Translating Semiconductor Device Physics into
Nanoparticle Films for Electronic Applications
by
Darcy Deborah Wanger
B.S. University of California- Los Angeles (2008)
M.S. University of California- Los Angeles (2008)
Submitted to the Department of Chemistry
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
MASSACHUSEM
&WM"
at the
OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUN 3 0 2014
June 2014
LIBRARIES
@ Massachusetts Institute of Technology 2014. All rights reserved.
Signature redacted
A uthor .............................
De'partment of Chemistry
February 28, 2014
C ertified by ..........................
Signature redacted
V
Moungi G. Bawendi
Lester Wolfe Professor of Chemistry
Thesis Supervisor
A ccepted by ..................................
Signature redacted
Robert W. Field
Chair. Department Committee on Graduate Students
This doctoral thesis has been examined by a Committee of the
Department of Chemistry as follows:
Signature redacted
Professor Keith A. Nelson..............
Thesis Committee Chair
Professor of Chemistry
Signature redacted
Professor Moungi G. Bawendi.........
Thesis Supervisor
Professor of Chemistry
Signature redacted
Professor Vladimir Bulovic........
Th'sis/Committee Member
Pr essor of Electrical Engineering
Translating Semiconductor Device Physics into Nanoparticle
Films for Electronic Applications
by
Darcy Deborah Wanger
Submitted to the Department of Chemistry
on February 28, 2014, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
This thesis explores and quantifies some of the important device physics, parameters,
and mechanisms of semiconductor nanocrystal quantum dot (QD) electronic devices,
and photovoltaic devices in particular. This involves a variety of characterization
techniques and their adaptations, as well as careful evaluation of their results to
assure the validity of assumptions. Chapter 1 provides an introduction of semiconductor band bending from a chemistry perspective and bulk semiconductor solar cells
to establish context for the QD analogs. Chapter 2 discusses the tradeoff between
absorption and conduction for QD thin films in a stacked architecture and the absorption percentage is calculated as a function of film thickness for the solar spectrum.
Chapter 3 presents a quantitative measurement of the number of trapped carriers and
a measurement of exciton quenching to assess limiting mechanisms for current losses
in PbS-quantum-dot-based photovoltaic devices. The trapped-carrier density ranges
from one in 10 to one in 10,000 quantum dots, depending on ligand treatment, and
non-radiative exciton quenching, as opposed to recombination with trapped carriers,
is likely the limiting mechanism in these devices. Chapter 4 presents a thorough study
of the dielectric constant of PbS QD films as a function of the volume fraction of QDs.
A capillary small-angle x-ray scattering (SAXS) technique is used to create a reliable
QD sizing curve, a pair-distribution function for QD spacing is extracted from SAXS
measurements of thin films, and a stacked-capacitor geometry is used to measure the
AC capacitance and determine the film dielectric constant. The resulting data yield
values of dielectric constants as a function of volume fraction of QDs in the thin films
that do not fit within any simple model that applies the bulk dielectric constant of
PbS, which suggests that surface or other size effects may play a role in altering the
dielectric constant of the individual QDs. Appendix A quantifies the number of ligands per particle present in a QD thin film using thermogravimetric analysis to find
that, in general, QD films can be heated under nitrogen to ~200'C without significant
mass loss. The number of ligands per QD in a thin film ranges from 300-3000 for 4.94nm-diameter particles, which suggests that there are many ligands in the thin film
that are not directly bound to the QD. Appendix B discusses the behavior of QD thin
films in thin-film transistors and the information that can and cannot be extracted
from these measurements. These discussions are accompanied by QD-FET transfer curve data for devices with each gold and titanium electrodes that show distinct
differences for the two electrodes. In Appendix C, steady-state and time-dependent
photoluminescence are evaluated as a metric for functioning QD-PV devices. The
steady-state photoluminescence varies as a function of voltage without shifting the
peak position; application of forward bias increases the total photoluminescence and
application of reverse bias decreases the total photoluminescence without reducing it
to zero. Time-dependent photoluminescence studies show only minimal changes in
PL decay time as a function of applied bias. Finally, Appendix D and E establish
liftoff techniques to create crack-free nanoscale patterns of QDs (Appendix D) and
controlled placement of small clusters of QDs (Appendix E) for use in smaller-scale
optoelectronic devices and experiments.
