carrier concentration, normalized to
absorbed excitation fluence. For both neat s-SWCNT films and s-SWCNT/C60 bilayers,
increases substantially with decreasing photon fluence. It has been shown elsewhere that this
fluence dependence can be accurately captured by the empirical equation,
AFBIA 01/ (2)
where A and B are empirical fitting parameters, and A represents the saturation value at low
fluencies approaching 1 sun AM1.5G condition ([]sat).64
For both fluence-dependent datasets
(bilayer and neat EOP), the resulting fits are good, and enable extrapolation to the behavior
expected for low-fluence. Equation 2 predicts []sat values of 0.17 and 0.84 cm2V
-1s
-1 for the
neat and bilayer EOP measurements, respectively (Figure 2a).
Assuming an invariant , the ratio of at 350 ns to at the EOP in the s-SWCNT/C60
bilayers indicates the fraction of initially photogenerated carriers that persist as long-lived
carriers at 350 ns. The ratio of at 350 ns to at the EOP is plotted versus fluence in Fig.
2B. At a high absorbed photon fluence of 4 1013
photons cm-2
, the fraction is only ~3%.
However, this fraction increases with decreasing fluence, increasing to ~16% at an absorbed
photon fluence of 6 1010
photons cm-2
and is expected to continue increasing with decreasing
65
fluence (as indicated by the extrapolated curve in Figure 2B). This observation is consistent with
a reduction in the carrier recombination rate, due to a reduction in the carrier density at low
fluences.
The fall off of with increasing fluence suggests a decreasing free carrier generation yield
through increased competition between exciton dissociation with collision-induced exciton
annihilation processes. In general, exciton collisions involving the net transfer of energy from
one exciton to another exciton or charge are referred to as Auger processes. It is useful to
distinguish between several such Auger processes. Exciton-exciton annihilation (EEA), also
commonly denoted Auger recombination, involves one exciton recombining by transferring
energy to a second exciton that is excited to a higher energy level, whereas for Auger ionization
(AI), the exciton receiving the excess energy is actually dissociated into free carriers. Exciton-
charge annihilation can also occur, in which the annihilated exciton transfers its energy to a free
charge.82,140,141
Figure 7.2 A. Absorbed photon fluence dependence of the yield-mobility product () at end-of-pulse (EOP, peak) for
Neat and Bilayer films. Solid lines represent fits with Eq. 2 (see main text). B. Fluence dependence of the long-lived (350ns)
fractional contribution for bilayer films, indicating a strong enhancement of the long-lived signal at low absorbed photon
fluences.
66
Exciton collisions become increasingly important as the fluence-dependent exciton and/or charge
density increases, and the balance between the different Auger pathways may also change with
increasing photon fluence. For our thin SWCNT films, an absorbed photon fluence of 4 1013
photons cm-2
in film of thickness 6 nm corresponds to volumetric absorbed photon density of 7
1019
photons cm-3
or a linear absorbed photon density of 280 photons μm-1
length of s-SWCNT,
equivalent to one exciton every 3.5 nm of s-SWCNT length (assuming a film density of 1.0
g.cm-3
and a 1:1 PFO:s-SWCNT volume ratio) for a ~4 ns pulse. However, we note that the 4 ns
pulse is significantly longer than values typically obtained for exciton lifetimes in s-SWCNTs,
meaning the peak exciton density is much lower than this value. For example, if the average
exciton lifetime is ~100 ps, the peak exciton density within the 4 ns pulse is ~7 μm-1
(an exciton
every ~140 nm of s-SWCNT length). Several studies have demonstrated the importance of
exciton collisions at these densities. For example, the TA studies of Yuma et al. suggest that AI
generates charges in isolated SWCNTs in solution at densities of a few excitons per micron.137
As another comparison, in excitation intensity dependent photoluminescence studies of isolated
nanotubes in solution, the Kanemitsu group estimates an Auger recombination (EEA) time of
800 fs when two excitons are present on the same, 1 μm long s-SWCNT, extending from an EEA
rate constant of 1.6 ps-1
.μm.142
In thin films, exciton collisions may even be enhanced due to the
strong electronic coupling of adjacent s-SWCNTs, and therefore the tendency of excitons to
accumulate on small bandgap species via inter-nanotube energy transfer.
It is important to note that while the exciton lifetime limits the peak exciton density, it does not
limit the peak carrier density. Assuming that a certain fraction of all excitons produce charge
carriers, and the lifetimes of free carriers are expected to be much longer than photogenerated
67
excitons, it is possible and even probable that the peak density of free carriers will exceed the
peak density of excitons in the limit of efficient exciton dissociation.
While it is important to consider these Auger-like processes, it is also important to note that the
saturation behavior at low fluences (i.e. with limited non-linear (Auger) loss processes) most
aptly describes the behavior expected in unconcentrated solar cell devices. The absorbed photon
fluences explored here (1010
–1014
photons.cm-2
per 4 ns) are much greater than what is found for
1 sun, AM1.5G conditions. For comparison, 10% absorption of the AM1.5G spectrum at photon
energies > 1 eV would result in an absorbed photon flux of only 1.2 108 photons.cm
-2 per 4 ns.
Therefore, based on the low fluence saturation behavior (Figures 2A and 4B), we expect that
most photogenerated carriers in s-SWCNT/C60 bilayer heterojunction devices with 6 nm thick s-
SWCNT films will be long-lived, facilitating their collection and extraction from devices.
However, the ‘fast’ recombination processes in s-SWCNT/C60 photovoltaic heterojunctions
observed at high fluence may become more relevant for concentrated solar applications or in
devices where poor charge extraction allows for significant buildup of carriers. The continued
presence of a fast decay component, even at the lowest absorbed photon fluencies measured here,
suggests that such devices will need to operate in a regime where free carrier collection times are
on the ns timescale.
The spectrally resolved dependence of photoconductance excitation contains valuable
information with regard to the mechanisms governing free carrier generation in both neat and
bilayer films. It is important to note that the films prepared here are heterogeneous, containing 7
distinct species: C60, the semiconducting dispersing polymer PFO, and five separate s-SWCNT
chiralities. Each species can be spectrally resolved separately by tuning the excitation
wavelength, with the exception of PFO due to overlap with the SWCNT S3 transitions and C60
68
absorption. We measure ΔG(t) transients at a fixed fluence of 1 1013
photons cm-2
and plot
ΔGEOP (normalized for incident photon flux I0) for both neat and bilayer films in Fig. 3A for λ in
the range of 400–1400 nm, and compare against the film absorptance. These photoconductance
action spectra contain spectral features unique to the s-SWCNT chiralities present and C60.
