Exciton Transport and Coherence
in Molecular and Nanostructured Materials
y .-0,
by
Gleb M. Akselrod
2 RA R IES
B.S., University of Illinois at Urbana-Champaign (2007)
Submitted to the Department of Physics
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2013
C 2013 Massachusetts Institute of Technology. All rights reserved
//
Signature of author.......................
Certified by...........
......................................................
Department of Physics
August 6, 2013
......................... ..
Vladimir Bulovic
Professor of Electrical Engineering and Computer Science
Thesis Supervisor
Certified by..............................
............
Erich Ippen
Professor of Physics
Thesis Co-supervisor
Accepted by...............
Krishna Rajagopal
Professor of Physics
Associate Department Head for Education
2
3
Exciton Transport and Coherence
in Molecular and Nanostructured Materials
by
Gleb M. Akselrod
Submitted to the Department of Physics on August 13, 2012, in partial fulfillment
of the requirements for the degree of Doctor of Philosophy in Physics
Abstract
Over the past 20 years a new classes of optically active materials have been
developed that are composites of nano-engineered constituents such as molecules,
polymers, and nanocrystals. These disordered materials have enabled devices such as
organic light emitting diodes, color tunable lasers, and low-cost photovoltaics, and hold
promise as a platform for all-optical computing. The defining optical and electronic
characteristic of molecular and nanostructured materials is the exciton, a bound electron-
hole pair. Excitons, which can be generated optically or electrically, are the nanoscale
carriers of energy, acting as intermediates between photons and electronic excitations.
The goal of this thesis is to add to the present understanding of two fundamental aspects
of excitons in molecular and nanostructured materials.
First we focus on the spatial transport of excitons, which is central to the operation
of photovoltaics, LEDs, and potential excitonic transistors. Despite its importance, the
precise dynamics of exciton transport and how it relates to disorder, the defining
characteristic of molecular and nanostructured materials, remains elusive. Here we
develop a technique for direct visualization
of exciton transport. We reveal
unambiguously that transport occurs by random walk diffusion and that it transitions to
subdiffusive as energetic disorder is increased. Furthermore, we harness exciton transport
in J-aggregate materials to build a platform for the enhancement of absorption and
fluorescence of organic molecules and quantum dots.
Second we turn to the interaction of excitons with optical microcavities. Using the
thermally stable excitons in molecular materials, it is possible to create strongly coupled
states of excitons and photons, known as polaritons. A longstanding research goal has
been creating polaritons at high densities in order to study condensation phenomena and
as a route to low threshold organic lasers. In this thesis we elucidate that a key
mechanism that prevents polariton condensation is exciton-exciton annihilation. In order
to circumvent annihilation, we develop a new microcavity architecture with an intra-
cavity excitation scheme and demonstrate room temperature lasing through a polariton
mode. Finally, we show superradiant lasing from an organic microcavity, an alternative
method over strong coupling that results in a substantially reduced lasing threshold.
4
Acknowledgements
As scientists we pride ourselves on our rationality, or at the very least the pursuit of
it. But often the most important decisions we make about research (and life in general)
are done more emotionally. This was certainly the case when I came to Vladimir BuloviP
and the rest of ONE Lab more than five years ago. I didn't know anything about organic
electronics or excitons, but I could tell this was a place filled with brilliant, enthusiastic,
and most importantly happy people, and I knew I could thrive in this environment. My
first thanks go to my adviser and mentor Vladimir Bulovic, who made ONE Lab and
everything in the following pages possible. His unwavering enthusiasm, intellectual
clarity, and support for his students are a rare combination in academia, and I was
fortunate to be a part of it.
My first on-the-ground experience in ONE Lab began humbly with Yaakov
Tischler showing me how to measure a spectrum. I thank him for training me by
throwing the kitchen sink at me, for introducing me to polaritons, and for his boundless
energy. Thank you to Scott Bradley for being my mentor in those early years and for
seemingly knowing everything.
Many late night laser measurement extravaganzas happened with Liz Young. I
thank Liz for being my partner-in-crime in the sometimes-dark world of polaritons and
for being a great friend. Much of our amazing optics lab would not be possible without
Kathy Stone, whose technical expertise on all laser matters I value greatly. To the rest of
the members of ONE Lab, both past and present: thank you all for making my time at
MIT a blast. I loved coming to work everyday and that was only possible because I had
amazing lab mates. Monica Pegis kept ONE Lab running, and I am grateful to her for
putting up with my occasional lack of organization with respect to packing slips.
My time at MIT was enriched by my collaboration and friendship with Will
Tisdale. I thank him for his boundless enthusiasm, clarity of thought and for calling me
5
out when I am not making any sense. I am indebted to Marc Baldo who organized the
Center for Excitonics, which became my intellectual home over the past years. I thank
him for his intellectual honesty, for always being constructively critical, and for being a
second informal thesis adviser.
The successes of the past year would not have been possible without Parag
Deotare, who never had doubt that we would do great and interesting things together. The
collaboration and friendship that we started this year is just the beginning. Parag and I
were fortunate to be joined by Vinod Menon, forming a fun and productive collaboration
that ended with the diffusion imaging work, although it was miles away from where we
started.
To my theory collaborators at Harvard, Semion Saikin, Stephanie Valleau, and
Alan Aspuru-Guzik: I thank you to your dedication to J-aggregates and insightful
conversations, and for helping to bridge the gap between experiment and theory that we
often avoid. I also had the pleasure of working with Brian Walker from the Bawendi
group, who taught me a lot of the chemistry knowledge I was sorely lacking. I am also
grateful for my other collaborators at MIT: Dylan Arias, Raoul Correa, Moungi Bawendi,
and Keith Nelson. Isaac Chuang was my research adviser during my first year at MIT,
and I am thankful to him for being a brilliant leader and for being supportive in finding a
new group.
The wide variety of projects and ideas I was able to explore would not have been
possible without the generous support of the Hertz Foundation Fellowship, endowed by
Nathan Myhrvold. The Hertz Foundation not only provided financial freedom but also
gave me the community of Hertz Fellows, which has enriched my graduate school
experience immensely. I acknowledge additional financial support from the National
Science Foundation Graduate Research Fellowship.
To my friends at 210 Enterprises, Greg and Ulric: this thesis is very much a product
of 210 and I thank you for years of loyal friendship. To Lauren: your love and support
make me a happier person, and I couldn't ask for anything more. Thank you to my family
for giving me every opportunity in life and for being encouraging along the way. In
particular I am thankful to my father who introduced me to research when I was still in
high school and who taught me to think like a scientist from an even earlier age.
Table of Contents
A bstract.............................................................................................................
3
A cknow ledgem ents..............................................................................................
4
Table of Contents ...................................................................................................
6
1 Introduction........................................................................................................
11
Thesis organization ...............................................................................
12
1.1
2 Excitons in Molecular and Nanostructured Materials ................................
14
2.1
Overview .................................................................................................
14
2.2
M olecular excited states ........................................................................
14
2.3
Singlet and triplet states ...........................................................................
16
2.4
Excitons...................................................................................................
17
2.5
Exciton transport .....................................................................................
18
2.5.1
Singlet transport .............................................................................
20
2.5.2
Triplet transport................................................................................
21
2.6
Excitonic materials utilized in this thesis................................................
22
2.6.1
M olecular crystals (tetracene)..........................................................
22
2.6.2
Small molecule amorphous solids (Alq3:DCM).............................
23
2.6.3
J-aggregates.....................................................................................
24
3 Visualization of Exciton Diffusion in Space, Time, and Energy .................
29
3.1
Overview .................................................................................................
29
3.2
Introduction............................................................................................
29
3.3
M ethods summ ary ..................................................................................
31
3.4
Results and discussion...........................................................................
31
3.5
Conclusion...............................................................................................
38
Table of Contents
7
3.6
Sam ple fabrication..................................................................................
38
3.7
Sample Characterization .......................................................................
40
3.7.1
Determination of crystal axes...........................................................
40
3.7.2
Absorption and emission spectrum .................................................
41
3.7.3
Fluorescence lifetim e .....................................................................
43
Diffusion imaging optical setup .............................................................
44
3.8
3.8.1
3.9
Spatial resolution of imaging setup ..................................................
47
Data analysis ..........................................................................................
47
3.9.1
The diffusion equation .....................................................................
47
3.9.2
Extracting the singlet exciton distribution ......................................
49
3.9.3
Inferring triplet density from singlet distribution.............. 50
3.9.4
Broadening of PSF due to dynamic redshift ....................................
3.10
52
Supplementary results and discussion..................................................
52
3.10.1
Energy dependence of emission lifetime ......................................
52
3.10.2
Excitation energy dependence of exciton diffusion ......................
55
3.10.3
Diffusion near crystal edge ............................................................
55
3.10.4
Radiative energy transfer ...............................................................
56
4 Disorder-Driven Exciton Transport in Quantum Dot Assemblies.............
58
4 .1
Overview ...............................................................................................
. . 58
4.2
Introduction ............................................................................................
. 58
4.3
M ethods Sum m ary .................................................................................
60
4.4
R esults and D iscussion...........................................................................
61
4 .5
C onclusion .............................................................................................
5 Harnessing Exciton Transport: The Excitonic Antenna .............................
. . 66
68
5.1
O verview ...............................................................................................
. . 68
5.2
Introduction ............................................................................................
. 68
5.3
Fundamentals of absorption cross-section ............................................
69
5.4
Existing approaches for absorption enhancement ..................................
70
5.5
Concept: the excitonic antenna ..............................................................
70
5.6
Excitonic antenna continuum model......................................................
71
5.7
A test system: J-aggregate antenna and DCM acceptors ............
74
8
Table of Contents
5.7.1
TCJ-DCM sample preparation ............................................................
75
5.7.2
TCJ-DCM sample characterization.....................................................
76
5.8
Optical measurement setup ......................................................................
79
5.9
Enhancement of DCM on TCJ...................................................................
79
5.10
Time-resolved measurements of DCM emission .................
82
5.11
M odeling the J-aggregate DCM system...................................................
84
5.12
Enhancement of Single QD fluorescence.............................................
87
5.12.1
Sample preparation........................................................................
87
5.12.2
Experimental setup ........................................................................
88
5.13
Results on single QD enhancement......................................................
90
5.14
Conclusion.............................................................................................
93
6 J-aggregate Critically Coupled Resonator for Fluorescence Enhancement. 94
6.1
Overview .................................................................................................
94
6.2
Introduction ............................................................................................
94
6.3
M ethods summary ...................................................................................
96
6.4
Results and discussion.............................................................................
97
6 .5
C on clu sion ................................................................................................
7 Strong Coupling in J-aggregate M icrocavities ..............................................
103
105
7 .1
O v erv iew ..................................................................................................
10 5
7.2
Introduction to polaritons .........................................................................
105
7.2.1
The optical microcavity.....................................................................
106
7.2.2
M icrocavity polaritons ......................................................................
108
7.2.3
Strong coupling using organic materials...........................................
109
7.2.4
Polariton lasing..................................................................................
110
7.3
Exciton-exciton annihilation in polariton microcavities ..........................
112
7.4
M ethods summary ....................................................................................
113
7.5
Results and discussion..............................................................................
115
7.6
C on clu sion ................................................................................................
119
8 Lasing Through a Strongly-Coupled Mode by Intra-Cavity Pumping.......120
8.1
O verv iew ..................................................................................................
120
Table of Contents
9
8.2
Introduction ..............................................................................................
120
8.3
M ethods sum m ary ....................................................................................
122
8.4
Results and discussion..............................................................................
125
8.5
Conclusion................................................................................................
128
9 Superradiant Lasing from Organic Microcavity ...................
129
9.1
O verview ..................................................................................................
129
9.2
Introduction ..............................................................................................
129
9.3
M ethods sum m ary ....................................................................................
131
9.4
Results and discussion..............................................................................
133
9.5
Conclusion................................................................................................
139
9.6
D etailed experim ental m ethods ................................................................
140
9.6.1
M easurem ent of pum p energy density ..............................................
140
9.6.2
Kerr shutter for time-resolved photoluminescence ...........................
140
9.6.3
Fourier space imaging of angular-resolved emission........................
142
9.7
Threshold reduction for varying cavity lengths .......................................
143
9.8
Sim ulation of conventional lasing............................................................
143
10 Conclusion and O utlook ................................................................................
148
10.1
O utlook for exciton transport .................................................................
148
10.2
Outlook for excitons in m icrocavities ....................................................
149
R eferences ............................................................................................................
151
C urriculum V itae ................................................................................................
166
1 Introduction
The photonics revolution of the past 60 years has given us transformative devices
such as light-emitting diodes, lasers, and solar cells, imaging sensors, and photodetectors.
These traditional devices rely on highly ordered and pure semiconducting materials and
achieving such high order requires energy intensive and expensive fabrication techniques
such as crystal growth and molecular beam epitaxy. Over the past 20 years a new class of
optically active materials have been developed which are composites of nano-engineered
constituents such as molecules, polymers, nanocrystals. These nanostructured materials
hold a number of advantages compared to inorganic semiconductors. The optical
properties are mostly determined by the properties of the constituent molecules or
nanocrystals, the variety of which is limited only by the enormous repertoire of synthetic
chemistry. Furthermore, these materials are amenable to low-temperature, large area, and
inexpensive deposition techniques on a wide range of substrates.
The defining optical and electronic feature of molecular and nanostructured
materials is the exciton, a bound pair of an excited electron and a hole [1]. Excitons can
be generated electrically or optically, manipulated spatially and energetically, and then be
converted back to electricity or light. In this sense, excitons are nanoscale packets of
energy that act as intermediates between photons and matter. Due to the weak van der
Waals forces joining the material constituents, excitons tend to be highly localized, with
the electron and hole located on the same molecule or nanocrystal. This confinement
makes excitons stable at room temperature and insensitive to the high degree of disorder
inherent to nanostructured materials.
The first technological success of excitonic materials has been the development and
commercialization of organic light emitting diodes [2], [3]. Current research on excitonic
materials is incredibly diverse, with work on thin film photovoltaics [4], photodetectors
[5], [6], lasers [7], [8], and sensors [9], among other devices . However, the application of
excitonic materials is not limited to producing the next generation of existing devices. For
example, all-optical switching is a long sought technology but is difficult to realize
Introduction
12
because photons are non-interacting particles. The nature of the exciton as a light-matter
intermediate makes them amenable to manipulation by electric fields, yet they retain the
ability to be readily converted to photons. This property makes excitons ideal as the basis
of all-optical or electro-optical switches. In the "excitonic transistor" [10], [11],
manipulation of excitons spatially through energy gradients offers the tantalizing
possibility of nanoscale transistors with a naturally built-in optical interface.
Central to the operation of photonic devices based on nanostructured materials is
the ability to manipulate the lifecycle of an exciton: from generation, to transport, to its
eventual demise as a photon or as electrical charges. For example in solar cells, the
transport of photogenerated excitons to a charge-separating interface is a key step that
determines device efficiency [12]. In contrast, in light emitting diodes, diffusion of
electrically generated excitons to quenching interfaces or with each other is a loss
mechanism that must be managed [13]. Yet despite the importance of exciton transport,
fundamental questions remain about how transport relates to nanoscale disorder, the
defining characteristic of nanostructured materials.
Along with device applications, the fundamental physics of collective exciton
interactions is similarly rich. The interaction of light and excitons can be extended to the
regime of strong coupling, resulting in coherent light-matter states known as excitonpolaritons. Polaritons forned by coupling of microcavity photons to excitons offer a rich
test-bed for collective exciton physics, such polariton condensation, superfluidity, as well
as possible applications such as optical parametric amplification and low-threshold lasing
[14], [15]. These phenomena have been studied extensively in inorganic semiconductors
at cryogenic temperatures, but molecular and nanostructured materials can reach the
strong light-matter coupling regime at room temperature because localized excitons are
thermally stable [16], [17].
1.1
Thesis organization
The main aim of this thesis is to add to the present understanding of the
fundamental processes governing excitons and to offer a number of novel applications of
excitonic materials. The thesis is organized into two parts. Chapters 2-5 will focus on the
fundamental properties of exciton transport in nanostructured materials and how transport
Introduction
13
can be harnessed for photonic applications. Chapter 2 will introduce the basic concepts of
exciton generation, transport, and decay and review the material systems that will be
studied in this thesis, including molecular crystals, amorphous molecular materials, and Jaggregates. Chapter 3 will present a direct spatial, temporal, and spectral visualization of
exciton transport in tetracene, an archetype molecular material using an imaging
technique that we developed for this work. Chapter 4 will extend the exciton imaging
technique to the study of exciton diffusion in quantum dot thin films. In Chapter 5, we
will propose and demonstrate the excitonic antenna, an approach for harnessing the large
diffusion length in J-aggregate thin films for the enhancement of molecular absorption
and fluorescence.
Chapters 6-9 will focus on the interaction of excitons with optical resonators.
Chapter 6 will extend the excitonic antenna concept by integrating J-aggregate thin films
with a resonant optical structure than enhances absorption and localizes optical energy in
the form of excitons with greater than 90% efficiency. Chapter 7 will present work on the
strong coupling of J-aggregate excitons to optical microcavities and show the hurdles that
must be overcome to achieve polariton lasing using organic materials. In Chapter 8, we
will present a cavity architecture that circumvents the limitations of J-aggregates and
demonstrate the first lasing through a strongly-coupled mode in a J-aggregate-based
microcavity. Chapter 9 will demonstrate a superradiant organic laser, the result of
collective emission from excitons at high density that are weakly coupled to a
microcavity. Chapter 10 offers concluding remarks and outlook for future work.
2 Excitons in Molecular and Nanostructured
Materials
2.1
Overview
The goal of this chapter is to discuss general aspects of excitons-in particular their
generation, transport, and decay and to summarize a subset of the excitonic materials
relevant to this thesis. The discussion here will be limited to the concepts critical to this
thesis, and more comprehensive reviews can be found elsewhere [1]. More detailed
concepts particular to each project will be introduced in the appropriate chapter.
2.2
Molecular excited states
To understand the origin and properties of an exciton, we will first consider the
excited states of isolated molecules. Many of the same concepts, in particular as it relates
to exciton transport, also hold true for nanocrystalline solids such as quantum dot thin
films.
Electronic transitions in molecules occur between the highest occupied molecular
orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The ground state
molecule contains two electrons in the spin singlet state in the HOMO level. While
orbitals and the transitions between them can be calculated directly for atoms, the
complexity of the vibrational and rotational states of molecules prevents us from doing
the same. As a result, the picture of molecular electronic transitions relies on the FrankCondon principle. In this approximation the heavy nuclei are considered to be fixed on
the time scale of electronic transitions, which occur on the time scale of -1 fs. In contrast,
the vibrational transitions occur on the scale of ~100 fs. As a result, we can consider an
electronic excitation to undergo four steps in its lifetime in the most simple case, as
shown in Figure 2-1: (1)
Upon absorption of a photon, an electron in the HOMO state
15
Ex-citons in Molecular and NanostructuredMaterials
(So) and in the ground vibrational state is promoted to an excited electronic and
vibrational state. (2) Because of the shift in the electron density, the nuclei are no longer
in the equilibrium positions and hence vibrational relaxation occurs to the ground
vibrational level of the excited electronic state (Si). (3) If we consider only radiative
decay of the excited state, the S, state will relax back down to the So state by emitting a
photon within a typical lifetime for organic molecules of -5 ns. (4) The final step is the
rearrangement of the nuclei in the ground electronic state, returning the molecule to the
original state. The symmetry of the vibrational relaxation after absorption and after
emission results in the mirror symmetry in the absorption and emission spectra typical of
organic molecules (Figure 2-1). The redshift between absorption and emission is known
as the Frank-Condon shift (or sometimes the Stokes shift), and is typically ~0.3 eV
comparable to the emission linewidth, making organic molecules nearly transparent to
their own radiation.
Vibrational states
Excited electronic
state S1
0)
0
Emission
0Absorption
CC
Ground electronic
state__
s oW
avelength,
X
Configuration coordinate
Figure 2-1 1 Molecular electronic and vibrational transitions in the Frank-Condon
approximation. Typical electronic transitions are -1 eV and typical vibrational level
spacing is ~0.1 eV. Right panel shows the typical absorption and emission spectra for an
organic molecular material.
16
.Ex-citons in Molecular and NanostructuredMaterials
2.3
Singlet and triplet states
The probability of transition between two states is proportional to the transition
square of the dipole moment between the initial and final electronic wavefunction
where
P=V
er Ie)
(2.1)
The transition probability also depends on the overlap of the vibrational states in each
electronic state, S(v,v')
. The absorption and emission of photons (transitions up or
down in electronic energy) are both governed by this same principle.
Besides wavefunction overlap, the spin state of the ground state and excited state
electrons determines whether emission is possible.
Due the exclusion principle, the
ground state electron spin configuration is in the singlet state
Co
=
[ [1
-
(2.2)
which has a total spin of S =0 . Electronic transitions between the ground and excited
state change the electron orbital angular momentum state but do not affect the spin state.
Therefore the excited electronic state is also (initially) in the S = 0 state. In certain
materials, the spin state can be altered by spin-orbit coupling due to the presence of a
heavy metal. The singlet state can then become mixed with triplet spin configuration,
which has a total spin S = I and has three possible states
o]= 1k[ ll)+ VP)]
'P)
=
(2.3)
A transition from the spin singlet state to the spin triplet state, or vice versa, is known as
inter-system crossing (ISC). The energetic driving force for ISC is an electron-electron
interaction that breaks the degeneracy of the singlet and triplet excited state energies. The
splitting occurs because the singlet spatial wavefunction is symmetric under exchange,
while the triplet spatial wavefunction is antisymmetric under exchange. Consequently
electrons in the triplet excited state experience less Coulomb repulsion, and this state has
Excitons in Molecular andNanostructuredMaterials
17
a lower energy (Figure 2-2). The singlet-triplet splitting is a particular feature of
molecular materials, which have localized excitations thus increasing the Coulomb
interaction.
Decay from the singlet excited state to the ground excited state, known as
fluorescence, is spin allowed, occurring rapidly with a typical lifetime ofT~ 5 ns (Figure
2-2). In contrast, transition from the triplet excited state to the singlet ground state is only
weakly allowed due to the spin restriction, with only second order effects contributing to
the emission. This emission is known as phosphorescence, and occurs with a typical
lifetime of ~ ps.
Singlet S = 0Qnter-system
crossing
S = 1 Triplet
Fluorescence
Phosphorescence
Singlet S = 0
Figure 2-2 1 Typical energy diagram for a molecule which has fluorescent and
phosphorescent transitions.
2.4
Excitons
So far we have discussed electronic excited states when the molecules are in
isolation. When the molecules are part of a solid, interactions between neighboring
constituents will determine the behavior of the excited states. An exciton is the bound
state of the excited electron and the ground state "hole", the absence of a ground state
electron, which has a net positive charge (Figure 2-3). Due to the weak coupling between
neighboring molecules, excitons are usually localized to one or a small number of
molecules and are known as Frenkel excitons. Consequently the Coulomb binding energy
of excitons in molecular solids is large (-200 meV), making Frenkel excitons stable at
room temperature. In contrast, in inorganic semiconductors such as silicon, excitons are
Excitons in Molecular and NanostructuredMaterials
18
highly delocalized due to the covalently bonded crystal structure, allowing large electron
hole separation and easy splitting of the electron and hole at room temperature. These
states are known as Wannier-Mott excitons.
Exciton
(bound electron-hole pair)
LUMO
HOMO
Spin 0
singlet
Spin 1
triplet
Figure 2-3 I Singlet and triplet Frenkel excitons in a molecular solid. (Adapted from [18])
2.5
Exciton transport
Transfer of excitons to neighboring molecular sites can occur by two mechanisms:
Dexter energy transfer and F6rster resonant energy transfer (FRET). Dexter transfer is the
simultaneous exchange of two electrons (Figure 2-4), the rate of which depends on the
wavefunction overlap between the donor and acceptor molecules. FRET is a near-field
dipole-dipole interaction, which depends on the radiative properties of the donor, the
absorption of the acceptor, and the distance between them. FRET is the dominant energy
transfer mechanism for radiative singlet excitons, while Dexter transfer dominates for
triplet excitons, which are spin-forbidden from radiating. Both transfer mechanisms are
short range, and hence exciton transport is predicted to occur by hopping, resulting in
random walk diffusion, although experimental verifications have been lacking to this
point.
Excitons in Molecular and NanostructuredMaterials
19
Dexter transfer
Simultaneous exchange of electrons
<1 n
Donor
Acceptor
Forster transfer
Dipole-dipole coupling
-5 nm
Donor
Acceptor
Figure 2-4 I Two types of excitonic energy transfer present in molecular solids.
Following the description of Yost et al. [19], the hopping rate (for FRET or Dexter
transfer) between a donor molecule and acceptor molecule can be approximated by
Fermi's Golden Rule
k
=
V
(FCWD)
(2.4)
where VJ1 is the electronic coupling between donor and acceptor. FCWD is the FrankCondon weighted density of states, which depends on the overlap between the density of
states of the donor and acceptor. The FWCD can by approximated by considering the
absorption spectral shape (Id)
and emission spectral shape (e)
of the donor and
acceptor, respectively. If both the emission and absorption spectra are approximated to be
have a Gaussian width a-, then
Excitons in Molecular andNanostructuredMaterials
FCWD= I
where
Ada
"
=
-exp_
2a
20
A(2.5)
4(52
is the energy difference between the center of the donor emission spectrum
and the acceptor absorption spectrum. The hopping rate then is seen to depend on both
the relative orientations and distances between the molecules (which determines Vda ) and
the energetic landscape of the material (which determines the FCWD). The differences
between singlet hopping and triplet hopping are then contained in the details of the
electronic coupling parameter Vda'
2.5.1
Singlet transport
The dipole-dipole interaction term is given by
VF
N2
da
(2.6)
3
where R is the center-of-mass separation between the donor and acceptor, A is the
magnitude of the transition dipole moment, n is the effective refractive index of the
medium, and
K
is a parameter that depends on the relative orientation of the donor and
acceptor dipoles and ranges between 0 and 2. This expression is the familiar FRET
interaction energy, which is an approximation that ignores second order effects that occur
when the donor-acceptor separation is smaller than the size of the transition dipole. The
FRET rate is then given by
2
2
do
F
3/2
=kexpi
n 4R
4
(2.7)
d.
4U2
The FRET hopping rate can be related to the diffusivity D by
D=
(2.8)
z
where z = 1,2,3 is the dimensionality of diffusion. The diffusion length
LD
is defined as
the root mean square displacement of an exciton from the point of generation within its
lifetime r
(2.9
LD
=
(2.9)
LExcitons in Molecular and NanostructuredMaterials
21
The exciton lifetime, in turn, depends on the radiative and nonradiative recombination
rates with 1 / -r = krd + k
and the radiative rate is
3c 3
krad
k 1
4Ep2
4E~u
2
(2.10)
where Es is the exciton energy. The diffusion length as defined above only has
significance in the situation where the diffusivity is not dependent on time. As will be
seen in later chapters, this assumption is not valid in systems with high degrees of
energetic disorder. The diffusion length of singlet excitons is ultimately limited by a
trade-off, as discussed by Yost et al. [19]: The hopping rate is increased with increasing
transition dipole moment p. However increasing the dipole moment decreases the
radiative lifetime, which limits the exciton lifetime, and consequently diffusion. As a
result the singlet diffusion length is fundamentally limited to 100-200 nm, while in most
actual materials the value is 10-20 nm [12].
2.5.2
Triplet transport
Triplet excitons cannot be transferred by dipole-dipole coupling due to their weak
transition dipole moment y. Instead energy transfer can occur by the simultaneous
exchange of two electrons, one between the ground states of the donor and acceptor, and
the other between the excited states of the donor and acceptor [20]. The Dexter coupling
is given by
Vd,
= V, = Aexp(-tR)
(2.11)
where R is the center-of-mass separation of the donor and acceptor, and q is the spatial
extent of the wavefunction overlap, and A is a scaling prefactor [21]. In contrast to the
1 / R' distance dependence of the FRET rate, the Dexter rate is exponentially sensitive to
donor-acceptor separation. In materials where singlet excitons are prevalent, the FRET
hopping rate is typically orders of magnitude larger than the Dexter hopping rate. The
Dexter rate, however, is not limited by the exciton radiative lifetime, and no trade-off
exists as discussed for singlet diffusion. The triplet diffusion length is consequently much
larger, exceeding 1 tm is some materials [20].
Excitons in Molecular and NanostructuredMaterials
2.6
22
Excitonic materials utilized in this thesis
Excitonic materials can be composed of a wide range of constituents, including
small molecules, polymers, and nanocrystals. The work in this thesis utilizes a set of
excitonic material systems, each chosen for its specific optical and excitonic properties.
Here we briefly discuss each, with more details introduced in the appropriate chapters.
2.6.1
Molecular crystals (tetracene)
One of the first excitonic materials to be studied were molecular crystals composed
polyacene molecules such as tetracene and anthracene [1]. Interest in molecular crystals
as an archetype organic solid stemmed from their high crystalline order, high
luminescence quantum efficiency, and good photostability, among other properties. In
Chapter 3 we use tetracene crystals to study the transport of triplet excitons. Triplet
excitons are the dominant energy carrier due to the efficiency of singlet fission in
tetracene, a process that splits one singlet exciton into two triplet excitons each with half
of the singlet energy. The exciton transport length in tetracene is known to be long [22]
compared to amorphous organic solids due to the high crystalline order and high purity.
Organic crystals such as tetracene are typically grown by thermal sublimation [23]
making the nanoscale control of their thickness and lateral dimensions extremely
challenging.
Figure 2-5 1 Tetracene crystal structure.
23
IExcitons in Molecular andNanostructuredMaterials
2.6.2
Small molecule amorphous solids (Alq3:DCM)
Small molecule amorphous solids lie at the opposite side of the crystallinity
spectrum. This class of materials is composed non-polymeric luminescent and absorptive
molecules with little orientational order between neighboring molecules. A prototypical
system from this material class is the Alq3:DCM blend in the which DCM dye molecules
are doped into a host matrix of Alq 3 molecules. Excitons generated on Alq 3 and emitting
at ~470 nm can be efficiently transferred via FRET onto the dopant DCM molecules
which have an absorption peak centered at ~470 nm (Figure 2-6). This energy transfer
scheme was utilized to achieve the first solid state organic lasing structure [24].
DCM is a robust dye with high luminescence quantum efficiency which was
previously used in liquid dye lasers [25]. In this thesis we utilize DCM in isolation as an
efficient exciton acceptor (Chapters 5 and 6) and as the excitonic material to achieve
superradiant lasing (Chapter 9). In Chapter 8 we use DCM doped in Alq 3 as an intracavity pump source for making a cavity which lases through a strongly-coupled mode.
DCM
Alcq
N C
L
[J
CN
N
I
1I
1
H3C
0
CH
H
N
'CH 3
FFNET
If
Figure 2-6 I Molecular structures of Alq 3 and DCM and the energy diagram showing
FRET from the host (Alq 3) to the guest (DCM). DCM is used either in isolation or as part
of the guest-host system.
Excitons in Molecular and NanostructuredMaterials
2.6.3
24
J-aggregates
J-aggregates are self-assembled aggregates of organic dye molecules in which the
interaction of the transition dipole moments causes a narrow and intense absorption
feature to form [26]. J-aggregates have the properties of both classes of molecular
materials discussed so far, having high crystalline order on the nanoscale yet little order
on the microscale [27]. These aggregates can be deposited into a thin film having
absorption coefficients of more than a = 106 cm-' [28]. This high absorption and narrow
linewidth make J-aggregate materials ideal for the energy focusing schemes described in
Chapters 5 and 6 and for achieving strong light-matter coupling in optical microcavities
as discussed in Chapters 7 and 8.
A typical absorption spectrum for a cyanine dye (TDBC) in the monomer and Jaggregate form is shown in Figure 2-7. The monomer absorption is broad (AA =50 nm )
and centered at A =520 nm , while the J-aggregate peak significantly narrowed (
AA
12 nm ) and is red shifted relative to the monomer.
TDBC
1.0
CN
J
"0.8
0.40.2-
0.6
400
46D
Soo
5SD
600
6SD
\tfeength (rm)
Figure 2-7 I Absorption of the cyanine dye TDBC in the monomer and J-aggregate form.
(From Scott Bradley and Yaakov Tischler).
The physics of J-aggregates can be understood by first considering dimerization of
just two monomers (Figure 2-8). When molecules are in close proximity, their transition
Excitons in Molecularand NanostructuredMaterials
25
dipoles can couple strongly enough to produce new energy states either above or below
the monomer dipole energy. The energy of the new states depends on the relative
orientation of the monomers as depicted in Figure 2-8. In the tip-to-tail orientation the
state with the non-zero transition dipole (with in-phase oscillators) is lower in energy
relative to the monomer energy. The dipole moment of the dimer state is P=
po
where pu
0 is the transition dipole of the monomer. This tip-to-tail interaction is what
gives J-aggregates their optical properties.
monomer
H-dimer
monomer
J-dimer
I
2U
2U
p=
mm,
p"= r2,
Figure 2-8 1 Two types of dimerization. The tip to tale interaction (J-type) lowers the
dimer energy relative to the monomer.
The dimerization picture can be extended for the case of N coupled molecules. The
lowest energy excited state corresponds to all transition dipoles of the individual
monomers being in phase. The J-aggregated system can be modeled as N coupled twolevel systems by considering the Hamiltonian (following [29] )
N
H= h=h
N
o 5b
n=I
+h
V,(Lb> +bb,)
n~z=1
n ,f
(2.12)
Excitons in Molecular andNanostructuredMaterials
26
where (o is the transition frequency of the nh molecule, b and b are the exciton
creation and annihilation operators on the n"' molecule, and Vnin is the dipole-dipole
coupling rate between the n'
and rnth molecule. Considering only nearest neighbor
interactions, the Hamiltonian can be diagonalized to obtain the energies of the new
eigenstates
Q
=o+2Vcos (fik
k
N+l1
(2.13)
where o is the frequency of a monomer transition, V is the nearest-neighbor coupling
rate, and k is the label for each state. The distribution of oscillator strength for each state
is given by [29]
p(k)=
2
N+1
1(1) Cot
2
irk
[2(N+1)_
(2.14)
For large N, most of the dipole moment strength is contained in the k = I state and the
above expression simplifies to
p(k = 0)=
O.81(N+1)p 0
(2.15)
This state is referred to as the J-aggregate state. The dipole strength contained in the
higher-k states is what gives the J-aggregate absorption spectrum its distinctive blue tail
in absorption and corresponding red tail in the emission. The typical number of
coherently coupled molecules at room temperature is N ~ 15 (Figure 2-9) with higher
values obtained with decreasing temperature [30]. It is important to point out that
although peak dipole moment is increased, to spectrally integrated absorption per
molecule remains constant upon J-aggregation.
Excitons in Molecular and NanostructuredMaterials
Monomer
Localized exciton
/10
J-aggregate
27
J-aggregate
Nc
coherently coupled molecules
2
=0.8
1(N
+I)pY
Figure 2-9 1 J-aggregation results in delocalization of the exciton and an increase in the
peak transition dipole moment proportional to the number of molecules.
A consequence of the delocalization of the exciton is the increased coupling to
neighboring molecules, resulting in rapid incoherent exciton transport of the coherent
exciton (Figure 2-10). Among organic materials J-aggregates are known to have some of
the longest exciton transport distances [31] of 50-100 nm, as we will show in Chapter 7.