Thesis Supervisor: Moungi G. Bawendi
Title: Lester Wolfe Professor of Chemistry
Acknowledgments
What a pleasant opportunity it is to publicly thank people who have contributed to my
positive experience procuring a PhD. For me, an academic achievement like a doctoral
degree is a testament both to the explicitly educational/intellectual environment, and
to the explicitly non-educational/intellectual environment. Don't get me wrong, I did
a lot too, but it would have been a lot harder and a lot less enjoyable were it not for
all of the people and things that populated those environments.
Academically, my advisor, Moungi Bawendi, has been the person who most defined
my PhD experience, and rightly so.
The most important aspect of my choice to
work in Moungi's group was his deep and sincere value of quality science, and that
has remained the most important thing I have taken away from these few years.
I'd like to thank Moungi for fostering a research group that values safety and is
made up of thoughtful, intelligent, and kind people. Because of Moungi, I've also
honed my skill of sitting and thinking in silence for a moment, thought more broadly
about product markets, adopted the black background on slides, become practiced
at concisely articulating "the big picture" to contextualize new experimental results,
and had way more fun skiing on the East Coast than I ever expected to coming from
Colorado.
The Fannie and John Hertz Foundation has generously provided my graduate
fellowship for all but my first year of graduate school (which was funded by the
DuPont-MIT Alliance).
I have appreciated the Hertz Foundation for deliberately
valuing good questions and thought processes, gathering Hertz fellows from across
the country and spanning a wide range of fellowship years to have creative and intellectually stimulating events, and for their earnest belief that science and engineering
can do very big and very positive things in the world.
The Bawendi lab has been a phenomenal place for me to do research, in significant
part because of my incoming cohort (Raoul Correa, Jian Cui, JM Lee, and myself)
who started figuring out quantum dots together in the first-year office, and a subset
of senior students in the group (Gautham Nair, Lisa Marshall, Scott Geyer, and
Brian Walker) who answered our questions and asked us new ones in those very early
phases. The lab atmosphere, intellectually and otherwise, has also been defined for
me by Tara Sarathi (our fist-pumping enthusiastic UROP), Dan Harris (partner in
glovebox maintenance and solution SAXS sizing, and the one who introduced me to
the wonders of spherical magnetic building blocks as a desktop toy), Dave Strasfeld (of
the boisterous laugh), Zoran Popvic (my original hood partner and laughing buddy),
and Jennifer Scherer (lab day brightener, lab-system-izer, LLB song and dance party
counterpart, wombat hider, straight face keeper, and one of my favorite people with
whom to talk science because she challenges me to understand things I already know).
Members of collaborating groups have also played a very positive role in my graduate research- in particular, Nirat Ray the precise and diligent, Tim Osedach the
thoughtful and receptive, and Joel Jean the sociable and semiconductor-y. Patrick
Brown has also been an integral part of my PhD experience- every time I talk about
science with him, it reminds me how meaningful and gratifying good science can be. I
also would like to acknowledge Jesus del Alamo, who taught the device physics course
in the Electrical Engineering department during my first semester at MIT, because
he securely established the premise on which much of my research and learning has
been based.
My decision to come to graduate school, to do research, and to be a scientist at
all was strongly influenced by mentors and teachers prior to my arrival at MIT. Ben
Schwartz was a superb undergraduate research advisor to me at UCLA because of his
enthusiasm, collaborative eye, and knack for traversing rigorous quantum mechanics and simple analogy explanations that made both difficult coursework and new
research problems fun and compelling. He was the one who said I should go to graduate school because I'd like it, and he was right. Sarah Tolbert taught how I desire to
teach, made presentation slides how I desire to make presentation slides, and made it
sound like it was obvious that I could excel at all of the components of professorship.
Alex Ayzner was a truly excellent research mentor and collaborator during my time
in the Schwartz group; I appreciated his deliberate and thoughtful explanations and
experimental design, and much of the way I approached my own graduate work was
with his experience and wisdom in mind. Alex and Sarah also take credit for my
identification as a P-chemist, correctly asserting that I like data too much not to be.
John Hanson and Tim Hoyt were my organic chemistry professors at the University
of Puget Sound during my freshman year there, and it was their incredible teaching
that prompted me to pursue chemistry and research. Jack Lundt coached the Science
Olympiad teams at Poudre High School- I credit him for my first exposure to materials chemistry, my belief that I can learn something from scratch and be competitively
knowledgeable about it, and the ever-useful-as-a-graduate-student skill of just trying
something when you aren't sure where to begin. When I decided not to major in psychology, it was because of my experience in Science Olympiad that I chose chemistry.