Strong signal is also observed at 400 nm excitation, however due to spectral congestion, it is not
possible to determine whether this signal is manifest of absorption by PFO, C60, or the s-SWCNT
components, all of which absorb strongly at this wavelength. While photoconductance signal is
clearly seen from absorption by C60 and all s-SWCNT components, not all of these materials
contribute equally. For example, the C60 film absorbs strongly in the bilayer films for λ < 700
nm, yet the photoconductance resulting from direct C60 excitation is less significant than that
arising from the s-SWCNT bandgap transitions in the near-infrared. This difference is most
likely due to the mismatch between the C60 film thickness (90 nm) and the expected value of C60
exciton diffusion length, measured to range from 14–40 nm).65,143,144
The weak absorption
coefficient exhibited by C60 across these wavelengths means that the absorption profile extends
across the entire film thickness, resulting in the generation of a large fraction of excitons that
cannot reach the interface with the s-SWCNT layer.
69
Also of note in bilayer samples is the
reduced ΔG for s-SWCNTs with optical
bandgaps at wavelengths > 1205 nm. To
better elucidate the s-SWCNT chirality
dependence on photogeneration yield, we
analyze the spectral dependence of the
EOP at constant fluence in Fig. 3B.
In the s-SWCNT/C60 bilayers, the
corresponding to the smaller bandgap (8,
7) and (9, 7) nanotubes are less than the
corresponding to the larger bandgap
(7, 5), (7, 6), and (8, 6) nanotubes.
Specifically, falls from 0.33, 0.37,
and 0.33 cm2V
-1s
-1 for the (7, 5) (7, 6)
and (8, 6) chiralities, to 0.13 and 0.11
cm2V
-1s
-1 for the (8, 7) and (9, 7)
chiralities, respectively. Since the TRMC
measurement is incapable of directly
decoupling the contributions of and
to the decrease in could potentially be explained by a reduced carrier yield or reduced high-
frequency mobility of holes on the (8, 7) and (9, 7) s-SWCNTs. However, it has been shown,
using semiclassical carrier transport theory, that the low-field carrier mobility increases with
decreasing s-SWCNT bandgap (by a factor of 2 going from the (7, 5) to the (9, 7) nanotube).11
Figure 7.3 A. Spectral dependence of end-of-pulse
photoconductance (GEOP), normalized to the incident photon
fluence (I0), for neat PFO-wrapped s-SWCNTs (Neat, Red
diamonds) and a PFO-wrapped s-SWCNT film in bilayers with C60
(Bilayer, Blue circles) compared to the absolute absorptance (1 –
Transmittance) for the same samples. B. Near-Infrared spectral
dependence of the yield-mobility product () at end-of-pulse for
Neat and Bilayer films. Vertical grey bars indicate wavelengths in
resonance with the S1 transition of the s-SWCNT chirality indicated.
70
Thus, it is more likely that the decrease in indicates a reduction in free-carrier generation
yield as the nanotube bandgap decreases. This trend is consistent with device studies in which
the IQE for exciton dissociation and charge collection from photoexcited (8, 7) and (9, 7)
SWCNTs is suppressed with respect to the larger bandgap species, due to an insufficient energy
offset between the conduction band of these nanotubes and the lowest unoccupied molecular
orbital of C60.11,83
In this case, free carrier generation is driven by electron transfer from the
SWCNT film to the C60 film. The spatial separation of the charge thereby suppresses the
recombination, which is consistent with the observation of long-lived carriers in the s-
SWCNT/C60 bilayer at low fluence.
This measurement technique provides an opportunity to estimate the electron affinity of s-
SWCNTs, specifically the (9, 7) chirality. Previous device-scale measurements of charge transfer
across this interface required the simultaneous measurement of photocarrier generation and
collection, potentially convoluting diametric/chirality trends in the charge transfer process with
diametric/chirality trends in the carrier collection process.79
This is nontrivial as it is expected
that free carriers will pool on larger diameter s-SWCNT species, which exist in lower relative
abundance and potentially do not form percolating networks for charge extraction. Here we
uniquely probe the photogeneration process, and are free from any concerns regarding collection.
The observation that the measured yield-mobility product is essentially equivalent with and
without the C60 interface when optically exciting the (9, 7) chirality (Figure 3B) allows us to
estimate the electron affinity (EA) and ionization potential (IP), related to the energies of the
lowest unoccupied and highest occupied molecular orbitals (LUMO and HOMO) respectively, of
the (9, 7) species. Because we see no significant photoconductivity gains with the addition of an
interface, we assert that the driving force for photoexcited electron transfer to C60 is
71
approximately 0 eV. If we take the EA of C60 to be 4.28 eV,145
and use the exciton binding
energy calculations of Capaz et al, with a relative dielectric constant of 4 to estimate the exciton
binding energy on the (9, 7) chirality as 0.2 eV,4 we can estimate the EA to reside 4.08 eV below
vacuum. Assuming that the electronic bandgap is given by the sum of the optical bandgap (with
an optical transition ca. 1375nm) and the exciton binding energy, we can then estimate the IP to
reside 5.18 eV below vacuum.
In contrast to the bilayer samples, photoconductivity measurements in the neat s-SWCNT films
reveal is relatively independent of nanotube diameter (chirality). In fact, the dependence of
on nanotube chirality appears to exhibit an opposite trend to the bilayer sample, increasing
slightly with decreasing s-SWCNT bandgap. This trend reversal suggests photocarriers are
produced via a different mechanism in neat versus bilayer samples. The observed diametric trend
in neat s-SWCNT films, specifically the increase in for the (8, 7) and (9, 7) SWCNTs may
simply be due to an increase in the carrier mobility, as mentioned above, and an equivalent
photogeneration yield across diameters.
The fact that free carriers are being photogenerated in neat polymer-wrapped s-SWCNT films at
all, let alone with yields up to 6.5% (see below) is rather surprising but consistent with our
previous THz82
and GHz146
spectroscopic studies, as well as several recent transient absorbance
or PL studies.147-149
In the absence of the C60 electron accepting layer, there is no intentional
driving force for overcoming the exciton binding energy, which is expected to be between 200
and 250 meV for the s-SWCNTs studied here, in a medium expected to exhibit a spatially
averaged relative dielectric permittivity of 4.4 Thermally driven ‘spontaneous’ exciton
72
dissociation cannot explain the relatively large charge generation yield because of the large
binding energy with respect to kBT. Furthermore, the dispersing polymer, PFO, and all chiralities
present are expected to form strong type-I heterojunction(s) and the work function across these
chiralities is not expected to vary significantly. Therefore, it would seem unlikely that free
carriers are being generated via charge transfer from one material component to another.79
As
discussed above, it is also possible that free carriers are being generated via AI, although we
must consider whether this mechanism is consistent with the fluence dependence of microwave
photoconductivity observed in these measurements (Fig. 2A). A recent transient absorption (TA)
measurement suggested free carriers were generated with yields on the order of a few percent for
uncoupled (6, 5) SWCNTs isolated in a gelatin matrix.147
Another recent pump-probe study
observed that probe pulses formed trions (bound exciton-charge complexes) following excitation
of (6, 5) SWCNTs with pump pulses of fluences ranging from 1012
to 1014
photons cm-2
per
pulse.149
The results of this study suggested a direct production of free charge carriers from the
photoexcited exciton population resulting from AI at high exciton densities. Furthermore, the
charge carrier yield (carriers per incident photon) decreased with increasing fluence, due to a
saturation of the exciton density created by pump photons. Our current study indicates a low-
fluence free carrier yield on the order of ~6.5% (see below) that decreases with increasing pump
fluence, both of which are consistent with the results of the TA studies discussed above. Another
possible source for carriers within our thin films is exciton dissociation at defects and/or traps. It
is conceivable that as these traps fill with increasing exciton and charge densities, a decreasing
proportion of excitons will dissociate, resulting in a decreasing free carrier generation yield with
increasing photon fluence, as observed in Fig. 2A.