The long transport lengths are attributed to the enhancement in FRET rate that occurs
when the donor and acceptor excitonic states are coherently delocalized, according to the
multichromophoric theory of energy transfer [32], [33].
I
I
T
1
Excitons in Molecularand NanostructuredMaterials
Figure 2-10 | Schematic of exciton diffusion in J-aggregate thin films, showing that
coherent exciton with a size of ~4 nm can propagate over a much larger incoherent
diffusion domain of ~50-100 nm.
28
Visualization of Exciton Diffusion in Space, Time, and Energy
29
3 Visualization of Exciton Diffusion in
Space, Time, and Energy
3.1
Overview
Transport of excitons is at the core of photosynthesis[34], [35] and it similarly
governs the operation of a wide array of nanostructured optoelectronic devices including
molecular, polymeric and colloidal-quantum-dot solar cells [12], [36], light emitting
diodes [37], and excitonic transistors[ 11]. Mapping and manipulating the flow of excitons
in such systems can enhance device performance[36] and can lead to development of
next-generation excitonic technologies. However, the precise dynamics of exciton
transport and how it relates to the nano-scale disorder, the defining characteristic of
molecular and nanostructured materials, remains elusive. In this chapter we present in
unprecedented detail a spatial, temporal, and spectral visualization of exciton transport in
molecular crystals and compare them to measurements in disordered films. Using
tetracane as an archetype organic semiconductor, we image time-resolved exciton
transport, showing that it follows random walk diffusion, with a clear transition from
normal to sub-diffusive transport as exciton traps are filled. Observation of the timedependent exciton dynamics is uniquely enabled by our measurement technique, which
maps the temporal exciton energy distribution of both mobile and trapped excitons. Our
measurements can be used to screen the properties of excitonic materials and to inform
their design. In particular, the effect of morphological disorder on the exciton energy
landscape and exciton transport dynamics can now be directly investigated.
3.2
Introduction
Energy transport in nanostructured thin films and crystals (such as those composed
of molecules, polymers and colloidal quantum dots) occurs by the motion of tightly
Visualization of Exciton Diffusion in Space, Time, andEnergy
bound electron-hole pairs, known as excitons [1].
30
For example, in molecular and
polymeric solar cells, excitons are generated by absorption of sunlight, and must be
moved efficiently to an interface where electron and hole are separated to produce charge
buildup, leading to photovoltage and photocurrent. Likewise, the efficient transport of
photogenerated excitons from the light-harvesting complex of a plant to the reaction
center is at the core of photosynthesis [34]. Transport of excitons in such systems is
thought to occur by hopping of the localized excitation to a neighboring molecular site,
resulting in random walk diffusion[19], [38]. Two types of hopping mechanisms are
possible: For excitons in the radiative spin singlet state (electronic spin of zero), hopping
occurs by Frster energy transfer (FRET), a near-field dipole-dipole interaction, with
interaction distance on the order of 5 nm. Excitons that are in the triplet state (electronic
spin of one) are spin-forbidden from emitting, and hence triplet exciton hopping is
dominated by Dexter energy transfer, the simultaneous exchange of two electrons
between nearest molecular neighbors.
While band transport of excitons has been studied extensively[39-41], mostly
indirect methods have been utilized to measure the exciton propagation in materials with
localized excitons due to their shorter propagation lengths. These techniques include
optoelectronic device modeling[42], exciton quenching at a surface or an interface[12],
[37], [43], [44], and exciton-density-dependent exciton-exciton annihilation[45]. Such
approaches produce an average "diffusion length", LD, defined as the mean displacement
of an exciton during its lifetime. However, these methods rely on assumptions about the
exciton interaction distance with an interface or with other excitons. A limited number of
studies have directly probed exciton transport spatially[46-48] but the nature of transport
and how it evolves in time remains elusive.
In the present work we spatially, temporally and spectrally visualize exciton
transport in tetracene, a well-studied organic semiconductor in which triplet excitons are
dominant [49], [50]. Tetracene is a valuable test bed for exciton transport both because
acenes are a promising class of photovoltaic materials[5 1] and because its morphology
and crystallinity can be precisely tuned. Upon optical excitation of tetracene, singlet
excitons are generated and undergo rapid fission into two triplet excitons, each with one
half the energy of the singlet (Figure 3-la). The triplet excitons undergo random hopping
31
Visualization of Exciton Diffusion in Space, Time, and Energy
to nearest neighbor molecular sites by Dexter energy transfer. When two diffusing triplets
encounter each other, triplet fusion can occur to produce a singlet exciton. The
subsequent radiative relaxation of the singlet exciton, known as delayed fluorescence, can
be optically detected and used as a direct probe of the triplet exciton density.
3.3
Methods summary
In our measurements of triplet exciton transport in tetracene we focus a k = 400 nm
wavelength pulsed excitation to a near-diffraction-limited spot, generating an in-plane
Gaussian distribution of singlet excitons within an absorption length
the surface, where aab,, is the absorption coefficient
l1/aas
=
1.3 pIm of
(Figure 3-1b). The delayed
fluorescence resulting from triplet fusion is imaged with 500x magnification onto a timeresolved single photon counting detector. The detector is then scanned across the image
to obtain a map of the time-dependent singlet exciton density as a function of position,
convolved with the point spread function of the imaging optics (See Methods for details).
Since fusion is a nonlinear process that requires the collision of two triplet excitons (see
Section 3.9.3), the triplet exciton density n,(x,t) is calculated from the measured singlet
exciton density ns(x,t) using n, oc n/ 2 [22], [52]. Detailed methods can be found at the
end of this chapter.
3.4
Results and discussion
Visualization of Exciton Diffusion in Space, Time, and Energy
a
b
= 1.4 ps
Delayed fluorescence
r,
Exiain
r,= 260 ps
Prompt fluorescence
Tetracene crystal
Objective lens
Pulsed excitation
A = 400 nm
Fusion
Triplet dIffusion
32
Dichroic
Excitation spot - 300 nm
r
mirror
Scanning APD
.50pm
Imaging lens
Image of emission spot
Fis'io
Photodetector (APD)
1
6
.
5
0.8 a
4
0.6
3
0.4
02
C
C~
:
106
* 0 ps
8
. 0. 5 s
2.25ps
0.6
0
0
2
0.8
0.4
2a,
-t
50Ox
q h
Subdiffusion __
a =0.57 ±0.07
10,
Normal diffusion
a =1.01 ± 0.01
D, =1.35x10' cm'/s
.*~~
0.2
104
0.
-1500 -1000 -500
0
500
Position (nm)
1000
1500
-1U0 -1000
-500
0
500
Position (nm)
1000
1500
0.1
10
Time (ps)
Figure 3-1 1 Imaging tetracene exciton diffusion in time and space. a, Excitonic processes in
tetracene that are relevant to this study. b, Schematic of the exciton diffusion imaging
setup. c, Map of exciton density as it evolves in space and time as measured along the
crystal a axis. The distribution at a particular time has been normalized to emphasize
changes in the distribution width. d, Cross-sections of the density map at 4 time points
showing broadening of the distribution. a, is the standard deviation of the Gaussian
distribution. e, Time evolution of mean square displacement of triplet excitons showing
transition from normal to subdiffusive transport.
Figure 3-ic shows the spatial and temporal evolution of the singlet exciton
distribution along the a axis of a tetracene single crystal after pulsed excitation at t = 0.
The spatial intensity distribution at each point in time has been normalized to a constant
maximum value to emphasize changes in the width of the distribution. The initial nearGaussian distribution of singlet excitons has a standard deviation of as(0) = 229 nm
(Figure 3-id) which rapidly broadens in the first 2 ps, with a subsequent slowing down of
the expansion, reaching as = 701 nm at t = 7 ps. Due to the Gaussian shape of ns at each
time, the triplet exciton distribution is also a Gaussian with (TT(t) = Vas . The observed
exciton transport can be understood in the context of diffusion by considering how the
mean squared displacement of the triplet excitons y (t) changes relative to the initial
mean squared displacement y (0). Diffusion is typically parameterized by
U (t)-
2 (0) = 2Dta
(3.1)
Visualization qf Exciton Diffusion in Space, Time, andEnergy
33
where a is the diffusion exponent and D is a scaling factor. For normal diffusion, a = I
because the particle hopping rate is independent of time, and D is the diffusivity,
expressed in units of cm 2/s. In contrast, anomalous diffusion is characterized by a # 1
and a time-dependent diffusivity. Subdiffusive transport (a < 1) is often caused by a
disordered landscape through which the particles diffuse, resulting in trapping and
decreased hopping rates. Superdiffusive transport such as ballistic motion is characterized
by a> 1.
Figure 3-le shows how the triplet exciton mean square displacement evolves in
time in a tetracene crystal along the a axis. For t < 2 pLs after excitation, the triplet exciton
transport follows a normal diffusive process with a = 1.01 ± 0.01 and a time independent
diffusion constant of Da = 1.35±0.01 x 10-3 cm 2 /s. Given the decay of the delayed
fluorescence, the average distance for exciton diffusion along the a axis within the
lifetime of the triplet excitons
TT =
1.37
ts is L, =
2DjrT =0.61 pm . While the
diffusion constant of tetracene is an intrinsic property that depends on wavefunction
overlap of adjacent molecules, the triplet lifetime can be limited by nonradiative
recombination at trap sites and defects. In ultra-pure tetracene crystals the lifetime has
been found to be up to 58 ps , which provides an upper limit to the a axis triplet diffusion
in tetracene of 4.0 .tm.
At longer times t > 2 ts, we find that a = 0.57 ± 0.07, indicating a transition to a
subdiffusive regime. Such anomalous diffusion is characteristic of particles diffusing in a
disordered potential and is observed in a wide range of physical systems from protein
diffusion in cells to charge diffusion in semiconductors [53], but to our knowledge has
not previously been observed in excitonic systems. Recent thoeretical work has predicted
that subdiffusive transport of excitons can occur in energy disordered systems with
excitonic energy trap levels at the low energy tail of the exciton distribution [54]. In
tetracene we attribute the subdiffusive transport to the excitons becoming trapped in
lower energy molecular sites, which decreases the hopping rate for a subpopulation of
excitons. We show below that this picture of subdiffusion is consistent with our
measurements of spectral distribution of excitons.
Due to the herringbone arrangement of molecules in tetracene, the 2-orbital overlap
is greater in the ab plane compared to the c axis. Consequently, a large anisotropy for
34
Visualization of Exciton Diffusion in Space, Time, and Energy
Dexter transfer rate and hence diffusivity is predicted[19], but until now has only been
observed experimentally in steady-state[47]. Our measurements show exciton diffusion in
both space and time along the b axis and the c axis (Figure 3-2). The exciton transport in
both axes follows normal diffusion with a ~1, but with a seven-fold anisotropy between
the b axis, Db = 2.28±0.07x10- cm 2 /s, and the c axis, Dc = 0.31±0.02x10-3 cm 2 /s. The
trend in diffusivity between the three axes follows the theoretical predictions of Yost et
al. [19]. Furthermore, the observed anisotropy is a direct verification that exciton energy
transfer in tetracene is dominated by triplet hopping rather than by photon emission
followed by reabsorption. If the radiative energy transfer was dominant, it is expected to
have the strongest anisotropy between the a and b axes due to alignment of the optical
transition dipoles[55], which is in contrast to our measurements that show a small (69%)
difference in the exciton diffusivity between the a and b axes .
a
b
baxis diffusion
Strong n-orbital overlap
c2
0
c axis diffusion
C
2
1
Weak
i-orbital
overlap0
d
10"6
b
1000
0
-1000
Position (nm)
b axis
a =1.10 ± 0.04
Db= 2.3 x10-3 cm 2/s
E
C
10
c axis
a =0.98 ±0.13
C"
10
0.1
D, = 3x10-cm2
Time (ss)
1
s
Visualization of Exciton Diffusion in Space, Time, andEnergy
35
Figure 3-2 1 Anisotropy of diffusion between the b axis and the c axis. a, Crystal
structure of tetracene in the bc plane showing overlap of the highest occupied
molecular orbitals. b and c, Normalized spacio-temporal map of exciton density as
measured along the b axis (b) and c axis (c). d. Time evolution of the mean squared
displacement along the b and c axes, showing large anisotropy.
In addition to spatial broadening of the exciton distribution, we find that the
spectrum of the delayed fluorescence also evolves in time and space. Figure 3-3a shows
that the fluorescence spectrum at t = 0 has a single peak at k = 535 nm ("SDD") which
decays with a concomitant appearance of lower-energy peaks at X = 570 nm and k = 615
nm ("SD,tr"). To understand the origin of the low energy emission, we visualize the
spectral evolution by measuring the shift of the average energy of the emission spectrum
at each position and time. Figure 3-3b shows that as exciton diffusion proceeds, the
emission spectrum red-shifts faster near the center of the spatial distribution than in
regions on the periphery of the distribution. This observation is consistent with the
presence of exciton energy traps [56]. Namely, as the diffusion proceeds, exciton traps
are filled faster in the center of the distribution, where the triplet density is higher. The
remaining sub-population of non-trapped excitons can diffuse. The diffusion process will
preferentially direct excitons towards lower energy sites in the exciton distribution
leading to a rapid red-shifting. The higher the free exciton density, the larger red-shift
will be observed.
The spectral signatures can then be assigned, where the two lower
energy peaks are due to the fusion of a diffusing triplet exciton and a trapped triplet
exciton and subsequent emission from the vicinity of the trap. The fluorescence peak at k
= 535 nm is the result of fusion of two diffusing triplet excitons (Figure 3-3a). This is
also consistent with our finding that the emission from red-shifted regions has a more
linear scaling with increasing triplet exciton density (adjusted by increasing the excitation
light intensity), confirming that the low energy emission is due to the fusion of diffusing
triplets and a fixed number of trapped excitons.
Visualization of Exciton Diffusion in Space, Time, and Energy
36
a
t
0
S0 ps
E 0.6 gs
* 2 ps
3.5 ps
t
520
540
560
580
600
Wavelength (nm)
620
b
640
0
0.5
-5
0.4
-10 E
w
ztf
0.3-15
0)
E
0.2
-20 E
0.1
- 25 w
0 -400
-200
0
200
400
30
Position (nm)
Figure 3-3 I Filling of exciton traps as diffusion proceeds. a, Tetracene crystal emission
spectrum at 4 time points after excitation, integrated over all space. Circles are
measured values and lines are spline interpolates. b, Spatio-temporal map of the
average energy of the emission spectrum showing more rapid red shifting in the center
of the distribution.
One of the defining features of organic and nanocrystalline materials is their high
morphological and energetic disorder. Consequently understanding how exciton transport
is affected by disorder is crucial for the design of new materials. To this end we measure
how exciton diffusion is affected as the disorder in tetracene is increased. Figure 3-4
shows how the mean squared displacement of the exciton distribution evolves in time for
a thermally evaporated film of tetracene that is polycrystalline. By atomic force
microscopy the crystalline domain size is measured to be -200 nm (Figure 3-4b), small
compared to the a axis diffusion length of La = 610 nm. We find that transport in the thin
film sample proceeds by normal diffusion for t < 350 ns with a diffusivity Dtf = 1.4 x
10-3 cm 2 /s. This value falls between the diffusivities found for the a and b crystal axes,
Visualization of Exciton Diffusion in Space, Time, and Energy
37
consistent with the film being composed of randomly oriented crystalline domains in the
ab plane. This agreement in diffusivities indicates that the trap density within the bulk of
a single domain of the film is similar to that of single crystal. However, in contrast to the
single crystal, transport in the film transitions to subdiffusive at t - 350 ns, much earlier
than the transition for the single crystal at t ~ 2 pts. The diffusion distance of an exciton in
350 ns is -500 nm, which indicates that a large fraction of diffusing excitons have
encountered a domain wall of the crystallite on which they were formed. Due to the
discontinuity in crystal order at the domain wall, the exciton trap density is expected to
increase[52],
leading to exciton trapping
and the concomitant observation of
subdiffusion.
a
Crystal a
bb
240
Thin film24
M
(D
Crystaline domain
00 1nm
1 Pill
-----
3
0
C
Crystal (a axis)
D, =1.35 x10-3 cm 2 /s
Thin film
E
Dt
1.4 x10-3 cm 2 /s
a1.00 ±0.1 0
10-
Trapping
wall
b
0.1
1
Time (gs)
Visualization of Exciton Diffusion in Space, Time, and Energy
38
Figure 3-4 1 Diffusion in tetracene polycrystalline film. a and b, Atomic force
microscopy images of a single crystal ab plane (a) and of a tetracene evaporated film
(500 nm average thickness) (b). Crystalline domains in the film are ~200 nm in size. c,
Time evolution of the mean squared displacement for the film and comparison to the fit
of the crystal a axis data.
3.5
Conclusion
In conclusion, our measurements demonstrate that transport of triplet excitons in
tetracene occurs by normal diffusion with a transition to subdiffusive transport that
depends on sample morphology and, consequently, trap density. These results are the first
direct spatial, temporal, and spectral observation of exciton transport in a molecular
system, which can be taken as an archetype for both natural and engineered, ordered and
disordered systems that rely on exciton transport. The imaging technique developed for
this study is a general tool that can be applied to exciton transport in a wide range of
materials, including those dominated by singlet exciton diffusion, characterized by a
much shorter exciton diffusion lengths of 10-50 nm[12]. Despite the relatively large
diffraction-limited size of the excitation and imaging point-spread function, the ultimate
spatial resolution of the measurement is limited by the precision with which the width of
the exciton distribution can be determined. The precision on the width, in turn, is only
limited by the number of photons collected[57] and the stability of the optical system.
Therefore no fundamental limit exists on the shortest diffusion length that can be
measured with this technique.
3.6
Sample fabrication
Tetracene was purchased from Luminescence Technology Corporation and further
purified three times by vacuum physical vapor transport [23]. Thin film samples were
fabricated on 170 pam thick microscope cover glass with no additional cleaning. The
tetracene thin films were thermally evaporated at pressures less than 3x10- 6 Torr at a rate
between 2-4 A/s. The film thickness was determined in-situ through use of a quartz
crystal oscillator and rotation of the substrate holder during thermal evaporation resulted
in a thickness variation of ±10% across the width of the substrate holder [51]. The
thermal evaporator was directly attached to the glovebox (with less than 1 ppm 02 and
Visualization of Exciton Diffusion in Space, Time, andEnergy
39
H2 0). The tetracene films were packaged in the dry nitrogen environment using UV
curing epoxy and a second cover slip. The thin film was shadowed from the UV light
during epoxy exposure by a square of aluminum foil.
Single crystals of tetracene are grown using the same purified tetracene by the
vapor phase method in Ar [23]. Crystallites had one large facet with a typical size of 1 xI
mm and a thickness of -20 micrometers. In order to avoid an air gap between the
crystallite and the cover glass, the cover glass is first wetted with immersion oil (Nikon, n
= 1.52). The crystallites were then placed in the oil and pressed with another cover glass
to make a sealed sandwich. We find that the tetracene was completely insoluble in the
immersion oil and that the oil had no effect on the fluorescence spectrum or intensity.
Most optical measurements of organic crystals are performed in the plane
perpendicular to the growth direction because of the difficulty in handling and orienting a
thin crystallite. Here we are interested in observing the large predicted anisotropy in
diffusion between the c axis and the ab plane. In order to image diffusion along the
crystal c axis a crystallite was wedged between two pieces of glass and the crystallite was
immersed in objective oil (Figure 3-5). From the small anisotropy in fluorescence
polarization in the image plane (Figure 3-5b) it was determined that the orthogonal axis
to the c axis for this crystal was the b axis.
a
Tetracene crystal
Immersion oil
b
Figure 3-5 1 a, Schematic of the sample setup for measurement of diffusion along the
crystal c axis. b,
Visualization of Exciton Diffusion in Space, Time, and Energy
3.7
40
Sample Characterization
3.7.1
Determination of crystal axes
To determine the crystallographic axes of crystals and the thin films, we used a
combination of x-ray diffraction and polarized light microscopy.
X-ray diffraction:
aX
104
"I
-
(001)
Single crystal
(0 )0
nm film
6
CO
C
2
(002)(03
0.
E
10
15
20
25
20 (deg)
Figure 3-6 1 X-ray diffraction pattern of tetracene single crystal and thin film.
X-ray diffraction patterns were taken of the single crystal and thin film tetracene on
glass cover slides in air. The crystal was oriented so that the largest facet was in contact
with the substrate. The X-ray source was copper k-alpha radiation and the scan was
measured in a coupled theta-two geometry. The (001) diffraction peak and its higher
orders were the only visible diffraction peaks. Scans measured to 60* 20 found no
additional diffraction. Thus we conclude that both the 500 nm film and the crystal have
the crystal c-axis oriented perpendicular to the substrate.
Wide-field fluorescence imaging:
The samples are imaged using the same inverted microscope and 1OOX oil
immersion objective as used for diffusion imaging. The samples were excited with a
mercury lamp at a wavelength of 470±15 nm and fluorescence was collected at all
wavelengths above 500 nm. The fluorescence is imaged onto a CCD camera (Q-Imaging
41
Visualization of Exciton Diffusion in Space, Time, and Energy
QIClick). A thin film linear polarizer is placed between the objective lens and the camera
in order to image selected polarization of fluorescence.
b
a
C
0.6
0
0.
4
.
0.2
0
0
Figure 3-7 1 Polarized fluorescence images of tetracene crystal in the ab plane. (a)
Polarizer is horizontally polarized and (b) polarizer is vertically polarized. (c) Image of the
degree of polarization obtained by taking the normalized difference of the two polarized
images.
a
b
C
0.2
-U
-0.1
-0.1
0
0
Figure 3-8 [ Polarized fluorescence images of a d = 500 nm tetracene thin film. (a)
Polarizer is horizontally polarized and (b) polarizer is vertically polarized. (c) Image of the
degree of polarization obtained by taking the normalized difference of the two polarized
images.
3.7.2
Absorption and emission spectrum
Absorption measurements of tetracene thin films are performed on a Varian Cary
5000 spectrophotometer. Figure 3-9 shows a representative normalized absorption
spectrum of a thin film of tetracene. Due to the thickness of tetracene crystals (~20 pm),
the optical density is extremely high (up to OD = 10), preventing direct measurements of
transmission to determine absorption. The thin film absorption is representative of the
typical absorption of a crystal, although peaks may be slightly shifted with redistributed
intensities.
Visualization of Exciton Diffusion in Space, Time, and Energy
42
The absorption coefficient at the excitation wavelength of k = 400 nm is found by
measuring the transmission through a 10 pm thick crystal. It was possible to measure the
transmission because at this wavelength the absorption is weaker compared to the peak at
~500 nm. The transmission light source was the same 400 nm doubled Ti:Sapphire
pulsed laser used for the imaging experiments but focused through a low-divergence 5X
objective onto a ~5 pm diameter spot on a flat facet of the crystal. The transmitted power
was measured above the sample and related to the transmission through the same setup
and substrate in the absence of the crystal. The absorption coefficient at 400 nm was
found to be a 4 00
Labs
=
7.5 x 10' cm-'
with a corresponding absorption length of
,
= 1 / a = 1.3 pm. Given this absorption length and the ~I ptm depth of field of the
diffusion imaging system, most of the incident light is absorbed within the detection
volume. [Power and exciton density here or somewhere later?]
1 am=
7.5 X103 CM.0.8
b
CO 0.8- CI
o
S0.6-
- - - Absorption
- -- Emission
400 nm
excitation f
I
El
0C 0.4.0-
'm
-v
0.2-
S50
400
450
500
550
Wavelength (nm)
600
650
700
Figure 3-9 1 Absorption spectrum of tetracene thin film and emission spectrum of a
tetracene crystal.
The steady-state emission spectrum of a tetracene crystal is shown in Figure 3-9.
Excitation and light collection is done in the same configuration as the diffusion imaging
experiments, but the fluorescence is directed to a different microscope port and imaged
onto a multimode fiber. The fiber output is mounted at the entrance slit of a spectrograph
(Princeton Instruments Acton SP2300,
f
= 300 mm, 300 g/mm grating, 500 nm blaze)
with a CCD imaging camera at the output port. The spectrum exhibits a main peak at 535
Visualization of Exciton Diffusion in Space, Time, and Energy
43
nm which corresponding to the fusion of diffusive triplet excitons. The two peaks at 570
nm and 615 nm are attributed to fusion of a diffusive triplet and a trapped triplet, as
elucidated by our spatially, temporally, and spectrally resolved measurements.
3.7.3
Fluorescence lifetime
The fluorescence lifetime for the single crystals and for the polycrystalline thin film
is shown in Figure 3-10. The fluorescence decay of tetracene has two characteristic time
scales. For the crystal, the fast component (inset) has a lifetime of TPF = 262
+
10 ps
which corresponds to prompt fluorescence from singlet excitons before fission occurs.
The singlet exciton lifetime is dominated by rapid fission into two triplets. In contrast to
the short total lifetime, the radiative lifetime of the singlet state has been found to be 12
ns in tetracene thin films[55]. At t > 3 ns, the fluorescence decays with a much longer,
non-exponential time-dependence resulting from triplet fusion and subsequent singlet
decay. The non-exponential decay occurs because fusion is a non-linear two-body
process which depends on triplet density. The decay is faster at early times because the
triplet density is highest. As the contribution from fusion of diffusing triplets decreases,
the decay becomes exponential. We attribute this long decay (r = 1.37 ps for the crystal)
to the fusion of a trapped triplet with a diffusing triplet. Since only one of the species is
mobile, the rate of this process is linearly dependent on the diffusing triplet density,
resulting in a mono-exponential decay.
Single Crystal
100
Prompt fluorescence
10-1
01
E0
C
TPF =
10 1
-2
26 2
±10 ps
10
To
- 10
(D 10 -3
0
1
3
2 3
Time (ns)
4
5
Delayed fluorescence
TDF=1. 37 ±0.01 ps
10
0
1
2
3
4
Time (gs)
5
6
7
Visualization of Exciton Diffusion in Space, Time, and Energy
44
Polycrystalline Thin Film
10
10'
Prompt fluorescence
TPF =310 ± 50 ps
10
~101
Z.C
-2
110
0
10'_
2
3
4
5
Time (ns)
Delayed fluorescence
1
.6 7 ±
PF
10-4[
0
0.5
1
1.5
Time (gs)
2
0.04S
2.5
3
Figure 3-10 I Time-resolved fluorescence of tetracene single crystal, showing both
prompt fluorescence and delayed fluorescence.
3.8
Diffusion imaging optical setup
Exciton transport in tetracene was measured using a custom-built fluorescence
microscope shown in Figure 3-11. The setup is similar to a laser scanning confocal
microscope but with a key modification. The -500 nm FWHM fluorescence spot is
magnified 50OX using the objective lens and a lens external to the microscope to produce
a spot with a FWHM of -250 ptm. The time-resolved photodetector with an active area of
50 pm is then scanned across the magnified fluorescence spot to obtain a map of
fluorescence intensity as a function of time and space on the sample. The fluorescence
intensity map is then assigned to a density of excitons, depending on whether singlet or
triplet excitons are the primary species in the material.
The laser excitation source is a Ti:Sapphire ultrafast laser producing pulses -100 fs
in duration at a repetition rate of 80 MHz at a wavelength of 800 nm. In order to observe
the long (-ps) dynamics of tetracene emission, the high repetition rate pulses are passed
through an electro-optic pulse picker (Conoptics Model 350-160 KDP Series ElectroOptic Modulator, with driver Model 25D, and Model 305 Synchronous Countdown
System). Typical repetition rates used for measurements of tetracene diffusion are 114
kHz, corresponding to a delay between pulses of 8.8 pts. The reduced repetition rate
pulses are focused with an f = 100 mm lens onto a frequency doubling BBO crystal
(Crystech Inc.). The crystal is cut for collinear phase-matching between the incoming and
Visualization of Exciton Diffusion in Space, Time, and Energy
45
outgoing upconverted light. The 400 nm beam is collimated and passed through a 750 nm
shortpass filter to remove the residual 800 nm laser light and then passed through a
390±20 nm bandpass filter (Semrock, Inc. FFO1-390/40-25). The beam is then sent into
an f = 18.4 mm fiber coupler (Thorlabs Inc. PAF-X-l 8-PC-A) to couple into a single
mode fiber with a length of 20 cm. The output of the single mode fiber is collimated with
a diffraction limited compound collimator to a diameter of 10 mm.
QD
Excitation spot
- 300 nm
thin film
Cover slide
Electro-optic
pulse picker
=
Objective lens
f = 2 mm, NA = 1.45
Fiber collimator
100 mm
Image of
BBO doubling
crystal
Dichroic mirror A = 405 nm
f = 100 mm
Long pass filter A = 405 nm
spot
Imaging lens
f = 1000 mm
750 nm short pass filter
390±15 nm bandpass filter
Single mode fiber
Variable ND filter
Fiber coupler
Figure 3-11
transport.
Photon counting system
Single photon APD
I
Schematic of fluorescence imaging microscope for imaging exciton
The single mode beam is directed into the back of an inverted optical microscope
(Nikon Ti-E) and reflected into the objective lens by a longpass dichroic mirror with a
cutoff wavelength of k = 415 nm (Semrock Inc., DiO2-R405-25x36). The lOOX oil
immersion objective lens (Nikon CFI PlanApo Lambda lOOX Oil, effective focal lengthf
= 2 mm) focuses the laser beam to a near diffraction limited spot with a FWHM of 200
nm, as determined from imaging the reflection spot.
The sample is mounted above the objective lens on a piezoelectric scanning stage
(Physik Instrumente, P-733.3CL with controller E-710.4CL). Each measurement of
tetracene crystals and thin films was done on a single spot and the piezoelectric stage was
used only to move to new areas between measurements. The fluorescence from the
Visualization of Exciton Diffusion in Space, Time, and Energy
46
sample is collected by the same objective and the resulting collimated beam passes
through the dichroic mirror and then through a longpass filter with a cutoff at k = 416 nm
(Semrock Inc., BLPO1-405R-25) to remove any residual scattered or reflected excitation
light. The fluorescence beam is then focused by an achromatic lens with a focal lengthf=
1000 mm (Thorlabs Inc., AC508-1000-A-ML) to a region outside the microscope. The
focal plane of the f= 1000 mm lens is determined by scanning an imaging CCD along the
optical axis to find the smallest fluorescence spot size.
A single photon detecting avalanche photodiode (APD) (MPD PDM Series 50 pm)
is mounted in the focal plane on a two-dimensional computer-controlled translation stage.
The output of the APD is connected to a timing module with a resolution of 4 ps
(PicoQuant PicoHarp 300) which detects the arrival time of each photon. This technique,
known as time-correlated single photon counting (TCSPC) results in a histogram of
photon arrival times which corresponds to the time-dependent rate of photon emission
from the sample. The APD detector is scanned with a velocity of 2.5 Im/s across the
excitation spot in either the vertical or horizontal direction. The time-resolved
fluorescence trace is recorded at each detector position resulting in a map of fluorescence
intensity along one axis of the sample as a function of time. The detector is shielded from
stray light and all measurements are done with room lights turned off, resulting in a dark
count rate in the presence of the excitation laser of 100 counts/s.
All measurements, with the exception of the power dependence in Section 3.10.2,
were done with an incident average power on the sample of 1 nW, corresponding to a
pulse energy of 9 fJ. Based on the absorption coefficient at X = 400 nm
a400
=
7.5xl 0 cm- 1 the estimated singlet exciton density at t = 0 is then
n(0) = 1.5 x
1017
-102
and as we see in Section 3.10.2 this density is also well below the onset of
cm-,
cm-3. This density is well below the tetracene molecular density of
exciton-exciton annihilation effects. Samples had excellent photostability under this
excitation power and consequently each measurement (-30 min) was done on the same
-300 nm spot on the sample.
Visualization of Exciton Diffusion in Space, Time, and Energy
3.8.1
47
Spatial resolution of imaging setup
FWHM
=
200 nm
600
20.
0
-1000
0
Position (nm)
1000
Figure 3-12 I Cross-section of single CdSe quantum dot (A = 610 nm) measured with a
100X, NA = 1.4 objective. The FWHM of the PSF of the system is y = 200 nm.
The spatial resolution of imaging setup was determined by imaging of single CdSe
quantum dots immobilized on a glass substrate. The resolution is near-diffraction limited
with a full-width at half-maximum of the point spread function of y = 200 nm.
3.9
3.9.1
Data analysis
The diffusion equation
The diffusion equation in the most general three-dimensional case is
a3n(r,t)
at - V r[D(n,r,t)Vn(r,t)]
aJt
(3.2)
where n(r,t) is the spatially-dependent and time-dependent density of excitons and
D(n,r,t) is the diffusion coefficient. In the simplest situation, the diffusion coefficient is
a constant. In our experiments, the exciton density is low-at most a fraction 10-4 of
molecular sites in tetracene are excited at t = 0 and we can therefore consider D to be
independent of n. We can also make the assumption that the diffusion coefficient is not
dependent on position because tetracene crystals are homogeneous on the length scale of
the exciton propagation distance. For tetracene thin films we can make this assumption
because the spot size averages several domains. Finally, we are left with the time
dependence of D, which in general is time-dependent. Since diffusion along different
Visualization of Exciton Diffusion in Space, Time, and Energy
48
directions is uncorrelated (i.e. the particle has no memory of the direction of the last hop)
we can separate the diffusion equation and only consider diffusion along one dimension,
therefore giving
'n(xt)
= D(t) a2'
-
k(t)n(x,t)
(3.3)
Ox
Mt
Here we have added an exciton decay term with a general time-dependent rate
k(t) = k,, (t)+ kr, where k(t),, is the non-radiative decay rate and k, is the radiative
decay rate. The exciton generation term is left out because optical excitation in the
experiments in this paper is pulsed, and hence will be given as the initial condition to the
equation.
The general solution to the diffusion equation with a constant diffusivity, and given
the general initial condition n(2,O), is
n(x,t)=
n(,0)exp
(x
4rDt
If
the
ns(x,0) = no exp(-x
initial
2
(3.4)
4Dt,
exciton
singlet
-4)
distribution
is
a
Gaussian
/ 2u2(0)), then the exciton density at time t is
n(x,t)=
n
4rDt
=
4rDt
exp
-72
exp
(o)
exp (x4j di
4Dt
(3.5)
x2
2(O)+ 4Dt,
where we have used the property that the convolution of two Gaussian functions with
variances
o
and
yr
results in a Gaussian with variance
&r +
U.
The variance of the
singlet exciton distribution, which is also termed the mean square displacement
Kx@)2)
evolves as
2Dt
(x(t)2) = a2(t)= a2(0) +
(3.6)
The relation derived for (x( t)( above is known as Fick's Law, in which the
hopping rates from site to site are not dependent on time. The linear relationship between
(x(t)2)
and t occurs in the special case of normal diffusion. In many physical systems
Visualization qf Exciton Diffusion in Space, Time, and Energy
49
where disorder is present, the distribution of particle hopping times has a heavy-tailed
distribution [53], [54], [58]. Consequently, Fick's law in one dimension is modified to
(x(t)2) = Ata
(3.7)
The exponent a characterizes the type of diffusion and A is an empirically observed
scaling factor which has fractional time units. For a = 1, we recover normal diffusion. For
a > 1, the transport is superdiffusive, in which the particles spread faster than in normal
diffusion. This is situation occurs in ballistic transport where the mean scattering time is
long relative to the observation time. For y < 1, the transport is said to subdiffusive. This
situation occurs when some fraction of the diffusing particles experience longer waiting
times between hops, thus slowing down diffusion. Subdiffusion occurs in disordered
physical systems because as diffusion proceeds, particles become trapped at sites from
which escape is less probable.