I also acknowledge the significant role that the International Baccalaureate program
played in my scholarly progress; my ability to think critically and articulate analysis
of complex problems were absolutely shaped by the program and the teachers within
it, particularly Lisa King, Chris Hays, and Russ Brown.
I am very grateful for the plentiful positive non-academic environments I've encountered at MIT. It started from the very beginning- Cathy Drennan and Beth
Taylor designed an excellent TA training that set a very positive tone for my first few
months at MIT, and led me to think deeply about learning and human psychology
in a way that has made me a better person. The music community at MIT has been
another reliable source of pleasant interactions- from the orchestra (and its kindly
leader, Adam Boyles) to chamber ensembles (in some lucky cases with coaching from
Jean Rife), to short engagements with the wind ensemble, pit orchestra, and groups
for special events- playing bassoon here, especially with the wonderful people I met in
the process, has been an absolute pleasure. The Women's Volleyball Club at MIT was
a surprising and very significant addition to my MIT experience- it is such a pleasant
and supportive group of people, it let me disengage my brain from sometimes very
tightly wound scientific ponderances and planning, and it was immensely rewarding
to become noticeably more skilled at something on a shorter timescale than my PhD
research. I give extraordinary credit to Tony Lee, the volleyball coach, for seeing in
me a capacity for athleticism and sports-mindedness that I didn't believe I had, and
then showing me that I did.
My close inner circle of friends and family has been, yet again, incredibly valuable
in building and maintaining my general feelings of happiness and consequently for
bolstering the self-motivation to do research where the results are unknown. My
parents, Dee and Mark Wanger, I thank for creating an atmosphere of confidence and
possibility to surround me through my life, both academic and otherwise. Samantha
Elliot and Hannah Leslie-Marshall, my youngest friends (and their respective sets of
parents, Cathy Drennan and Sean Elliot, and Lisa Marshall and Kate Leslie), I thank
for welcoming me into their childhood spheres of curiosity, transparency, joy, comfort,
and play. My dear friends Duhita Mahatmya, Alex Johnson, Jennifer Scherer, and
Kristin Vicari, and my sister Renee Wanger have been a particular joy and comfort
to me in my time as a graduate student because they know me well, say thoughtful
things, and are very willing to laugh with me. And Mike Grinolds, my partner and
best friend, in all his wit and sincerity, has been a wonderful teammate the whole
time.
And finally, in the spirit of "it would have been a lot harder without", I'd like to
acknowledge Sara Bareilles, Ingrid Michaelson, Florence and the Machine, Mumford
and Sons, and The J Band for being my go-to working music, and Trader Joe's
chocolate-covered almonds and Pentel R.S.V.P pens (violet) for keeping my desk
happy.
Contents
1
Introduction
33
1.1
Energy bands and band-bending . . . . . . . . . . . . . . . . . . . . .
34
1.1.1
Energy bands: the chemists approach . . . . . . . . . . . . . .
34
1.1.2
Electron and hole motion: the chemist's approach . . . . . . .
36
1.1.3
The Ferm i level . . . . . . . . . . . . . . . . . . . . . . . . . .
37
1.1.4
Band bending . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
1.1.5
Heterojunction effects
44
1.1.6
Common types of band diagrams
1.1.7
Electrical contacts
1.2
1.3
2
3
. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
46
. . . . . . . . . . . . . . . . . . . . . . . .
46
Bulk semiconductor solar cells . . . . . . . . . . . . . . . . . . . . . .
48
1.2.1
Photocurrent and diode current and photovoltaic metric
. . .
48
1.2.2
Solar cell testing as compared to solar cells in the field
. . . .
49
1.2.3
Equivalent circuit modeling
. . . . . . . . . . . . . . . . . . .
50
QD films as semiconductor analogs: thesis overview . . . . . . . . . .
52
The QD Absorption Spectrum and Ideal Bandgaps for Tandem Cells 53
2.1
Introduction........
................................
53
2.2
Percent absorption of the solar spectrum by a QD thin film . . . . . .
54
2.3
"Ideal" band gaps for tandem cells
. . . . . . . . . . . . . . . . . . .
55
2.4
Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . . . .
56
The Dominant Role of Exciton Quenching in PbS Quantum-DotBased Photovoltaic Devices
57
11
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.2
Measuring the density of trapped carriers . . . . . . . . . . . . . . . .
58
3.3
Measuring non-radiative exciton quenching . . . . . . . . . . . . . . .
68
3.4
D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.5
C onclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
3.6
Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
71
. . . . . . . . . . . . . . . . . . . . . . . .
71
. . . . . . . . .
71
. . . . . . . . . . . . . . .
72
3.6.1
PbS QD Synthesis
3.6.2
Top-gated lateral geometry device fabrication
3.6.3
Photoluminescent film preparation
3.6.4
Photovoltaic device fabrication
. . . . . . . . . . . . . . . . .
72
3.6.5
Top-gated lateral geometry device testing . . . . . . . . . . . .
73
3.6.6
Photoluminescence lifetime measurement . . . . . . . . . . . .
73
3.6.7
Photovoltaic device testing . . . . . . . . . . . . . . . . . . . .
74
3.7
Data tables for all ligands and concentrations
. . . . . . . . . . . . .
74
3.8
Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . . . .
79
4 Quantum Dot Size and Thin-Film Dielectric Constant: Precision
81
Measurement and Dielectric Constant Reduction
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.2
Q D sizing curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4.3
Solution SAXS simulations . . . . . . . . . . . . . . . . . . . . . . . .
84
. . . . . . . . . .
84
. . . . .
90
. . . . . . . . . . . . . . . . . . . . . . . . . . .
90
. . . . . . . . . . . . . . . . . . . . . . .
90
4.4
4.5
4.6
4.3.1
Single-size simulation of scattering intensity
4.3.2
Signal variation with particle size and polydispersity
SAXS measurements
4.4.1
Solution SAXS data
4.4.2
Matching simulations with experimental data
. . . . . . . . .
93
QD spacing in a film . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
. . . . .
93
. . . . . . . . . . . . . . . . . . . . . . . . .
95
Dielectric measurement using stacked architecture . . . . . . . . . . .
96
4.5.1
Spacing determined from pair-distribution function
4.5.2
Film SAXS data
12
4.7
Detailed values for samples used in stacked-capacitor measurements
98
4.7.1
Absorption spectra . . . . . . . . . . . . . . . . . . . . . . .
98
4.7.2
Random close packing . . . . . . . . . . . . . . . . . . . . .
98
4.8
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
4.9
C onclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
4.10 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . .
103
4.10.1 PbS QD synthesis and purification
. . . . . . . . . . . . . .
103
. . . . . . . . . . . . . . . . . . .
103
4.10.3 Stacked capacitor device fabrication . . . . . . . . . . . . . .
104
4.10.4 SAXS measurement . . . . . . . . . . . . . . . . . . . . . . .
104
4.10.5 Capacitor measurement
. . . . . . . . . . . . . . . . . . . .
105
4.11 Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . . .
105
A Ligand Quantification using Thermogravimetric Analysis (TGA)
107
4.10.2 SAXS sample preparation
A .1 Introduction . . . . . . . . . . . . . . . . . . . . .
107
A.2 Sample preparation . . . . . . . . . . . . . . . . .
108
A.3 TGA method . . . . . . . . . . . . . . . . . . . .
108
A.4 Mass loss and ligand quantification . . . . . . . .
109
A.4.1
Size variation . . . . . . . . . . . . . . . .
109
A.4.2
Ligand variation
. . . . . . . . . . . . . .
109
A.4.3
Ligand quantification . . . . . . . . . . . .
111
A.5 Species lost at each temperature . . . . . . . . . .
114
A.5.1
Mass-loss derivative analysis . . . . . . . .
114
A.5.2
Bulk study to probe Pb evaporation
. . .
114
A.5.3
TGA-MS
. . . . . . . . . . . . . . . . . .
117
A .6 Conclusions . . . . . . . . . . . . . . . . . . . . .
117
A.7 Chapter-specific acknowledgments . . . . . . . . .
120
B QD Films in Transistor Geometries
121
B.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121
B.2
Length scales and electric-field boundaries
122
13
. . . . . . . . . . . . . .
B .3 Charge injection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
122
B.4
Importance of Ohmic contacts . . . . . . . . . . . . . . . . . . . .
124
B.5
Mobility measurements using FETs . . . . . . . . . . . . . . . . .
125
B.6
Carrier-type characterization . . . . . . . . . . . . . . . . . . . . .