73
Finally, in an effort to deconstruct the yield-mobility product (), we use photoluminescence
quenching measurements as an estimate of for s-SWCNT films with a C60 overlayer (see Fig.
4). For films equivalent in thickness and of identical composition to those studied in TRMC here,
we measure photoluminescence quenching (PLQ) efficiencies of 0.65. We also note that
previous work measuring the thickness dependence of photocurrent generation in thin film
photovoltaics fabricated using very similar active layers extracted IQE values > 0.65 for
equivalent film thicknesses of similar s-SWCNT composition.95
We couple this estimate ( =
0.65) with the low-fluence yield-mobility product extrapolation of = 0.84 cm2V
-1s
-1 for
excitation at λ = 1205 nm, estimated earlier from the empirical fit using Eq. 2. This results in a
lower limit for the high frequency (@ ~9 GHz) mobility sum in the bilayer of = 1.29 cm2V
-1s
-
1 (assuming that PL quenching results solely from interfacial electron transfer). This carrier
mobility sum represents the sum of the electron mobility in C60 with the hole mobility in the s-
SWCNT phase. Recent time-resolved terahertz spectroscopy measurements indicate that the
high-frequency (~1 THz) electron mobility in a thin, thermally-evaporated C60 film is of the
order of 50 cm2V
-1s
-1, decaying to around 25 cm
2V
-1s
-1 in the first several tens of picoseconds.
150
Previous pulse-radiolysis TRMC measurements, carried out at ~32 GHz, of carrier transport in
C60 powders estimated to have a minimum value of ~0.3 cm2V
-1s
-1, and assuming an equal
contribution of electrons and holes to the measured radiation-induced conductivity a value for
e,min of ~ 0.15 cm2V
-1s
-1.151,152
In Figure S1, we estimate the measured high-frequency mobility
as a function of probe frequency, calculated by solving the 3-dimensional diffusion equation
inside a cube of edge-length a, with reflecting boundary conditions at the sides of the cube.153,154
If one assumes a cube with edge-length a = 50 nm, corresponding roughly to the crystallite sizes
observed for thermally-evaporated thin films,155
such as those deposited here, and in the TRTS
74
study,150
the high-frequency electron
mobility detected at 32 GHz and 9 GHz
would be e,32GHz ~ 21.7 cm2V
-1s
-1 and
e,9GHz ~ 5.1 cm2V
-1s
-1, respectively.
These values appear to be unrealistically
large, suggesting that the true scattering
length is smaller than the crystallite
dimensions. In fact, a value of a = 10
nm results in the high-frequency
electron mobility detected at 32 GHz
and 9 GHz of e,32GHz ~ 0.15 cm2V
-1s
-1
and e,9GHz ~ 0.01 cm2V
-1s
-1,
respectively, which are more reasonable
in the context of previously published
results. This suggests that the scattering
length, which limits the measured
mobility at the microwave frequencies
employed in TRMC measurements, lies
in the range 10 nm < a < 50 nm. It should be noted that this value is on the order of that
measured for the electron mobility in domains of the soluble fullerene derivative [6,6]-phenyl-
C61-butyric acid methyl ester (PCBM) blended with poly(3-hexylthiophene) (P3HT).140
We now use the lower limit for the electron mobility at 9 GHz (e,9GHz ~ 0.01 cm2V
-1s
-1) to
estimate the contribution of mobile holes in the SWCNT layer. Since the high frequency (@ ~9
Figure 7.4 A. Photoluminescence emission of PFO-wrapped s-
SWCNT films before (Red diamonds) and after (blue circles)
deposition of C60.. B. Fluence dependence of the calculated free
carrier generation yield (ϕ ) for neat films (Red diamonds) and
bilayers with C60 (blue circles)
75
GHz) mobility sum in the bilayer is = 1.29 cm2V
-1s
-1, and we estimate e,9GHz > 0.01 cm
2V
-1s
-
1, the high-frequency mobility of holes in the SWCNT layer is estimated to be h,9GHz < 1.28
cm2V
-1s
-1. In the case of the neat s-SWCNT film we assume that mobile holes and electrons
contribute equally to the measured photoconductance, which results in a high-frequency mobility
sum of ~ 2.6 cm2V
-1s
-1. Similar to the process described above for the s-SWCNT/C60 bilayer,
we use the low-fluence yield-mobility product extrapolation of = 0.17 cm2V
-1s
-1 for
excitation of the neat s-SWCNT film at λ = 1205nm, estimated from the empirical fit using Eq. 2,
and estimate the low-fluence saturation photogenerated free carrier yield () in the neat s-
SWCNT film to be ~ 6.5 %, with experimental, fluence-dependent values shown in Fig. 4. It is
important to keep in mind that this estimate is informed by several assumptions, each of which
comes with associated uncertainties. These uncertainties are discussed in more detail in the
Supporting Information.
While a free carrier photogeneration yield of 6.5% is not promising in-and-of itself for high
efficiency photovoltaics, it is significant. More problematic is that without a mechanism for rapid
spatial separation of these free carriers, they rapidly recombine, as shown in Figure 1C. It is
interesting to note that utilizing very similar polymer wrapped s-SWCNT samples and
dispersions, studies designed specifically to look for free carrier photogeneration and collection
failed to measure photocurrent from the excitation of neat, polymer wrapped s-SWCNT films79
,
likely due to the fast recombination for neat s-SWCNT films, ca. 10 ns. However, Soavi et al.
recently demonstrated photocurrent generation from a neat s-SWCNT film sandwiched between
ITO and an aluminum cathode.139
The predominant differences between our previous device
studies and the Soavi study include (1) the absence of non-covalent surface modification by PFO
in the Soavi study, and (2) the additional presence of a s-SWCNT/Al interface. It is possible that
76
free carrier mobilities are much greater in s-SWCNT films without PFO, enabling the rapid
extraction of photocurrent. It is also possible that s-SWCNT exciton dissociation is occurring at
the Al interface, effectively accomplishing exciton dissociation and charge extraction through a
single photoexcited electron or hole transfer event.