In organic molecular materials, charge conduction is known to increase as electron
or hole traps are filled [1]. This phenomenon is markedly different from what we observe
with exciton transport, where trap filling reduces exciton hopping. The reason for this
difference is that charge lifetimes are much longer than exciton lifetimes. As charge is
injected into the material, traps are filled, and subsequent passing charges can no longer
be captured by the filled traps, and hence conductivity increases. In contrast, the exciton
lifetime is so short that the probability of multiple excitons sampling the same molecular
site within the the exciton lifetime is very small. This situation could change in the case
of higher exciton densities, although other complications will arise such as excitonexciton annihilation.
3.9.2
Extracting the singlet exciton distribution
The measured image of emitted photons is actually a spatial convolution of the
exciton distribution n(x,t) , the point spread function (PSF) for the emission photons
f,
(x) , and the APD detector fd(x)
I(x,t)= n(x,t)* f f(x)fd(x)
(3.8)
The PSF of emitted photons is an Airy disk pattern but can be approximated by a
Gaussian function. From single quantum dot imaging studies using our experimental
Visualization of Exciton Diffusion in Space, Time, and Energy
50
setup, we find that the typical FWHM of the point source image is 200 nm for quantum
dots emitting at 610 nm, corresponding to a standard deviation o = 133 nm . This value
agrees well with the theoretical Rayleigh resolution of 0.6 1X / NA = 265 nm , when using
an NA = 1.4 objective, indicating that our optical setup is near diffraction-limited. The
APD detector size is 50 tm, and when imaged in the sample plane at 50OX
demagnification, the size is 100 nm, which small compared to the spot size.
Using the fact the convolution of Gaussians results in a Gaussian profile having a
variance which is a sum of the constituent variances, we find that
(t)+
o(t)=
F =O(0)OSF
+ 2Dt
(3.9)
where a (t) is the variance of the intensity distribution, o2(t) is the variance of the
singlet exciton distribution, and
o2SF
(t) is the variance of the detection point spread
function. The change in mean square displacement (also termed the change in variance of
the distribution) is then
AMSD
=
(x(t)2)(x(0)2=
2 to(t)-r (0)
= 2Dt
(3.10)
Importantly, we can see that AMSD does not depend on convolution with the Gaussian
point spread function or on the width of the initial distribution.
3.9.3
Inferring triplet density from singlet distribution
The time-resolved fluorescence intensity distribution measured in our setup is
proportional to the singlet density in the material. However, energy transport in tetracene
is dominated by triplet excitons. Hence we must determine the triplet exciton density
based on the singlet exciton density. We start by considering the simplified rate equation
for the density of singlet excitons n [52]:
dns = ksns +y
dt
T
Here ks is the total singlet exciton decay rate rate, yJ,
(3.11)
is the triplet-triplet fusion rate
constant, and nT is the triplet exciton density. The singlet decay rate is a sum of rates
ks = k
+ knr + kISC + kic + k,
(3.12)
Visualization qf Exciton Diffusion in Space, Time, and Energy
51
where krd is the radiative decay rate, knr is the nonradiative decay rare not captured by
other processes such as recombination on a defect, k.Sc is the inter-system crossing rate,
k,C is the internal conversion rate, and kf is the singlet fission rate. As discussed by
Burdett et al. [52], the total decay rate is dominated by the fission rate with
ki ~ 1 / 250 ps in our measurements. Therefore, solving for the triplet density, we find:
n, =T
[lr
dni
YTTF
dt
-
1/2
(3.13)
+ k .5ns
Y
We can make the assumption that dns / dt <ksn, because the term dns / dt is obtained
experimentally as the slope of the measured time-resolved fluorescence. The measured
delayed fluorescence lifetime is much longer than the fission lifetime for all times after
the prompt fluorescence. Therefore the triplet density is given by:
n,(~)
-XE ns (x,t)
12(3.14)
If the distribution of singlet excitons ns(x,t) is a Gaussian at all times with
variance aj(t), as is the case in this work, then the triplet distribution variance is
S
T=
2j(t) It follows from Eqs. (3.9) and (3.10) that
AC =2Ar (t)=2D t
(3.15)
The rate equation from which Eq. (3.14) was derived was simplified and did not
include the effect of exciton traps. In the presence of traps, the relationship between
singlet exciton density and the free triplet exciton density (those not in a trap) becomes
more linear as traps are filled. Therefore Eq. (3.11) is modified at longer times[52].
However, generation of a singlet still requires the fusion two triplets, regardless of
whether one of them is trapped. Therefore at a particular time, the variance of the total
triplet exciton distribution (both free and trapped) is still given by Eq. (3.15).
In the above discussion we have ignored geminate recombination of correlated
triplet pairs. As has been shown by Burdett et al.[59], correlations between pairs of
triplets can persist up to ~10 ns after fission. Such correlations modify the rate equation
and early times and give a linear relationship between triplet and singlet exciton density.
Visualization of Exciton Diffusion in Space, Time, andEnergy
52
However, our measurements are primarily concerned with much longer time scales (- s),
and hence geminate recombination can be ignored in calculating the triplet density.
3.9.4
Broadening of PSF due to dynamic redshift
As diffusion proceeds, the emission spectrum redshifts, translating into a small
change in the detection point spread function (PSF). Here we estimate the size of this
effect on the measurement of the exciton distribution broadening. The change in the
FWHM of the PSF due to dynamic red shifting of the tetracene fluorescence is given by
Ay = y
(3.16)
where y is the FWHM of the initial PSF, X, is the center wavelength of the initial
emission spectrum, and AX is the wavelength shift in the emission spectrum. The
nominal detection PSF was found by imaging a single a CdSe colloidal quantum dot
(Section 3.8.1) giving y = 200 nm . For a dynamic redshift in crystalline tetracene of
AX =7 nm and a center wavelength of X0 =550 nm, we find that Ay = 2.5 nm , which
is much smaller than the -1000 nm observed change in the FWHM of the intensity
distribution due to diffusion. Therefore we can consider spectral broadening of the PSF to
be a small effect and therefore can be neglected.
3.10 Supplementary results and discussion
3.10.1 Energy dependence of emission lifetime
To verify the origins of the delayed fluorescence component of the emission (t > 10
ns) and the prompt fluorescence component of the emission (t < 10 ns), we measure the
time-resolved fluorescence from crystalline tetracene (not spatially resolved) at varying
excitation powers (Figure 3-13a). We can quantify the type of fluorescence mechanism in
two time regimes by considering how the emission intensity scales with incident pump
energy. Figure 3-13b shows that the time-integrated intensity of delayed fluorescence
increases nonlinearly with pump energy. The nonlinearity in the power dependence is
consistent with delayed fluorescence occurring as a result of the encounter of two triplet
Visualization of Exciton Diffusion in Space, Time, and Energy
53
excitons to produce a singlet exciton, consistent with earlier work [50]. As will be
discussed below, the power law exponent for the scaling with pump energy is 'y < 2
because of processes that compete with fusion. It is of note that this increase in
fluorescence quantum yield with increasing pump energy is unusual among organic
materials, in which destructive two-body processes (such as annihilation) dominate at
high exciton densities.
a
b
-0
10
-
f
10-
0.2
1 fJ
-- 16
4fJ
1 ---
6 fJ
-- 60fJ
8
--
Delayed
--
Prompt
--
Total
2
1i0
- -- 1:1
line-
10
o 10
10
1
E2
_10
0
0
1
2
3
4
Timne (ps)
5
6
7100,
0
1010
101
Incident pulse energy (fJ)
Figure 3-13 I a, Time-resolved fluorescence from tetracene crystal at varying excitation
energies. The glitch at t - 100 ns is due to the stitching of two data sets, one for short
time scales and the other for long time scales. b, Integrated delayed and prompt
fluorescence as a function of pump energy and comparison to a 1:1 line (power law
slope y = 1) as guide to the eye.
In contrast, the prompt fluorescence component (t < 10 ns) has a linear scaling with
pump energy at energies < 100 fJ, at which point exciton-exciton annihilation effects
reduce the quantum yield of prompt fluorescence. We note here that all measurements of
diffusion were done at powers below the onset of annihilation. Prompt fluorescence is the
result of singlet exciton decay, which is a single-body process, consistent with the
measured pump energy dependence.
Visualization of Exciton Diffusion in Space, Time, and Energy
a
54
b
1.3
1.3.
1.2-1.2
1
0.9 e
0
,
20
,
40
60
Time (ns)
,
80
0.
$00
- ----
400
-
-
600
Time (ns)
-
-
800
1000
Figure 3-14 1 Power exponent y of the relationship between pump energy and
fluorescence intensity at a, short time scale and b, long time scale. The small mismatch
in y between the two time scales occurs because energy-dependent measurements
were done separately. This was done because of the large dynamic range of
fluorescence intensity in tetracene between prompt fluorescence and delayed
fluorescence.
We can further quantify the evolution of the fluorescence by considering how the
emission intensity at a particular time after excitation scales with the initial exciton
density (proportional to the pump energy) (Figure 3-14). The power law exponent is y
1I
at t = 0 ns, corresponding to prompt fluorescence, and rapidly increases to y = 1.25 at t =
10 ns, corresponding to exciton fusion becoming the dominant mechanism. The power
exponent is y < 2 because of processes that compete with fusion, such as triplet-triplet
annihilation and triplet-singlet annihilation as has been discussed in previous works [1].
As time proceeds, the power exponent again approaches y = 1, indicating a return to a
fluorescence-producing process with a rate proportional to initial exciton density. Based
on this result and our measurements of spectrally resolved exciton diffusion discussed
earlier, we propose the following mechanism: As exciton diffusion proceeds, lower
energy molecular states are filled with diffusing triplets, saturating to a fixed density N,.
The remaining diffusing excitons can encounter the trapped excitons and undergo fusion,
but this process occurs with a rate proportional to nN,, where n, is the density of nontrapped excitons. Consequently, the dependence of fluorescence intensity on exciton
density is expected to be linear with triplet density, since N, is fixed by the trap density,
which agrees with our observation.
Visualization of Exciton Diffusion in Space, Time, and Energy
55
3.10.2 Excitation energy dependence of exciton diffusion
In order to assign the observed exciton distribution broadening to exciton transport,
it is important to verify that the broadening is not dependent on the excitation pulse
energy. Apparent distribution broadening could be observed due to destructive exciton
processes such as singlet-triplet annihilation. If strong annihilation is present, the exciton
lifetime will be shorter in the center of the distribution where the density is highest,
relative to the periphery of the distribution. As a result, the normalized exciton
distribution will broaden, a process that could contribute to the broadening due to
diffusion. Figure 3-15 shows the measured singlet exciton distribution broadening for
three different excitation pulse energies ranging from 2 fJ to 8 fJ. We find excellent
overlap of the data indicating that at these energy densities tetracene is well below the
annihilation regime. Indeed if annihilation was present, a 4-fold increase in power would
result in a 16-fold increase in the annihilation rate, but no such excitation energy
dependence is observed.
1000
0 2U
5
0
800240
8 fJi
600 400
'i)
2000'
0
1
2
3
4
5
6
Time (gs)
Figure 3-15 1 Singlet exciton distribution standard deviation CTS as for three different
pump energies, showing that the broadening is independent of excitation energy.
3.10.3 Diffusion near crystal edge
As a demonstration of passive control of exciton transport, we measure diffusion
near the edge of a tetracene crystal. The excitation spot is focused -500 nm from the edge
Visualization of Exciton Diffusion in Space, Time, and Energy
56
of a crystal facet, where the crystal ab plane is in the objective lens focal plane. Figure
3-16 shows that broadening proceeds only in the direction away from the crystal
boundary. This result is a clear and direct vizualozation that exciton transport can be
guided by tailoring the morphology of the material. In future work, we anticipate that
nano-patterning organic thin films using the nano-imprinting technique we developed
will allow for more precise manipulation of exciton transport.
b
Crystal edge
a
1
4.5
01
0 pis
1
,1
C,0.8.-
3
--
-
-15p
3-5ps
S0.6X
~
E
0.40 0.2z
-1000
-500
0
0
500
Position (nm)
1000
0
0
500
-1500 -1000 -500
Position (nm)
1000 1500
Figure 3-16 I Triplet exciton diffusion near the edge of a crystal. a, Two dimensional
map of the normalized singlet exciton distribution. b, Singlet exciton distribution at
three time intervals showing diffusion only in the direction away from the crystal edge.
3.10.4 Radiative energy transfer
Along with near-field hopping, the emission and reabsorption of a photon is
another mechanism that can give rise to energy transport. This radiative form of energy
transport is often difficult to distinguish from exciton hopping in exciton transport
measurements, as has been discussed by Powell et al.[60]. In particular, photon emission
followed by reabsorption (ERA) is itself a random walk process due to the randomization
of the photon direction with each emission event. In materials dominated by singlet
excitons, hopping transport and ERA transport occurs along the same axes because both
mechanisms rely on the interaction of two dipoles-hopping in the near-field and ERA in
the far-field.
Visualization of Exciton Diffusion in Space, Time, and Energy
a
b
57
Strong ERA
Strong n-orbital overlap
Strong ERA
Weak n-orbital overlap
Transition
dipole
morment
Weak ERA
Strong n-orbital overlap
Figure 3-17 1 a, Structural formula of tetracene and orientation of the transition dipole
moment. b, Structure of a tetracene crystal showing the transition dipole moments and
relative strengths of emission-reabsorption and n-orbital overlap.
Tetracene, in contrast, is dominated by triplet excitons, the transport of which
depends on wavefunction overlap. Transition dipole alignment and wavefunction overlap
do not necessarily occur most efficiently along the same axes. Unlike most conjugated
organic molecules, the dipole moment of tetracene is perpendicular to the long molecular
axis (Figure 3-17a). Based on the orientation of the dipole moment and the crystal
structure we can see from Figure 3-17b that the strongest dipole alignment, and hence
ERA rate, occurs along the b crystal axis and the c crystal axis, with the weakest ERA
occurring along the a axis. Consequently, the largest anisotropy in ERA is expected to be
between the a and b axes, and a much smaller anisotropy is expected between the b and c
axes. Indeed, the observed anisotropy in both absorption and emission between the a and
b axes is ~3-fold as measured by Tavazzi et al.[61]. In contrast, the largest a-orbital
overlap anisotropy, and hence the triplet exciton hopping anisotropy, is between the b and
c axes, as seen in Figure 2 in the main text. Based on the observed anisotropy, we can
conclude that the observed distribution broadening is due to triplet exciton hopping and
not ERA.
Disorder-DrivenExciton Transportin Quantum Dot Assemblies
58
4 Disorder-Driven Exciton Transport in
Quantum Dot Assemblies
4.1
Overview
Colloidal quantum dots (QDs) are promising materials for use in solar cells, light
emitting diodes, lasers, and photodetectors, but the mechanism and length of exciton
diffusion in QD materials is not well understood. In this chapter we use time-resolved
optical microscopy to directly visualize exciton transport in CdSe/ZnCdS core/shell QD
assemblies. Contrary to expectations, we find that energetic disorder is the principle
driving force for exciton diffusion in these materials, resulting in an exciton diffusion
length exceeding 30 nm. Moreover, the diffusion length can be tuned by adjusting the
inorganic shell thickness and organic ligand length, offering a powerful strategy for
controlling exciton transport. These findings reveal new insights into exciton dynamics in
QD assemblies and provide strategies for rationally designing QD materials and devices.
Introduction
4.2
Introduction
Colloidal quantum dots (QDs) are semiconductor nanocrystals with size-tunable
optical properties [62]. QDs are promising components of next-generation optoelectronic
technologies due to solution processability, [63] narrow and size-tunable emission
spectrum, [64] and the possibility for novel physics at the nanoscale that might enable
enhanced power conversion efficiency [65],
[66]. Indeed, a number of device
architectures now employ QDs as the active optical material with great success: QDbased light emitting diodes have recently been demonstrated with external quantum
efficiency as high as 18%,[67], and solar cells based on QDs have obtained overall power
conversion efficiencies exceeding 7% [68], QD photodetectors have been fabricated that
Disorder-DrivenExciton Transportin Quantum Dot Assemblies
59
surpass the performance of epitaxial devices [69], and lasers based on QD materials have
shown tunable emission across the entire visible range [70].
Central to the operation of these devices is the formation, transport, and decay of
bound electron-hole pairs, known as excitons. For instance, in excitonic solar cells, the
efficient diffusion of excitons to charge-separating interfaces is an essential step in
photocurrent generation [63]. On the other hand, exciton diffusion to quenching
interfaces in QD light emitting diodes is a process that limits luminescence efficiency
[67]. While considerable effort has been dedicated to the investigation and manipulation
of charge transport in QD assemblies [71-74], comparatively little is known about
exciton transport. Kagan et al. first showed that the ensemble photoluminescence
spectrum of a close-packed QD solid is red-shifted due to resonant energy transfer within
the sample inhomogeneous distribution [75]. Later, Crooker et al. used spectrallyresolved transient photoluminescence to monitor downhill excitonic energy migration in
the time domain [76]. More recent studies have continued to focus on the dynamics of
QD energy transfer [77] [78] [79]. The distance of exciton propagation, however, has
remained elusive. Furthenore, it is unclear what effect downhill energy migration has on
exciton transport in inhomogeneously broadened QD assemblies, and what strategies may
be employed to control exciton diffusion length.
We report the direct visualization of exciton transport in colloidal QD assemblies
using time-resolved optical microscopy, as described in Chapter 3. By combining direct
spatial imaging experiments with measurements of spectral dynamics we reveal the
details of exciton transport in space, time, and energy, and furthermore show that the
exciton diffusion length can be controlled by modification of QD surface properties.
Disorder-DrivenExciton Transport in Quantum Dot Assemblies
A
Exciton distribution
60
B
40
30
20
0.5
20
=0
-500
D
C
3500
,1.5x0
0
m
0
x (nm)
5000
E
d, 8.05nm
sbdIffuslon
CIS
C 1000 -
6'
,''
e
,d
10
.0.5
20
Time (ns)
12.6 nm
30
40
00
10
20
Time (ns)
30
40
Figure 4-1 1 a, Concept for exciton transport measurement, showing initial exciton
distribution spreading spatially. b, Map of normalized exciton density in the place of the
sample as a function of time. c, Change in the mean square displacement of the exciton
distribution as a function of time for three QD samples. d, Schematic of the three
different QD samples used with different average center-to-center QD spacing in each. e,
Time-dependent diffusivity calculated from the mean square displacement data in part c.
4.3
Methods Summary
To measure exciton transport spatially, a pulsed laser (k
=
405 nm) focused to a
near-diffraction-limited spot excites an initial distribution of excitons in the plane of a z
70 nm thick QD film. The initial distribution broadens in time as excitons diffuse from
areas of higher exciton density to areas of lower exciton density (Figure 4-la). By
measuring photoluminescence emission intensity as a function of position and time, the
time-dependent exciton distribution can be reconstructed. Results from one of these
experiments are shown in Figure 4-lb. The exciton distribution at time t = 0 has a
standard deviation of a(0) = 204 nm, which broadens to a(t) = 214 nm at t = 40 ns.
Although the initial size of the exciton distribution is limited by the smallest focal spot
possible with far-field optics, the large signal-to-noise ratio in our measurement makes it
possible to observe even small changes in the exciton distribution.
Disorder-DrivenExciton Transportin Quantum Dot Assemblies
61
Results and Discussion
4.4
We compare exciton transport in three QD materials, which differ in inter-QD
spacing (Figure 4-id). All three samples are based on CdSe cores of nearly identical size
(diameter ~ 4.2 nm, X ~ 600 nm) with photoluminescence quantum efficiency exceeding
60%. Inter-QD spacing is tuned by varying the molecular ligand length and inorganic
shell thickness. As measured by electron microscopy, the average center-to-center
spacing in each sample is d, = 8.0 ± 0.3 nm, d2 = 8.5 ± 0.3 nm, and d3 = 12.6 ± 0.8 nm.
To quantitatively analyze the time-dependent broadening of the exciton distribution,
we plot the change in variance a 2 versus time for the three samples (Figure 4-1c).
Broadening of the exciton distribution is slower for samples with larger QD center-tocenter separation, consistent with theories of excitonic energy transfer based on
electromagnetic coupling [60], [80]. For a simple random walk, or normal diffusion, the
variance grows linearly with time,
C2 (t)where
C
2
(t) is the variance at time t,
2
(4.1)
(0)= 2Dt
is the variance of the initial distribution, and
y 2 (0)
D is the diffusivity. However, in all three QD samples the variance is observed to grow
sub-linearly (see Figure 4-1c). The measured change in variance can in this case be
parameterized by,
a 2 (t)-
2
(4.2)
(0)= Ata
where A is a proportionality factor with fractional time units and a is the diffusion
exponent. For a = I, we recover Eq. (4.1) for normal diffusion. If a <1, the transport is
said to be subdiffusive [58] with a time-dependent diffusivity D(t) = 1 / 2A-
1.
D(t) for
each of the three samples is shown in Figure 4-le. In each case, rapid initial diffusion is
followed by an approach toward a slower, quasi-static diffusivity.
Disorder-DrivenExciton Transportin Quantum Dot Assemblies
62
A
kBT
Time
B
580
0
600
-5
620
-
-10_
E 580
d
(*
-15-
:r>600
C
-
-)
>620
-20
--
600
-
-25
dW
25
620
-.30
640
0
-
.
)
---
0.1
0
-Distance
5
0
1020
Time (ns)
6
10
14
(nm)
10
15
Time (ns)
20
25
Figure 4-2 1 a, Schematic showing how the exciton energy distribution evolves as
diffusion proceeds, with fast initial diffusion and slow diffusion at later times. b,
Evolution of the emission spectrum in time for the three QD samples with white lines
showing the mean emission wavelength at each time. c, Shift in the mean emission
energy vs. time for each sample with a fit to a decaying and offset exponential function
with decay rate k,
. Inset shows the decay rate as a function of QD separation distance.
The dashed line shows a 1/d
6
FRET rate scaling for comparison.
Disorder-DrivenExciton Transport in Quantum Dot Assemblies
63
Subdiffusive transport can result from variable site-to-site hopping rates in a
disordered energy landscape [58]. In our system, excitons are generated with equal
probability at any site in the QD ensemble (Figure 4-2a). Over time, the exciton moves
energetically downhill due to energy transfer from higher-energy sites to lower-energy
sites. The thermalized exciton reaches a final average energy that is determined by site
energy disorder and the available thermal energy (Figure 4-2a) [81], [82].
QD materials are known to have energetic disorder arising from size polydispersity
[75], [76]. To characterize this aspect of our material system, we performed spectrallyresolved transient photoluminescence measurements of exciton dynamics. The temporal
evolution of the photoluminescence spectrum and intensity for the three QD samples is
shown in Figure 4-2b. In all three samples the median emission energy red-shifts with
time. This transient red-shift is absent in solution, where QDs are spaced too far apart for
exciton diffusion to occur. The time-dependent shift of the peak relative to its initial
position
is
plotted
in
Figure
4-2c.
Solid
lines
are
fits
to
the
form
AE = AE [I - exp(-kat)].
The dynamic red-shift is direct evidence of energetic disorder in our system.
Bassler [81] showed that, for a Gaussian distribution of site energies, the median
occupied energy saturates at long time to a value,
AE=
'.kBT
(4.3)
where ai is the width of the inhomogeneous distribution of site energies, and
kB T = 25 meV is the thermal energy per degree of freedom at room temperature. The
energy shift is determined by a balance between the width of the density of states and
thermal excitation out of the lowest energy states.
To quantify the energetic disorder in our system, we use Eq. (4.3) to calculate the
inhomogeneous broadening. For samples dj, d2, and cA, we find that the inhomogeneous
broadening (reported as FWHM = 2N2 n 2 -ah ) is 54 meV, 54 meV, and 47 meV,
respectively.
From knowledge of the inhomogeneous broadening and the total
photoluminescence linewidth, the homogeneous photoluminescence linewidth can be
determined from
o"
=
+lorn h.
We find that the homogeneous linewidth (FWHM) is
Disorder-DrivenExciton Transport in Quantum Dot Assemblies
64
70 meV, 68 meV, and 63 meV for samples dl, d2 , and d 3, respectively, in agreement with
recent measurements of similar materials [83]. The similarity in homogeneous and
inhomogeneous broadening for all three samples allows us to make comparisons based
primarily on inter-QD spacing.
The rate at which the exciton population approaches a thermalized energy
distribution is determined by the site sampling frequency, which is directly proportional
to the average energy transfer rate between neighboring nanocrystals. The exponential
decay constant kAE obtained from analysis of the data in Figure 4-2c is plotted in the inset
as a function of QD center-to-center distance. The dotted line shows l/d 6 scaling, as
expected for energy transfer dominated by dipole-dipole interactions [60], [80], although
higher-order multipoles may play a role [84].
If energetic disorder is the origin of subdiffusive transport, then excitons of
different energy should have different diffusivities. In Figure 4-3a we show spectrallyresolved measurements of exciton transport. Diffusion is faster for excitons in the higher
energy portion of the inhomogeneous distribution than excitons near the bottom of the
distribution. Excitons at high energy sites within the sample have larger cumulative
hopping rates due to greater probability of finding a lower-energy acceptor nearby. This
is confirmed by measuring the exciton lifetime as a function of exciton energy (Figure
4-3b). The highest-energy excitons have the shortest lifetime (fastest energy transfer
rate), whereas the lifetime of low-energy excitons approaches the lifetime of isolated
QDs, as measured in solution.
A
B
2500
12
2000E
1500
622
588
Wavelength (nm)
6
1000 -C
S
-
500-
2
5
10
Time (ns)
15
$75
600
625
Wavelength (nm)
650
Disorder-DrivenExciton Transportin Quantum Dot Assemblies
65
Figure 4-3 1 a, Evolution of the mean square displacement for three spectral regions of
the QD emission. The spectral regions are shown in the inset. b, QD emission lifetime as
a function of emission wavelength. The lifetime approaches the lifetime of QDs in
solution for lower energy excitons.
Energetic disorder is typically regarded as detrimental to diffusive transport [81].
Our results indicate, however, that in QD assemblies energetic disorder can provide an
additional driving force for exciton transport. Due to a limited exciton lifetime (10-20 ns
in these materials), an exciton spends the majority of its time in the transient approach to
thermal equilibrium (see Figure 4-2c). Consequently, transport occurs mainly during the
first few nanoseconds following photoexcitation, when the exciton population is large
and the downhill energetic driving force is greatest. The beneficial effect of this initial
rapid diffusion on the overall exciton diffusion length, LD, is demonstrated in Figure 4-4.
Here, we plot the fraction of excitons surviving to some time t vs. the net spatial
displacement (in one dimension) during that time. The solid curves shown in Figure 4-4
are generated directly from measurements of the exciton spatial distribution and the
ensemble population decay. By convention, we define the exciton diffusion length, LD, as
the minimum net displacement in one dimension achieved by 37% (i.e. Ile) of the exciton
population. Exciton diffusion lengths for samples dl, d 2, and d3 are found to be 32 nm, 25
nm, and 21 nm, respectively. These values are 2-5 times larger than typical singlet
exciton diffusion lengths in organic molecular thin films [12].
The dashed curve in Figure 4-4 is a hypothetical case of normal diffusion for
sample d, assuming a constant limiting diffusivity of D(t-coo) =
x 10-4
cm 2/s. Comparing
it to the measured (solid) curve for dl, we see that the initial rapid disorder-driven phase
of transport leads to an exciton diffusion length that is more than twice as large as one
would expect assuming thermalized exciton diffusivity. This shows that the initial phase
of transient approach to a thermalized population should not be neglected when modeling
hopping-type exciton transport in disordered materials.
Disorder-DrivenExciton Transport in Quantum Dot Assemblies
66
1d
0.8
d2
d
-
-O -dD(t-yo
0.6
.0
0
C
0
10
20
30
40
50
Propagation distance (nm)
Figure 4-4
I
Distribution of exciton propagation lengths for the three QD samples
obtained from measurements of the mean square displacement and the exciton lifetime.
Dashed line shows the hypothetical case in which the diffusivity is constant and has a
value of D = 10~4 cm 2/s.
While it is evident that energetic disorder provides an additional driving force for
exciton transport in these QD samples, it is not clear what the optimum amount of
disorder would be for maximizing exciton diffusion length. Increasing inhomogeneous
broadening would augment the initial rapid phase, but also slow transport at later times.
The effect of energetic disorder is expected to be system-specific, and a function of
exciton lifetime, hopping rate, homogeneous linewidth, and Stokes shift. Additionally,
we note that not all energetic disorder is good. For instance, heavy-tailed distributions
with very deep energetic traps have deleterious effects on exciton transport [54].
4.5
Conclusion
We have showed that energetic disorder, QD center-to-center distance, and
photoluminescence quantum efficiency are important factors in determining exciton
diffusion length in QD materials. Additionally, emission wavelength (i.e. band gap) is
expected to strongly influence exciton diffusion length. For a random walk of dipolemediated energy transfer events, LD scales as L 5' 2 [36].
In a film of near-infrared (? z
1200 nm) emitting QDs with similar polydispersity, size, and photoluminescence
quantum efficiency to our sample d1 , exciton diffusion lengths exceeding 150 nm could
Disorder-DrivenExciton Transport in Quantum Dot Assemblies
67
be expected. The flexibility in tuning exciton transport allows QD materials to be
engineered for a particular device application. For example, in excitonic solar cells where
a long diffusion length is desired, QDs with a thin shell, short ligand, and long exciton
lifetime are desirable. For light-emitting devices and lasers where isolated, noninteracting excitons are desired, QDs with thick shells and little inhomogeneous
broadening are ideal.
5 Harnessing Exciton Transport: The
Excitonic Antenna
5.1
Overview
In this chapter we show how exciton transport in molecular materials can be
harnessed for addressing a fundamental limitation: the small optical absorption crosssection of nanoscale items such as molecules and quantum dots. This limitation is
relevant to a number of applications including single-molecule sensing, single photon
generation, and down-conversion for lighting applications. Here we develop the concept
of the excitonic antenna, which relies on the strong excitonic absorption and exciton
transport of J-aggregates to funnel excitons to acceptor molecules and quantum dots, thus
increasing their absorption cross-section. We show that on a per-molecule basis, the
absorption cross-section, and the subsequent fluorescence, of DCM molecules coupled to
the excitonic antenna is enhanced by a factor of ~1000. Furthermore, we demonstrate
how fluorescence enhancement occurs on the single quantum dot level.
5.2
Introduction
Nature presents us with a fundamental size mismatch in photonics. While the size
of the smallest optical mode in free space is a microscopic A/2 ~ 250 nm, the size of the
optical absorption cross-section of a typical organic molecule is
~ 0.1 nm .
Consequently, the probability that a single photon will be absorbed by a single molecule
is ~10-7. The small absorption probability then leads to low external quantum efficiency
(EQE) of molecular fluorescence, where EQE is defined as the fraction of incident
photons that are reemitted.
harnessingExciton Transport: The Excitonic Antenna
69
A number of technological applications would benefit by increasing the absorption
performance and fluorescence of organic and nanostructured materials. These include
chemical sensing, lasers, solar concentrators, photodetectors, single-photon generation,
and optical frequency down shifting. These applications in the context of our system are
discussed at the end of Chapter 6.
5.3
Fundamentals of absorption cross-section
Several factors contribute to the low absorption probability. First, the absorption
features in most organic and nanostructured materials are spectrally broad, with the
transition dipole moment of the transition distributed over this spectral bandwidth. For an
optical transition with Einstein spontaneous emission cross-section A, and lineshape
function g(v) where v is the frequency, is [85]:
or,,9
ab()=
1X
2
(5.1)
g(X)
The broadening of an optical transition has three components: (1) the natural linewidth
AE determined by the transition dipole moment, (2) the homogeneous linewidth AEh,
and (3) the inhomogeneous linewidth AElh, with the total linewidth given by
AE = AE + AEh AEih
(5.2)
Inhomogeneous broadening is caused by site-specific disorder in the material, with each
molecular site experiencing a different environment causing energy shifts. The main
source of homogeneous broadening in solid-state systems is due to molecular vibrations.
Even in a perfectly ordered system with no inhomogeneous broadening, the linewidth at
room
temperature
will
still be
dominated
by the
homogeneous
broadening
AE=~kT = 25 meV. This broadening then sets a limit on the absorption. For a two-level
transition Eq. (5.1) can be rewritten as [86], [87]
=' 3X2
abs
AEh
2AE
(5.3)
We see that while fundamentally the absorption cross-section is ~A2 , the cross-section is
reduced by a factor of AEh / AE 0 due to homogeneous broadening.
HarnessingExciton Transport: The ExcitonicAntenna
5.4
70
Existing approaches for absorption enhancement
Over the past decade, work on the control of radiative properties of luminescent
materials has led to the development of strategies for enhancement of fluorescence by
near-field coupling of constituent lumophores to optical fields associated with metal
nanostructures [88-91]. Plasmonic metal nanostructures can increase the fluorescence of
lumophores by locally enhancing the incident optical field, by modifying the lumophore
radiative rate, and by increasing the outcoupling of light. For example, fluorescence
enhancements of up to 1340-fold have been demonstrated in bowtie nano-antennas,[90]
in the vicinity of scanning probe tips,[92-95] and even in large-area structures.[91], [96]
While providing high local fields and large enhancement factors, such schemes are highly
sensitive to the nano-scale geometry of the plasmonic structures, resulting in either large
enhancement or effective quenching.[89], [94]
5.5
Concept: the excitonic antenna
Here we propose and demonstrate a purely excitonic approach to absorption
enhancement by harnessing the absorption and exciton transport properties of organic
thin films. Figure 5-1 shows the schematic of the excitonic antenna. Molecules or other
absorbers to be enhanced such as quantum dots are deposited on a material (the antenna
material) with a large absorption cross-section and having a long exciton diffusion length.
The antenna material is optically excited generating excitons. The excitons diffuse and
eventually encounter an acceptor molecule or quantum dot. The emission of the antenna
material and the absorption of the acceptor are chosen to overlap in order to produce
efficient FRET to the acceptor. The exciton on the acceptor can now be emitted
radiatively or the energy can be further transferred as needed.
HarnessingExciton Transport: The Excitonic Antenna
71
71
HarnessingExciton Transport. The Excitonic Antenna
O X=600
emission
nm
excitation
A=400nm
1
J-aggregate film
(5 nm)
IR-
T
A~k~d&
single
acceptors
exciton diffusion
by random walk
Figure 5-1 | Schematic of the excitonic antenna for absorption and fluorescence
enhancement
In this scheme, the dimensionality of the incident photon energy is reduced in
several steps. The incident three-dimensional microscopic photon mode is first localized
in a quasi two-dimensional film in the form of excitons. Exciton diffusion and energy
transfer to the acceptor further localize the energy onto a zero-dimensional acceptor. The
absorption cross-section of the acceptor is effectively increased by a factor corresponding
to the number of molecular sites that can be sampled by the diffusing exciton within its
lifetime. In this work we will generally refer to the enhancement in fluorescence because
fluorescence is the experimental observable, while recognizing that in the absence of
saturation of the excited state, fluorescence is proportional to the absorption crosssection.