126
. . . . . . . . . .
126
B.6.1
Misinterpretation of FET measurements
B.6.2
QD FET mobility variation as a function of contact metal
127
B.6.3
Accurate carrier-type characterization . . . . . . . . . . . .
128
B.6.4
Evaluating Ohmic contacts . . . . . . . . . . . . . . . . . .
131
B.7 Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . .
132
C Photoluminensce as a Metric for Functioning Electronic QD Devices 133
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
133
C.2 Steady-state photoluminescence . . . . . . . . . . . . . . . . . . . . .
133
C .1
C.2.1
Increased PL with voltage in PV architecture
. . . . . . . . .
133
C.2.2
Consistent PL with voltage in capacitive architecture . . . . .
138
C.3 Lifetime invariance with voltage . . . . . . . . . . . . . . . . . . . . .
140
C.4 Device encapsulation and testing experimental details . . . . . . . . .
143
C .5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
144
C.6 Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . . . . 145
D Nanopatterned Electrically Conductive Films of Semiconductor Nanocrystals
147
D .1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
148
D .2 Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
150
. . . . . . . . . . . . . . . . . . . . .
154
D.4 Patterns and their properties . . . . . . . . . . . . . . . . . . . . .
157
D .5 C onclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
164
D.6 Chapter-specific acknowledgments . . . . . . . . . . . . . . . . . .
164
D.3 Detailed patterning process
E Controlled Placement of Colloidal Quantum Dots in Sub-15 nm
165
Clusters
14
E.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
E.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 167
E.3
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171
E.4
Experimental
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
173
E.4.1
Synthesis of CdSe(ZnxCdl-xS) core(shell) QDs . . . . . . . . .
173
E.4.2
Electron-beam Lithography (EBL)
E.4.3
Scanning Electron Microscopy . . . . . . . . . . . . . . . . . .
174
E.4.4
Transmission Electron Microscopy . . . . . . . . . . . . . . . .
174
E.4.5
Optical Chracterization . . . . . . . . . . . . . . . . . . . . . . 174
15
. . . . . . . . . . . . . . . 174
16
List of Figures
1-1
(a) Simple MO diagram for two one-valence-electron atom. (b) The
addition of more atoms to the MO diagram creates closely spaced bonding and antibonding orbitals (c) At the many-atom limit these orbitals
form a "band" (indicated by orange box of filled orbitals and white
box of empty orbitals). The distance between the two bands is referred to as the "band gap" between the "valence band" (occupied by
electrons) and the "conduction band" (devoid of electrons).
(d) The
absorption spectrum of a semiconductor has an onset at the bandgap
and continues into the UV. This image is from pveducation.org. [40]
1-2
.
35
(a) Schematic of two molecules with simple MO diagrams where one
is shifted lower in energy. (b) The two molecules when an electron
is added to the left molecule, resulting in electron motion from the
left antibonding orbital to the right antibonding orbital. (c) The two
molecules when an electron is taken away from the right molecule,
result in electron motion from the left bonding orbital to the right
bonding orbital. (d) The scenario in (c) using hole notation rather
than electron notation. . . . . . . . . . . . . . . . . . . . . . . . . . .
1-3
36
The density of states in the band, the Boltzmann distribution, and the
temperature of the system define the electron and hole populations in
the conduction and values bands, respectively. . . . . . . . . . . . . .
17
38
1-4
Cartoon of the series of steps that would take place if an n-type and ptype material were brought into contact. a) Semiconductors are chargeneutral. b) Free carriers diffuse into free states in the other material,
and recombine with excess carriers of the opposite type. c) Uncompensated atoms (red) create an electric field across the interface in the
opposite direction of the diffusion effects. . . . . . . . . . . . . . . . .
1-5
Plots of (a) charge density, (b) electric field, (c) electric potential, (d)
energy level, and (e) energy band diagram for a p-n homojunction. . .
1-6
41
43
a) Illustration of vacuum level in a standard band diagram. b) Illustration of a p-n junction band diagram if a constant vacuum level rather
than constant Fermi level were enforced.
1-7
. . . . . . . . . . . . . . . .
Band diagrams of heterojunction architectures, showing the discontinuity in the band levels and continuity in the vacuum level . . . . . .
1-8
45
Band diagram examples for some common architectures.a) Schottky
junction b) p-i-n junction c) MOS structure. . . . . . . . . . . . . . .