A possible explanation for the enhanced yield estimated in this study involves trions, which are
understood to be readily created in s-SWCNTs optically excited at high fluence when there is an
overlap between the optically excited exciton and charge populations.114-116,137
The relatively
long duration of the pump pulse, relative to exciton lifetimes and collision rates, coupled with the
finite free carrier yield, results in a population of both charges and excitons within the duration
of the pulse, enhancing the probability of trion formation. Although it is unclear how, or even if,
trions (irrespective of polarity) will influence microwave conductivity in our measurements, it is
reasonable to expect that trions may behave as ‘heavy’ electrons and holes, i.e. charges with
comparatively high effective masses and thus, lower mobilities. Thus, it is possible that our free
carrier yield estimates are artificially inflated due to the presence and potential photoconductivity
contributions of trions. In contrast, TA measurements presumably generate an exciton population
within an ultrafast (< 100 fs) pulse that is much shorter than the exciton lifetimes and collision
rates. A delayed probe pulse then elucidates the pump-induced formation of charges through
either the generation of trions137
or by probing Stark-induced shifts of exciton transitions.139
In conclusion, we have studied the photogeneration and subsequent recombination of free
carriers in polymer-wrapped s-SWCNT films and thin-film bilayers with C60. We have identified
a competition between recombination processes in bilayer s-SWCNT/C60 samples: fast
recombination via processes intrinsic to the s-SWCNT films occurs on the timescale of ns and is
77
dominant at high photon fluences, while recombination across the s-SWCNT/C60 heterointerface
occurs on timescales of 100’s of ns and contributes much more strongly at low fluences.
Photoconductance action spectra support long-lived free carrier photogeneration in s-
SWCNT/C60 bilayers via charge transfer to C60, and that the driving force, and therefore yield,
for free carrier generation is dependent on the diameter (bandgap) of the s-SWCNT species. In
addition, fluence dependence datasets provide insight regarding potential mechanisms for carrier
generation in neat s-SWCNT films. Photoluminescence quenching coupled with yield-mobility
product values measured using TRMC enable the estimation of the s-SWCNT hole mobility of
ca. 1.25 cm2V
-1s
-1, and for the free carrier generation yield of ~6.5% in neat s-SWCNT films.
78
8. Summary and Outlook
The work described and presented in this dissertation represents an enabling advance in our
understanding of photocurrent generation from light absorption by semiconducting carbon nanotubes.
Specifically, we demonstrate that photocurrent can be generated by dissociating photogenerated
excitons on s-SWCNTs at type-II heterojunction interfaces where electronic offsets exceed the binding
energy of the photogenerated charges. We demonstrate this in a photocapacitive device architecture
and further demonstrate that photocurrent generation can occur via charge transfer of both polarities.
We focus on the heterojunction interface between small diameter s-SWCNTs and C60, and measure
internal quantum efficiencies of > 85%, consequently establishing a lower limit for the dissociation
efficiency at this interface. We also demonstrate a s-SWCNT diametric dependence to the charge
transfer efficiency with highest efficiencies occurring for s-SWCNT diameters < 1.0nm.
Thickness dependence studies of preliminary thin-film planar photovoltaic devices reveal a rapid fall in
the IQE with s-SWCNT film thicknesses exceeding ca. 5 nm; a thickness we understand to be related to
the diffusion length of photogenerated excitons in those films. We go further to study the diffusion of
excitons in disordered s-SWCNT films with varying amounts of the dispersing polymer and demonstrate
that net exciton diffusion is a cooperate process between inter- and intra- nanotube energy transfer. We
demonstrate the pooling of excitons on limited populations of small band-gap (large diameter) s-SWCNT
chiralities. We further demonstrate an increase in photocurrent generation with decreasing amounts of
the initial dispersing polymer, primarily related to a consequential reduction in the NIR absorption
length of light. We also demonstrate that limitations manifest of exciton diffusion lengths can be
overcome via formation of a bulk heterojunction with C61 – PCBM.
79
Using more monodisperse s-SWCNT samples, we study the optical transition dependence of
photocurrent generation. Increased monochirality enables the spectral resolution of photocurrent
generation from optical transitions creating excitons in a higher subband, and ‘dark’ excitons. We
measure photocurrent generation of these transitions in identical efficiencies as the IQE of photocurrent
generation via groundstate exciton formation.
We corroborate these device-level studies with time-resolved microwave conductivity studies, directly
tracking the generation and recombination of free carriers in neat s-SWCNT films, and s-SWCNT/C60
bilayers. We observed both greatly increased yield and carrier lifetimes in bilayer samples, with lifetimes
exceeding 850ns. The spectral dependence of microwave photoconductivity in these studies
corroborates device level measurements of s-SWCNT diameter dependence in photocurrent generation,
and further, enables the extraction of an electron affinity value of the (9,7) chirality.
We demonstrate the practicality and relevance of these insights through various photovoltaic device
demonstrations, achieving 1% power conversion efficiency of broadband near-infrared light and 7%
power conversion efficiency under monochromatic, NIR irradiance. The key findings of this dissertation
have greatly advanced our ability to generate photocurrent from light absorption by semiconducting
carbon nanotubes. There are many opportunities to extend this work and realize some of the suggested
applications. I will outline a number of outstanding research questions, and postulate some reaserch
directions to achieve these applications, below.
8.1 Enhancing the performance of planar heterojunctions
The ultimate goal, motivating the work described in this dissertation, is high current responsivities
consequent to light absorption by semiconducting carbon nanotubes. This goal can potentially be
achieved through the use of active films consisting of either planar film stacks of acceptor atop s-
80
SWCNTs (or vice versa), or blended, bulk heterojunctions of s-SWCNTs with acceptor materials. Here, I
will suggest research areas which enable the former.
We have previously demonstrated a rapidly deteriorating IQE of planar devices with increasing s-SWCNT
film thickness. The mismatch between the absorption length necessary for complete light absorption,
and the maximum length available for high IQE has thus far limited the performance of planar devices.
We understood this mismatch to be principally manifest of a ‘short’ exciton diffusion length (ca. 3nm)
which stands in stark contrast to the ultralong (ca. 600nm) intrananotube exciton diffusion length
measured elsewhere in isolated, well dispersed s-SWCNTs. What remains unclear is what fundamentally
limits the diffusion length of photogenerated excitons in our disordered films. As the diffusion length is
proportional to the square root of the lifetime-exciton diffusivity product, many materials parameters
influence the net diffusion length. An incomplete list of factors which could limit exciton lifetimes
and/or exciton diffusivities includes: 1.)covalent or noncovalent defects at s-SWCNT ends or sidewalls,
2.)dilute, small EG s-SWCNTs 3.)dilute metallic SWCNTs, 4.)persistent dispersing polymer in cast films,
and/or 5.)excessively disordered s-SWCNT films which result in exciton and/or charge traps at or away
from tube/junctions. Understanding which factors limit the diffusivity of excitons and designing schemes
to minimize or eliminate the source of limited diffusivity will result in greatly improved performance.