5.6
Excitonic antenna continuum model
In this section we quantitatively consider the dynamics of the excitonic antenna to
determine the acceptor fluorescence enhancement. The rate equations describing the twodimensional densities of antenna excitons n,(t) and acceptor excitons n,(t) are
dn
pjklS=
- knJ-y(NA - nA)nj
dn
dnA = PA - kAnA
+y(NA - nA)nj
dt
(5.4)
harnessingExciton Transport: The Excitonic Antenna
where /, and
PA
72
are the excitation rates per unit area, kj and kA are the total exciton
decay rates (including radiative and nonradiative components), NA is the density of
acceptors. The parameter il is the fraction of donor excitons that are mobile and can
couple to the acceptors. It is reasonable to expect that many generated donor excitons are
not mobile due to the many unknowns of the morphology of the J-aggregate antenna
material, which will be discussed below. Hence, q is the only fit parameter used in the
model.
The last term in the rate equations represents the total energy transfer rate to the
acceptors due to diffusion and FRET. The parameter y is the donor-acceptor FRET rate
constant in units of cm 2 /s which is given by [1]
y = 4rDRF / dj
(5.5)
where D is the diffusivity of the donor excitons, dj is the thickness of the donor film. The
capture radius RF is the distance between donor and acceptor below which energy transfer
happens instantaneously. This is a common approximation made for two-body reactions
such as this [1]. Here we make the approximation that the capture radius is equal to the
FRET radius. We solve our system in the two-dimensional case where the donor film
thickness dj is on the order of the FRET radius, dj ~ RF. Hence to obtain the twodimensional FRET rate constant y, we reduce Eq. (5.5) by di. In two dimensions, the
diffusivity of the donor excitons D can be related to the diffusion length LD by [1], [19]
LD =
D
4D
k
(5.6)
where 1 / k. is the lifetime of the donor excitons. The FRET rate constant is then given
by
iL2D kJ RF
ff=
(5.7)
d,
which can be regarded as the surface area sampled by a diffusing exciton within the
exciton lifetime.
HarnessingExciton Transport: The Excitonic Antenna
73
The rate equations can be solved in steady-state to yield the total density of
excited acceptor molecules. The total rate of emission from the acceptor molecules is
given by
IA= k'k A(ki PA + #P
A
+ yN A
(5.8)
where kAx is the radiative rate of the acceptors. Here we have made the assumption that
saturation of the acceptor transitions is negligible, which is a reasonable approximation in
the limit of low-intensity, continuous-wave excitation that is used in our experiments.
The first term,
3A,,
is the direct pumping rate of the acceptors by the incident excitation
light. This occurs because of spectral overlap between donor and acceptor absorption,
which can be large or small depending on the choice of donor and acceptor materials, as
we will see below. The second term in Eq. (5.8) is the acceptor excitation due to the
FRET from diffusing donor excitons. The rate of emission per molecule is given by
A=
'
kA
AJ+
N AN
J+
'Na
Ak,+
yN A
(5.9)
The enhancement in fluorescence intensity from the acceptors is then given by the ratio
of the excitonic pumping term and the direct pumping term of Eq. (5.9)
EF = excitonic pump + optical pump
optical pump
fl
yNA
=1+11
PA k + yNA
The pump rates
#,
and
#A can be rewritten
(5.10)
as
fP=
ICJNJ
P,
I
(5.11)
NA
A
where I is the pump rate in photons/cm 2, and uT and o A are the absorption crosssections of the donor and acceptor materials, respectively, at the excitation wavelength.
The enhancement rate is then
EF = 1+ 77
yNj
A kJ+yNA
(5.12)
HarnessingExciton Transport: The Excitonic Antenna
74
This expression is further simplified by noting that
k
N
NF
=(5.13)
where 1/ N F is the surface area sampled by a diffusing exciton given by
N F=
(5.14)
7(L\JRF
Therefore the final expression for the enhancement factor is
EF=1+
a
A
N
N Nj
(5.15)
NF +NA
A surprising feature of Eq. (5.15) is that EF is a function of the acceptor concentration
N A. As we will see in subsequent sections, this dependence is a consequence of the
ability of a single acceptor to scavenge donor excitons from an area much larger than the
FRET radius due to the mobility of the donor excitons.
5.7
A test system: J-aggregate antenna and DCM acceptors
The key criteria to increasing this enhancement factor are the ratio between the
recombination of donor excitons, k. and the rate at which donor excitons diffuse and
energy transfer to acceptors, YNA , as well the ratio between the absorption of the antenna
material and the acceptor material. For these reasons J-aggregate thin films are ideal
candidates as donors for large enhancement factors. As discussed in Section 2.6.3, Jaggregates are characterized by a narrow and intense absorption feature and are known to
have long (~50 nm) exciton diffusion lengths. As the acceptors, we use will consider
molecules of DCM, a stable organic laser dye discussed in Section 2.6.2.
The J-aggregate thin films are composed of aggregated thiocyanine molecules, with
the J-peak absorption resonance centered at k = 465 nm (Figure 5-2). Due to the small
Frank-Condon shift in J-aggregates, the emission is centered at k = 467 nm. The DCM
molecules are deposited on the thiacyanine J-aggregate (TCJ) film with varying
concentrations. DCM is chosen because its absorption spectrum, center at X = 460 nm,
has excellent overlap with the J-aggregate emission spectrum, resulting in efficient
FRET. The emission of DCM is measured to be centered at ~600 nm in the dielectric
HarnessingExciton Transport: The Excitonic Antenna
75
environment of the underlying TCJ film and the surrounding air [97]. The DCM emission
is therefore well spectrally separated from the peak of the J-aggregate emission, making it
possible to discriminate acceptor enhancement from background antenna material
emission.
antenna:
thiocyanine J-aggregate
0.
absJ
acceptor:
DCM dye
abs
%
~
Forster
e
'
energy
-- transfer
(FRET)
em
OCM
"C
CN
350
400
450
500
550
Wavelength (nm)
600
650
700
Figure 5-2 1 The TCJ-DCM system in which TCJ acts as the excitonic antenna and DCM
molecules as acceptors.
5.7.1
TCJ-DCM sample preparation
TCJ thin films are prepared via layer-by-layer dip coating using the technique
described by Bradley et al [28]. The 4.5-bilayer films are deposited on glass slides having
a 1 mm thickness. The thickness of the J-aggregate films is estimated to be -5 nm, based
on AFM measurements of similar cyanine-based layer-by-layer thin films [28].
DCM
(4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran)
is
prepared by dissolving DCM powder (Exciton Inc.) in chloroform at a range of
concentrations from 10- mg/mL to 10- mg/mL. The DCM solutions are deposited onto
TCJ films by spin coating at a rotational speed of 1500 RPM and with an acceleration of
1500 RPM/s. All depositions of DCM were done in an N2 inert atmosphere glovebox to
minimize degradation of the DCM dye. We verified that TCJ samples are insoluble in
chloroform with now measurable change in the optical properties after immersion in
chloroform. The samples are encapsulated by first depositing a bead of Torr Seal two-part
solvent free vacuum epoxy on the perimeter of the sample. The film is then sealed in the
76
HarnessingExciton Transport: The Excitonic Antenna
glovebox by placing a glass coverslip on the epoxy bead, thereby creating a sealed N2
pocket around the central region of the film.
A set of control samples is fabricated by spin-coating the same DCM solutions on
glass slides that had been coated with a single layer of PDAC, the positive polyelectrolyte
constituent of the layer-by-layer J-aggregate thin films. The PDAC layer is used in order
to make the surface of the control sample similar in hydrophilicity to the top surface of
the J-aggregate films, which also has PDAC as the top layer. This ensures that a
particular DCM concentration in solution will result in the same DCM surface density
after spin coating on both TCJ and the control samples.
5.7.2
TCJ-DCM sample characterization
The absorption of TCJ films was determined by measuring the thin film
transmission (Figure 5-3). The reflection of the film is ignored here because only an
approximate value of absorption is required for the subsequent analysis. Based on the
peak absorption of the film (A = 49% at X = 466 nm), the film thickness of -5 nm, and
the peak absorption coefficient of TCJ is a= 1.4 x 106 cm-'. The typical molecular
density for organic small molecules such as cyanine dyes is n ~ 2 nm-3 . The absorption
cross-section is related to the molecular density n and the absorption coefficient a by
a,
For TCJ we find that the absorption cross-section per molecule is
the peak of absorption.
(5.16)
n
cabs
=
7 x 10-16 cm
2
at
HarnessingExciton Transport: The Excitonic Antenna
77
400
30 0
0 2010-
0-
Figure 5-3
= 466 nm.
I Absorption
400
450
500
Wavelength (nm)
550
600
of 4.5 bilayer TCJ thin film, showing a 49% peak absorption at X
To compare the experimental results to the above model, it is necessary to obtain
the density of DCM acceptors on the TCJ film. This quantity cannot be obtained directly
because at low surface densities the absorption is very difficult to measure by
transmission methods. Instead two solutions with higher DCM concentrations
1
(
' mg/mL and 102 mg/mL) were prepared and spin coated onto PDAC coated glass
slides. The absorption of these samples is shown in Figure 5-4. From the peak absorption
of 1.9% at k = 461 nm for the 10-' mg/mL solution concentration, and a previously
obtained peak absorption cross-section for DCM of aUDCA =1.3x 10-16 cm 2 , we find that
the surface density of DCM molecules is NDC
=1.4x 1014 cm
2
. This value is obtained
using the relationship
NDCM
A
(5.17)
DCM
where A is the absorption. The surface density corresponding to a particular solution
concentration can now be extrapolated based on the value obtained for the 10' mg/mL
solution. To ensure that the surface density scales linearly with solution concentration we
measure the PL intensity from the control samples.
Figure 5-5a shows the emission
spectra from DCM control samples fabricated from a range of solution concentrations.
Figure 5-5b near-linear relationship between solution concentration and the integrated
harnessing Exciton Transport: The Excitonic Antenna
78
PL, with a power law exponent of y = 0.9. This result confirms that extrapolating the
DCM surface density based on solution concentration is a valid assumption.
10-1 mg/mL
10-2 mg/mL
-
1.5-
0
0
CO)
0.5
0
350
400
- ---450
500
550
Wavelength (nm)
600
650
Figure 5-4 I Absorption of DCM on glass (control samples), at two DCM concentrations
in solution.
a
X
10,b
10 10_
-10- 3 mg/mL
-- 10' mg/ML
10-
.
-- 10-5 mg/mL
-0mg/mL-
42 8
86 -
'
-
10 9
Power law fit
y= 0.9
"R 10,
406
10 6
2 --
-i-
500
550
600
650
Wavelength (nm)
-
700
-4o2
100
10-
10
10DCM concentration (mg/mL)
Figure 5-5 I Analysis of the PL from DCM control samples. a, PL of DCM control samples
at three solution concentrations. b, Integrated PL counts as a function of solution
concentration, showing a near-linear power law dependence with a power exponent of
y = 0.9.
HarnessingExciton Transport: The Excitonic Antenna
5.8
79
Optical measurement setup
Spectrally resolved measurements are carried out on an inverted optical microscope
(Nikon Ti-U). Samples were excited with a mercury lamp in an epifluorescence
configuration, with the excitation bandpass filter of k = 390 ± 10 nm. The excitation light
is focused to 100 pm diameter spot with a 20X objective and the sample was
continuously scanned during measurement in order to avoid photobleaching. The
excitation power density as measured at the sample is 1 W/cm 2 . A k = 405 nm longpass
dichroic filter and emission filter were used to select the fluorescence, which was coupled
into a CCD spectrograph.
Time-resolved measurements are carried out on the same microscope, but with
pulsed excitation from a supercontinuum white light source (NKT Photonics SuperK
Blue). The supercontinuum laser produces pulses with ~100 ps duration at a repetition
rate of 40 MHz. The laser output is fiber coupled to an acouso-optic tunable filter
(AOTF) (NKT Photonics), which is used to select the excitation wavelength, exc = 475
nm. The excitation light is focused to 100 ptm diameter spot with a 20X objective. The
fluorescence is collected and filtered as above, and then focused onto a single photon
detecting avalanche photodiode (APD) (MPD PDM Series 50 tm). The output of the
APD is connected to a timing module with a resolution of 4 ps (PicoQuant PicoHarp
300), which detects the arrival time of each photon to build a time-resolved trace of the
PL emission.
5.9
Enhancement of DCM on TCJ
Figure 5-6 shows the spectrally resolved emission from the TCJ-DCM system for
samples having a range of DCM surface densities under CW excitation. A range of DCM
surface densities is used in order to probe the ability of a single acceptor to scavenge
excitons from a large area of the antenna material. The spectra show two emission
regions. At wavelengths k < 505 nm, the PL is dominated by the J-aggregate peak. For k
< 505 nm the PL consists of a superposition of the tail emission states from TCJ and the
PL of the DCM layer. We see that as the DCM surface density is reduced over two orders
HarnessingExciton Transport: The Excitonic Antenna
80
of magnitude, the reduction in the DCM component is significantly less. The J-aggregate
PL tail is a ubiquitous feature of J-aggregates in both solution and thin film form.
J-aggregate peak
emission
DCM + J-aggregate tail
emission
I.'
12 CM-2
101 cM-2
-10"
0CM -2
NoDCM
I-
3.5
3-
IR2.5-
450
500
550
600
650
Wavelength (nm)
700
Figure 5-6 I PL of the TCJ-DCM system showing two spectral regions corresponding to Jaggregate peak emission and the DCM emission.
The DCM component is quantified by subtracting the TCJ component from the
total PL spectrum. To reduce the contribution of the TCJ emission, we use
=
575 nm as
the cutoff wavelength at which the DCM component is normalized to zero. This approach
will slightly underestimate the DCM emission because the DCM emission is centered at
= 600 nm, as can be seen in Figure 5-6. We found that this analysis step was necessary
because of the variation in the J-aggregate peak intensity between TCJ samples that were
otherwise prepared in identical conditions and in the same layer-by-layer growth.
However, despite the peak height variation, the normalized shape of the TCJ tail
spectrum (when normalized at k = 575 nm) was identical across samples, making any
changes in that shape attributable to the DCM contribution.
HarnessingExciton Transport:The Excitonic Antenna
81
Figure 5-7 shows the DCM component of the emission for both the TCJ-DCM
system and the DCM control samples. As was seen in Figure 5-6, the reduction in the
DCM component is not proportional with the reduction in acceptor surface density. In
contrast, Figure 5-6b shows that the control DCM samples show a decrease PL intensity
that is proportional to surface density. The integrated DCM PL intensity as a function of
surface density for both sets of samples is shown in Figure 5-8a, quantifying the
observations in Figure 5-7. At a surface density of N A =1012 Cm- 2 the PL from the TCJ-
DCM sample is a factor of 6 higher than the corresponding control sample. Therefore the
enhancement factor at NA
=1012
cM- 2 is EF = 6.
The enhancement factors at other
surface densities are calculated similarly and are shown in Figure 5-8b. At a
concentration of N A=109 cM- 2 the enhancement factor per DCM molecule is EF
2000.
DCM on J-aggregates
DCM on glass
DCM density
2
30
-1'c
cm-
-)- 10
cm
-25 10
20
10
30
25
m
--- 10
cm~
cm~
cm2'-1
-2
15
10
10
0
-0
-2
15
5
DCM2 density
35
5
600
650
Wavelength (nm)
700
500
550
600
650
700
Wavelength (nm)
Figure 5-7 I DCM component of the total emission for the TCJ-DCM system (left panel)
and the DCM control samples (right panel).
82
HarnessingExciton Transport: The Excitonic Antenna
a
10
1000
Mean DCM spacing (nm)
100
10
b
Mean DCM spacing (nm)
41000
1000101
100
10
D1000-fold
100
C 10
J-aggregate
enhancement
10
0110
10-21
DCM on glass
10
10-1
10
r
10
12
10
DCM surface density (cm 2)
10
10O
10
0'
1010
DCM surface density (cm- 2)
10
22
Figure 5-8 1 a, Total DCM emission as a function of DCM surface density for the TCJDCM system and the DCM control samples. b, Enhancement factor per molecule with
varying DCm surface density, showing > 1000-fold enhancement for low DCM densities.
5.10 Time-resolved measurements of DCM emission
The same enhancement effect can be seen by measuring the time-resolved
fluorescence from the TCJ-DCM samples. Figure 5-9a shows the emission for k > 565
nm for a range of DCM concentrations. The PL is dominated by TCJ emission at early
times, while the DCM contribution is significant at longer times (t > 1 ns). The TCJ
lifetime in the absence of DCM is ~1 ns in this spectral range, with the more paid decay
exciton decay occurring at wavelengths corresponding to the J-aggregate peak. After
decay of the TCJ excitons by radiative recombination, nonradiative recombination, or
FRET to DCM, the longer DCM exciton lifetime (T = 5 ns) is dominant in the emission.
The DCM component is obtained by subtracting the normalized PL decay for the sample
with DCM from the normalized PL decay curves obtained from the DCM coated samples
(Figure 5-9). Figure 5-10 shows the time-resolved DCM PL component for DCM coated
on glass and for DCM coated on TCJ with the same surface density. The peak of the
emission from the TCJ-DCM sample is delayed relative to the PL trace from the control
sample. This delay could be attributed to the time required for TCJ excitons to diffuse
after excitation and subsequently FRET to the acceptors. However, this interpretation is
complicated by the fact that the DCM emission is obtained by subtraction of one semi-
HarnessingExciton Transport: The Excitonic Antenna
83
exponential decay trace from another, a mathematical procedure which naturally results
in a peak delayed from t = 0. To further elucidate the origin of the delay, samples with
thinner TCJ layers and fewer "fixed" excitons are needed (as discussed in Section 5.13).
a
b
Total emission > 565 nm
100
DCM component
10-1
-i10 mg/mL
5 mg/mL
-10-
increasing
-
IT
increasing
DCM density
No DOM
-
DCM density
1
0
8
0.
0.
10-2
0
2
4
6
8
10
12
I
. ..
1.
10 -3
2
Time (ns)
4
,
6
8
Time (ns)
10
Figure 5-9 1 a, Time-resolved PL from TCJ-DCM samples, filtered for wavelengths A > 565
nm. b, The DCM PL component.
-1 ns delay due to exciton diffusion and FRET time
100
DCM on TCJ
1012 CM-2
C
10-
II
DCM
1012 cm-
2
I
10-21
J
I
0
2
I
4
I
6
8
Time (ns)
I
R
10
12
Ii
Figure 5-10 1 Time-resolved PL from a DCM control sample (on glass) and from DCM on
TCJ, at the same acceptor surface density.
TI
12
HarnessingExciton Transport: The Excitonic Antenna
84
5.11 Modeling the J-aggregate DCM system
In this section we return to the model developed in Section 5.6 in order to interpret
the enhancement factors and the dependence on acceptor density that is found
experimentally. The model is evaluated using the optical parameters for TCJ thin films
and for DCM, which are shown in Table 5-1.
Parameter
Value
Notes
41
1.4 x 10-" cm 2
TCJ absorption cross-section at 390 nm
9D
3.9 x 10-
NJ
5 x 10" cm- 2
Density of TCJ donor molecules
d
5 nm
TCJ film thickness
RF
5 nm
TCJ to DCM FRET radius
'1
0.02
Fraction of excitons which are mobile
cm 2
DCM absorption cross-section at 390 nm
Table 5-11 Parameters used in model of DCM enhancement.
Figure 5-11 shows the fluorescence enhancement factor per DCM molecule, as
obtained from Eq. (5.15), as a function of the acceptor density NA and for a range of
exciton diffusion lengths LD. The enhancement factor dependence on acceptor density
has three clear regimes. For NA >> 1012 cm- 2 (corresponding to a mean acceptor spacing
of dA <10 nm), EF approaches 1 independent of the diffusion length. This occurs
because a smaller area on TCJ acceptors is available to each DCM acceptor and therefore
the direct optical excitation rate of the acceptors exceeds the pump rate due to FRET. In
the second regime, the acceptor spacing becomes comparable with the diffusion length
dA ~ LD . In this regime, each DCM acceptor can "see" an increasing area of the TCJ film
as the acceptor density is decreased. At these densities, the largest increase in
enhancement factor is observed. In the third regime, the acceptor separation exceeds the
diffusion length, dA
>
LD . The enhancement factor hence saturates because a single
harnessingExciton Transport: The Excitonic Antenna
85
acceptor cannot access TCJ excitons that were created at a distance farther than the
diffusion length.
Mean acceptor spacing (nm)
100
10
1000
1
_> 10
o
E
nm
L=100
0
L
=0n
10
CO)
LD
L
10
ED
nm
L=>
0
-C
C
r
LD
L
10
lnm
108
101
101
101
DCM density (cm-)
LD <sacengo
D spacing
LD > accetor
D
spacingJ
pJ <lOD
D
Figure 5-11 I Simulated enhancement factor per DCM acceptor as a function of DCM
density for a range of J-aggregate exciton diffusion lengths.
J-aggregates are known to have long diffusion lengths, which motivated our choice
of this material as the excitonic antenna. In similar layer-by-layer thin films, we have
measured the exciton diffusion length to be 50-100 nm (see Chapter Error! Reference
source not found.). Figure 5-12 shows a comparison between the simulated
enhancement factor for a diffusion length of LD = 100 nm and the experimental data. The
data shows good agreement with the simulation, indicating that the range of DCM
densities chosen for this experiment puts the system in the second regime described
above, with dA ~ LD. The only fit parameter in the model is j7 = 0.02, the fraction of TCJ
excitons that can diffuse and FRET to DCM. If this parameter was set to a higher value,
the predicted enhancement factors are significantly larger, in disagreement with the
86
Harnessing Exciton Transport: The Excitonic Antenna
experiment. This result suggests that most of the excitons generated in the TCJ film are
not mobile.
The consequence of these "fixed" excitons is that despite the large enhancement
factors, the J-aggregate emission spectrum remains dominant and largely unaffected in
the presence of DCM due to the large mismatch between the number of donors and
acceptors. This is in contrast to other "superquenching" systems that have been studied
[98] [99], in which the donors can be heavily quenched. In our system the majority of
donor excitons appear to not participate in the diffusion and FRET process.
A more complete understanding of the morphology of J-aggregate films and how it
relates to exciton transport is needed. Indeed the exciton transport techniques developed
in the previous chapters offer a path for future studies of J-aggregate exciton diffusion.
With better control of film morphology and the potential to embed the acceptors directly
into the antenna material could significantly increased the fraction of coupled excitons
and hence further increase the fluorescence enhancement factor.
7 10
_
___
Sim with L
-
Measured
= 100 nm
0
E
2 10
0
CL 2
10
L
CO,
a)
E
10
C)J
10-
c
108
10
101
101
DCM surface density (cm-2)
Figure 5-12 1 Simulated and measured DCM enhancement factor. A diffusion length of
100 nm is used in the calculation.
HaJrnessingExciton Transport: The Excitonic Antenna
87
5.12 Enhancement of Single QD fluorescence
One of the ultimate functions of the excitonic antenna is the ability to enhance the
absorption and fluorescence of individual emitters for sensing and single-photon
generation applications. To this end, we show in this section the ability to enhance the
fluorescence of individual quantum dots (QDs) coupled to a J-aggregate thin film.
5.12.1 Sample preparation
TCJ samples are prepared by the same technique described in Section 5.7.1, but on
#1.5 glass microscope cover slides with a thickness of 170 tm. The TCJ samples are
prepared with only 1.5 bilayers in order to minimize the TCJ PL background. The QDs
were synthesized by the Bawendi group at MIT and are composed of CdSe core with a
CdS shell, having a total diameter of 6.8 nm and a peak PL wavelength of X = 624 nm.
The solution absorption spectrum of the CdSe QDs is shown in Figure 5-13. The stock
QD solution with an unknown starting concentration was sequentially diluted in loX
steps to the desired surface density after spin coating. QDs were deposited on the TCJ
surface by spin coating the solution at 1500 RPM with an acceleration of 1500 RPM/s in
an inert glovebox environment. The samples are encapsulated by first depositing a bead
of Torr Seal two-part solvent free vacuum epoxy on the perimeter of the sample. The film
is then sealed in the glovebox by placing a glass coverslip on the epoxy bead, thereby
creating a sealed N2 pocket around the central region of the film.
HarnessingExciton Transport: The Excitonic Antenna
A,,c
F1xc =485 nm
=465 nm I
6
88
'1 F.
I
I
II
I
I
0
__
0
C
I
0
I
-
S2I
01
450
I
500
550
600
Wavelength (nm)
650
700
Figure 5-13 1 Absorption of CdSe QDs in chloroform solution.
5.12.2 Experimental setup
The TCJ-QD samples were imaged on a custom-built confocal microscope shown
in Figure 5-14. Output from a supercontinuum white light source (NKT Photonics
SuperK Blue) is fiber coupled to an acouso-optic tunable filter (AOTF) (NKT Photonics).
The supercontinuum laser produces pulses with -100 ps duration at a repetition rate of 40
MHz. The AOTF output, which has a bandwidth of -1 nm, is coupled into a multi-mode
fiber that output of which is collimated to produce a near-diffraction-limited beam with
-10 mm diameter. The beam is passed through a neutral density filter (OD = 2.0), a
vertically oriented polarizer and a 50:50 non-polarizing beamsplitter, with reflected beam
aligned onto a power meter for real time monitoring of power. The transmitted beam is
directed into the microscope (Nikon Ti-U) and reflected into the objective by a dichroic
beamsplitter (longpass k = 488 nm, Semrock Di02-R488). The 100X oil immersion
objective (Nikon CFI PlanApo Lambda 100X Oil, effective focal length
f
= 2 mm)
focuses the excitation light on the surface of the sample. All measurements were done at
an excitation power (as measured at the sample) of 50 nW.
HarnessingExciton Transport: The Excitonic Antenna
89
The sample is mounted above the objective lens on a piezoelectric scanning stage
(Physik Instrumente, P-733.3CL with controller E-710.4CL). The fluorescence is
collected by the same objective and is focused by the microscope tube lens (f= 200 mm)
to a region outside the microscope body. Two filters are mounted before the detector: a
longpass filter at k = 561 nm and bandpass filter k = 612±34 nm.
A single photon detecting avalanche photodiode (APD) (MPD PDM Series 50 tm)
is mounted in the focal plane of the tube lens. The output of the APD is connected to a
timing module with a resolution of 4 ps (PicoQuant PicoHarp 300) which detects the
arrival time of each photon. This technique, known as time-correlated single photon
counting (TCSPC) results in a histogram of photon arrival times which corresponds to the
time-dependent rate of photon emission from the sample. The detector is shielded from
stray light and all measurements are done with room lights turned off, resulting in a dark
count rate in the presence of the excitation laser of~100 counts/s.
microscope
sample on XYZ piezo
objective lens, Plan Apo Nanocoat
10OX 1.4S NA
ND 2.0
polarizer (V)
SuperK
5050
10DM:
488 nm dichroic
f=200mm
Newport
power meter
sgepoo
APD
561 LP Semrock
612-69 Semrock
Figure 5-14
TCJ.
I Optical diagram
of experimental setup for imaging single quantum dots on
harnessingExciton Transport: The Excitonic Antenna
90
5.13 Results on single QD enhancement
Images of the sample are obtained by raster scanning the piezo stage and collecting
the time-resolved PL at each location. Figure 5-15 shows the same region of the sample
under excitation at
ex
= 485 nm and keXe = 465 nm. Excitation at exc = 485 nm is at an
energy below the J-aggregate absorption and hence only the QDs are excited directly. Hot
spots corresponding to QD emission are visible under direct excitation, but with poor
signal to noise. Upon shifting the excitation by only 20 nm to x.c = 465 nm, the TCJ film
is excited, generating excitons which can pump the QD absorption. The same region
under
Xexc
= 465 nm excitation shows much better contrast, suggesting enhancement of
the QD fluorescence. The increase in QD fluorescence intensity is not due to the shift in
excitation wavelength because the change in QD absorption over this wavelength range is
small (Figure 5-13). Some of the bright regions which are present under ke
= 465 nm
excitation are due to inhomogeneous regions of the TCJ film and are hence not present
under direct QD pumping.
a
J-aggregate + QD excitation
Direct OD excitation
km = 485 nm
45C
J-aggregate film
(5 nm)
b
Direct QD excitation
c
J-aggregate + QD excitation
250
200
150
100
50
0
HarnessingExciton Transport: The Excitonic Antenna
91
Figure 5-15 1 a, Diagram of QD situated on J-aggregate thin film, showing direct
excitation and indirect excitation of QDs via the excitonic antenna. b, PL image under
direct excitation. c, Same region under excitonic pumping.
Blinking of single QD:
200
1
1
.
1
3-fold fluo escence enhancement
150
4
+-
E
J-aggregate + QD
excitation
b 100
0
direct QD
excitation
50
0
0
1
2
3
4
5
Time (s)
6
7
8
9
10
Figure 5-16 I Blinking of a single QD under direct and excitonic pumping, showing a 3fold enhancement in fluorescence.
Figure 5-16 shows the PL time trace of a single QD under the two types of
excitation. Under direct excitation the QD shows typical blinking behavior with an
ON/OFF amplitude of 20 counts/50 ms (Figure 5-17a). Under excitonic pumping at
Xexc
=
465 nm, the blinking amplitude increases to 60 counts/50 ms, representing a 3-fold
enhancement in fluorescence (Figure 5-16 and Figure 5-17b). The remaining PL in the
QD OFF state under excitonic pumping is a result of the TCJ emission tail, as seen in the
TCJ-DCM system. The bimodal intensity distribution in Figure 5-17 indicates that a
single QD is present in the laser focal spot. Figure 5-18 shows the time-resolved PL from
the same QD. Under direct excitation, the emission is nearly monoexponential with a
lifetime of ~20 ns, typical for core-shell CdSe QDs with good quantum yield. Under
excitonic pumping, the PL has distinct temporal components. At t < 2 ns the PL is
dominated by TCJ emission which is not quenched by the QD. After decay of the TCJ
excitons, the PL is dominated by the excited QDs with a lifetime at long times matching
the lifetime observed under direct excitation.
The 3-fold QD fluorescence enhancement is significantly smaller than the ~2000fold enhancement seen for DCM. This is likely due to the much larger physical size of
the core-shell QD (-2 nn shell and -5 nm core) relative to a DCM molecule (-
nm
92
HarnessingExciton Transport: The Excitonic Antenna
size), which significantly reduces the maximum FRET rate that can obtained. Due to the
three-dimensional nature of the QD system (QD size is larger than TCJ film thickness)
the continuum model developed in the previous sections is not applicable to this system.
With the use of QDs with thinner shells and by embedding the QDs in the TCJ film
during growth, we anticipate larger enhancement factors should be achievable.
a
LXexc = 485 nm
40 0
I
I
I
OFF |ON
300
C
200
0)
U-
100
0u
0
50
b
100
Counts/50 ms
150
200
150
200
Xexc =465nm
:ON
OFFi
400F
I
300
0
2
200
U_
100F
0
50
100
Counts/50 ms
Figure 5-17 1 Histogram of emission intensities for a, direct QD excitation and b,
excitonic pumping.
93
HarnessingExciton Transport:The Excitonic Antenna
ex,
-
exc = 465 nm
--
TCJ PL
= 485 nm
CO,
0.102
Enhanced OD PL
0
10 1
0
1
1
10
5
15
Time (ns)
Figure 5-18 1 Time-resolved PL for a single QD under two types of excitation.
5.14 Conclusion
In this chapter we have demonstrated a new excitonic approach to absorption and
fluorescence enhancement. The observed enhancement factors of -2000 in molecular
fluorescence compare well with the best plasmonic enhancements which have been
observed [90]. The excitonic antenna approach was also shown to operate on the single
acceptor level by imaging the fluorescence enhancement of single QDs. As will be
discussed in the following chapter, this work can be extended by incorporating optical
resonator structures to further increase light absorption in J-aggregate thin films.
J-aggregateCritically CoupledResonatorfor FluorescenceEnhancement
94
6 J-aggregate Critically Coupled Resonator
for Fluorescence Enhancement
6.1
Overview
In this chapter we extend the excitonic antenna approach by coupling J-aggregate
thin films to optical resonator. The resulting structure, known as a J-aggregate critically
coupled resonator (JCCR), can absorb > 90% of the incident light in a 5 nm J-aggregate
film. We show here that the absorption of the JCCR is surprisingly insensitive to the
incident optical wavelength and angle. Using DCM as the acceptor material, we show
that this structure functions as the excitonic antenna described in Chapter 5 but with
increased absorption efficiency. The JCCR-DCM system represents a method for
localizing highly-delocalized three-dimensional optical energy onto a zero-dimensional
molecule in the form of an exciton. Finally we discuss the excitonic antenna and the
JCCR in the context of technological applications.
6.2
Introduction
The absorption and fluorescence enhancement structure in this chapter contains a
thin film of strongly absorbing molecular J-aggregates [27] placed at the anti-node of the
electric field at a distance 10/4 away from a mirror, where Ao is the wavelength of incident
light. The resulting structure, referred to as a J-aggregate critically coupled resonator
(JCCR), absorbs nearly all the incident light due to destructive interference between light
reflected by the mirror and light reflected by the J-aggregate. Earlier work demonstrated
97% absorption in 3 molecular layers, corresponding to a 5-nm thick film of J-aggregates
in a JCCR structure [100] and the same principle has been used to enhance the signal in
surface enhanced Raman spectroscopy [101]. The optical energy incident and absorbed in
the JCCR structure is localized in the form of J-aggregate excitons. Target lumophores
J-aggregate CriticallyCoupledResonatorfor FluorescenceEnhancement
95
placed on the surface of the JCCR are coupled to these localized excitons by Fbrster
resonant energy transfer (FRET) (Figure 6-la). As a result, the JCCR acts as a platform
for strongly enhancing the effective optical absorption cross-section of the target
lumophores, increasing their emission under fixed optical excitation. The presence of the
mirror in this structure increases the absorption of the J-aggregate film but does not
modify the rate of FRET between J-aggregate excitons and donor lumophores, which is a
near-field interaction. Likewise, the emission rate of the donor lumophores is unaffected
because the target lumophore emission is not resonant with the critically coupled
resonator. The presence of the mirror does however increase the forward outcoupling of
the lumophore emission by a factor of -2.
The absorption and emission spectrum of J-aggregated films of different
molecules can be tuned across the entire visible spectrum and into the near infrared [27],
thus enabling broad tunability in the spectral response of JCCRs.
With this broad
spectral coverage, the fluorescence of a wide range of target lumophores, such as organic
molecules or inorganic quantum dots, can be enhanced by simply choosing the
appropriate J-aggregate material for the JCCR. Furthermore, due to the small Stokes shift
of J-aggregates (-5 nm), the fluorescence of the target lumophores is enhanced by
increasing the absorption at the spectral peak of their uncoupled absorption. The study
presented in this paper demonstrates a 20-fold enhancement in the emission of the laser
dye
DCM
(4-dicyanmethylene-2-methyl-6-(p-dimethylaminostyryl)-4H
utilizing the JCCR excitonic enhancement structure.
-pyran)
by
J-aggregateCritically Coupled Resonatorfor FluorescenceEnhancement
(a)
96
(b)
Alq3 :DCM (2.5 nm)
100
80
SIO2 spacer (49 nm)
-0
0
60
0.