1-9
44
47
Band diagram for an semiconductor with a Fermi level in the middle of
the bandgap that is symmetrically contacted by two deep-workfunction
electrodes a) prior to contact and b) in equilibrium. . . . . . . . . . .
48
1-10 Illustration of p-n junction band diagram in a) reverse bias b) equilibrium c) forward bias and d) the corresponding current-voltage curve
for diodic and photocurrent
. . . . . . . . . . . . . . . . . . . . . . .
50
1-11 Solar cells in practice can be modeled using an equivalent circuit. High
shunt resistance is beneficial for the device performance, and manifests as a shallow slope in the current-voltage curve at the short-circuit
current point. Low series resistance is beneficial for the device performance, and manifests as a steep slope at the open-circuit voltage
p oin t.
2-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
Thin films (left) allow excited carriers to reach the edges of the film.
Thick films (right) suffer recombinative losses. . . . . . . . . . . . . .
18
54
2-2
Data and line of best fit for the OD of QD thin films as a function of
film thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
2-3
Percentage of solar spectrum absorbed as a function of film thickness.
56
3-1
The intensity dependence of the photocurrent is used to determine the
ratio of free to effective trapped carriers (n/N,*).
(a) Schematic of a
top-gated field-effect transistor device, which is illuminated through
the underlying glass substrate at varying intensities with a 532-nm cw
laser. Measurements of photocurrent are made between the source and
drain (IDS) under illumination. In a separate measurement (Figure 32), mobilities are extracted from the slopes of the IDS curves as a
function of the gate voltage (VG) in the dark. (b) Full data set for one
n/Nt* measurement. A voltage sweep is made at each light intensity.
The projections (in green) show that the current density is nonlinear
as a function of light intensity, and linear as a function of voltage. . .
3-2
59
Quantitative determination of the FET mobility for both electrons and
holes using a top-gated transistor geometry. The IDS values over a full
sweep of VG are shown on a semilog scale (upper plots) for TBAC
(VDS
= 10 V), TBABr and TBAI (VDS = 5 V), where the gate leakage
(grey) is shown to be insignificant on the order of magnitude of the
signal changes.
Linear fits (solid lines in both panels) to the data
sweeping away from zero (+ signs) are applied to the n-channel and
p-channel of each device (lower plots) to extract the electron and hole
mobilities, respectively. All mobility measurements were taken in the
dark........
.....................................
19
61
3-3
Carrier data extracted from photocurrent intensity measurement and
calculations. (a) Photocurrents and free-carrier densities for a full voltage (VDS) sweep as a function of laser intensity with a representative fit
to I = aJ 2 +-J at a single voltage, for three halogen-salt ligand treatments. The value of n is calculated by multiplying the photocurrent
density (left axes, matched in color to data points) by a (of Equation 3.2).The spread of values at a given laser intensity is the variation
in the measurement made at different voltages (seen in panel (d)). (b)
Free-carrier density and a representative fit as a function of laser intensity, plotted on a logarithmic scale in laser intensity. The logarithmic
scale of the x-axis more readily shows the fit to the data over a wide
range of points. (c) Ratio of free carriers to effective trapped carriers,
nINt* = 2Ja/3 as a function of laser intensity. The spread of values
at a given laser intensity is the variation in the measurement made at
different voltages (seen in panel (d)). (d) Trapped-carrier density as a
function of voltage, calculated at each voltage by dividing the values
in panel (c) by those in panels (a) and (b). These values are independent of voltage, which is consistent with the assumption of linear
current-voltage behavior. . . . . . . . . . . . . . . . . . . . . . . . . .
20
63
3-4
Ligands affect the effective density of trapped carriers and density
of dark free carriers, though all N* values remain significantly below one trapped carrier per QD. Dark free-carrier values (pink diamonds) are lower than trapped-carrier values (blue circles).
Values
for free carriers in the dark are not calculated for the high-gain ligand (TBACl) because the average mobility assumption does not hold.
13BDT is 1,3 benzenedithiol, MPA is mercaptopropionic acid, and
CTAB is cetyltrimethylammonium bromide (see Table 3.1 and 3.7 for
all ligand concentrations and solvents). Dark free-carrier densities are
extracted from the lateral current using Equation 3.2 and trappedcarrier densities are extracted from the photocurrent intensity dependence. ........
3-5
...................................
65
Small-Angle X-ray Scattering (SAXS) to determine inter-dot spacing.