Beyond this, much is yet to be learned about charge transfer at these interfaces. For instance, what are
the kinetics of electron transfer at the s-SWCNT/C60 interface? And beyond this, what diameters s-
SWCNTs are optimal for ultrafast, ultraefficient electron transfer? Does a Marcus-inverted regime exist,
where the driving energy is so great it can actually slow charge transfer? It would be greatly enabling to
develop electron acceptor materials which serve as alternatives to C60 and C61-PCBM. This could enable
exciton dissociation across a wider range of s-SWCNT diameters, and potentially result in materials such
as TiO2 or ZnO which offer superior thermal and chemical stability to fullerenes.
81
8.2 Enhancing the performance of bulk heterojunctions
The goal of highly efficient photocurrent generation via light absorption by semiconducting carbon
nanotubes can also potentially be realized through the formation of blended heterojunctions between s-
SWCNTs and charge accepting materials. This is perhaps the most obvious route, mirroring the
developments of polymer and small molecule organic photovoltaics. Indeed, preliminary work outlined
in chapter 4 demonstrates gains achieved by overcoming exciton diffusion limitations in such an
architecture. Building on these gains is a promising route to high efficiency.
The performance of BHJs will also be greatly and positively influenced by answering questions outlined
in section 8.2 regarding exciton diffusivity limitations. However, additional questions must be answered
in order to enable BHJs.
One of the more practical, but real challenges associated with the gains achieved in Chapter 4 is
associated with processing. While s-SWCNTs can be solubilized by PFO, solubility remains limited to ca.
100 μg mL-1, which is partially why the work demonstrated throughout this dissertation is based on films
which have been Dr. Blade cast. Dr. Blading allows s-SWCNT films of increasing thickness to be built up
by iterative methods. However, such an interative technique is not viable for blends, as the highly
soluble PCBM (or even C60) component is readily re-dissolved and removed. To overcome this,
alternative deposition methods are needed to achieve smooth films of blended heterojunctions.
Following the development of these deposition methods, optimization of the film morphology through
processing conditions and/or composition is needed in order to suppress recombination, promote
dissociation, and enhance carrier extraction rates.
8.3 Perspective The presented dissertation outlines techniques for the extraction of photocurrent from optically excited
semiconducting carbon nanotubes, and detailed understanding regarding the mechanism of the same.
82
The most natural application of this technological advance is in thin film photovoltaic devices and
photodetectors, as outlined in Chapter 1. Beyond this, the fundamental insights provided are potentially
relevant to a host of other materials systems and applications involving energy and charge transport
within discrete, quantum confined systems.
83
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APPENDIX A: s-SWCNT Solution Preparation
General s-SWCNT Isolation and Dispersion Device quality solutions of s-SWCNTs are prepared by dispersing 1mg mL-1 HiPco® single walled carbon
nanotubes (Unidym) with 4 mg mL-1 PFO (American Dye Source) in toluene using a titanium sonotrode
for 1 hour, utilizing a water bath to cool the solution.11 The resulting suspension is then centrifuged for
15 minutes at 50,000 g over an 11 cm pathlength in a swing-bucket rotor, the supernatant collected and
the pellet discarded. The supernatant is then filtered through a 5 µm Millex Millipore-SV ® syringe filter.
The resulting, dilute, solution was concentrated while simultaneously removing excess PFO by pelleting
the s-SWCNTs out of solution at 50,000 g in 11 cm long fluoropolymer centrifuge tubes in a 30 degree
fixed angle rotor held at 4 °C over a period of time approaching 90 hours for high extraction yields. The
pellet was then redispersed, and dissolved in fresh tetrahydrofuran (THF) by heating on a hotplate set to
90 °C for iterative pelleting, or redispersed into chlorobenzene to yield a stable solution. The resulting
solutions consisted of primarily the (7, 5), (7, 6), (8, 6), (8, 7), and (9, 7) chiralities of semiconducting
nanotubes wrapped by tunable amounts of PFO, with minimal quantities of metallic nanotubes,
amorphous carbon, aggregates, or residual catalyst.
(7,5) s-SWCNT Isolation and Dispersion Suspensions of 1 mg mL-1 SG65 (now SG65i) CoMoCAT single walled carbon nanotubes (SWeNT) and 2
mg mL-1 poly(9,9 dioctylfluorene 2,7-diyl) (PFO, American Dye Source) in 100 mL toluene were
ultrasonicated for 1 hour at 40% amplitude with a horn-type sonic dismembrator (Fisher Scientific,
400W). The ultrasonicated suspensions were immediately centrifuged at 50,000g for 15 min. The
collected supernatant was filtered with 5 μm Millipore Millex-SV syringe filters and concentrated via
vacuum distillation. PFO-wrapped s-SWCNTs were then removed from the supernatant by centrifuging
102
at 4 °C for 24 hours, at 50,000g. This rinsing was repeated 3x times by redispersing the s-SWCNT pellet
into tetrahydrofuran (THF), heating the solution for 5 minutes on a hotplate set to 90° C and repelleting.
The final, low PFO content s-SWCNT pellet was redispersed into ortho-dichlorobenzene (o-DCB).
Immediately before casting films, persistent aggregates were removed by centrifuging the o-DCB
solution for 10 minutes at 30,000g and extracting the supernatant for use.
(6,5) s-SWCNT Isolation and Dispersion Suspensions of 1 mg mL-1 SG65 (now SG65i) CoMoCAT single walled carbon nanotubes (SWeNT) and 2
mg mL-1 poly[(9,9 dioctylfluorene 2,7-diyl)-alt-co-(6,6’-{2,2’-bipyridine})] (PFO-BPy, American Dye
Source) in 100 mL toluene were ultrasonicated for 1 hour at 40% amplitude with a horn-type sonic
dismembrator (Fisher Scientific, 400W). The ultrasonicated suspensions were immediately centrifuged
at 50,000g for 15 min. The collected supernatant was filtered with 5 μm Millipore Millex-SV syringe
filters and concentrated via vacuum distillation. PFO-BPy -wrapped s-SWCNTs were then removed from
the supernatant by centrifuging at 4 °C for 24 hours, at 50,000g. This rinsing was repeated up to 6x
times by redispersing the s-SWCNT pellet into tetrahydrofuran (THF), heating the solution for 5 minutes
on a hotplate set to 90° C and repelleting. The final, s-SWCNT pellet contained a, roughly 3:1 BPY6,5)
ratio, and can be stably redispersed into chlorobenzene. Further removal of BPy to result in a ratio much
closer to 1:1 requires excessive dilution into either toluene or THF and aging.