40
0
Substrate
20
---------------------J-aggregate critically
coupled resonator (JCCR)
(C)
'
J-aggregate
on CCR
80
1
11
0.8
0
C
0 60
0.6
0
40
'r
0
J-aggregate
500
550
Wavelength (nm)
0.6 E
J-aggregate:
PL
0
0.4 J-aggregate
~0.2
450
Alq3:DC
abs.
0.4 I
o
20
V
400
50
100
SiO 2 spacer thickness (nm)
E 0.8
0
0
O'
0
(d)
100
'00'0
0
abs.
400
:A q3:DC
500
600
Wavelength (nm)
a.
PL
0.2
0
700
Figure 6-1 1 a, J-aggregate critically coupled resonator (JCCR) fluorescence enhancement
structure with 2.5 nm of DCM:Alq 3 (2.5% w/w) deposited on top as the exciton acceptor
layer. b, Calculated absorption of the JCCR as a function of SiO 2 spacer layer thickness,
showing a maximum at 50 nm, corresponding to a resonant condition. c, Absorption of
the 15-nm thick J-aggregate thin film on quartz and increased absorption of the same
film when placed on the critically coupled resonator and excited at 70 relative to normal
incidence. d, Normalized absorption (solid lines) and emission (dashed lines) spectra of
the J-aggregate and DCM:Alq 3 layers.
6.3
Methods summary
The key feature of the enhancement scheme is the localization of optical energy in
a thin nanocrystalline film of J-aggregates with a thickness comparable to the FRET
radius for energy transfer from J-aggregates to DCM molecules. The J-aggregates used in
this study are characterized by a narrow and intense absorption band centered at
A = 465 nm (Figure 6-lb), red-shifted relative to the monomer absorption, which is a
result of coherent transition-dipole coupling between molecules within the aggregate.[27]
J-aggregateCriticallyCoupled Resonatorfor FluorescenceEnhancement
97
The J-aggregate solution is prepared by dissolving a thiacyanine dye [102] in 2,2,2trifluoroethanol at a concentration of 1.5 mg/mL. The solution is then spin deposited
either on a cleaned quartz substrate or on previously prepared critically coupled resonator
(CCR) substrates rotated at 2000 RPM for 60 s. The resulting J-aggregate film is 15 nm
thick, as measured by atomic force microscopy step height analysis, and has a 20 nm
FWHM absorption line with a peak absorption of 36%, corresponding to the absorption
coefficient of a = 3 x 10 cm-.
To form the CCRs, a 300 nm thick Ag mirror is thermally evaporated on a 1 mm
thick quartz substrate at a pressure of 3x 10-6 Torr and a growth rate of 0.5 nm/s,
producing a mirror with 97% reflectivity. The spacer layer, which separates the overlying
J-aggregate film from the mirror, is formed by sputter depositing 50 nm of SiO 2 on the
Ag mirror. The 15 nm J-aggregate film is subsequently spin deposited on the SiO 2 spacer
layer. The spacer layer thickness is chosen such that the sum of the optical path length in
SiO 2 and the 30 nm optical penetration of the A = 465 nm light incident onto the Ag
mirror [103] results in the J-aggregate film being positioned at the anti-node of the
electric field. Transfer matrix simulations [104], plotted in Figure 6-lb, show that
maximum absorption of the JCCR is achieved when the SiO 2 spacer layer thickness is 50
nm, corresponding to the resonant condition.
6.4
Results and discussion
At the resonant condition, the peak absorption of the JCCR is 86% (Figure 6-1c),
measured by probing the reflectivity of the structure with unpolarized light at nearnormal incidence (70 away from the normal). The linewidth of the J-aggregate film
absorption in the JCCR geometry is increased from 17 to 25 nm due to the broad
absorption tail to the blue of the main peak. Figure 2 shows that the absorption of the
JCCR is largely independent of angle for TE polarized excitation and falls off only
slightly under TM polarized excitation. These measurements are in agreement with the
transfer matrix simulations of the JCCR, as plotted in the insets of Figure 6-2.
J-aggregateCritically CoupledResonatorfor FluorescenceEnhancement
100-
80
(Angle
100100
(o)
TM
600
4
(a 80 4,4
S60
20
)
98
40
60
20
Angle (0)
20
20
0
400
450
500
550
Wavelength (nm)
600
100
(b)
80
c
0 100
Angle (o)
TE
*eO60
080
60
40
.=
406
20
0400
450
500
550
600
Wavelength (nm)
Figure 6-2 1 Absorption spectrum of the JCCR structure as a function of angle of the
incident a TM and b TE polarized light. Insets show the measured peak absorption at
each angle (blue dots) and the absorption calculated using the transfer matrix formalism
(black lines).
The JCCR structure can be used as a general platform for enhancing the
absorption and fluorescence of luminescent nanostructures, such as organic molecules or
quantum dots, deposited on top of the JCCR. The greatest fluorescence enhancement will
occur when the overlap between the J-aggregate emission and the absorption of the
overlying material is maximized, as this condition maximizes the rate of FRET. To that
end, in the present work the J-aggregate emission spectrum (centered at A = 470 nm)
overlaps with the absorption spectrum (centered at A = 495 nm) of the overlying DCM
molecules, that will act as energy acceptors (Figure 6-1d), resulting in a calculated FRET
radius, RF, for J-aggregate to DCM energy transfer of 2.75 nm [105]. Furthermore, the
J-aggregateCritically Coupled Resonatorfor FluorescenceEnhancement
99
DCM emission is centered at A = 610 nm, ensuring that the J-aggregate and DCM
luminescence are spectrally separated, and is hence easy to resolve in optical
measurements.
DCM molecules are coated on top of the JCCR as a dilute thin film of DCM
doped at 2.5% w/w into Alq 3 (tris(8-hydroxyquinolinato)aluminum) molecular host
material. Alq 3 molecules are optically transparent at the J-aggregate and DCM emission
wavelengths. The DCM:Alq 3 film is 2.5 nm thick and is deposited on the JCCR structure
by simultaneous thermal vacuum evaporation of Alq 3 and DCM at rates of 4 A/s and 0.1
A/s, respectively, and at a pressure of 3 x 10-
Torr. The resulting effective thickness of
the deposited DCM molecules is 0.06 nm, which is much thinner than a single molecular
layer, and implies an incomplete DCM monolayer with an average separation between
DCM molecules of 4 nm (as sketched in Figure 6-la). Figure 6-3 shows the surface
morphology of the JCCR samples, characterized by atomic force microscopy (AFM) at
various points in the fabrication process, with surface roughness of (1.7 ± 0.4) nm for the
completed structures. The low roughness allows the JCCR to be approximated as a onedimensional structure, making it more conducive to modeling of FRET, exciton diffusion,
and other dynamics in the system. The layered geometry is advantageous because it
allows for the fluorescence enhancement of a range of materials that can be deposited by
vacuum or solution methods directly onto the JCCR. To prevent degradation of the
organic layers under atmospheric exposure, the samples are encapsulated in a nitrogen
glovebox using a ring of UV-curing air-impermeable epoxy and a quartz cover slip
(Figure 6-4b).
(a)
J-aggregate
on CCR
(b)
9.4 nm
-47 nm
AIq3: DCM
on CCR
(c)
10.9 nm
-58 nm
Alq3:DCM on
J-agg., atop CCR
5.0 nm
-6.4 nm
J-aggregateCriticallyCoupled Resonatorfor FluorescenceEnhancement
100
Figure 6-3 1 AFM images of a J-aggregate on the CCR structure (RMS roughness 1.2 ± 0.2
nm), b DCM:Alq 3 on the CCR structure (RMS roughness 1.2 ± 0.1 nm) and, c DCM:Alq3
on the J-aggregate layer atop the CCR (RMS roughness 1.7 ± 0.4 nm).
The enhancement of DCM fluorescence when on top of the JCCR is characterized
by measuring both the internal quantum efficiency (IQE) and external quantum efficiency
(EQE) of the structures in an integrating sphere following the technique of de Mello et al
[106]. In this measurement the samples are situated at the center of the integrating sphere
and illuminated with the output of a grating monochromator and a tungsten halogen lamp
at an intensity of 60 ptW/cm 2 at A = 465 nm and a spectral bandwidth of 6 nm. The PL is
collected with an optical fiber and imaged on a CCD spectrograph. All collected spectra
are corrected by calibrating the system using a halogen light source with a known
spectrum.
As a control sample, the 2.5 nm film of DCM:Alq 3 is also simultaneously
deposited on a quartz substrate and encapsulated in the nitrogen glove box. The
absorption of the control film is measured to be 0.5%, with an IQE of 20%, and hence an
EQE of 0.1%. Due to the low intensity of emission from the 2.5-nm film, the IQE of
DCM:Alq 3 was determined by measuring the absorption and PL of a thick, 140-nm film
deposited on quartz. The PL spectrum of the 2.5-nm DCM:Alq 3 control film is shown in
Figure 4a. An optical image of this sample under the same 60 pW/cm 2 illumination taken
with a digital SLR camera at 0.1 s exposure and a A = 550 nm longpass filter shows
almost no visible emission (Figure 6-4c).
Upon deposition of the same DCM:Alq 3 film on the JCCR structure, the DCM
emission is dramatically enhanced. Figure 6-4a shows the emission spectrum from the
DCM-on-JCCR structure, which is a sum of the enhanced DCM emission and the red tail
of the J-aggregate emission. Subtraction of the J-aggregate tail from the total PL
spectrum isolates the DCM contribution. This wavelength-integrated JCCR-enhanced
DCM emission is 20 times greater than the wavelength-integrated emission from the
control DCM sample. The optical image of the enhanced DCM sample (Figure 6-4d),
taken under the same conditions as the control sample (Figure 6-4c), shows visual
verification of the dramatic enhancement in fluorescence from a sub-monolayer
equivalent of DCM molecules. The EQE of the DCM is enhanced to 2.2%, while the
J-aggregateCritically Coupled Resonatorfor Fluorescence Enhancement
101
IQE remains unchanged at 20%. In other words, the effect of the FRET coupling to the
JCCR is to increase the effective absorption cross-section of the DCM molecules (and
hence absorption coefficient of the film). The original cross-section of the DCM
molecules is
c-D =
1.3x10- 6 cm 2 (aD = 2x10 cm') for the control DCM film. When
coupled to the JCCR the DCM cross-section is effectively enhanced to aD,JccR 2.6x 10
15 cm 2 (aDJCCR= 4x 105 cm'1). The enhancement factors produced
in this study can be
increased by decreasing the DCM molecule separation, as discussed in Chapter 5.
(a)
,
_
_
,
_
_(b)
2
+-
DCM on JCCR
1.5
DCM
contribution
1
a0.5
DCM on quartz
(C)
DCM on quartz
0
0
500
700
600
Wavelength (nm)
(e)
1 CM-
100
80
.80
20
_
D15
-
i
6O0C
-
(d)
DCM oni JCCR
10
.40c0
CI
(5
20
0
440
cm -
-1
460
480
Excitation wavelength
500
Figure 6-4 I a Emission spectra of isolated DCM film, DCM film on JCCR, and the DCM
contribution when atop the JCCR showing a 20-fold enhancement in the spectrally
integrated DCM emission. b Ambient light image of the DCM film deposited on the JCCR,
and encapsulated with UV curing epoxy and a quartz cover slip. c-d Images of DCM
emission on quartz substrate (c) and on JCCR (d) under A = 465 nm excitation. Images
taken with 0.1 s exposure and a A = 550 nm longpass filter. e Enhancement factor of
DCM emission as a function of excitation wavelength and comparison to the absorption
spectrum of the JCCR.
J-aggregateCritically Coupled Resonatorfor FluorescenceEnhancement
102
The fluorescence enhancement factor is maximized when the excitation is
resonant with the J-aggregate absorption and the CCR spacing (A = 465 nm). Figure 6-4e
shows the enhancement factor for a range of excitation wavelengths, and is observed to
follow the absorption spectrum of the JCCR. Significant enhancement (> 7 fold) occurs
over a 40 nm range, making this excitonic approach to fluorescence enhancement suitable
for applications where the incident illumination has appreciable spectral bandwidth.
It is instructive to compare the fluorescence enhancement provided by the JCCR
structure to the enhancement achieved when the DCM is excited by FRET from the Alq 3
host material. Enhancement in DCM emission is expected because a large number of
Alq 3 molecules within the FRET radius can excite the DCM molecule. Such a guest-host
excitation scheme has previously been used in the excitation of organic LEDs [2] and
organic solid state lasers [24]. A DCM:Alq 3 film (140 nm thick) was prepared on a quartz
substrate and excited at two wavelengths: at A = 400 nm, where Alq 3 absorption
dominates, and at A = 490 nm, the peak of the DCM absoprtion. The integrated intensity
of the DCM emission when pumping the DCM indirectly by energy transfer from Alq 3 is
found to be only a factor of 2 higher than when exciting the DCM directly (Figure 6-5) 10 times less enhancement than achieved with the JCCR structure.
400 nm
100
$
-0f\exc.
1xc
3
80' I\2
8
60
0
I
490 nm
exc. n
~
040
20
0'
400
500
600
700
Wavelength (nm)
0
800
Figure 6-5 | A factor of 2 enhancement in DCM emission is observed due to energy
transfer from Alq 3 in a 140 nm thick film of DCM:Alq 3, significantly less than the 20-fold
enhancement observed when using the JCCR. The DCM was excited directly at A = 490
nm, while the Alq 3 is excited at A = 400 nm at the same intensity.
J-aggregateCriticallyCoupled ResonatorJbr FluorescenceEnhancement
6.5
103
Conclusion
The presented JCCR structure is a general platform for absorption (and hence
fluorescence) enhancement of a wide range of nanostructured materials, including
organic molecules and semiconductor quantum dots. In this work, a model system is
studied showing a 20-fold enhancement in the absorption cross-section of the organic dye
DCM measured through the enhancement of the molecular fluorescence.
The
enhancement is obtained due to FRET coupling of the DCM molecules to the strongly
absorbing JCCR structure. The absorption of the JCCR is found to be over 80% for
incidence angles from 7' to 70' and the fluorescence enhancement greater than a factor
of 7 was observed over a 40 nm excitation bandwidth, making this approach appropriate
for applications where the incident light is spectrally broad and not directional. The
fluorescence enhancement factor can be improved by optimizing the J-aggregate material
for increased exciton diffusion length in the direction transverse to the plane of the film,
thus transferring a larger fraction of the generated excitons to the acceptor layer.
The JCCR system shows promise as a platform for a number of applications
where efficient absorption and reemission of light is critical. For example (with
acknowledgement to William Tisdale):
High efficiency lighting: In novel quantum dot (QD) LEDs, for instance, the
material cost of the QDs themselves may constitute a significant fraction of the total
product price. By using the luminescence enhancement scheme shown here, 20 times
fewer QDs are needed to achieve the desired brightness, decreasing manufacturing costs.
The exact reduction of the QD use would vary depending on the specific design.
Chemical sensing: Some chemical sensors rely on luminescence or luminescence
quenching of a thin film when exposed to an explosive or a toxic substance. By
enhancing the brightness of the luminescent thin film using the scheme disclosed here,
detection of analytes at lower concentrations will be possible, increasing the overall
sensitivity and efficacy of the chemical sensor.
Lasers: The heterojunction device discussed here may be a highly effective gain
medium for monolithically integrated lasers. The absorptive layer acts as an exciton
reservoir constantly supplying excitations to the lumophores in the luminescent layer and
facilitating population inversion.
J-aggregateCritically CoupledResonatorfor FluorescenceEnhancement
104
Solar concentrators: Many photovoltaic devices are known to operate at higher
power conversion efficiencies when irradiated with sunlight at levels higher than those
found at the Earth's surface. The excitonic antenna could act as a type of solar
concentrator, funneling incident sunlight in the form of excitons and delivering that
energy efficiently to small photovoltaic devices, enabling higher power conversion
efficiencies and reducing the overall material cost of the solar cell.
Photodetectors: The device provides a means for efficient light absorption and
subsequent transfer of that energy to another medium for detection. Such a scheme might
be advantageous for the efficient detection of low intensity light.
Near-field microscopy: The strategy discussed here is an effective way to focus
incident radiation that is originally dispersed over a large area down to a single
lumophore. This lumophore could then act as a nano-scale "beacon of light" for imaging
analytes dispersed on a surface.
Quantum computing and quantum cryptography: Quantum computers and quantum
encryption algorithms rely on single photons to carry information. Single lumophores
supported on an absorptive layer as described here could serve as ultrabright singlephoton sources for quantum computing and quantum cryptography.
Optical down-conversion: The device could be a method for converting light of a
given color to a lower-frequency (i.e. longer wavelength) color with the potential for
near-unity quantum efficiencies.
In summary, the JCCR-DCM system represents a method for localizing highlydelocalized three-dimensional optical energy onto a zero-dimensional molecule in the
form of an exciton. At present the J-aggregate material produces losses in the system,
with most excitons never reaching an acceptor. The goal of future work is to optimize Jaggregate exciton transport, quantum yield, and to tailor the exciton energy landscape in
order to guide excitons to acceptors instead of relying on diffusion.
7 Strong Coupling in J-aggregate
Microcavities
7.1
Overview
In this chapter we further utilize the unique absorption properties of J-aggregate
materials to achieve the regime of strong light-matter coupling. When excitons are
coupled to an optical microcavity, coherent photon-exciton states known as polaritons
can form. Polaritons in planar microcavities enable the study of polariton condensation,
superfluidity and related condensed matter phenomena, and opens a path to a radically
new class of optoelectronic devices based on the macroscopic coherence of light and
matter [14], [107-110]. Notably, strong coupling in molecular organic materials [16],
[17] could enable lasing and condensation to be achieved at room temperature, as the
high absorption constant of many molecular films and crystals can lead to strong
coupling even for low quality microcavity structures. In this chapter we show that a
critical obstacle to achieving polariton condensation in J-aggregate microcavities is
exciton-exciton annihilation, a competing process with the buildup of a polariton
population in the polariton trap.
7.2
Introduction to polaritons
Here we briefly review how the regime of strong coupling and the main features of
organic polariton microcavities. More complete reviews of polaritons in inorganic [14],
[15] and organic [17] systems can be found elsewhere.
When molecules with optical transition moments are situated in an optical
resonator, the absorption and emission rates under most conditions are perturbed only
weakly by the modification of the density of photonic states. The situation is markedly
different when the decay rate of the exciton y, and the decay rate of the cavity mode y,
Strong Coupling in J-aggregateMicrocavities
106
are both smaller than the rate of interaction between the dipoles and the cavity mode, g".
The interaction rate Q = 2g 0 , which is known as the Rabi splitting, is large when the
resonance of the exciton is matched to the resonance of the cavity. The Rabi splitting
represents the rate of coherent energy exchange between the excitons and the cavity
mode. In this regime of strong exciton-photon coupling, the initially matched cavity
resonance and exciton resonance are split into two new modes, one above and one below
the energy of the uncoupled states. These eigenstates of the coupled cavity-exciton
system are known as polaritons (Figure 7-1).
Light: Microcavity
Matter: Exciton
6
We x
100
90-
50-
1100.
40-
90.
C
0
S80
0 80
C
a 30-
@70
~20
060.
10
50
500 550 600 650 700
Wavelength (nm)
Light and Matter:
Strona Coupling
70
0-
50
500 550
600
650 700
Wavelength (nm)
!
I
-
"
500 550 600 650 700
Wavelength (nm)
Figure 7-1 | Strong coupling is obtained by matching the resonance of a cavity to the
resonance of an excitonic material. If the interaction is stronger than the decay rates of
the cavity and exciton, then two new modes in the reflectivity are seen. (Reproduced
from [17])
7.2.1
The optical microcavity
Here we review the quantitative model of polariton microcavities following the
notation of Deng et al. [14]. We begin by considering the planar microcavity, the optical
Strong Coupling in J-aggregateMicrocavities
107
structure most commonly employed in studies of polaritons due to its experimental
advantages in accessing the moment and energy of the polariton states. A planar
microcavity consists of two parallel mirrors separated by a distance L. The mirrors can be
composed of metal or of dielectric Bragg reflectors (DBRs), which are stacks of
alternating high and low index dielectrics. Metal mirrors have a maximum reflectivity of
~98%, while DBRs can reach reflectivities of >99.9999%, depending on the number of
layers in the stack and the quality of the materials. In the case of a cavity composed of
two DBRs, the transmission depends on the reflectivities of the two mirrors, RJ and R2,
and the optical phase acquired by a photon round trip in the cavity, 0. The transmission T
is given by
T=
(1- R1 )(1-R2)
(1-
RR
2
(7.1)
R2R sin (0 /2)
)2+4)
2
where 0 is the round-trip phase
(7.2)
L=
AO
The cavity quality factor
Q is a measure
of the sharpness of the resonance defined as
2zcnL
kO
(RR21 )
4
/
-O
2
l-(RR 2 )1/
A.
(7.3)
where n is the refractive index of the medium between the mirrors, Ak is the cavity
resonance wavelength, and A/1 is the width of the resonance.
The distance between the mirrors quantizes the optical field in the direction
perpendicular to the mirrors (z), but the photon momentum is continuously variable in the
xy plane. The energy of a cavity photon with in-plane momentum k,, and z momentum
k, is
E = nCc
+k
(7.4)
The perpendicular component is determined by the resonance wavelength
k = f
AO
(7.5)
108
Strong Coupling in J-aggregateMicrocavities
while the in-plane component is the related to the angle of incidence & relative to normal
2nn(
.
ki = 27ntan sin'sm
_i (sin6
(7.6)
Therefore the cavity resonance energy as a function of angle is
E= E I- si
(7.7)
2
n,
In the limit of small incidence angles, the microcavity dispersion has a parabolic
dispersion.
7.2.2
Microcavity polaritons
When an excitonic material is placed at the anti-nodes of the microcavity electric
field, and the interaction rate between the excitons and cavity is faster than the decay
rates, the system must be described by a combined Hamiltonian. In the second
quantization notation the total system Hamiltonian is
H0 = HC + He + H1
A(7.8)
+ : E b'b + I hgo (55 1b+a^ b'
= E(k ,k )6&{,
In this expression a and
a are the
creation and annihilation operators for a photon with
in-plane momentum k11 and kt and b are the creation and annihilation operators for an
exciton. Unlike in inorganic semiconductors, the excitons in molecular materials are
localized and hence do not posses a well-defined momentum. Consequently, we consider
the uncoupled exciton to have a fixed energy. The last term in Eq. (7.8) represents the
exciton-photon coupling, with the interaction rate go given by [111]
g = _
2h2 oV,
oc n 1/2
(7.9)
In this expression N is the number of participating dipoles on which an exciton can be
generated, y is the transition dipole moment, and V is the mode volume. As we can see
interaction rate scales as the square root of the dipole volume density, n.
Strong Coupling in J-aggregateMicrocavities
109
The above Hamiltonian can be diagonalized using the transformation described by
Deng et al., giving the form
H
where P and
Q
=XELP(k)P
+X E,,(k)Qp
(7.10)
are the operators for the lower polariton and the upper polariton, the
new eigenstates of the system that composites of photons and excitons. The eigenstate
energies of the polariton states are given by
E + Ee±
ELP,P
4g +(E -E
(7.11)
)2
The difference between the exciton cavity resonance and the exciton resonance is known
as the detuning, and is defined as
A = E(6 = 0)- E
(7.12)
A typical dispersion for the upper polariton and lower polariton states is shown
schematically at zero detuning in Figure 7-2, demonstrating the characteristic anticrossing of the two modes. The contribution to each polariton state from the exciton or
photon uncoupled eigenstates is expressed as the exciton fraction X(&) and photon
fraction C(6) [112]:
2
AE(6)
1
X(O)
C2
C()=-
AE()2+4g
1,
2
I-
AE(O)
AE(6)
2
(
!(7.13)
+4g2
where AE = E - E (0) is the energy difference between the uncoupled states.
7.2.3
Strong coupling using organic materials
The basic requirement for strong coupling in the system described above is that the
linewidth of the cavity AEC and the linewidth of the exciton resonance AEe be larger
than the Rabi splitting hQ = 2hgo. Semiconductor quantum well excitons have been the
traditional medium for achieving strong coupling due to their narrow excitonic peaks.
However, due to the weak binding energy of Wannier-Mott excitons, these systems do
Strong Coupling in J-aggregateMicrocavities
110
not have excitonic absorption at room temperature. Frenkel excitons in molecular
materials, on the other hand, have binding energies of hundreds of meV [1], making them
highly stable at room temperature.
Thin films of J-aggregates were the first molecular materials to show strong
coupling in a cavity at room temperature [16]. The optical properties of J-aggregates
proved to be ideal for studies of polaritons, possessing narrow exciton linewidths (AEe
-
50 meV) and high absorption coefficients of up to 106 cm-' [28]. This remarkable
absorption coefficient allows for Rabi splittings of up to 200 meV to be obtained [113].
For these reasons, the work in the following two chapters will focus on J-aggregates as
the excitonic material for strong coupling.
UP
Ene rgy
Cavity
---------------
ff
-2---------
Exciton
LP
k-vector (angle)
Figure 7-2 1 Dispersion diagram showing the uncoupled cavity and exciton modes as
well as the upper and lower polariton branch. This schematic represents zero excitonphoton detuning (A = 0 ). The Rabi splitting is hQ .
7.2.4
Polariton lasing
Polaritons are bosonic particles, and owing to the shape of the lower polariton
dispersion, these particles can collect at the bottom of the energy trap (Figure 7-3). At
Strong Coupling in J-aggregateMicrocavities
III
high polariton densities condensation can occur creating a new coherent state, known as a
polariton condensate. The coherent photon emission from the condensate is sometimes
referred to as polariton lasing. Polariton lasers have been demonstrated in semiconductor
systems [114], [115], but only a single organic system has been shown to undergo lasing
in the conditions of strong coupling [116]. Achieving polariton lasing in organic
materials is a worthwhile goal, as it allows for the study of coherent polariton physics at
room temperatures and promises to be a route towards low-threshold lasing [15] [117].
The physics of a polaritonic device can best be visualized by considering the
dispersion (i.e. the relationship between energy and k-vector) of a J-aggregate thin film
strongly coupled to its surrounding cavity. Figure Figure 7-3 shows how the polariton
modes (solid curves) are the result of splitting between exciton mode (flat dashed line)
and the cavity mode (parabolic dashed curve).
The system is pumped, either optically
or electrically, far above the shared resonance of the cavity and exciton. These excitations
can exist either as upper-branch polaritons or simply as uncoupled excitons. These
excitations quickly relax via emission of photons to the "exciton reservoir," which
consists of uncoupled or only slightly coupled, large wavevector excitons. From this
reservoir, excitons relax into the lower polariton branch and relax via phonon emission or
polariton-polariton scattering to the k = 0 state. When the occupation of the k = 0 state
becomes populated on average with at least one excitation for all time, final-state
stimulated scattering of polaritons into the lower branch massively populate the k = 0
state, creating a coherent exciton-polariton condensate. The coherent light that is emitted
is actually spontaneous emission of the polaritons, which are all coherent. This emission
is known as polariton lasing. This is in contrast to a regular "photon laser" where the
coherent emission is due to stimulation. The threshold for this kind of lasing is inherently
low because no population inversion has to be created [118]. For a more complete
comparison of polariton lasing to photon lasing see [117]
112
112
Strong Coupling in J-aggregateMicrocavities
Strong Coupling in J-aggregateMicrocavides
Below threshold
Pump
emg
Enel rgy
hQ
Polariton-polariton scattering or
Polariton-phonon scattering
-------- M
k-vector (angle)
Above threshold
Pump
Enei rgy
-h--- -
-Sg
........................
k-vector (angle)
Coherent PL ="Polariton lasing"
Figure 7-3 1 Polariton population along the lower branch below and above threshold.
7.3
Exciton-exciton annihilation in polariton microcavities
Previous work has demonstrated strong coupling in J-aggregate microcavities [16],
[119], as well as polariton electroluminescence [120] and ultra-fast relaxation between
polariton branches [121]. However, J-aggregate polariton lasing remains elusive. In this
Strong Coupling in J-aggregateMicrocavities
1 13
chapter we study exciton dynamics in highly absorbing J-aggregated organic films in
polariton microcavities [17]. We show that the J-aggregate excitonic material exhibits
significant exciton-exciton annihilation, which competes with the build up of a threshold
polariton population necessary for lasing action. The annihilation process is attributed to
the large incoherent diffusion radius of excitons in the J-aggregated film.
7.4
Methods summary
The J-aggregate material is studied both as an isolated thin film and as the excitonic
layer of a polaritonic cavity. The isolated thin film is grown by sequential immersion of a
glass substrate in solutions of the J-aggregating cyanine dye TDBC (5,6-dichloro-2-[3[5,6-dichloro- 1-ethyl-3-(3-sulfopropyl)- 2(3H)-benzimidazolidene]-1 -propenyl]- I-ethyl3-(3-sulfopropyl) benzimidazolium hydroxide, inner salt, sodium salt, N. K. Dye Chem)
and a solution of PDAC (polydialylldimethylammonium chloride) following Bradley et al
[28]. This layer-by layer growth produces a (5.1±0.1) nm thick films with an absorption
linewidth of 46 meV (13 nm), peaked at the exciton resonant energy of Ev = 2.10 eV
(591 nm), with a peak absorption of a
=
106 cm'
114
Strong Coupling in J-aggregateMicrocavities
100
(a)
(b)
80
r 60
A/2
L
$40
-
0
20,
1.8
2.0
2.2
2.4
2.6
2.3
1.0 _(c)
(d)
Detuning:
-
2.2
160 meV-
-
2.1
40 meV
-- 40 meV
exciton -
-
,c
C/
*
W2.0 -
1.9
0-
-
0.0
'
-100
0
100
Detuning (meV)
-120 meV
-
'
'
1.8
2.0
2.2
2.4
2.6
Energy (eV)
Figure 7-4 1 a, DBR-metal microcavity with a J-aggregate excitonic layer and a total
optical path length of A/2 where /I = 591nm. b, The reflectivity of devices having
different cavity-exciton detunings achieved by varying the TAZ thickness. c, The
corresponding photoluminescence. d, Energies of the upper and lower polaritons as a
function of exciton-cavity detuning extracted from the reflection plots of part b. The
bare exciton and cavity dispersions are shown as dashed lines.
The microcavity samples (Figure 7-4a) are formed by sputter-depositing a 4.5 pair
distributed Bragg reflector (DBR) on a quartz substrate, followed by a A / 4n SiO 2 spacer
layer, where n is the index of refraction and A = 591 nm . The J-aggregate film is then
deposited, followed by a 100 nm thick spin-coated layer of PVA (polyvinyl alcohol,
99.8% hydrolized, Sigma Aldrich). The PVA layer acts as the top spacer layer of the
cavity and enhances the PL external quantum yield of the film from 7% to 42%. A
thermally
evaporated
TAZ
[3-(Biphenyl-4-yl)-4-phenyl-5-(4-tert-butylphenyl)-1,2,4-
triazole] layer forms the remainder of the cavity spacer. The structure is capped with a
300 nm thick thermally evaporated silver mirror, resulting in a cavity
Q of 60.
The total
thickness of the cavity region is tuned by varying the thickness of the TAZ layer, thereby
11 5
Strong Coupling in J-aggregateMicrocavities
changing the detuning between the J-aggregate exciton (E , = 2.10 eV ) and the cavity
mode.
7.5
Results and discussion
Figure 7-4b shows the mode splitting observed in the reflectivity of devices with
different cavity-exciton detunings. The peak energy of the lower polariton branch
photoluminescence (PL) is observed to follow the lower polariton reflectivity (Figure
7-4c), indicating that the observed emission originates from the decay of polaritons. The
reflectivity and PL data are collected at normal incidence to the cavity. The polaritonic
dispersion relation for these devices is shown in Figure 7-4d, demonstrating characteristic
polaritonic anti-crossing at zero detuning with a Rabi splitting of 160 meV.
The polariton dynamics are investigated by pumping the cavities non-resonantly
with TM polarized light at A = 535 nm though the DBR at 60' relative to normal. The
polariton PL is collected at normal incidence to the sample and imaged on a CCD
spectrometer. To fully characterize the behavior of the devices in a wide range of
excitation power regimes, three pump sources are utilized: a continuous wave (CW) laser
at A = 532 nm, a 10 ns pulsed laser at A = 535 nm (10 Hz repetition rate), and a 150 fs
pulsed laser at A =535 nm (1 kHz repetition rate). With CW excitation, the devices show a
linear increase in PL intensity with increasing excitation power. With 10 ns excitation
pulses, the PL begins to show a sublinear power law dependence as a function of the
pump intensity ( PL oc
JO.54)
with the effect becoming more pronounced with 150 fs
excitation pulses (PL oc 1.35 ) (Figure 7-5a and b). Devices with a range of cavity-exciton
tunings as well as cavities with higher
Q of 115
were tested and all show qualitatively
similar sublinear behavior.
To elucidate the role of the microcavity versus the excitonic layer in the sublinear
PL dependence, we tested J-aggregate thin films grown on glass substrates (i.e. the active
layer without the cavity). A similar, but less pronounced, sublinear dependence is
observed for the thin film (PL C JO.68 with 10 ns excitation, and PL c>
jO.48
with 150 fs
excitation), indicating that the excitonic component of the device is responsible for the
sublinear response of the microcavity (Figure 7-5c and d). We rule out the sublinear
116
Strong Coupling in J-aggregateMicrocavities
power dependence as being due to absorption saturation, as only 1% of the molecules are
excited at the highest powers. Furthermore, the films show no PL or absorption
degradation under 10 ns excitation (4 mW/cm 2 maximum average power density) and
only slight degradation under 150 fs excitation (40 mW/cm 2 maximum average power
density) that is insufficient to account for the sharp roll off in PL quantum yield.
.....-
(a)
(b)
PL OC IO.-54
PL oc
-
*..-.
C
Microcavity pumped with:
150 fs pulses
Microcavity pumped with:
10 ns pulses
S
I
*
*
I
*
I
(d)
0
PL ocI 0
PL oc I'0.6"
48
.
y
Thin film pumped with:
ni
0
10
Incident
. j dit
Thin film pumped with:
150 fs pulses
p'
10 ns pulses
JWm
40
20
30
power density (kW/cm2)
0
10
20
30
Incident energy density (pJ/cm 2 )
Figure 7-5 | PL intensity dependence for: a microcavity pumped with A = 535 nm a, 10
ns pulses and b, 150 fs pulses; and a J-aggregate thin film pumped with c, 10 ns pulses
and d, 150 fs pulses. The solid lines are fits to Eq. (7.15) (parts a and c), while dashed
lines are fits to a power law. Fits overlap in parts a and c.