103
Appendix B: Supplmentary information for chapter 3
Characterization of film morphology
Figure S1. Comparative scanning electron micrographs of SWCNT thin films. (A) Thin film of mixed-SWCNTs on ITO,
scalebar = 200 nm. (B) Thin film of semi-SWCNTs on ITO, scalebar = 200 nm.
Thickness trends of external QE and film reflectance for mixed-SWCNT
devices
Figure S2. (A) External quantum efficiency (EQE) of mixed-SWCNT/C60 heterojunction devices for increasing mixed-
SWCNT film thickness. Each EQE spectrum is offset by 2% from the previous spectrum, starting with the thinnest
film (blue curve) to the thickest film (red curve). (B) 1-Reflectance curves for each device shown in part A, data is
not offset.
Photovoltaic response of mixed-SWCNT device
104
Figure S3. Typical photovoltaic response of mixed-SWCNT devices to 17 mWcm
-2 NIR irradiance. The power
conversion efficiency is limited to ~0.001%, and is Voc limited.
Device area independence
Figure S4. Demonstration of area-independent external quantum efficiency (EQE) and a lack of current spreading.
Device diameter, d, ranged from 0.1 to 1.0 mm.
Photovoltaic spectrum
105
Figure S5. Spectrum of near-IR irradiance used for NIR photovoltaic efficiency measurements. The spectrum is that
of a 100 watt quartz-tungsten halogen lamp filtered by both 1365 nm short-pass and 1000 nm long-pass filters.
Absorption Efficiency Calculation
Figure S6. Fitting of 1 – Reflectance data. Experimentally measured data = solid blue curve. Fit Lorentzians
(corresponding to the five s-SWCNT chiralities present) = black dotted curves. The sum of the fit Lorentzians = the
solid red curve. The fit ITO loss = the dashed green curve. The combined sum of the fit Lorentzians and the fit ITO
loss = pink dash-dot curve.
Discussion
The internal QE was related to the external QE by the thin film absorption efficiency, ηA, according to
external QE = internal QE · ηA. We specifically determined ηA by measuring the spectrally resolved
reflectance from the devices stacks and fitting the s-SWCNT contribution. The experimentally measured
1 – Reflectance data was fit to the sum of (a) a broad background corresponding to ITO loss and (b) 5
Lorentzians corresponding to absorption from the 5 chiralities of s-SWCNTs.
(a) Fitting of the ITO loss: The ITO loss in the NIR originates from free carrier absorption, which
increases with increasing λ in the NIR. The modulation of the free carrier absorption with microcavity
effects (e.g. constructive and destructive interference) is manifested as a broad, asymmetric peak in the
NIR, as shown in Fig. 3B. With increasing SWCNT film thickness, the maximum of the ITO loss is red-
shifted (due to a red-shifting of the constructive interference) and the ITO loss increases in magnitude.
106
For each device stack, the ITO losses were fit as: a*(loss0(λ+Δλ)+b), where loss0(λ) was the measured
ITO loss without s-SWCNTs (Fig. 3B) and a, b, and Δλ were scalar fitting parameters to account for the
red-shifting of the microcavity effects.
(b) Fitting of the s-SWCNT absorption and ηA: The band gap absorption of each semi-SWCNT was
described by a Lorentzian of FWHM ~ 30-40 meV.
The ITO loss and the sum of the 5 Lorentzians were fit to the measured 1- Reflectance data (Fig. S6). The
sum of the Lorentzians corresponds to ηA (red solid curve) in Fig. S6.
Integrated external QE/Jsc matching The wavelength-dependent product of the external QE and the photovoltaic photon flux (calculated from Fig. S5),
integrated over the entire spectrum, matches the photovoltaic short-circuit current density Jsc = 0.8 mA/cm2 to within
5%. Thus both the external QE and Jsc are consistent with one-another.
Optical cross-section of semi-SWCNTs We determined the peak E11 optical cross-section by two methods:
(1.) The E22 cross-section of Tsyboulski et al.21
(3.5x106 cm
2mol
-1, assumed to be the natural
cross section) was corrected to account for spectral broadening, the in-plane alignment of
our films, and the increased amplitudes of the E11 transitions. Accordingly, the resulting
optical cross-section for E11 absorption in our films was calculated to be 1.16x107 cm
2
mol-1
.
(2.) The natural E11 un-polarized optical cross-section of Luer et al.25
(7x10-18
cm2
atom-1
)
was corrected to account for spectral broadening and the alignment of our nanotubes in-
plane in our films. Accordingly, the resulting optical cross-section for E11 absorption in
our films was calculated to be 1.19x107 cm
2 mol
-1.
107
These optical cross sections were in good agreement, and a value of 1.2 x107 cm
2 mol
-1 was
used.
Estimation of absorption length, LA LA at 1205 nm (the peak of the E11 transition for the (8, 6) chirality) was estimated using the E11
cross-section calculated in the preceding section, assuming a thin film density of 1.5 g cm-3
,
accounting for a PFO:s-SWCNT mass ratio of 3:1, using a (8, 6) abundance fraction of 0.32, and
using an intensity enhancement factor of 4 to account for constructive interference. LA is then
given by,
25.0
1
32.0
1
5.1
101.12
4
1
102.1
1 3
27
g
cm
mol
g
cm
mol
xLA = 21 nm. (eqn.
S1)
I. One-dimensional diffusion model
The following differential equation was used to model one-dimensional exciton diffusion,
, (eqn. S2)
where D,G, , and τ represent the one-dimensional exciton diffusion coefficient normal to the
substrate plane, the exciton generation rate via optical absorption (assumed to be spatially
uniform), the exciton density, and the exciton lifetime, respectively. We assumed that the
exciton flux at the ITO/semi-SWCNT interface was zero (no dissociation), and that the exciton
density at the semi-SWCNT/C60 interface was zero (perfect dissociation). In this case, the
02
2
G
xD
108
internal QE is equal to the ratio of the exciton flux at the semi-SWCNT/C60 interface and the
product of G and the film thickness, t. Accordingly, the thickness-dependent IQE goes as,
D
DD
L
t
L
t
t
LIQE
2exp1
2exp1
. (eqn. S3)
109
Preparation of mixed-SWCNTs
Mixed-SWCNT solutions were prepared by sonicating 1 mg/mL HiPCO in a chlorobenzene
solution of 0.3 mg/mL PFO for 45 minutes. Bundles and catalyst material were removed through
a 1 hr centrifugation at 30,000 g in a fixed angle rotor (Eppendorf FA-45-24-11-HS.) The
supernatant (top 50% of a 3 cm vial) was extracted, diluted to 50% its initial concentration with
THF and pelleted at 30,130 g. Additional PFO was removed by iterating this process. The final
PFO:mixed-SWCNT mass ratio that was used for the device studies, here, was approximately
3:1, determined from the nanotube optical cross-section and the absorption spectrum in Fig. 1C.