The sublinear behavior of the J-aggregate thin films and the microcavities is well
modeled by exciton-exciton annihilation, a procees in which excitons at high densities
can be nonradiatively destroyed via exciton-exciton interactions[29], [122], [123]. The
kinetics of excitons in organic materials are modeled by the two-body rate equation
pln
at
= -Fn-
-yn2
2
Ia
+ I
'""n
(7.14)
Strong Coupling in J-aggregateMicrocavities
117
where n is exciton density in Cm 3 , a is the absorption cross-section at the pump
wavelength in cm 2 ,
In
is the pump intensity in photons/cm 2, F is the single exciton
decay rate (radiative and nonradiative components), nMOI is the three-dimensional density
of dye molecules in cm 3 , and y is the annihilation rate constant in cm 3/s. Under 10 ns
pulsed excitation the material can be considered in quasi steady state (rpuse >> 1/ F), and
the solution to Eq. (7.14) is
F
n
1+
27
2nn
(7.15)
-11
The observed power dependence shows a good fit to Eq. (7.15) (Figure 7-5a and c),
suggesting that exciton-exciton annihilation is present in the excitonic material. The
absorption cross-section of a single dye molecule at A = 535 nm is found to be
a = 6.25 x 10-17 cm 2 and the in-plane density is n2D =-201 cm 2 given a 5 nm film
thickness and a molecular density 2 nm 3 . The single exciton decay rate is determined
from time-resolved PL measurements to be 45 ps. Based on the fit of Eq. (7.15), the
annihilation
rate
constant
is
y=5.2x 10-6 cm 3 / s
in
the
microcavity
and
y = 1.1 x 10-6 cm 3 / s in the isolated J-aggregate thin film.
The annihilation rate constant can be related to the exciton diffusion constant D
using [124]
y = 47rDRC
(7.16)
where R is the maximum distance between two excitons at which annihilation occurs.
Annihilation of singlet excitons is dominated by dipole-dipole interactions; hence, RC is
approximated to be the F~rster radius which we calculate to be 4 nm in these J-aggregate
thin films . If the diffusion in the 5 nm thin film is taken to be two-dimensional, then the
in-plane diffusion length, in the absence of annihilation is
L=
4D
(7.17)
For the quasi steady state excitation of the isolated thin films, we find L = 44 nm,
which is substantially longer than the < 20 nm singlet exciton diffusion lengths typically
Strong Coupling in J-aggregateMicrocavities
118
found in amorphous organic materials [12]. In the microcavity, the annihilation rate
constant is significantly larger than in the thin film, giving a diffusion length of
L = 115 nm in the absence of annihilation. The increased annihilation rate in the cavity is
attributed to coupling of the excitons to the cavity mode [125], which increases the
effective diffusion length of the excitons due to the oscillatory exchange of energy
characteristic of strong coupling.
The time dependence of the exciton population also shows that annihilation is a
valid model for exciton dynamics in the film. We investigate the exciton population
relaxation by exciting the thin films with 5 ps pulses at A = 532 nm at varying incident
energy densities (Figure 7-6) and collecting the time-dependent PL. The PL is imaged by
a streak camera and a CCD spectrometer, having a Gaussian instrument response
function with a full-width at half maximum of 6 ps. In this regime of short pulse
excitation (,r,, <1 / F ), the pumping term in Eq. (7.14) is set to zero, and the solution
is
1,=
'"(718
er' 1+ 2
n(O)
2
n(O)
where n(0) is the number of excitons per unit volume at t = 0. The time-dependent PL
fits to a convolution of Eq. (7.18) with the instrument response function (Figure 7-6),
which again shows that exciton-exciton annihilation is a valid model for exciton
dynamics in the film. Fitted values of y vary from 3.9 x 10-5 cm 3 /s at low intensity
excitation (0.147 pJ/cm 2 ) to 8.1 x 10-6 cm 3 /s at high intensity excitation (1.30 pJ/cm 2 )
while the single exciton decay rate is 1/ F = 45 ps, independent of excitation energy.
Using Eqs. (7.16) and (7.17) the diffusion length is found to be 245 nm at low intensity
excitation and 135 nm at high intensity excitation. This incoherent delocalization size is
much larger than the coherent size of a J-aggregate exciton which is typically - 16
molecules (radius of 3 nm) [30]. The apparent reduction in the annihilation-free diffusion
length at higher intensities can be attributed to rapid annihilation of non-relaxed excitons
at times < 100 fs after excitation [126], [127], which cannot be resolved with our
measurement setup.
1 19
Strong Coupling in J-aggregateMicrocavities
600
_400
S10-
0.0
05
1.0
1.5
Enrgy cnsity (jim
7
Eio IRF
2
0 0. 147 p/cm0 0.455 W/cm
10
% E 1.302
0
IS0
/acm,
100
150
200
-Trme pa)
Figure 7-6 |Time-dependent PL at A = 591nm from a J-aggregate thin film excited with 5
ps pulses at /1 = 535 nm with varying energy densities. The data is fit to the convolution
of the nonexponential population decay (Eq. 5) and the instrument response function
(IRF). The inset shows the in-plane diffusion length in the absence of annihilation.
7.6
Conclusion
The sublinear PL power dependence and the nonexponential PL time-dependence
support exciton-exciton annihilation as the nonlinear mechanism in the J-aggregate thin
film active layer of the microcavities. This result has important implications for achieving
polariton lasing using J-aggregate materials. Annihilation processes decrease the exciton
lifetime, and hence the polariton lifetime, which increases the polariton lasing threshold
density. Furthermore, annihilation competes with polariton-polariton scattering, which is
one of the possible mechanisms for populating the k =0 state of the polartion dispersion
(the polariton trap) [125], [128] Our results show that achieving low threshold polariton
lasing in organic materials will require materials that do not exhibit exciton-exciton
annihilation and still posses the necessary properties for strong coupling to a cavity, such
as high oscillator strength, narrow linewidth and small Stokes shift. Exciton-exciton
interactions can also be minimized by either nanopatterning the excitonic layer of the
microcavity to reduce the diffusion length, or by doping the excitonic material into a
wider gap host matrix. In the next chapter we will present another approach to
overcoming annihilation by introducing a new cavity pumping scheme and cavity design.
8 Lasing Through a Strongly-Coupled Mode
by Intra-Cavity Pumping
8.1
Overview
Previous work has shown the first polariton laser based on organic materials using
crystalline anthracene[129], [130]. However, the anthracene laser, as well as other
attempts at achieving polariton lasing using J-aggregates as the strong-coupling material,
have all encountered the phenomenon of exciton-exciton annihilation as a significant loss
mechanism [131], as was seen in the last chapter. Exciton-exciton annihilation [1], [123]
in polariton microcavities is a competing process with the buildup of a threshold
population of polaritons at the k = 0 point of the dispersion. Furthermore, due to the slow
exciton-phonon scattering rate and the short polariton lifetime, only a small fraction (103)
of the photogenerated excitons become cavity polaritons[132], [133]. Here we
demonstrate a new approach to populating the lower polariton (LP) branch of a
microcavity that circumvents losses due to exciton-exciton annihilation [134] and the
small polariton fraction, and provides a flexible design architecture for organic and
hybrid organic-inorganic polariton devices.
8.2
Introduction
The traditional non-resonant pumping scheme for populating the LP branch
involves off-normal-angle excitation of the polariton microcavity with incident light of
photon energy well above the LP energy (Figure 8-la) [135]. The photogenerated hot
excitons then relax to the exciton reservoir and subsequently relax to the bottom of the
LP branch by polariton-polariton scattering or phonon-polariton scattering. In contrast, in
the intra-cavity pumping scheme (Figure 8-1b), described in this work, a second,
emissive material inside the cavity acts as the LP pump [134]. The broadband emission
121
Lasing Through a Strongly-Coupled Mode by Intra-CavityPumping
spectrum of the pump material is chosen to overlap with the entire dispersion of the LP
branch. Therefore, any cavity emission from the pump material, either spontaneous or
stimulated, occurs through the strongly-coupled LP mode. By utilizing this intra-cavity
pump scheme, scattering from the exciton reservoir can be avoided, hence reducing the
amount of exciton-exciton annihilation. Furthermore, if the intra-cavity pump material
has a large stimulated emission cross-section, lasing of the pump material will occur
through the strongly coupled mode, thus not requiring LP-LP scattering to create lasing
from a polaritonic cavity. In particular, the four-level structure of organic materials is
responsible for low (-10 pJ/cm 2 ) lasing thresholds [8][136], which suggests that similarly
low thresholds should be possible from a cavity in strong coupling. Lasing through the
strongly coupled mode has been suggested to explain the room temperature polariton
[137]. Regardless of the mechanism of amplification-LP-LP
lasing in anthracene
scattering or stimulated emission-the result is coherent emission through a stronglycoupled mode with a single nonlinear threshold. In the case of organic microcavities, the
use of two optically active materials creates a cavity architecture that relaxes the stringent
material requirements to achieve organic lasing in a strongly coupled mode by employing
one strongly coupled material to create the polariton mode and another material to
populate the LP branch and creating lasing.
Non-resonant pumping
(a)
Energy
Intra-cavity pumping
Pump
(b)
Energy
Intra-cavity
hR
h-
pump
Lower
polariton
Exciton-exciton
annihilation
k-vector
V*
E mission
k-vector
n
E mission
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
122
Figure 8-1 1 a, Non-resonant excitation scheme for polariton microcavities showing
exciton-exciton annihilation as a lossy process. b, Intra-cavity pumping scheme utilizing
broadband emission from a second organic material in the cavity to pump the entire LP
branch thereby removing the need for polariton-polariton scattering to populate the
bottom of the LP dispersion.
8.3
Methods summary
In this work, the strongly coupled material is a highly optically absorbing 5-nm
thick J-aggregate thin film with an absorption line centered at energy E = 2.100 eV
(corresponding to the wavelength A = 591 nm), with a linewidth of 87 meV, and a peak
absorption coefficient of 4x 105 cm'. The intra-cavity pump material is the laser dye
DCM
(4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran),
with
broadband emission centered at E = 2.03 eV (A = 612 nm), which overlaps well with the
entire LP branch (Figure 8-2b). The absorption of DCM is negligible at the LP energy
(Figure 8-2b). The cavity is fabricated on a quartz substrate by first depositing a 7.5
bilayer SiO 2 /TiO 2 distributed Bragg reflector (DBR) by RF magnetron sputtering. A LO/4
SiO 2 spacer layer is deposited on the DBR (where A0 = 605 nm is the average position of
the lower polariton branch across the sample) in order to position the subsequently
deposited J-aggregate layer at the anti-node of the cavity electric field. The J-aggregate
thin film is grown by sequential immersion of the sample into solutions containing the
anionic cyanine dye TDBC (5,6-dichloro-2- [3-[5,6-dichloro-I-ethyl-3-(3-sulfopropyl)2(3H)-
benzimidazolidene]-1-propenyl]-1-ethyl-3-(3-sulfopropyl)
benzimidazolium
hydroxide)) and the cationic polyelectrolyte PDAC (poly(diallyldimethylammonium
chloride)) [28]. The remainder of the A-thick cavity is filled with DCM doped at 2.5%
w/w in Alq 3 (aluminum tris(8-hydroxyquinoline))[138]
deposited by thermal co-
evaporation. In addition, a 15 nm spacer layer of Alq 3 containing no DCM is deposited
on the J-aggregate film to avoid Fbrster resonant energy transfer (FRET) between the
TDBC and the DCM. The top mirror is a thermally evaporated film of Ag with a
thickness of 300 nm. The 30 nm effective optical path length at the Ag mirror due to
phase shift upon reflection is taken into account in the cavity design. The Alq 3 :DCM
layer is grown with a spatial gradient to achieve a variable cavity thickness, and hence
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
123
cavity-exciton detuning, across the sample, with a detuning of 0 meV at the center of the
sample. The complete microcavity structure is shown in Figure 8-2a.
The cavity is excited with near transform-limited k = 400 nm, 100 fs pulses with a
repetition rate of I kHz focused through a 0.7 NA microscope objective to a spot size of
20 im in diameter. The excitation is linearly polarized. The X = 400 nm excitation creates
Alq 3 excitons which undergo an efficient Fdrster-resonant-energy-transfer (FRET) to the
DCM molecules [138]. Photoluminescence (PL) is collected from the sample through the
same objective with the Fourier plane of the objective imaged onto a fiber coupled to a
spectrograph. The fiber is scanned across the momentum space image to obtain the PL
dispersion of the cavity with 0.50 angular resolution. Alternatively, an imaging CCD is
positioned at the same image plane to obtain the momentum space image [139]. All
experiments are performed at room temperature in ambient atmosphere. Angle-resolved
PL is shown in (Figure 8-2c) for three cavity-exciton detunings (A = 10, -50, -90 meV)
corresponding to three points on the surface of the sample. A fit of the dispersion to the
polariton two-level model results in a Rabi splitting of 60±5 meV and demonstrates that
the cavity is in strong coupling.
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
(a)
E-fled
Ag
DCM:Alq%-
-OW
Ak6-L
TDBC J-aggregate DBRQuartzMaterial to Romo Dolariton
mode and orovide gain:
DCM
(thin film emission)
(b)
MeIa
otooping:
TDBC J-aggregate
(thin film absorption)
-
-
20.8
0.6
Lower
I
DCM:A%
absorption
E 0.4
4W nm
_ Pu
~0.2 I
1.5
(C)
2.1
0I
2
- - - --
3
2.5
Energy (eV)
---
--
- -----
--
-
2.08
2.06
0
A = -50 meV
2.04
2.02
A = -90 meV
2
-20
Figure 8-2
0
Angle (deg)
20
1 a, Schematic of the cavity structure along with an approximate
representation of the cavity electric field with the TDBC J-aggregate film at one of the
cavity antinodes. b, Absorption spectrum of TDBC J-aggregates and the emission
spectrum of DCM showing overlap with the LP energy. The DCM:Alq 3 absorption is
negligible at the LP energy. c, PL of the LP branch as a function of angle for three cavityexciton detunings, showing a fit to the LP dispersion, demonstrating that the cavity is in
strong coupling.
124
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
8.4
125
Results and discussion
Figure 8-3a shows the two-dimensional PL dispersion of the polariton cavity with
negative cavity-exciton detuning (A = -43 meV) under low excitation pulse energy (3.5
At this detuning, the exciton and photon fractions are 0.15 and 0.85,
respectively. The LP linewidth is 17 meV corresponding to a polariton lifetime of 40 fs.
pJ/cm 2 ).
The LP linewidth is determined primarily by the J-aggregate homogeneous and
inhomogeneous broadening and is not further broadened by the minimal residual
absorption of DCM at the cavity resonance energy. The momentum space distribution of
the PL shows a wide ±20' cone emission profile with no observed linear polarization.
2.14
>
(a)
2.12near
below E,
scale)
UP2.14
E
E
2.1
>, 2.08 2)
2.06
(b)
2.2(log
>
2.1
>%2.08
~LP
2
2.
2.04
2.04
2.02
2.02
-20
0
above E
scale)
20
-20
Angle (deg)
0
10
7
(C
(d)
Below Et
,Above Eh
6-6
CuC
-D
20
Angle (deg)
5
-0
-10
-11
-5
0
X angle (deg)
5
-40
-20
0
Angle (deg)
20
40
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
126
Figure 8-3 1 a, Photoluminescence dispersion from a cavity with -43 meV detuning
pumped below the lasing threshold, Eth (shown in linear scale). The plot shows the LP
emission maximum at each angle (black circles) and a fit to the LP and UP energy (white
solid lines), as well as the energy dispersion of the uncoupled cavity, Ecv, and the
uncoupled exciton energy, Eex (white dashed lines). b, Dispersion of same cavity above
the lasing threshold, with the intensity shown in logarithmic scale to emphasize that
cavity remains in strong coupling above threshold based on the median energies of
emission that is not part of the lasing lines (black dots). c, Emission in momentum space
above threshold. d, Degree of polarization of the emission as a function of angle above
and below threshold.
Under increasing pump energy (7 ptJ/cm 2 ), a collapse in the spectral energy width
and momentum dispersion of the polariton emission is observed for the cavity with -43
meV detuning (0.15 exciton fraction) (Figure 8-3b).
Appearance of multiple narrow
linewidth modes with a flat dispersion is indicative of the multimode lasing. The nonlasing emission follows the same polariton dispersion as below threshold, with the lasing
lines superimposed in energy onto this polariton mode, indicating that the cavity remains
in strong coupling above the lasing threshold. The relative intensity of the multiple lasing
modes varies with power, but the energy spacing is nearly uniform at ~2.5 meV. Above
the lasing threshold, the momentum space distribution shows a narrow
+5'
emission cone
angle. The multiple emission spots produce interference fringes in the overlapping
regions in momentum space, indicating that the regions in momentum space are coherent
with each other (Figure 8-3c). A weak coupling cavity with only the DCM gain layer and
no J-aggregate layer showed only a single lasing mode. In the strongly coupled cavity,
the emission above threshold shows a high degree of linear polarization (ratio of 6) along
the direction of the pump laser polarization, despite the FRET that occurs between Alq 3
and DCM molecules, behavior which is also observed in DCM microcavity lasers in
weak coupling [140]. Due to the amorphous nature of the organic materials, a preferred
emission polarization is expected to be set by the pump polarization and not by the cavity
structure. The emission in the center of the lasing cone is the most polarized, with
spontaneous non-lasing emission at higher angles showing no linear polarization (Figure
8-3d).
127
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
(b)
(a)
103
8
300-
30.
250-
8
Eth
1.8E, -
c 200-
E 102
0E
-4
00
0 150
-
100
10-
101
5020
30
40
50
Pulse energy (pJ/cm2)
60
0
or
2.02
2.03
2.04
2.05
2.06
Wavelength (nm)
2.07
Figure 8-4 | a, Dependence of PL emission intensity at k = 0 as a function of the
excitation pulse energy showing a lasing threshold at 6 pJ/cm 2 . A reduction in the
emission linewidth from 7 meV to 0.5 meV is observed at the lasing threshold. b,
Emission spectrum below (0.8Eth excitation energy) and above (1.8Eth excitation energy)
the lasing threshold.
The threshold of nonlinear emission occurs at an absorbed excitation energy
density of 6 pJ/cm 2 , accompanied by a narrowing of the emission line from 17 meV
(below threshold) to 0.5 meV (above threshold) (Figure 8-4). Saturation of the emission
occurs at 8 pJ/cm 2 . We note that the threshold occurs at an energy density below the
onset of exciton-exciton annihilation [131], which we found to be -10
pJ/cm 2 . This
input-output dependence is similar to what is observed in DCM VCSELs in weak
coupling but the threshold for the polariton cavity at -43 meV detuning is -2-fold higher
than the threshold we find for a DCM VCSEL due to losses in the polariton mode. A
nonlinear lasing threshold occurs for polariton cavities with detunings ranging from -35
meV (0.15 exciton fraction at k = 0) to -110 meV (0.04 exciton fraction at k = 0), with a
lower lasing energy threshold for more negative detunings. No threshold was observed
for detunings of less than -35 meV due to J-aggregate photobleaching on the time scale of
measurement time (-30 s). In addition, for detunings of less than -35 meV, an increased
exciton fraction results in higher nonradiative loses due to the increasing J-aggregate
exciton portion of the exciton-polariton, which was measured to have a PL quantum yield
at room temperature of (1 0±2)%. The multiple spectral lasing modes were only observed
Lasing Through a Strongly-CoupledMode by Intra-CavityPumping
128
for cavities containing J-aggregates, at all detunings, and not for weak coupling cavities
containing DCM. The relative intensity of the multiple spectral peaks varies with
increasing excitation energy, with a single mode dominating at higher power. The
multiple modes can likely be attributed to disorder in the J-aggregate film across the
excitation spot, an effect that is also observed in GaN polariton lasing[ 110].
8.5
Conclusion
In conclusion, we demonstrate lasing through a strongly coupled mode, achieved by
intra-cavity pumping of a J-aggregate organic microcavity at room temperature. The laser
shows spectral and momentum space collapse of the emission above threshold while the
cavity remains in strong coupling. The laser employs a new architecture in which the
strong coupling material is separated from the material that populates the lower polariton
branch and creates gain in the cavity. This architecture opens the possibility for building
lasers operating through a strongly-coupled mode at a wide range of wavelengths (from
UV to NIR) simply by choosing a J-aggregating molecule with the appropriate absorption
line and a corresponding, spectrally overlapping organic pump material. Furthermore,
organic materials such as DCM could be incorporated with inorganic quantum wells to
create hybrid polariton structures with intra-cavity pumping [141].
SuperradiantLasingfrom OrganicMicrocavity
129
9 Superradiant Lasing from Organic
Microcavity
9.1
Overview
Coherent exciton interactions in organic materials are responsible for a number of optical
phenomena including enhanced energy-transfer[142], exciton-polariton condensation
[143], anomalous second order phase transitions [144], and more recently photon BoseEinstein condensation [145]. However, until now, exciton coherence has not been
harnessed to improve organic optoelectronic device performance, with organic polariton
lasers showing a higher threshold than their photonic counterparts, as was seen in the
previous chapter. In this chapter we demonstrate that cooperative interaction between
excitons in a microcavity containing a solid-state organic gain layer leads to superradiant
emission, manifested as a 10-fold reduction in lasing threshold, resulting in a record low
threshold for an organic microcavity of 400 nJ/cm 2 . While great emphasis has been
placed on polariton lasers as a route to low-threshold coherent emission [14], including
the work on J-aggregates in the previous chapter, this system shows that coherent
interactions between excitons, rather than strong coupling with the photon field, is a route
towards low-threshold lasing.
9.2
Introduction
In conventional lasing, threshold occurs when the rate of stimulated emission into
the cavity mode is equal to the rate of energy flow out of the cavity given by [146]
nthSEC
(9.1)
SuperradiantLasingfrom OrganicMicrocavity
130
where n1 h is the inversion density of excitons at threshold,
USE
is the stimulated emission
cross-section, c is the speed of light, and TC is the photon lifetime in the cavity. In this
expression, the time scale on which the inversion density is created relative to the
dephasing time is not considered, because the conventional lasing action does not rely on
coherence between the excited states of matter, which in our study are excitons in a
molecular organic solid-state gain layer (Figure 9-1b). However, if the excitons are
created at sufficient density and in a time rm
spontaneous emission lifetime of the exciton r,
can result in superradiant
emission
which is much shorter than the
coherent interactions between excitons
,
[147],
[148]'[149].
Superradiance
(SR)
is
characterized by a fast, intense, and directional emission pulse with a characteristic
timescale
VR
r,
where r, is the spontaneous emission lifetime of the excitons.
Furthermore, the presence of an optical cavity can increase the SR rate by a factor
proportional to the finesse of the cavity, by creating a longer effective sample length
[147], [150].
Below we demonstrate that under conditions of SR lasing in which both the
matter and photon components are coherent (Figure 9-1c), the effective stimulated
emission cross-section is enhanced by a factor
I e, resulting in a substantial reduction
rR
in threshold density. At the same time, the emission pulses from the cavity above
threshold are governed by the SR time rR rather than by the cavity photon lifetime r,, as
expected from conventional lasing. The observed lasing threshold energy density is a
record low for an organic vertical microcavity [151], surpassing the performance of
higher-Q microcavities [152] and organic polariton microcavities[116].
The low
threshold was achieved by tailoring the optical excitation to create SR conditions, rather
than by engineering the cavity to have a higher quality factor or to have a polariton
dispersion. We show here that SR lasing is a general phenomenon and method for ultralow thresholds that should be attainable with other 4-level organic lasing materials and in
geometries beyond microcavities, such as microring resonators and distributed feedback
lasers [8], [151].
SuperradiantLasingfrom Organic Microcavity
131
A = 532 nm
(a)
Conventional lasing
(b)
8 ns or 80 fs
USE small
excitons
not in phase
Superradiant lasing
(c)
DBR
pulse width
photons
in phase
USE enhanced
Ag (low-0)
DBR (hig-)
I
excitons
in phase
pulse width
photons
In phase
Figure 9-1 1 Conventional and superradiant lasing. a, Architecture and cross-sectional
transmission electron microscope image of organic microcavity with DCM gain material.
Bottom mirror consists of Ag (low-Q cavity) or a DBR (high-Q cavity). b, Schematic
representation of regular lasing illustrates that photons in the microcavity are in phase
while the radiating excitons are not, and under pulsed excitation, the emission pulse is
determined by the cavity lifetime T. . c, In superradiant lasing, the excitons are also
coherently coupled to one another and hence radiate with an effective cross-section
enhanced by TR / T. and the emission pulse is determined by the SR time TRJ resulting
in a dramatically reduced lasing threshold excitation density.
9.3
Methods summary
The microcavities measured in this study are comprised of an organic thin film gain
layer sandwiched between a distributed Bragg reflector (DBR) and an Ag or DBR mirror,
as shown in Figure 9-la. For the low-Q cavity the DBR mirror is formed from 6.5 pairs
of sputter-coated TiO 2 and SiO 2 thin films that serve as the high and low refractive index
layers (qT1 02 = 2.41 and qsio2 = 1.46) of thickness 62 nm and 102 nm, respectively. The
organic gain layer is a thin film of laser dye DCM (4-Dicyanmethylene-2-methyl-6-(pdimethylaminostyryl)-4H
-pyran)
doped
at
2.8%
by
weight
into
aluminum
tris-(8-hydroxyquinoline) (Alq 3) host material, where the mixed DCM:Alq 3 film is
deposited by thermal co-evaporation onto the DBR mirror. DCM is a 4-level laser dye
with a stimulated emission cross-section of USE
=
1.1XIO
cm 2 [146], a spontaneous
emission lifetime of r,= 3 ns, and a broad (AADcM = 80 nm) luminescence emission
SuperradiantLasingfrom Organic Microcavity
132
spectrum centered at ADCA = 620 nm. The gain layer thickness is varied across the
sample to allow for probing at the desired cavity tuning of A = 600 ± 5 nm. The 500-nm
thick Ag mirror is deposited by thermal evaporation onto the gain layer. Photon lifetimes
low-Q cavity is 100 fs, derived from the relation c = QA / 21fc , where the cavity quality
factor
Q was
obtained from emission spectra (AX
=
2 nm) and confirmed by transfer
matrix modeling [104].
Due to the difficulty of sputtering dielectric mirrors on organic thin films, the high-
Q cavity
is fabricated by a stamping technique. DBRs with 14.5 pairs of SiO 2 and Ta 20 5
are commercially grown on flat substrates and on substrates with 10 m radius of
curvature. DCM was deposited on the flat substrate as described above and the curved
DBR mirror was aligned, pressed, and sealed onto the flat substrate, forming the kthickness microcavity. Photon lifetimes high-Q cavity is 100 fs (AX = 2 nm).
The microcavities are optically excited through the substrate with a TM polarized
pump, incident at 6= 600 from normal, with the excitation focused to a spot size of 300
pim in diameter. To vary the duration of the excitation pulses, three pump lasers are used:
frequency doubled Q-switched Nd:YAG lasers emitting 0.9-ns or 8-ns pulses at 1'ex = 532
nm and a mode-locked regeneratively amplified laser system that pumps an optical
parametric amplifier (OPA) to deliver -80 fs duration pulses at A = 532 nm. The duration
of the 80-fs pulses is varied using a grating based pulse stretcher with spectral windowing
[153]. Cavity emission spectra are collected via an optical fiber coupled into a
spectrograph and imaged onto a CCD camera. Angle-resolved measurements were
obtained using Fourier space imaging [154]. Time-resolved measurements of cavity
emission were obtained by Kerr optical gating [155] with a temporal resolution of 250 fs.
The excitation wavelength in all cases was 1ex = 532 nm in order to pump DCM
molecules and to avoid excitation of Alq 3 , with on average 25% of the incident light
absorbed in the 2/2 cavity. Due to fast, sub-picosecond Frank-Condon relaxation of
excited DCM molecules to the meta-stable excited state [156], the instantaneous hot
exciton density can be considered equal to the emissive state exciton density.
SuperradiantLasingfrom Organic Microcavity
9.4
133
Results and discussion
Microcavities of k-thickness with two different Q-factors were excited in regimes
of slow excitation with ,p-
2,,
, and fast excitation with r,,wn,,
-
T2 <
SI)
where T2
=
50-200 fs is the optical dephasing time of typical organic dyes at room temperature [157159]. Under slow excitation (r,,ntp = 8 ns ), the absorbed energy density at threshold is
80± 4
gJ/cm
2
for the
Q = 300 cavity and
4.0 ± 0.5 pJ/cm 2 for the
Q = 4000
cavity (Figure
9-2). From Eq. (9.1) the expected threshold exciton densities are nth= 3.Ox 1018 cm- 3 and
nth =
2.3 x 1017 Cm- 3 corresponding to absorbed energy densities of 39 pj/Cm 2 and 2.9
pJ/cm 2 for the low-Q and high-Q cavities, respectively. These value agree well with the
measured thresholds when we consider that the slow excitation duration r,,in, is ~2 times
longer than r , which reduces the energy absorbed per spontaneous emission lifetime.
When the same cavities are tested under fast excitation (,r,,,n
=
80 fs ), the low-Q
and high-Q cavities exhibit absorbed energy thresholds of 4 ± 0.2 j/cm2 (nh = 3x 1017
cm~3) and 0.4 ± 0.02 pJ/cm 2 (nth= 3x 1016 cm-3), a remarkable 10-20 fold reduction in
lasing threshold as compared to slow excitation (Figure 9-2). These thresholds are -10
times below what is expected from the lasing threshold condition (Eq. (9.1)), which
depends only on the exciton density created within the exciton lifetime and therefore
should be independent of the excitation rate as long as
< T,
<,,,,,,
. The 400 nJ/cm 2
threshold observed for the high-Q cavity represents a record low threshold for organic
microcavity lasers.
SuperradiantLasingfrom Organic Microcavity
134
134
SuperradiantLasingfrom Organic Microcavity
Excitation density (cm- 3)
1016
10
1017
101
p
104 (a) Q = 300
.
0V
E
10
I-
pump
0
C
C,
E
C
0 80 fs
0 8 ns
0
0
0
Sof
12
10 1
80
w
pJ/CM2
40
AA Inrr
p1m
a
2
10
(b) Q =4000
10
Spump
0
104
10
0
C,
10
E
w
10
o 80 fs
e 8 ns
0
1
+
-4
pJ/cm
2
10
0.4 pJ/cm
9d
10~
100
10
2
102
Absorbed energy density (pJ/cm2)
Figure 9-2 1 Threshold reduction under fast (80-fs) excitation. Comparison of emission
intensity in the surface normal direction as a function of absorbed excitation energy
density for a, low-Q cavity, and b, high-Q cavity, upon excitation at Lex = 532 nm with
fast 80-fs pulses (open data points) and slow 8-ns pulses (filled data points). Under fast
excitation both cavities show a 10-20 fold reduction in threshold energy compared to
slow excitation.
The markedly reduced thresholds cannot be attributed to pump-induced coherence
because the cavities are excited far away from resonance, nor to circumventing polaron
losses [160] or losses due to inter-system crossing since the DCM is being excited
directly and there is good agreement between the measured 8-ns pump threshold and
predicted values from Eq. (9.1). In addition, the reduction in threshold cannot be
SuperradiantLasingfrom Organic Microcavity
135
attributed to small microcavity effects [144] because the reduction was observed to be
independent of cavity length.
.1
4
0
(a)
(b)
_
O.6E,
E
1. 2 Eth
-
' 0.5
N
-1 .0 EM
103
-
-
-0.
8 Eth
0
th
CZ
1. 2 Eh
0
-0.2Eth
0
-20
-10
0
Angle (deg)
10
20
1
(C)
10 2
N 0.5
CL
a.~
10 4
590
'.
'
-
'
595
600
605
Wavelength (nm)
610
:.Oth
1.OE
.
--
100
10
102
Absorbed energy density (pJ/cm2)
Figure 9-3 I Signatures of lasing. Cavity emission under fast (80 fs) excitation. a,
Emission spectra collected over angles -20* to 20* for the low-Q cavity at various
excitation densities, showing spectral line narrowing to 1 nm above threshold, where Eth
is the threshold energy density. b, Wide emission cone below threshold narrows to a
width of 8* above threshold. c, Degree of polarization of the emission
(TM - TE) /(TM +E)
as a function of excitation density shows highly polarized emission
above threshold.
In addition to the threshold behavior, the emission of the cavities under fast
excitation exhibits characteristic features of lasing. Spectrally-resolved emission from the
low-Q cavity is peaked at the resonance of A = 605 nm, with a linewidth of 2.5 nm below
threshold and a long 15 nm blue tail corresponding to off-angle emission (Figure 9-3a
and b). Above threshold, the spectral linewidth narrows to 1 nm and the angular width
narrows from ±300 to ±40. Furthermore, at threshold the emission becomes highly
polarized in the TM direction, along the pump polarization, a signature of lasing in solidstate organic microcavity lasers [138] (Figure 9-3c). This behavior indicates that,
although the cavity is far below the threshold density for conventional lasing, the
SuperradiantLasingfrom Organic Microcavity
136
observed transition exhibits the spectral, angular and polarization features characteristic
of coherence.
The unexpectedly low lasing threshold density can be understood in the context of
cooperative emission. As known from the Dicke SR model [149], the collective system
radiates at an enhanced rate given by [148]
1
_1
-- SR
nA 2 L
- nA(9.2)
,
8 7r
sVP
where n is the volume density of excitons, L is the length of the sample, and A = A0 / 77 is
the emission wavelength A0 reduced by the refractive index '1 of the material. It has
been shown that in an optical cavity the effective length of the material is increased,
which enhances the SR rate in proportion to the finesse of the cavity [147]. Bj~rk et al.
[150] have calculated the overlap between SR emission and a microcavity mode to show
that the enhancement factor is given by (I+
R
-R)
, where Re
is the
geometric average of the microcavity mirror reflectivities. For the low-Q cavity, which
will be the focus of the remainder of the paper, Rff= 0.98 and the enhancement factor is
190. Furthermore, the SR rate is modified by the mismatch between the cavity spectral
linewidth and the inhomogeneous linewidth of DCM emission. This mismatch results in
only a fraction of the excitons, T* /r , being coupled to the cavity-enhanced SR mode,
where T* = 2.8 fs is the inhomogeneous dephasing time of DCM obtained from the
emission spectral width, and rC = 86 fs is the photon lifetime of the low-Q cavity.
Finally, the expression for the cavity-enhanced SR rate in the A-thickness cavity is
1
TR
I nA2L
t
SP
1+
TR9
87c
1-T2
(9.3)
f
Therefore, at the threshold exciton density with fast excitation of n = nlh = 3x 1017
cm~3, the SR time is
ZR
= 620 ± 50 fs. Using Eq. 3 and the expression for the stimulated
emission cross-section, the lasing threshold condition from Eq. (9.1) is reduced to
1/
TC
=
nthc(TR
/
conditions of SR.
)SE
, where (rR / ,
)CrSE=
7 is the enhanced cross-section under
137
SuperradiantLasingfrom Organic Microcavity
The condition for "strong SR", in which all light is emitted coherently, requires
that the optical dephasing time is longer than the SR time, T2
> ZR
, which our system
does not satisfy. However SR can still occur in the "limited SR" regime, as discussed by
MacGillivray et al. [148], in which T2
< ZR
and only a fraction of emission occurs
coherently. Temnov et al. [161] have shown that a substantial fraction is emitted
superradiantly as long as T2 /
R >
0.1. Due to the cavity, the inhomogeneous broadening
T*2 is removed and the SR dynamics are determined only by the DCM homogeneous
dephasing time T2 as long as T2~
Zc.
Typical 12 values for organic laser dyes at room
temperature have been measured to be in the range of 50 fs to 200 fs [157-159]. This
value of T2 and the SR time of rR= 620 ± 50 fs puts the system in the limited SR regime
under fast excitation at the observed threshold density of n,h
=
3x 1017 cm 3 .
We further explored the onset of SR lasing by varying the excitation time rp.