The exact determination of the concentration of the mixed-SWCNTs from the optical spectra in
Fig. 1C was compounded by the spectral broadening and congestion, as well as by the unknown
optical cross-section of the metallic-SWCNTs.
XI. Device characterization The external QE was measured using a home built setup consisting of a quartz tungsten halogen
lamp modulated by a chopper wheel and a monochromator. The modulated photoresponse of the
devices was measuring using a Stanford Research Systems lock-in amplifier at zero-bias in
conjunction with calibrated photodiodes (818 series, Newport). The current-voltage response
was measured using a Keithley 2636 source-meter.
110
Appendix C: Supplmentary information for chapter 5
Quantification of PFO Content We determined absorbance contributions from PFO, s-SWCNT E33 and E44, and s-SWCNT background
using the following assumptions:
- The absorbance spectrum and strength of PFO is constant whether free in solution or wrapping
a s-SWCNT.
- Constant energetic shift of E33 and E44 transition energies for each chirality with respect to those
values reported by the Weisman group.2
- Lorentzian line-shape for E33 and E44 absorption peaks.
- Constant ratio of E33 and E44 width to fit E11 width for each chirality.
- Constant ratio of E33 and E44 amplitude to fit E11 amplitude for each chirality.
Once background values, peak shift, amplitude and width values were extracted for the 43 s-SWCNT
solution, they were held constant across all solution absorbance fits. Extracted PFO absorption peaks
were correlated to an optical cross section extracted from the measurement of standard concentration
solutions created from raw PFO powders in chlorobenzene.
Figure S1. Representative fit of solution UV absorbance using predicted contributions from E33 and E44 transitions
of 5 chiralities present, absorbance background and PFO.
111
Determining Absorption Efficiency To determine the absorption efficiency of each photodiode in full consideration of optical interference,
optical reflectance of each individual device was quantified in a normal incidence configuration. To
achieve fully normal incidence, a beamsplitter was used in-line with incident beam to redirect reflected
light into a detector.
1 – Reflectance values were extracted for each device at 1195 nm, and are plotted in Figure S2.
Absorption losses at λ = 1195nm due to ITO were assumed to be constant with respect to thickness for
each dataset and fit to be approximately 30%, in good agreement with control devices fabricated in the
absence of PFO wrapped s-SWCNT films, shown in Figure S3. A polynomial fit of the overall absorption
efficiency (taken to be equivalent to the 1 – Reflectance measurement and therefore serving as an
upper limit of the absorption efficiency,) minus the ITO losses were used in conjunction with exciton
diffusion efficiencies (discussed below) in fitting thickness dependent EQE datasets.
Figure S2. Measured and extrapolated absorption efficiencies for devices cast from 22%, 36% and 43% s-SWCNT
solutions, left to right, respectively, as a function of s-SWCNT film thickness. Total absorption efficiencies plotted
represent absorption due to s-SWCNT, ITO, transmission losses and scattering losses.
Measured 1 – Reflectance values were assumed to represent absorption only; that is, scattering and
transmission losses were assumed to be negligible. To support this assumption, we utilized an
112
integrating sphere to measure total and diffuse reflectance (scattering) from s-SWNT films of various
thickness on ITO, shown in Figure S3. In all cases, contribution to light extinction from diffuse scattering
was negligible (< 1%) and the majority of specular reflection occurs in response to the ITO, presumably
at the glass/ITO interface. The measured reflectance was observed to be minimal and relatively constant
with respect to s-SWCNT film thickness (i.e. absorptance) at any given wavelength, shown at 1200nm for
illustration.
Figure S3. Measured 1 – Reflectance spectra for a control device stack, without s-SWCNTs present (blue) and for a
full device stack containing s-SWCNTs. In the absence of s-SWCNTs, a large absorption peak in the NIR is clearly
visible, resulting from free carrier absorption in the ITO.
Modeling Exciton Diffusion
Model 1, that is, the 1-D exciton diffusion model was reproduced here verbatim from other work,
included in references 8, 27 and 28. Briefly, the following differential equation describes one-
dimensional exciton diffusion,
, (eqn. S1) 0
2
2
G
xD
113
where D,G, , and τ represent the out of plane, one-dimensional exciton diffusion coefficient, the
exciton generation rate via optical absorption (which we assume to be spatially uniform), exciton
density, and the exciton lifetime, respectively. We assume that exciton flux at the ITO/s-SWCNT
interface is zero (e.g. that the ITO is a perfectly non-quenching contact, consistent with our
measurements of relatively bright photoluminescence from sub-monolayer films of nanotubes (and
thicker films) cast on ITO, and with our measurements of high absorbed photon-to-collected
electron/hole pair conversion efficiency at the E11 transition of devices based on thin films of nanotubes
lying on ITO and over-coated by C60 (7)), and that the exciton density at the semi-SWCNT/C60 interface
is zero (perfect dissociation). Accordingly, the thickness-dependent exciton diffusion efficiency goes as,
D
DDED
L
t
L
t
t
L
2exp1
2exp1
Where LD = (Dτ)0.5, is the 1-D exciton diffusion-length, and t is the s-SWCNT film thickness.
Model 2, that is, the exciton wicking model, assumes perfect exciton transfer up to a certain penetration
depth, LP, beyond which the probably that an exciton will diffuse the heterointerface is 0. Accordingly,
the exciton diffusion efficiency will vary as:
P
P
P
ED Ltt
L
Lt
,
,1
114
Appendix D: Supplmentary information for chapter 6
IQE of E11 and E11 + X transitions:
Both EQE and 1 – Reflectance (ηA) measurements were taken on each device analyzed, in
response to chopped light from a tungsten-halogen lamp spectrally filtered via a Horiba-Jvon
monochromator.
No NIR photocurrent results from absorption by the ITO; and C60 does not absorb in the
same spectral range as the (7, 5) E11, or E11 + X transitions. For these reasons, measured EQE at
the peak of both these transitions represents contribution exclusively from absorption by the (7,
5) phase (ηA_cnt). To quantify ηA_cnt , ηA spectra of control devices (containing no (7, 5) phase)
were first subtracted from ηA spectra of full devices, as mentioned in the main text and defined
as ΔηA. The resulting ΔηA spectra are approximations of ηA_cnt which also contain broad
backgrounds and offsets, resulting from the deviations outlined in the main text, briefly: (1)
slight sample to sample variations in alignment, (2) slight deviations in the optical interference
profile within the C60 and ITO films due to the presence of the (7, 5) film, (3) the addition of two
interfaces for light reflection and/or scattering to occur, (C60 / (7, 5) and (7, 5) / ITO), and (4)
sample to sample variation in the ITO free carrier absorption.