FFigure 9-4 shows that the threshold energy density for lasing decreases dramatically
from n~h = 4x10
18
cm~3 when r,,U,, = 900 ps to n
= 3x 10
7
cm-3 when rpunp = 1 ps .
Consistent with SR, the threshold is constant as the excitation pulse width is reduced to
below 1 ps because the excitations are created in a time shorter than the SR time,
pump
R *
1019
2
10
Conventional lasing
simulation
E
E
CD
a)
(D
75
-
a
C
&-1
-Fn
0
18 '18
10 1
10
10
Superradiant lasing
experiment
nX
101
100
101
Pulse width r
102
(ps)
10
SuperradiantLasingfrom Organic Microcavity
138
Figure 9-4 1 Threshold energy density vs. excitation pulse width. Experiment shows
dramatic reduction in threshold energy density for shorter pulses, while simulation of
the conventional lasing threshold does not show same dependence, indicating that
phenomena beyond conventional lasing are responsible for the reduced threshold.
To contrast the observed threshold behavior with a conventional
lasing
mechanism, the DCM microcavity is modeled using the rate equation formalism
described by Koschorreck et al. [136] (see Section 9.8). As expected, Figure 9-4 shows
that the simulated lasing threshold is independent of excitation pulse width for
T,,M, <100 ps and is equal to nh = 2.7x 10
threshold
density
18 cm-3.
The modest increase in the simulated
for r,,, > 100 ps occurs because
approaches the radiative lifetime of the excitons rS.
the excitation pulse length
Using 80-fs pulsed excitation, the
ratio of the simulated to the observed threshold densities is 7, which agrees well with the
enhancement of the effective stimulated emission cross-section (rR / T,)cSE ~ 7USE *
Superradiant Lasing
Experiment
10 0
(a)
**
*
10-2
.
Conventional Lasing
Simulation
.
(C)
hE
2 Eth
z=110 fs
=
200 fs
0
* .0
.
10-4
N
10 0
(b)
(d)
3Eth
0
0
z
10-2
~
3Eth
t
r=690 fs
=
110 fs
.*
10-
4
.0
0
2
4
6
Time (ps)
8
10
0
2
4
6
Time (ps)
8
10
SuperradiantLasingfrom OrganicMicrocavity
139
Figure 9-5 1 Temporal dynamics of cavity emission. Measured and simulated emission
following the 80-fs pulsed excitation for the low-Q cavity. Above threshold, the pulse
decay time is a, 1100 fs for excitation density 2 Eth and b, 690 fs for excitation density
3
Eth. The observed pulse decay times are ~2 rR, in agreement with SR regime of
operation. The pulse decay times predicted from a conventional laser model are c, 200
fs for excitation density 2Eth and d, 110 fs for excitation density 3Eth, approaching rc = 95
fs for high excitation densities.
To further confirm our interpretation of threshold reduction as SR, we measured
the temporal dynamics of the emitted pulses using a Kerr gating technique with 250 fs
resolution. At a density of 2 nth = 6x 10 cm
3
(Figure 9-5a), the emitted pulse is peaked
at 4 ps after excitation and has a decay time constant of 1100 fs, which is
2rR, as
expected from the typical hyperbolic secant shape of SR pulses [150]. As the excitation
density is increased to
3
nth (Figure 9-5b), the decay time constant is reduced to 690 fs,
proportional with the decrease in rR * The modeled microcavity emission under the same
excitation conditions (Fig. 5c and d) shows decay time constants of 200 fs and 110 fs for
the two excitation densities, respectively. These decay times approach the cavity photon
lifetime TC with increasing density, in stark contrast to the measured pulses.
9.5
Conclusion
In conclusion, we demonstrated that an organic microcavity shows a pronounced
~10 fold decrease in threshold density under short pulsed excitation as compared to a
conventional lasing threshold. The record low threshold for an organic microcavity is
attributed to limited cavity-enhanced SR based on the predicted SR time and the
homogeneous dephasing time of DCM. SR is further supported by the observed temporal
dynamics of the emission, which agrees with SR pulse dynamics, and differs substantially
from the predictions of a conventional lasing model. This work demonstrates that
cooperative exciton emission can be a dominant effect even at room temperature that can
be utilized to control and improve the performance of optoelectronic devices that rely on
large exciton densities.
SuperradiantLasingfrom OrganicMicrocavity
9.6
9.6.1
140
Detailed experimental methods
Measurement of pump energy density
For all measurements other than the time-resolved data, the excitation spot size is
determined by scanning a knife-edge across the focused excitation beam at the position of
the sample. The obtained spot diameter is 300 pm at the Ile intensity points.
To obtain the incident energy density per pulse on the sample, the average power of
the incident beam was measured using a calibrated Si photodetector (Ophir-1Z0241.3
with power meter Ophir-lZ01803). The measurement range of the power meter was
chosen such that the detector was not saturated due to the pulsed excitation. To verify the
accuracy of the power measurements, we measured the power with a calibrated
thermopile detector (Newport 818P-0 10-12 with power meter 1918-C), which in contrast
to a photo-diode is not susceptible to pulsed excitation saturation. The observed
agreement between the two types of measurements allowed us to use the Ophir Si
photodetector for the low excitation powers needed for cavity experiments.
For the lower-Q, metal-DBR microcavities, the fraction of incident light that is
absorbed in the gain medium is obtained by measuring the power of the excitation light
reflected by the sample compared with the power incident on the sample. For the lower-Q
cavities the back mirror of the cavity is a 500-nm thick Ag layer, and the bottom DBR
mirror has low optical losses. Hence any light not reflected by the sample is absorbed by
the gain layer. At an angle of incidence of 60' relative to normal, the typical absorption
of the
Q = 300
cavity at the excitation wavelength of 532 nm is 25%. By combining the
measurements of spot size, incident power, and reflected power, we obtain the absorbed
energy densities and subsequently exciton densities reported in this work. For the high-Q
double-DBR cavity, a similar procedure was followed but transmission through the
sample was also measured to obtain the absorption.
9.6.2
Kerr shutter for time-resolved photoluminescence
Time-resolved measurements of cavity emission were performed using a Kerr
shutter gating technique following the method of Kinoshita et al.[155] (Figure 9-6). The
detailed optical diagram of our setup is shown in Figure 9-7. The output of the optical
SuperradiantLasingfrom Organic Microcavity
141
parametric amplifier (k = 532 nm, 1kHz repetition rate) is sent through an optical delay
line and then focused onto the surface of the sample with a 50X objective lens to a spot
diameter of 20 pm. The photoluminescence (PL) emission is collected with the same
objective lens, passes through a dichroic mirror, and is imaged onto a SrTiO 3 crystal. In
the absence of the gate beam, the PL is cross-polarized between two polarizers, one
before and one after the SrTiO 3 crystal, with an attenuation of ~10-6. The PL image spot
is spatially overlapped in the crystal with a gate beam of wavelength k = 800 nm,
polarized at 450 relative to the PL. In the presence of the gate beam, the polarization of
the PL signal in that time slice is rotated, passed through the crossed polarizer, and then
imaged onto the slit of a CCD spectrograph. The delay of the excitation beam is scanned
to obtain a time-resolved and spectrally-resolved PL trace. The rise time of the Kerr
medium response was found to be 250 fs by performing a time-resolved measurement of
the 80 fs excitation pulses directly.
gate pulse, width = 150 fs
A= 800 nm
PL
vertical
polarizer
Kerr material
to spectrometer
vertical
polarizer
Figure 9-6 | Conceptual diagram of Kerr shutter setup for measuring time-resolved
photoluminescence.
SuperradiantLasingfrom OrganicMicrocavity
142
spectrograph
real space
f = 100 mm (ach.)
FES700
polarizer
delay line
f= 100 inm (ach.)
I
SriO, crystal
real space
microscope
in rotation mount
r--microcavity
to Kerr shutter
sample
d
=
50mm
I
50X
laser power controller
OPA
HWP
polak
100 fs
pladize
I
5
0.45 NA, 17 mm %
f,= 150 mm(ach.)
m
7DM:
800 nm
Ti:sapph Regen
d = 150mm
objective lens
564 nm dichroic
and emitter
d=-200mm
800 nm from NDfilter
OPA dumo n n
HWP
@22.S deg
f =200 m
polarizer
k-spacef
realspace
periscope
32 mm
f =200 mm
d=200mm
d=200mm
d=200mm
Figure 9-7 | Diagram of Kerr shutter experimental setup.
9.6.3
Fourier space imaging of angular-resolved emission
Angle-resolved emission from the cavities was measured following the method of
Richard et al.[154] (Figure 9-8). Emission from the cavity is collected with a 20X (0.45
NA) objective and the Fourier plane of the objective is imaged onto the slit of a CCD
spectrograph to obtain a two-dimensional dispersion (energy vs. angle).
real space
(image of sample)
k-space
k-space
Sample
spectrograph
k-space
toy
after spectrograph slit
tI9
after spectrograph grating
on CCD
e
SuperradiantLasingfrom Organic Microcavity
143
Figure 9-8 1 Dispersion imaging setup for obtaining angle-resolved emission data.
9.7
Threshold reduction for varying cavity lengths
The superradiant reduction in threshold was observed to be independent of cavity
length, and hence cannot be attributed alternatively to microcavity effects such as those
described by de Martini et al.[162] . The same low-Q microcavity as described in the
Methods section was fabricated with lengths of k/2, X, and 312. Figure 9-9 shows that for
the X and 3X/2 cavities, we observe a similar 20-fold reduction in lasing threshold under
fast excitation. The A/2-thickness cavity does not exhibit a lasing threshold under slow
pumping because the required threshold exciton density of 6x 1018 cm-3 would be close to
the DCM molecule density nDCM
=
2.5x1019 cm- 3 , thus requiring almost complete
saturation and because a larger fraction of DCM excitons are quenched by the metal
mirror compared to longer cavities.
Excitation density (cm-3
10 1
10
10
10
10
10
(a) V/2 cavity
10
10 1
101
(b) X cavity
010
10
10
10
10
(c) 3/2 cavity
106
C
10
0
U
5
0
00
4
0
0 0
80 pJ/cm 2
*
100 pJ/cm 2
10
0000 0.
102
10
10
mt
10
p
0
3 pJcm
10
10
p
5 pj/cm2
4 [pJ/cm 2
100
10
10
10
100
01
10
Absorbed energy density (gJ/cm2)
Figure 9-91 Threshold reduction under fast excitation for 3 cavity lengths. a, X/2 cavity. b,
A cavity. c, 3 X/2 cavity. Open circles are data for slow (8 ns) excitation and filled circles
are fast (80 fs) excitation.
9.8
Simulation of conventional lasing
The experimental results for time-resolved cavity emission and the lasing threshold
were compared with simulations of conventional lasing dynamics. The dynamics of the
DCM microcavities are modeled by considering the 4-level structure of DCM, which in
SuperradiantLasingfrom Organic Microcavity
144
our experiments is optically pumped directly, without Fbrster energy transfer from the
Alq 3 host matrix. The energy level diagram of DCM is shown Figure 9-10, in which m is
the population of the pump state, n is the population of the relaxed excited state, and q is
the number of photons in the cavity mode. To model the dynamics of this system, we
consider the coupled differential equations describing the three species following the
notation of Bruckner et al.[163]:
dm
S=
dt
dn
p(M,- 2m)- kbm
A= kvbm - (I- 0) A n - PA, (I+qn
n- Fn
(9.4)
dt
dq = A, (1+q)n-yq
dt
where p is the normalized pump rate, m,0 , is the total number of DCM molecules in the
volume of one cavity mode, kvib is the vibrational relaxation rate,
p
is the spontaneous
emission coupling factor into the cavity, At is spontaneous emission rate into free space,
Af is the cavity-enhanced spontaneous emission rate into the cavity mode, F is the decay
rate of the relaxed excited state n, and y is the leakage rate of photons from the cavity.
The populations, m, n, and p, are per mode volume.
kvib
In
p
4,,3AJ1+q)
r
Figure 9-10 j Energy level diagram of DCM. The pump state is m and the fluorescent
state is n.
The equation for the pump state population m includes a saturation term determined
by the total number of molecules within the volume of the cavity mode, V. The mode
volume is V
=
r
where L = 350 nm is the thickness of the cavity gain layer for a k-
SuperradiantLasingfrom OrganicMicrocavity
145
thickness cavity, and ret is the effective transverse mode radius. The effective mode
radius is given by[164]
-1/2
-
r =(9.5)
qf 8n( - R )
where A = 600 nm is the cavity resonance free space wavelength, n = 1.62 is the cavity
refractive index, L = 350 nm is the cavity length, and Reg= 0.98 is the geometric mean of
the cavity mirror reflectivities. From these values we find rej = 1.5 pm. Based on the
2.5% doping of DCM in Alq 3 and the molecular weights of each molecule, the estimated
two-dimensional density of DCM molecules is ND
=
number of molecules per mode volume is m,, = ir'N
1
x
1015 cm 2 . Consequently, the
= 7 x 107.
The vibrational relaxation rate from the pump state to the relaxed excited state is
assumed to be rapid with kvib = 1/(500 fs)[138], [163], although changes in this parameter
did not affect the results significantly. The spontaneous emission coupling factor is
estimated to be l = 0.002 following the results of Bjbrk et al.[165], using the linewidths
of the cavity
(Akcav
= 2 nm) and DCM emission (AXD= 80 nm). For the total exciton
decay rate we use F = 1/(2 ns), the spontaneous emission rate into free space is Af = 1/(3
ns). The cavity-enhanced spontaneous emission rate is A = FAA , where FP is the
Purcell factor given by [15]:
= 3Q(A 0 / n) 3
(9.6)
41r2 V
Using the parameters for the Q = 300 cavity, we find Fp = 1.9 and consequently A,
=
1/(1.6 ns). The cavity photon escape rate y is determined from the cavity lifetime which is
given by rc = QAO / 21rc, where c is the speed of light. For the low-Q cavity, y = 1/(95
fs).
The dynamics of the cavity emission are simulated by numerically solving Eqs.
(9.4) in MATLAB. The initial conditions for the simulation are that the DCM molecules
are in the ground state with no intra-cavity photons, m = 0, n = 0, q = 0. The excitation is
a time-dependent pump term
SuperradiantLasingfrom Organic Microcavity
p(t)= po exp -
146
( t2
(9.7)
2
2a P/2
The full width of the pulse at Ile intensity is ri,
= 2Jha, and this is the value referred
to as the pulse width. The total energy delivered by one pulse per unit area is then
calculated from
hc/lX
E -h
where hc /
,
L p(t)(m 0,, -2m)dt
(9.8)
is the energy of one pump photon.
The simulated dynamics of cavity emission are shown below and above the
nonlinear threshold in the two excitation regimes, ru,
=
100 fs (fast) and rm
=
1 ns
(slow). Under both kinds of excitation, the lifetime of the emission pulse is determined by
the pump pulse width. Under even shorter excitation, the emission pulse width becomes
limited by the cavity photon lifetime. As described in the manuscript, due to SR, the
pulse duration above threshold under fast excitation is ~5 times longer than conventional
lasing simulation predicts.
a
_b
10 0-
Below Eth
-Above
(n
E
y,,,, =10 fs
c
10
Below E
h7
r
0
U)
Et
=1n
E
15
15
CO
0
-Above
1
2
cc
6
Time (ps)
4
8
10
110-
0
1000
2000 3000
Time (ps)
4000
5000
Figure 9-11 I Comparison of cavity dynamics for fast and slow pumping. a, 100 fs
excitation pulse width. b, 1 ns excitation pulse width. The emission pulse is offset from t
= 0 because the excitation pulse has a positive offset to avoid negative time values in
the simulation. The oscillations above threshold are due to repumping of state n from
state m due to vibrational relaxation.
SuperradiantLasingfrom Organic Microcavity
147
Figure 9-12a shows the simulated cavity emission as a function of absorbed energy
density. The regimes of spontaneous emission, lasing, and saturation are seen for all the
simulated pump pulse widths. The lasing threshold is defined by the inflection point of
the input-output dependence, as shown with the dashed line in Figure 9-12a. Despite the
widely varying duration of the excitation and subsequent emission pulses, the inputoutput curves are insensitive to changes in pump pulse width. Figure 9-12b shows how
the lasing threshold depends on rmn.
density for
The modest increase in the simulated threshold
,, > 100 ps occurs because the excitation pulse length approaches the
radiative lifetime of the excitons rS. The simulated dependence stands in stark contrast
to the observed experimental values due to the presence of SR.
a
b
102
---
700 fs
4.8 ps
340 ps
-- 230 ps
1ns
10
1019
2
102
0fs
-
E
E
1
C
2)
-10
0101
a))
F-
101
102
2
Absorbed energy density (pJ/cm )
10~1
100
101
102
Pulse width (ps)
103
Figure 9-12 1 Simulation of cavity emission vs. pump energy. a, Simulated cavity
emission as a function of pump energy density for a range of pump pulse widths.
Dashed line indicates level at which the threshold was determined. b, Lasing threshold
as a function of pump pulse width and comparison to experimental results.
Conclusion and Outlook
Conclusion and Outlook
148
148
10 Conclusion and Outlook
In this thesis we have demonstrated the rich variety of physical phenomena in
excitonic materials. We have learned a great deal about the fundamentals of exciton
transport and how it relates to disorder, knowledge that will aid the design of existing
devices such as photovoltaics that rely on moving excitons. We demonstrated a new
application for excitonic materials that takes advantage of exciton transport to make the
interaction of molecules with light more efficient. Finally, we studied two approaches to
coherent emission from excitons in a microcavity. Using J-aggregates as a strongly
coupled material, and DCM as the gain material, we demonstrated lasing through a
strongly coupled mode. In a complimentary approach, the spontaneous emission of
excitons in the weak coupling regime was synchronized to produce superradiant lasing at
room temperature with a significantly reduced lasing threshold.
10.1 Outlook for exciton transport
The lessons learned about exciton transport in tetracene and QD thin films are just
the beginning. The direct imaging technique is a versatile approach to extracting many
parameters about exciton diffusion and can be applied to materials dominated by triplet
and singlet transport. As we showed with QD thin films, the resolution of the
measurement is only limited by the signal-to-noise ratio. At present our measurements
were limited to about 30 min in duration due to focus drift on the microscope. This is a
technical limitation that can easily be overcome. Having multiple photodetectors imaging
along one or two spatial dimensions in parallel will greatly enhance the data collection
efficiency. In the future, we envision our imaging technique to be used as a high
throughput method for quickly screening exciton transport in the large library of
materials currently used in photovoltaic research and as new materials are synthesized.
Conclusion and Outlook
149
Many questions about the role of disorder, whether structural or energetic, still
remain. Is the observation of disorder-driven exciton transport in QD films a general, yet
counterintuitive, phenomenon that could be applied to other materials? What other
strategies could be used to enhance exciton diffusion length? These are rich areas for
further exploration.
While our imaging technique is powerful in providing a spatial average of exciton
transport in time, visualization of transport in nanopatterned structures is not possible due
to the diffraction limit. For this reason, the future belongs to near-field microscopy.
While a challenging and often-signal limited technique, near-field imaging is the most
direct method for looking at excitons near nano-scale interfaces, the regions most critical
to excitonic device performance.
The J-aggregate antenna produced dramatic fluorescence enhancement values,
previously only obtained with plasmonic structures. However, the losses inherent to Jaggregates make the overall efficiency of the system, from photons to photons out, quite
low. The ultimate goal of the excitonic antenna is for one input photon to result in one
generated exciton on the desired acceptor. While the absorption efficiency can approach
100% using the JCCR, the transport and FRET to the acceptor is the limiting step. Most
excitons are either not mobile or decay before reaching an acceptor. Improving the
fluorescence quantum yield of J-aggregates and exploring materials other than Jaggregates is a worthwhile goal. However, the most promising approach is to tailor the
energy landscape in which the excitons diffuse, moving from the regime of diffusion to
the regime of drift. Applying nanoscale pressure or nanopatteming the materials to
confine and guide excitons are just two methods to molding the flow of excitons that we
are currently exploring.
10.2 Outlook for excitons in microcavities
In this thesis we showed two complimentary approaches to generating coherent
excitons and coherent emission that fundamentally differ from traditional lasing. While
much has been made of polaritonic structures as a way to low-threshold lasing, material
losses have so far prevented this from becoming a reality. Indeed in the anthracene
polariton laser [129] and in our J-aggregate-DCM laser, the lasing threshold is higher in
Conclusion and Outlook
1 50
the strongly-coupled system relative to the equivalent photon laser. In the case of Jaggregates, the higher threshold arises most likely as a result of the short exciton lifetime,
making interaction of photons with the polariton mode very lossy.
To our initial surprise, the route to low threshold came not through modifying the
cavity mode but by changing the rate of excitation, thus putting the system in the regime
of superradiance. Thus the same DCM laser, though in weak coupling showed a
dramatically lower threshold. Superradiance in organic microcavities must be explored in
other resonator geometries and with other excitonic materials in order to determine if the
observed behavior is a general phenomenon or is specific to DCM in planar
microcavities.
The studies presented here are part of an explosion in work in recent years on
coherent exciton states such as superradiance [166], polariton lasing [167], and photon
Bose-Einstein condensation [168], to name a few. Understanding the connection and
mapping the transition between these coherent regimes is a rich avenue for future
research. While the interest in these topics has generally been from the point of view of
fundamental physics, intriguing possibilities could be considered in the application of
coherent exciton states. In particular, could exciton coherence, either with the photon
field or between excitons, result in enhanced exciton transport, allowing us to overcome
the inherent disorder in molecular materials that limits exciton transport? The
implications could be far-reaching, from solar cell design to artificial photosynthesis to
potential excitonic transistors.
References
[1]
C. Swenberg and M. Pope, Electronicprocesses in organiccrystals and polymers.
Oxford University Press, 1999.
[2]
C. W. Tang, S. A. van Slyke, and C. H. Chen, "Electroluminescence of doped
organic thin films," J. Appl. Phys., vol. 65, no. 9, p. 3610, 1989.
[3]
M. A. Baldo and S. R. Forrest, "Highly efficient phosphorescent emission from
organic electroluminescent devices," Nature, vol. 395, no. September, pp. 151154, 1998.
[4]
B. Kippelen and J.-L. Bredas, "Organic photovoltaics," Energy & Environmental
Science, vol. 2, no. 3, p. 251, 2009.
[5]
J. Clark and G. Lanzani, "Organic photonics for communications," Nat. Photon.,
vol. 4, no. 7, pp. 438-446, Jul. 2010.
[6]
T. P. Osedach, S. M. Geyer, J. C. Ho, A. C. Arango, M. G. Bawendi, and V.
Bulovic, "Lateral heterojunction photodetector consisting of molecular organic and
colloidal quantum dot thin films," Appl. Phys. Lett., vol. 94, no. 4, p. 43307, Jan.
2009.
[7]
V. Bulovic, V. Kozlov, V. Khalfin, and S. Forrest, "Transform-limited, narrowlinewidth lasing action in organic semiconductor microcavities," Science (New
York, N.Y.), vol. 279, no. 5350, pp. 553-5, Jan. 1998.
[8]
I. D. W. Samuel and G. A. Turnbull, "Organic semiconductor lasers," Chem. Rev.,
vol. 107, no. 4, pp. 1272-1295, Apr. 2007.
[9]
A. Rose, Z. Zhu, C. Madigan, T. M. Swager, and V. Bulovid, "Sensitivity gains in
chemosensing by lasing action in organic polymers," Nature, vol. 434, no. April,
pp. 1-4,2005.
[10]
M. Baldo and V. Stojanovid, "Optical switching: Excitonic interconnects," Nat.
Photon., vol. 3, no. 10, pp. 558-560, Oct. 2009.
[11]
A. A. High, E. E. Novitskaya, L. V Butov, M. Hanson, and A. C. Gossard,
"Control of exciton fluxes in an excitonic integrated circuit.," Science, vol. 321,
no. 5886, pp. 229-231, Jul. 2008.
Conclusion and Outlook
1 52
[12]
R. R. Lunt, N. C. Giebink, A. A. Belak, J. B. Benziger, and S. R. Forrest, "Exciton
diffusion lengths of organic semiconductor thin films measured by spectrally
resolved photoluminescence quenching," J. Appl. Phys., vol. 105, no. 5, p. 53711,
Jan. 2009.
[13]
S. Reineke, K. Walzer, and K. Leo, "Triplet-exciton quenching in organic
phosphorescent light-emitting diodes with Ir-based emitters," Phys. Rev. B, vol.
75, no. 12, p. 125328, Mar. 2007.
[14]
H. Deng and Y. Yamamoto, "Exciton-polariton Bose-Einstein condensation," Rev.
Mod. Phys., vol. 82, no. 2, pp. 1489-1537, May 2010.
[15]
A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities. OUP
Oxford, 2011.
[16]
D. G. Lidzey, D. D. C. Bradley, M. S. Skolnick, T. Virgili, S. Walker, and D. M.
Whittaker, "Strong exciton-photon coupling in an organic semiconductor
microcavity," Nature, vol. 395, no. 6697, pp. 53-55, Jan. 1998.
[17]
J. R. Tischler, M. S. Bradley, Q. Zhang, T. Atay, A. Nurmikko, and V. Bulovic,
"Solid state cavity QED: strong coupling in organic thin films," Org. Electron.,
vol. 8, no. 2-3, pp. 9 4 - 1 13 , 20 0 7 .
[18]
C. Madigan, "Theory and Simulation of Amorphous Organic Electronic Devices,"
Massachusetts Institute of Technology, 2006.
[19]
S. R. Yost, E. Hontz, S. Yeganeh, and T. Van Voorhis, "Triplet vs singlet energy
transfer in organic semiconductors: the tortoise and the hare," J. Phys. Chem. C,
vol. 116, no. 33, pp. 17369-17377, Aug. 2012.
[20]
A. Kdhler and H. Bdssler, "Triplet states in organic semiconductors," Materials
Science and Engineering:Reports, vol. 66, no. 4-6, pp. 71-109, Nov. 2009.
[21]
Z.-Q. You and C.-P. Hsu, "The fragment spin difference scheme for triplet-triplet
energy transfer coupling.," The Journal of chemical physics, vol. 133, no. 7, p.
074105, Aug. 2010.
[22]
J. B. Aladekomo, S. Arnold, and M. Pope, "Triplet exciton diffusion and double
photon absorption in tetracene," Physica Status Solidi (b), vol. 80, no. 1, pp. 333340, Mar. 1977.
[23]
H. Jiang and C. Kloc, "Single-crystal growth of organic semiconductors," MRS
Bull., vol. 38, no. 01, pp. 28-33, Jan. 2013.
Conclusion and Outlook
1 53
[24]
V. Bulovic, V. Kozlov, V. Khalfin, and S. Forrest, "Transform-limited, narrowlinewidth lasing action in organic semiconductor microcavities," Science, vol. 279,
no. 5350, pp. 553-5, Jan. 1998.
[25]
M. Broyer and J. Chevaleyre, "CVL-Pumped Dye Laser for Spectroscopic," vol.
36, pp. 31-36, 1984.
[26]
E. E. Jelley, "Molecular, nematic and crystal states of 1,
cyaninechloride," Nature (London, vol. 139, p. 631, 1937.
[27]
T. Kobayashi, J-aggregates.World Scientific, 1996.
[28]
M. S. Bradley, J. R. Tischler, and V. Bulovic, "Layer-by-layer J-aggregate thin
films with a peak absorption constant of 10(6) cm(-1)," Adv. Mater., vol. 17, no.
15,pp. 1881-1886, 2005.
[29]
M. van Burgel, D. A. Wiersma, and K. Duppen, "The dynamics of onedimensional excitons in liquids," The Journalof Chemical Physics, vol. 102, no. 1,
p. 20, 1995.
[30]
D. H. Arias, K. W. Stone, S. M. Vlaming, B. J. Walker, M. G. Bawendi, R. J.
Silbey, V. Bulovi6, and K. a Nelson, "Thermally-Limited Exciton Delocalization
1-Diethyl-c-
in Superradiant Molecular Aggregates.," The journal of physical chemistry. B,
Dec. 2012.
[31]
S. Valleau, S. Saikin, M. Yung, and A. Guzik, "Exciton transport in thin-film
cyanine dye J-aggregates," The Journalof Chemical ... , pp. 1-16, 2012.
[32]
S. Jang, M. Newton, and R. Silbey, "Multichromophoric F6rster Resonance
Energy Transfer," Phys. Rev. Lett., vol. 92, no. 21, pp. 21-24, May 2004.
[33]
E. N. Zimanyi and R. J. Silbey, "Unified treatment of coherent and incoherent
electronic energy transfer dynamics using classical electrodynamics.," The Journal
of chemical physics, vol. 133, no. 14, p. 144107, Oct. 2010.
[34]
G. D. Scholes, G. R. Fleming, A. Olaya-Castro, and R. van Grondelle, "Lessons
from nature about solar light harvesting.," Nat. Chem., vol. 3, no. 10, pp. 763-74,
Oct. 2011.
[35]
M. Escalante, A. Lenferink, Y. Zhao, N. Tas, J. Huskens, C. N. Hunter, V.
Subramaniam, and C. Otto, "Long-range energy propagation in nanometer arrays
of light harvesting antenna complexes.," Nano Lett., vol. 10, no. 4, pp. 1450-1457,
Apr. 2010.
Conclusion and Outlook
[36]
1 54
S. M. Menke, W. A. Luhman, and R. J. Holmes, "Tailored exciton diffusion in
organic photovoltaic cells for enhanced power conversion efficiency.," Nat.
Mater., vol. 12, no. 2, pp. 152-157, Feb. 2013.
[37]
S. Hofmann, T. C. Rosenow, M. C. Gather, B. LUssem, and K. Leo, "Singlet
exciton diffusion length in organic light-emitting diodes," Phys. Rev. B, vol. 85,
no.24,p.245209,Jun.2012.
[38]
Z. Soos and R. Powell, "Generalized Random-Walk Model for Singlet-Exciton
Energy Transfer," Phys. Rev. B, vol. 6, no. 10, pp. 4035-4046, 1972.
[39]
D. Sanvitto, F. Pulizzi, A. J. Shields, P. C. Christianen, S. N. Holmes, M. Y.
Simmons, D. A. Ritchie, J. C. Maan, and M. Pepper, "Observation of charge
transport by negatively charged excitons.," Science, vol. 294, no. 5543, pp. 837839, Oct. 2001.
[40]
B. A. Ruzicka, R. Wang, J. Lohrman, S. Ren, and H. Zhao, "Exciton diffusion in
semiconducting single-walled carbon nanotubes studied by transient absorption
microscopy," Phys. Rev. B, vol. 86, no. 20, p. 205417, Nov. 2012.
[41]
H. Hillmer, S. Hansmann, A. Forchel, M. Morohashi, E. Lopez, H. P. Meier, and
K. Ploog, "Two-dimensional exciton transport in GaAs/GaAlAs quantum wells,"
Appl. Phys. Lett., vol. 53, no. 20, pp. 1937-1939, 1988.
[42]
A. K. Ghosh and T. Feng, "Merocynanine organic solar cells," J. Appl. Phys., vol.
49,no.12,p.5982,1978.
[43]
J. Mei, M. Bradley, and V. Bulovid, "Photoluminescence quenching of tris-(8hydroxyquinoline) aluminum thin films at interfaces with metal oxide films of
different conductivities," Phys. Rev. B, vol. 79, no. 23, p. 235205, Jun. 2009.
[44]
H. Najafov, B. Lee, Q. Zhou, L. C. Feldman, and V. Podzorov, "Observation of
long-range exciton diffusion in highly ordered organic semiconductors.," Nat.
Mater., vol. 9, no. 11, pp. 938-43, Nov. 2010.
[45]
V. Sundstrom, T. Gillbro, R. A. Gadonas, and A. Piskarskas, "Annihilation of
singlet excitons in J aggregates of pseudoisocyanine (PIC) studied by pico- and
subpicosecond spectroscopy," J. Chem. Phys., vol. 89, no. 5, pp. 2754-2762, 1988.
[46]
V. Ern, P. Avakian, and R. Merrifield, "Diffusion of triplet excitons in anthracene
crystals," Phys. Rev., vol. 541, no. 1186, pp. 862-867, 1966.
[47]
P. Irkhin and I. Biaggio, "Direct imaging of anisotropic exciton diffusion and
triplet diffusion length in rubrene single crystals," Phys. Rev. Lett., vol. 107, no. 1,
p. 017402, Jul. 2011.
Conclusion and Outlook
1 55
[48]
J. Salcedo and A. Siegman, "Dynamics of energy transport in molecular crystals:
the picosecond transient-grating method," Phys. Rev. Lett., vol. 4, no. 2, pp. 131134, 1978.
[49]
C. J. Bardeen, "Excitonic processes in molecular crystalline materials," MRS Bull.,
vol. 38, no. 01, pp. 65-71, Jan. 2013.
[50]
R. Groff, P. Avakian, and R. Merrifield, "Coexistence of exciton fission and fusion
in tetracene crystals," Phvs. Rev. B, vol. 26, no. January, pp. 815-817, 1970.
[51]
D. N. Congreve, J. Lee, N. J. Thompson, E. Hontz, S. R. Yost, P. D. Reusswig, M.
E. Bahlke, S. Reineke, T. Van Voorhis, and M. A. Baldo, "External quantum
efficiency above 100% in a singlet-exciton-fission-based organic photovoltaic
cell.," Science, vol. 340, no. 6130, pp. 334-337, Apr. 2013.
[52]
J. J. Burdett, A. M. MUller, D. Gosztola, and C. J. Bardeen, "Excited state
dynamics in solid and monomeric tetracene: The roles of superradiance and
exciton fission.," The Journal of Chemical Physics, vol. 133, no. 14, p. 144506,
Oct. 2010.
[53]
J. Klafler and I. Sokolov, "Anomalous diffusion spreads its wings," Physics world,
2005.
[54]
S. M. Vlaming, V. A. Malyshev, A. Eisfeld, and J. Knoester, "Subdiffusive exciton
motion in systems with heavy-tailed disorder.," J. Chem. Phys., vol. 138, no. 21, p.
214316, Jun. 2013.
[55]
S.-H. Lim, T. Bjorklund, F. Spano, and C. Bardeen, "Exciton delocalization and
superradiance in tetracene thin films and nanoaggregates," Phys. Rev. Lett., vol.
92, no. 10, p. 107402, Mar. 2004.
[56]
M. Voigt, A. Langner, P. Schouwink, J. M. Lupton, R. F. Mahrt, and M.
Sokolowski, "Picosecond time resolved photoluminescence spectroscopy of a
tetracene film on highly oriented pyrolytic graphite: dynamical relaxation, trap
emission, and superradiance.," J. Chem. Phys., vol. 127, no. 11, p. 114705, Sep.
2007.
[57]
L. Novotny and B. Hecht, Principles of Nano-Optics. Cambridge University Press,
2006.
[58]
J.-P. Bouchaud and A. Georges, "Anomalous diffusion in disordered media:
Statistical mechanisms, models and physical applications," Physics Reports, vol.
195, no. 4-5, pp. 127-293, Nov. 1990.
Conclusion and Outlook
1 56
[59]
J. J. Burdett and C. J. Bardeen, "Quantum beats in crystalline tetracene delayed
fluorescence due to triplet pair coherences produced by direct singlet fission.," J.
Am. Chem. Soc., vol. 134, no. 20, pp. 8597-607, May 2012.
[60]
R. Powell and Z. Soos, "Singlet exciton energy transfer in organic solids," J.
Lumin., vol. 11, 1975.
[61]
S. Tavazzi, L. Raimondo, L. Silvestri, P. Spearman, A. Camposeo, M. Polo, and D.
Pisignano, "Dielectric tensor of tetracene single crystals: the effect of anisotropy
on polarized absorption and emission spectra.," The Journalof Chemical Physics,
vol. 128, no. 15, p. 154709, Apr. 2008.
[62]
A. Alivisatos, "Semiconductor Clusters, Nanocrystals, and Quantum Dots,"
Science, vol. 271, no. 5251, pp. 933-937, 1996.
[63]
M. Graetzel, R. a J. Janssen, D. B. Mitzi, and E. H. Sargent, "Materials interface
engineering for solution-processed photovoltaics.," Nature, vol. 488, no. 7411, pp.
304-12, Aug. 2012.
[64]
Y. Shirasaki, G. Supran, M. Bawendi, and V. Bulovid, "Emergence of colloidal
quantum-dot light-emitting technologies," Nat. Photon., vol. 7, no. December
2012, 2012.
[65]
0. E. Semonin, J. M. Luther, S. Choi, H.-Y. Chen, J. Gao, A. J. Nozik, and M. C.
Beard, "Peak external photocurrent quantum efficiency exceeding 100% via MEG
in a quantum dot solar cell.," Science (New York, N.Y.), vol. 334, no. 6062, pp.
1530-3, Dec. 2011.
[66]
W. A. Tisdale, "Hot Electron Dynamics at Semiconductor Surfaces: Implications
for Quantum Dot Photovoltaics," University of Minnesota, 2010.
[67]
B. Mashford, M. Stevenson, and Z. Popovic, "High-efficiency quantum-dot lightemitting devices with enhanced charge injection," Nature, vol. 7, no. April, pp.
407-412,2013.
[68]
A. H. Ip, S. M. Thon, S. Hoogland, 0. Voznyy, D. Zhitomirsky, R. Debnath, L.
Levina, L. R. Rollny, G. H. Carey, A. Fischer, K. W. Kemp, I. J. Kramer, Z. Ning,
A. J. Labelle, K. W. Chou, A. Amassian, and E. H. Sargent, "Hybrid passivated
colloidal quantum dot solids.," Nature Nanotechnology, vol. 7, no. 9, pp. 577-82,
Sep. 2012.
[69]
G. Konstantatos, I. Howard, A. Fischer, S. Hoogland, J. Clifford, E. Klem, L.
Levina, and E. H. Sargent, "Ultrasensitive solution-cast quantum dot
photodetectors.," Nature, vol. 442, no. 7099, pp. 180-3, Jul. 2006.
Conclusion and Outlook
1 57
[70]
C. Dang, J. Lee, C. Breen, J. S. Steckel, S. Coe-Sullivan, and A. Nurmikko, "Red,
green and blue lasing enabled by single-exciton gain in colloidal quantum dot
films," Nature Nanotechnology, vol. 7, no. 5, pp. 335-339, Apr. 2012.
[71]
D. Yu, C. Wang, and P. Guyot-Sionnest, "n-Type conducting CdSe nanocrystal
solids.," Science (New York, N.Y.), vol. 300, no. 5623, pp. 1277-80, May 2003.
[72]
Y. Liu, M. Gibbs, J. Puthussery, S. Gaik, R. Ihly, H. W. Hillhouse, and M. Law,
"Dependence of carrier mobility on nanocrystal size and ligand length in PbSe
nanocrystal solids.," Nano Lett., vol. 10, no. 5, pp. 1960-9, May 2010.
173]
J.-S. Lee, M. V Kovalenko, J. Huang, D. S. Chung, and D. V Talapin, "Band-like
transport, high electron mobility and high photoconductivity in all-inorganic
nanocrystal arrays.," Nature nanotechnology, vol. 6, no. 6, pp. 348-52, Jun. 2011.
[74]
D. V Talapin and C. B. Murray, "PbSe nanocrystal solids for n- and p-channel thin
film field-effect transistors.," Science (New York, N.Y.), vol. 310, no. 5745, pp. 869, Oct. 2005.
[75]
C. Kagan, C. Murray, and M. Bawendi, "Long-range resonance transfer of
electronic excitations in close-packed CdSe quantum-dot solids.," Phys. Rev. B,
vol. 54, no. 12, pp. 8633-8643, Sep. 1996.
[76]
S. Crooker, J. Hollingsworth, S. Tretiak, and V. Klimov, "Spectrally Resolved
Dynamics of Energy Transfer in Quantum-Dot Assemblies: Towards Engineered
Energy Flows in Artificial Materials," Phys. Rev. Lett., vol. 89, no. 18, p. 186802,
Oct. 2002.
[77]
M. Achermann, M. a. Petruska, S. a. Crooker, and V. I. Klimov, "Picosecond
Energy Transfer in Quantum Dot Langmuir-Blodgett Nanoassemblies," The
Journal of Physical Chemistry B, vol. 107, no. 50, pp. 13782-13787, Dec. 2003.
[78]
J. Miyazaki and S. Kinoshita, "Site-selective spectroscopic study on the dynamics
of exciton hopping in an array of inhomogeneously broadened quantum dots,"
Phys. Rev. B, vol. 86, no. 3, p. 035303, Jul. 2012.
[79]
F. Xu, X. Ma, C. Haughn, and J. Benavides, "Efficient Exciton Funneling in
Cascaded PbS Quantum Dot Superstructures," ACS Nano, no. 12, pp. 9950-9957,
2011.
[80]
T. F6rster, "Zwischenmolekulare Energiewanderung und Fluoreszenz," Annalen
der physik, vol. 248, no. 1938, 1948.
[81]
H. Bassler, "Charge Transport in Disordered Organic Photoconductors," Physica
Status Solidi (B), vol. 15, no. 175, 1993.
Conclusion and Outlook
1 58
[82]
F. Fennel and S. Lochbrunner, "F6rster-mediated spectral diffusion in disordered
organic materials," Phys. Rev. B, vol. 85, no. 9, p. 094203, Mar. 2012.
[83]
J. Cui, A. P. Beyler, L. F. Marshall, 0. Chen, D. K. Harris, D. D. Wanger, X.
Brokmann, and M. G. Bawendi, "Direct probe of spectral inhomogeneity reveals
synthetic tunability of single-nanocrystal spectral linewidths.," Nat. Chem., vol. 5,
no. 7, pp. 602-6, Jul. 2013.
[84]
R. Baer and E. Rabani, "Theory of resonance energy transfer involving
nanocrystals: the role of high multipoles.," J. Chem. Phys., vol. 128, no. 18, p.
184710, May 2008.
[85]
J. T. Verdeyen, Laser electronics. Prentice Hall, 1995.
[86]
I. Gerhardt, G. Wrigge, P. Bushev, G. Zumofen, M. Agio, R. Pfab, and V.
Sandoghdar, "Strong Extinction of a Laser Beam by a Single Molecule," Phys.
Rev. Lett., vol. 98, no. 3, pp. 1-4, Jan. 2007.
[87]
R. Loudon, The Quantum Theory of Light. OUP Oxford, 2000.
[88]
Y. Chen, K. Munechika, and D. S. Ginger, "Dependence of fluorescence intensity
on the spectral overlap between fluorophores and plasmon resonant single silver
nanoparticles.," Nano Lett., vol. 7, no. 3, pp. 690-6, Mar. 2007.
[89]
Y. Ito, K. Matsuda, and Y. Kanemitsu, "Mechanism of photoluminescence
enhancement in single semiconductor nanocrystals on metal surfaces," Phys. Rev.
B, vol. 75, no. 3, pp. 1-4, Jan. 2007.
[90]
A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. Moerner,
"Large single-molecule fluorescence enhancements produced by a bowtie
nanoantenna," Nat. Photon., vol. 3, no. 11, pp. 654-657, 2009.
[91]
J.-H. Song, T. Atay, S. Shi, H. Urabe, and A. V Nurmikko, "Large enhancement of
fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant
coupling to spatially controlled surface plasmons.," Nano Lett., vol. 5, no. 8, pp.
1557-61, Aug. 2005.
[92]
H. F. Hamann, M. Kuno, a. Gallagher, and D. J. Nesbitt, "Molecular fluorescence
in the vicinity of a nanoscopic probe," The Journal of Chemical Physics, vol. 114,
no. 19, p. 8596, 2001.
[93]
S. Kuhn, U. Hfikanson, L. Rogobete, and V. Sandoghdar, "Enhancement of SingleMolecule Fluorescence Using a Gold Nanoparticle as an Optical Nanoantenna,"
Phys. Rev. Lett., vol. 97, no. 1, pp. 1-4, Jul. 2006.
Conclusion and Outlook
1 59
[94]
P. Anger, P. Bharadwaj, and L. Novotny, "Enhancement and Quenching of SingleMolecule Fluorescence," Phys. Rev. Lett., vol. 96, no. 11, pp. 3-6, Mar. 2006.
[95]
J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, "Single Quantum Dot
Coupled to a Scanning Optical Antenna: A Tunable Superemitter," Phys. Rev.
Lett., vol. 95, no. 1, pp. 1-4, Jun. 2005.
[96]
J. R. Lakowicz, "Plasmonics in Biology and Plasmon-Controlled Fluorescence.,"
Plasmonics, vol. 1, no. 1, pp. 5-33, Mar. 2006.
[97]
C. Madigan and V. Bulovik, "Solid State Solvation in Amorphous Organic Thin
Films," Phys. Rev. Lett., vol. 91, no. 24, pp. 1-4, Dec. 2003.
[98]
R. M. Jones, L. D. Lu, R. Helgeson, T. S. Bergstedt, D. W. McBranch, and D. G.
Whitten, "Building highly sensitive dye assemblies for biosensing from molecular
building blocks," P Natl Acad Sci, vol. 98, no. 26, pp. 14769-14772, Jan. 2001.
[99]
S. W. Thomas, G. D. Joly, and T. M. Swager, "Chemical sensors based on
amplifying fluorescent conjugated polymers," Chem. Rev., vol. 107, no. 4, pp.
1339-1386, Apr. 2007.
[100] J. R. Tischler, M. S. Bradley, and V. Bulovic, "Critically coupled resonators in
vertical geometry using a planar mirror and a 5 nm thick absorbing film," Opt.
Lett., vol. 31, no. 13, pp. 2 04 5 - 2 0 4 7 , 20 0 6 .
[101] L. C. T. Shoute, A. J. Bergren, A. M. Mahmoud, K. D. Harris, and R. L.
McCreery, "Optical interference effects in the design of substrates for surfaceenhanced Raman spectroscopy," Appl. Spectrosc., vol. 63, no. 2, pp. 133-140,
2009.
[102] B. J. Walker, G. P. Nair, L. F. Marshall, V. Bulovi6, and M. G. Bawendi,
"Narrow-band absorption-enhanced quantum dot/J-aggregate conjugates.," J. Am.
Chem. Soc., vol. 131, no. 28, pp. 9624-5, Jul. 2009.
[103] F. Ma and X. Liu, "Phase shift and penetration depth of metal mirrors in a
microcavity structure.," Applied optics, vol. 46, no. 25, pp. 6247-6250, Sep. 2007.
1104] M. S. Bradley, J. R. Tischler, Y. Shirasaki, V. Bulovic, and V. Bulovi6,
"Predicting the linear optical response of J -aggregate microcavity excitonpolariton devices," Phys. Rev. B, vol. 78, no. 19, p. 4, Nov. 2008.
[105] Y. Shirasaki, P. 0. Anikeeva, J. R. Tischler, M. Scott Bradley, and V. Bulovi6,
"Efficient F6rster energy transfer from phosphorescent organic molecules to Jaggregate thin films," Chem. Phys. Lett., vol. 485, no. 1-3, pp. 243-246, Jan.
2010.
Conclusion and Outlook
160
[106] J. C. de Mello, H. F. Wittmann, and R. H. Friend, "An improved experimental
determination of external photoluminescence quantum efficiency," Adv. Mater.,
vol. 9, no. 3, pp. 230-232, Feb. 1997.
[107] D. Sanvitto, F. M. Marchetti, M. H. Szymanfska, G. Tosi, M. Baudisch, F. P.
Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch,
C. Tejedor, and L. Vifia, "Persistent currents and quantized vortices in a polariton
superfluid," Nat. Phys., vol. 6, no. May, pp. 527-533, May 2010.
[108] K. G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. Andr6, L. S.
Dang, and B. Deveaud-Plddran, "Quantized vortices in an exciton-polariton
condensate," Nat. Phys., vol. 4, no. 9, pp. 706-7 10, Aug. 2008.
[109] R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, "Bose-Einstein
condensation of microcavity polaritons in a trap," Science, vol. 316, no. 5827, pp.
1007-10 10, May 2007.
[110] S. Christopoulos, G. von H6gersthal, A. Grundy, P. Lagoudakis, A. Kavokin, J.
Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, and N. Grandjean,
"Room-temperature polariton lasing in semiconductor microcavities," Phys. Rev.
Lett., vol. 98, no. 12, p. 126405, Mar. 2007.
[111] P. R. Berman, Advances in atomic, molecular, and optical physics. Academic
Press, 1994.
[112] J. Hopfield, "Theory of the Contribution of Excitons to the Complex Dielectric
Constant of Crystals," Phys. Rev., vol. 112, no. 5, p. 1555, Dec. 1958.
[113] J. R. Tischler, "Solid State Cavity QED," Massachusetts Institute of Technology,
2007.
[114] J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling,
F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B.
Littlewood, B. Deveaud, and L. S. Dang, "Bose-Einstein condensation of exciton
polaritons," Nature, vol. 443, no. 7110, pp. 409-414, Sep. 2006.
[115] H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, "Condensation of
semiconductor microcavity exciton polaritons," Science, vol. 298, no. 5591, pp.
199-202, Jan. 2002.
[116] S. Kena-Cohen and S. R. Forrest, "Room-temperature polariton lasing in an
organic single-crystal microcavity," Nat. Photon., vol. 4, no. 6, pp. 371-375, Apr.
2010.
[117] M. S. Bradley, "Engineering J-Aggregate Cavity Exciton-Polariton Devices,"
Massachusetts Institute of Technology, 2009.
Conclusion and Outlook
161
[118] G. Malpuech, A. Di Carlo, A. Kavokin, J. J. Baumberg, M. Zamfirescu, and P.
Lugli, "Room-temperature polariton lasers based on GaN microcavities," Appl.
Phys. Lett., vol. 81, no. 3, pp. 412-414, Jan. 2002.
[119] D. Lidzey, D. Bradley, T. Virgili, a. Armitage, M. Skolnick, and S. Walker,
"Room Temperature Polariton Emission from Strongly Coupled Organic
Semiconductor Microcavities," Phys. Rev. Lett., vol. 82, no. 16, pp. 3316-3319,
Apr. 1999.
[120] J. R. Tischler, M. S. Bradley, V. Bulovic, J. H. Song, and A. Nurmikko, "Strong
coupling in a microcavity LED.," Phys Rev Lett, vol. 95, no. 3, p. 36401, 2005.
[121] D. Lidzey, "Enhanced Raman scattering in a strongly coupled microcavity
containing J-aggregates," Synth. Met., vol. 127, no. 1-3, pp. 151-154, Mar. 2002.
[122] J. Moll, W. J. Harrison, D. V Brumbaugh, and A. A. Muenter, "Exciton
annihilation in J-aggregates probed by femtosecond fluorescence upconversion," J.
Phys. Chem. A, vol. 104, no. 39, pp. 8847-8854, Jan. 2000.
[123] C. E. Swenberg, N. E. Geacintov, and M. Pope, "Bimolecular quenching of
excitons and fluorescence in the photosynthetic unit.," Biophys. J., vol. 16, no. 12,
pp. 1447-1452, Dec. 1976.
[124] P. E. Shaw, A. Ruseckas, J. Peet, G. C. Bazan, and I. D. W. Samuel, "ExcitonExciton Annihilation in Mixed-Phase Polyfluorene Films," Adv. Funct. Mater.,
vol. 20, no. 1, pp. 155-161, Jan. 2010.
[125] M. Litinskaya, "Exciton polariton kinematic interaction in crystalline organic
microcavities," Phys. Rev. B, vol. 77, no. 15, p. 12, Apr. 2008.
[1261 a. Ruseckas, P. Wood, 1. Samuel, G. Webster, W. Mitchell, P. Burn, and V.
Sundstr6m, "Ultrafast depolarization of the fluorescence in a conjugated polymer,"
Phys. Rev. B, vol. 72, no. 11, pp. 1-5, Sep. 2005.
[127] A. Lewis, A. Ruseckas, 0. Gaudin, G. Webster, P. Burn, and 1. Samuel, "Singlet
exciton diffusion in MEH-PPV films studied by exciton-exciton annihilation,"
Org. Electron., vol. 7, no. 6, pp. 452-456, Dec. 2006.
[128] M. Litinskaya, P. Reineker, and V. Agranovich, "Fast polariton relaxation in
strongly coupled organic microcavities," J. Lumin., vol. 110, no. 4, pp. 364-372,
Dec. 2004.
[129] S. Kena-Cohen and S. R. Forrest, "Room-temperature polariton lasing in an
organic single-crystal microcavity," Nat. Photon., vol. 4, no. 6, pp. 371-375, Apr.
2010.
Conclusion and Outlook
162
[130] M. Slootsky, Y. Zhang, and S. R. Forrest, "Temperature dependence of polariton
lasing in a crystalline anthracene microcavity," Phys. Rev. B, vol. 86, no. 4, p.
045312, Jul. 2012.
[131] G. M. Akselrod, Y. R. Tischler, E. R. Young, D. G. Nocera, and V. Bulovic,
"Exciton-exciton annihilation in organic polariton microcavities," Phys. Rev. B,
vol. 82, no. ll, p. 113106, Sep. 2010.
[132] P. Michetti and G. La Rocca, "Simulation of J-aggregate microcavity
photoluminescence," Phys. Rev. B, vol. 77, no. 19, p. 195301, May 2008.
[133] D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G.
Lidzey, "Vibrationally assisted polariton-relaxation processes in strongly coupled
organic-semiconductor microcavities," Adv. Funct. Mater., vol. 2011, no. 21, pp.
3691-3696, Jul. 2011.
[134] M. Bradley and V. Bulovi6, "Intracavity optical pumping of J-aggregate
microcavity exciton polaritons," Phys. Rev. B, vol. 82, no. 3, pp. 1-4, Jul. 2010.
[135] J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling,
F. M. Marchetti, M. H. Szymaniska, R. Andre, J. L. Staehli, V. Savona, P. B.
Littlewood, B. Deveaud, and L. S. Dang, "Bose-Einstein condensation of exciton
polaritons," Nature, vol. 443, no. 7110, pp. 409-414, Sep. 2006.
[136] M. Koschorreck, R. Gehlhaar, V. G. Lyssenko, M. Swoboda, M. Hoffmann, and
K. Leo, "Dynamics of a high-Q vertical-cavity organic laser," Appl. Phys. Lett.,
vol.87,no. 18,p. 181108,2005.
[137] G. C. La Rocca, "Organic photonics: polariton lasing," Nat. Photon., vol. 4, no. 6,
pp. 343-345, Jun. 2010.
[138] V. Kozlov and V. Bulovic, "Study of lasing action based on F6rster energy transfer
in optically pumped organic semiconductor thin films," J. Appl. Phys., vol. 84, no.
8, pp. 4096-4108, Jan. 1998.
[139] C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T.
Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, "Coherent zerostate and pi-state in an exciton-polariton condensate array.," Nature, vol. 450, no.
7169, pp. 529-32, Nov. 2007.
[140] V. G. Kozlov, V. Bulovic, and S. R. Forrest, "Temperature independent
performance of organic semiconductor lasers," Appl. Phys. Lett., vol. 71, no. 18, p.
2575, 1997.
Conclusion and Outlook
163
[141] V. M. Agranovich, D. M. Basko, and G. C. La Rocca, "Efficient optical pumping
of organic-inorganic heterostructures for nonlinear optics," Phys. Rev. B, vol. 86,
no. 16, p. 165204, Oct. 2012.
[142] P. Andrew, "Forster Energy Transfer in an Optical Microcavity," Science, vol.
290, no. 5492, pp. 785-788, Oct. 2000.
[143] S. Kena-Cohen and S. R. Forrest, "Room-temperature polariton lasing in an
organic single-crystal microcavity," Nat. Photon., vol. 4, no. 6, pp. 371-375, Apr.
2010.
1144] F. De Martini and G. Jacobovitz, "Anomalous spontaneous-stimulated-decay
phase transition and zero-threshold laser action in a microscopic cavity," Phys.
Rev. Lett., vol. 60, no. 17, pp. 1711-1714, 1988.
[145] J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, "Bose-Einstein condensation of
photons in an optical microcavity," Nature, vol. 468, no. 7323, pp. 545-548, Nov.
2010.
[146] B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Wiley-Interscience,
2007.
[147] L. Moi, P. Goy, M. Gross, J. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom
masers. I. A theoretical and experimental study of super-radiant systems in the
millimeter-wave domain," Phys. Rev. A, vol. 27, no. 4, p. 2043, 1983.
[148] J. C. MacGillivray and M. Feld, "Theory of superradiance in an extended,
optically thick medium," Phys. Rev. A, vol. 14, no. 3, p. 1169, 1976.
[149] R. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev., vol. 93, no.
l,p.99, 1954.
[150] G. Bjdrk, S. Pau, J. Jacobson, and Y. Yamamoto, "Wannier exciton superradiance
in a quantum-well microcavity," Phys. Rev. B, vol. 50, no. 23, 1994.
[151] S. Chenais and S. Forget, "Recent advances in solid-state organic lasers," Polym.
Int., vol. 61, no. 3, pp. 390-406, Mar. 2012.
[152] M. Koschorreck, R. Gehhaar, V. G. Lyssenko, M. Swoboda, M. Hoffmann, and
K. Leo, "Dynamics of a high-Q vertical-cavity organic laser," Appl. Phys. Lett.,
vol. 87, no. 18, p. 181108, 2005.
[153] A. M. Weiner, J. P. Heritage, and E. Kirschner, "High-resolution femtosecond
pulse shaping," JOSA B, vol. 5, no. 8, pp. 1563-1572, 1988.
Conclusion and Outlook
164
[154] M. Richard, J. Kasprzak, R. Romestain, R. Andre, and L. Dang, "Spontaneous
Coherent Phase Transition of Polaritons in CdTe Microcavities," Phys. Rev. Lett.,
vol. 94, no. 18, p. 187401, May 2005.
[155] S. Kinoshita, H. Ozawa, Y. Kanematsu, I. Tanaka, N. Sugimoto, and S. Fujiwara,
"Efficient optical Kerr shutter for femtosecond time-resolved luminescence
spectroscopy," Rev. Sci. Instrum., vol. 71, no. 9, p. 3317, 2000.
[156] P. Van Der Meulen, H. Zhang, A. M. Jonkman, and M. Glasbeek, "Subpicosecond
solvation
relaxation
of
4-(dicyanomethylene
)-2-methyl-6-(p(dimethylamino)styryl )-4H-pyran in polar liquids," J. Phys. Chem., vol. 100, pp.
5367-5373, 1996.
[157] S. Frolov, W. Gellermann, M. Ozaki, K. Yoshino, and Z. Vardeny, "Cooperative
Emission in a-Conjugated Polymer Thin Films," Phys. Rev. Lett., vol. 78, no. 4,
pp. 729-732, Jan. 1997.
[158] M. Barnes, W. Whitten, S. Arnold, and J. Ramsey, "Homogeneous linewidths of
Rhodamine 6G at room temperature from cavity-enhanced spontaneous emission
rates," J. Chem. Phys., vol. 97, no. 10, pp. 7842-5, 1992.
[159] C. B. Cruz, R. Fork, W. Knox, and C. Shank, "Spectral hole burning in large
molecules probed with 10 fs optical pulses," Chemical physics letters, vol. 132, no.
4,pp. 341-344, 1986.
[160] V. G. Kozlov, P. E. Burrows, G. Parthasarathy, and S. R. Forrest, "Optical
properties of molecular organic semiconductor thin films under intense electrical
excitation," Appl. Phys. Lett., vol. 74, no. 8, p. 1057, 1999.
[161] V. Temnov and U. Woggon, "Superradiance and subradiance in an
inhomogeneously broadened ensemble of two-level systems coupled to a low-Q
cavity," Phys. Rev. Lett., vol. 95, no. 24, p. 243602, Dec. 2005.
[162] F. De Martini and G. Jacobovitz, "Anomalous spontaneous-stimulated-decay
phase transition and zero-threshold laser action in a microscopic cavity," Physical
review letters, vol. 60, no. 17, pp. 1711-1714, 1988.
[163] R. Brnikner, M. Sudzius, H. Frdb, V. G. Lyssenko, and K. Leo, "Saturation of
laser emission in a small mode volume organic microcavity," J. Appl. Phys., vol.
109, no. 10,p. 103116, 2011.
[164] T. Enomoto, T. Sasaki, K. Sekiguchi, Y. Okada, and K. Ujihara, "Intensity
fluctuation of a pulsed planar microcavity laser," J. Appl. Phys., vol. 80, no. 12, p.
6595, 1996.
Conclusion and Outlook
165
[165] G. Bj6rk, H. Heitmann, and Y. Yamamoto, "Spontaneous-emission coupling factor
and mode characteristics of planar dielectric microcavity lasers," Phys. Rev. A, vol.
47, no. 5,p. 4451, 1993.
[166] J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K.
Thompson, "A steady-state superradiant laser with less than one intracavity
photon.," Nature, vol. 484, no. 7392, pp. 78-81, Apr. 2012.
[167] a Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, a
Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vifia,
"Collective fluid dynamics of a polariton condensate in a semiconductor
microcavity.," Nature, vol. 457, no. 7227, pp. 291-5, Jan. 2009.
[168] J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, "Bose-Einstein condensation of
photons in an optical microcavity," Nature, vol. 468, no. 7323, pp. 545-548, Nov.
2010.
Curriculum Vitae
166
166
Curriculum Vitae
GLEB M. AKSELROD
akselrod@mit.edu
EDUCATION
Massachusetts Institute of Technology (MIT)
August 2007 - August 2013
Ph.D. in Experimental Condensed Matter Physics
Department of Physics
Thesis: "Exciton Transport and Coherence in Molecular and Nanostructured Materials"
University of Illinois at Urbana-Champaign (U. of Illinois)
B.S. with Honors in Engineering Physics
Department of Physics
Thesis: "Numerical Simulation of Type-I Entangled Photon Sources"
August 2003 - May 2007
AWARDS
Hertz Graduate Fellowship (Endowed by Nathan Myhrvold)
National Science Foundation Graduate Research Fellowship
Lester Wolfe Fellowship, MIT
American Physical Society Best Student Paper Award, Quantum Info. Theory
Outstanding Physics Senior Thesis Award, U. of Illinois
Barry M. Goldwater Scholarship
Lorella M. Jones Research Fellowship, U. of Illinois
Rensselaer Mathematics and Science Medal
RESEARCH
EXPERIENCE
Duke University
Metamaterials and Plasmonics
Advisors: Professor David Smith and Professor Maiken Mikkelsen
2007-2012
2007-2012
2007-2008
2007
2007
2006
2006
2003
September 2013 - present
Massachusetts Institute of Technology
Organic and Nanostructured Electronics Laboratory
Advisor: Professor Vladimir Bulovic
Graduate Research Assistant
May 2008 - August 2013
Massachusetts Institute of Technology
Quantum Computing Group
Advisor: Professor Isaac Chuang
Graduate Research Assistant
August 2007 - May 2008
University of Illinois at Urbana-Champaign
Quantum Optics and Quantum Information Group
Advisor: Professor Paul Kwiat
Undergraduate Research Assistant
University of Illinois at Urbana-Champaign
Biophysics and Photonics Group
Advisor: Professor Gregory Timp
Undergraduate Research Assistant
April 2006 - May 2007
August 2004 - April 2006
Landauer, Inc., Stillwater, OK
April 2002 - August 2003, May 2004 - August 2004
Optical and Radiation Physics Research Group
Supervisor: R. Craig Yoder
Research Associate
Curriculum Vitae
PUBLICATIO
NS
167
[18] W. Chang, G. M. Akselrod, V. Bulovic, "Mechanical Pressure-Induced Solid State Solvation
and Forster Mediated Spectral Diffusion Effects in Organics Thin Films." Manuscript in
preparation.
[17] G. M. Akselrod*, F. Prins*, L. Poulikakos, V. Bulovic, W. Tisdale, "Exciton diffusion in CdSe
quantum dot thin films probed spectrally, temporally and spatially." Manuscript in preparation.
[16] C. H. Lui, A. J. Frenzel, D. V. Pilon, Y.-H. Lee, G. M. Akselrod, J. Kong, N. Gedik, "Trion
induced negative photoconductivity in monolayer MoS 2 ." Submitted.
[15] G. M. Akselrod, P. Deatore, V. Menon, N. Thompson, M. A. Baldo, and V. Bulovic, "Direction
observation of exciton diffusion in tetracene." Manuscript in preparation.
[14] G. M. Akselrod and V. Bulovic, "Excitonic Antenna for Fluorescence Enhancement of Single
Quantum Dots." Manuscript in preparation.
[13] G. M. Akselrod, E. R. Young, K. W. Stone, A. Palatnik, V. Bulovic, and J. R. Tischler,
"Superradiant Lasing from Organic Microcavities." Submitted (2013).
[12] G. M. Akselrod, E. R. Young, M. S. Bradley, and V. Bulovic, "Lasing Through a StronglyCoupled Mode by Intra-Cavity Pumping." Optics Express, 21: 12122-12128 (2013).
[11] A. M. Eltony, S. X. Wang, G. M. Akselrod, P. F. Herskind, and I. L. Chuang, "Transparent ion
trap with integrated photodetector." Applied Physics Letters, 102: 054106 (2013).
[10] T. P. Osedach, A. lacchetti, R. R. Lunt, T. L. Andrew, P. R. Brown, G. M. Akselrod, and V.
Bulovic, "Near-Infrared Photodetector Consisting of J-Aggregating Cyanine Dye and Metal
Oxide Thin Films." Applied Physics Letters, 101: 113303 (2012).
[9] G.M. Akselrod, B. J. Walker, W. Tisdale, M. Baewendi, and V. Bulovic, "20-fold
Enhancement of Molecular Fluorescence by Coupling to a J-aggregate Critically Coupled
Resonator." ACS Nano, 6: 467-471 (2011).
[8] G. M. Akselrod, J. R. Tischler, E. R. Young, D. G. Nocera, and V. Bulovic, "Exciton-exciton
annihilation in organic polariton microcavities." Physical Review B, 82: 113106 (2010).
[7] P. B. Antohi, J. Labaziewicz, D. Schuster, Y. Ge, G. M. Akselrod, Z. Lin, W. S. Bakr, and I. L.
Chuang, "Cryogenic ion trapping systems with surface-electrode traps." Review of Scientific
Instruments, 80: 013103 (2009).
[6] M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, "Photon arrival time quantum
random number generation." Journal of Modern Optics, 56: 516-522 (2009).
[5] G. M. Akselrod, J. B. Altepeter, E. R. Jeffrey and P. G. Kwiat, "Phase-Compensated UltraBright Source of Polarization Entangled Photons: Erratum." Optics Express, 15: 5260-5261
(2007).
[4] G. M. Akselrod, W. Timp, Q. Zhao, P. Matsudaira, R. Timp, K. Timp, and G. Timp, "LaserGuided Assembly of Heterotypic Three-Dimensional Living Cell Microarrays." Biophysical
Journal, 91: 3465-3473 (2006).
[3] G. M. Akselrod, M. S. Akselrod, E. R. Benton, and N. Yasuda, "A Novel A12 0 3 Fluorescent
Nuclear Track Detector for Heavy Charged Particles and Neutrons." Nuclear Instruments and
Methods B, 247: 295-306 (2006).
Curriculum Vitae
168
[2] M. S. Akselrod, R. C. Yoder, and G. M. Akselrod, "Confocal Fluorescent Imaging of Tracks
and 3D Dose Distribution From Heavy Charged Particles Utilizing New A12O3:C,Mg Crystals."
Radiation Protection Dosimetry, 119: 357-362 (2006).
[1] M. S. Akselrod, S. S. Orlov, and G. M. Akselrod, "Bit-Wise Volumetric Optical Memory
Utilizing Two-Photon Absorption in Aluminum Oxide Medium." Japanese Journal of Applied
Physics, 43: 4908-4911 (2004).
PATENTS
G. M. Akselrod, M. G. Bawendi, V. Bulovic, J. R. Tischler, W. A. Tisdale, and B. J. Walker,
"Device and method for luminescence enhancement by resonant energy transfer from an organic
thin film." U.S. patent application 20120188633 (2012).
V. Bulovic, C. E. Packard, V. C. Wood, A. Murarka, and G. M. Akselrod, "Method and Apparatus
for Forming MEMS Device." U.S. patent application 2010018879 (2010).
M. S. Akselrod, R. C. Yoder, and G. M. Akselrod, "Detection of Neutrons and Heavy Charged
Particles." U.S. Patent 7,141,804 (2006).
INVITED
TALKS AND
G. M. Akselrod, W. Tisdale, B. J. Walker, and V. Bulovic, "Excitonic Antenna for Large
Fluorescence Enhancement of Single Molecules and Quantum Dots." Invited talk presented at
ES
MIT Modern Optics and Spectroscopy Seminar, Cambridge, MA (2013).
G. M. Akselrod, W. Tisdale, B. J. Walker, and V. Bulovic, "Excitonic Antenna for Large
Fluorescence Enhancement of Single Molecules and Quantum Dots." Materials Research Society
Spring Meeting, San Francisco, CA (2013).
G. M. Akselrod, E. R. Young, M. S. Bradley, V. Bulovic, "Room Temperature Organic Polariton
Lasing by Intra-Cavity Pumping." Optics of Excitons in Confined Systems (OECS12), Paris,
France (2011).
G. M. Akselrod, E. R. Young, M. S. Bradley, V. Bulovic, "Room Temperature Organic Polariton
Lasing by Intra-Cavity Pumping." Workshop on Spontaneous Coherence and Collective
Dynamics, Telluride, CO (2011).
G. M. Akselrod, E. R. Young, and V. Bulovic, "Ultra-fast Laser Modulation Mediated by Strong
Light-Matter Coupling." 8th International Conference on Electroluminescence and Organic
Optoelectronics, Ann Arbor, MI (2010).
G. M. Akselrod, J. R. Tischler, E. R. Young, M. S. Bradley, D. G. Nocera, and V. Bulovic,
"Exciton-Exciton Annihilation in Organic Polariton Microcavities." International Quantum
Electronics Conference, Baltimore, MD (2009).
G. M. Akselrod, D. Schuster, P. Antohi, Z. Lin, R. Schoelkopf, and I. L. Chuang, "Trapping and
Detecting Polar Molecular Ions in a Closed-Cycle 4 K Ion Trap." American Physical Society March
Meeting, New Orleans, LA (2008).
G. M. Akselrod, J. Altepeter, M. Goggin, J. Valle, J. Yasi, and P. G. Kwiat, "Numerical Modeling
and Optimization of Type-I Entangled-Photon Sources." American Physical Society March
Meeting, Denver, CO (2007).