115
To account for these various sources of broad backgrounds and absolute offsets, we fit
measured ΔηA (Figure S1A, blue) as a linear sum of ηA_cnt (Fig. S1B and S1C, orange dashed)
and a smooth background (S1B, purple dashed) from 835 – 1170 nm, defined as ηA_bg. ηA_cnt was
determined by multiplying a measured (7, 5) film absorption spectra by an ‘optical interference’
constant (I), which was chosen to vary quadratically with wavelength (Figure S1B, black solid).
The orange, dashed curve was specifically determined as:
, (Eq. S1)
Where is the measured thin film absorption coefficient and
, (Eq. S2)
is the spectrally varying intensity with m2, m1 and m0 as fitting parameters. In all cases the fit m2
was small, resulting in an approximately linear . A simple quadratic expression:
, (Eq. S3)
Iexp1
01
2
2 10521052 mmmI
I
01
2
2 10521052 bbbBG
116
was sufficient to account for the smooth background (Figure S1B purple, dashed) where b2, b1
and b0 are fitting constants. In all cases, the background was small and approximately flat.
In all cases, the ηA fit (green) to the raw data (blue) was excellent. The curvature of the
background was substantially smaller than the E11 and E11 + X transitions, providing confidence
that the background subtraction does not artificially affect ηA_cnt for these transitions. Rather, the
lineshapes for the E11 and E11 + X transitions are picked out nearly perfectly for the modulated
absorption spectra.
The IQE for each transition was determined from the peak EQE of the E11 and E11+X and
the peak of ηA_cnt for each E11 and E11+X. We analyzed the IQE for the E11 transition for all 7
devices measured. We only analyzed the IQE for the E11 + X transition for the 3 thickest devices
in which the signal was the strongest. We limited ourselves to these 3 thickest devices because
the E11+X absorption is comparatively weak. However, the IQE of the E11+X transition on the
other 4 devices was qualitatively very similar.
117
Complete dataset: Each row corresponds to an independent device, and each column represents
datasets analogous to those presented in Figure S1.
118
IQE of E22 transition: We extracted the IQE of photocurrent generation from E22 absorption in a process very
similar to that described and implemented for fitting the E11 and E11 + X transitions.
The process used to extract ηA_cnt from C60 absorbance was identical to that implemented
for lower energy transitions, with the only exception being adjustment of the spectral range to
550 – 770 nm. Additionally, the spectrally varying intensity, which represents optical
interference, was again observed to be approximately linear and also observed to increase with
wavelength in this spectral range, consistent with expectations from optical transfer matrix
modeling of the system.
In determining the background absorbance (purple, dashed) b2 was found to be virtually
zero in all cases, resulting in a linear background with respect to wavelength. In all cases, the
background was found to be small and the ηA fit to the raw data was found to be excellent. Again,
the curvature of the background was observed to be significantly less than that of the E22
transition, which allows us to assert that the background subtraction does not affect ηA_cnt for the
Figure S2. (A, Left) Measured EQE (red, solid) and measured ΔηA (blue, solid determined by subtracting
average ηA of control device from measured ηA of full device.) EQE contribution from the (7, 5) phase
(red, dotted) extracted by subtracting off C60 contribution. Fit ΔηA (green) is decomposed in (B, Center)
as the sum of extracted absorption efficiency of the (7, 5) film (ηA_cnt, orange dashed) and the extracted
background (ηA_bg , purple dashed). ηA_cnt is determined by multiplying a measured film absorption
spectrum by a spectrally varying constant (I, black solid) which represents the internal optical field in
the (7,5) film. (C, Right) is a direct comparison of EQE from (7,5) component (red, dotted) against
extracted ηA_cnt (orange dashed).
119
E22 transitions. The lineshapes for the E22 transition is picked out nearly perfectly from the
modulated s-SWCNT spectrum.
Unique from fitting the E11 and E11 + X transitions, it is necessary to subtract off
photocurrent contributions from C60 absorbance in the analysis of the EQE arising from the s-
SWCNTs. To account for this, we used the lineshape of the EQE extracted from control devices
without s-SWCNTs. We scaled the C60 EQE from these devices, assuming that the EQE at λ
=450 nm in the full (7, 5)/C60 device is entirely due to the C60 component. The resulting decrease
in EQE at the E22 transition was less than 10% of the measured value, and if anything,
overestimates the EQE arising from the C60 component at the s-SWCNT E22 transition and
consequently underestimates the contribution from (7, 5) absorbance. The ultimate result would
be an underestimation of the IQE for E22 excitation. The small shifts between the peaks of the Eii
transitions in the ηA_cnt and EQE spectra in Figs. S1-2 are due to measurement-to-measurement
variation in the calibration of the monochromator and are not physical.
We analyzed the E22 IQE for the 3 thickest devices in which the signal was the strongest.
However, the IQE of the E22 transition on the other 4 devices is qualitatively similar.
120
Complete Dataset: Each row corresponds to an independent device, and each column represents
datasets analogous to those presented in Figure S2.
121
Appendix E: Supplmentary information for chapter 7
The discussion of the high-frequency hole (h,9GHz) and electron (e,9GHz) mobilities, in the s-
SWCNTs and C60 respectively, and the subsequent estimation of the free carrier yield in neat
films of s-SWCNTs relies on several assumptions. Below, we discuss these assumptions and/or
approximations and their implications:
If the scattering length in the C60 domains is larger than 10 nm the resulting high-
frequency electron mobility in the C60 layer, as measured by TRMC, will increase, with a
concomitant decrease in the mobility of holes in the SWCNTs.
In contrast, the photoluminescence (PL) quenching yield represents an upper limit for .
If the free carrier yield is smaller than the PL quenching yield the ‘true’ peak mobility
sum () would be larger, resulting in a possible increase in the high-frequency
mobilities of both carriers.
There may be unresolved fast carrier loss processes that result in the current study
underestimating the peak yield-mobility product (), which would also result in an
increase in the mobility sum ().
Should (1) the low-fluence extrapolation prove too optimistic/pessimistic, (2) the PL
quenching yield data too high/low an estimate of of the free carrier yield () in bilayer
samples, or (3) the expected 9 GHz electron mobility (e,9GHz) of 0.01 cm2V
-1s
-1 on C60
too low/high, the resulting free carrier generation yield in neat films of s-SWCNTs will
be significantly lower/higher, respectively.
122
In Figure S1 we present data where we estimate the measured high-frequency mobility as a
function of either the scattering length (for different probe frequencies) or probe frequency (for
different scattering lengths), calculated by solving the 3-dimensional diffusion equation inside a
cube of edge-length a, with reflecting boundary conditions at the sides of the cube.153,154
Figure S1. (A) Dependence of the measured high-frequency electron mobility in a C60 domain on the
scattering length, for probe frequencies of 1 THz, 32 GHz and 9 GHz. (B) Dependence of the measured
high-frequency electron mobility in a C60 domain on the probe frequency, for scattering lengths between
10 and 50 nm, in intervals of 5 nm.