Integrated counts over a cone of signal (excluding surface reflection)
for films of PbS QDs deposited as for photovoltaic devices but on crystalline Si substrates with no surrounding layers show no appreciable
change in inter-dot distance as a function of ligand-exchange solution
concentration. The inter-dot spacing as determined from the peak is
4.5 nm. Extracting the pair-distribution function for a QD film of the
same size particles (see Chapter 4) yields a larger spacing of ~5.3 nm.
3-6
66
Increasing TBAI concentration results in higher PL lifetimes and an
increase in short-circuit currents without changing the density ofeffective trapped carriers. (a) SWIR-PL decay traces for encapsulated QD
films on glass, as treated with TBAI ligand-exchange solutions of three
different concentrations. (b) Trapped-carrier densities (blue/black circles) and dark free-carrier densities (pink diamonds) plotted as a function of TBAI concentration. (c) Current-voltage curves for the three
TBAI concentrations under AM1.5 solar illumination. Inset shows device architecture. Shading shows standard deviation.
21
. . . . . . . . .
67
3-7
Increasing TBAI concentration changes the peaks in FTIR from the
native oleic acid ligand peaks. . . . . . . . . . . . . . . . . . . . . . .
3-8
69
Surface trapping control experiment using ungated films. The nI/N*
values are within the same range for bare glass and silated (octadecyltrimethoxysilane) glass surfaces. The device architecture used to
make these measurements uses the same glass substrates as top-gated
devices used for the Nt* measurements, but the fabrication ends after
the deposition of the QD layer. If surface trapping at the glass interface contributed significantly to the values measured for Nt*, one would
expect the value for n to be higher and the value of Nt* to be lower
for the silated glass, making the n/Nt* ratio significantly larger for the
silated surface.
4-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Development of the PbS QD sizing curve. (a) Absorption and photoluminescence spectra for all sizing samples. (b) Solution SAXS data and
simulated fits for all sizing samples. Absorption and photoluminescence peak positions are noted in addition to the matching simulated
diam eter.
4-2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
Sizing curve plotted with literature sizing values. This solution-SAXS
sizing method maps a given diameter to a larger bandgap than other
methods[51, 120, 76, 46, 10, 50], or a given peak location to a larger
diameter. This result suggests that other methods may underestimate
the size of the QD particles, which is consistent with previous observations of a poorly resolved surface layer in TEM images of CdSe QDs
that is resolved in x-ray analysis[77].
4-3
. . . . . . . . . . . . . . . . . .
86
Simulated PbS QD at a particular radius, in units of lattice spacings.
Blue and green points represent Pb and S atoms, respectively. We note
that faceting is not included in this model; atoms are only located on
points within the radius input for any particular particle size.
22
. . . .
87
4-4
Simulated scattering intensity due to Pb-Pb scattering (blue), S-S scattering (green), and Pb-S scattering (red). These are the scattering values prior to the addition of the (constant) atomic scattering factors;
the negative value of the Pb-Pb baseline does not result in a simulated
negative scattering value. . . . . . . . . . . . . . . . . . . . . . . . . .
4-5
Simulated x-ray scattering in both the small-angle and wide-angle region s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-6
88
89
Simulated x-ray scattering with increasing diameters from 12 A to 66
A where the standard deviation of the normal distribution is set at 5%
of the particle size. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-7
Simulated x-ray scattering with increasing polydispersity from 0% to
6% for an unchanging average particle size of 50 A. . . . . . . . . . .
4-8
92
2D-detector intensity for the solution-SAXS measurement for a size
series of Q D s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-9
91
92
a) Raw film SAXS data (open data points) and GNOM fit (solid black
line). The minor peaks at larger 20 values are self-scatter peaks like
those shown in Figure 4-1. b) Extracted pair-distribution function for
fits in (a) using GNOM. Error bars are calculated by GNOM. The
peaks of the P(r) curves are the center-to-center spacings for nearest
neighbors and other features of the curves are a result of self-scattering
and limited measurement range. . . . . . . . . . . . . . . . . . . . . .
94
4-10 Images of the 2D-detector intensity for the film-SAXS measurement
for the four film samples in the text.
. . . . . . . . . . . . . . . . . .
4-11 Measurement and evaluation of the film dielectric constant.
96
(a) Di-
electric measurements as converted from capacitance as a function of
frequency, after control subtraction. (b) Impedance phase angle as a
function of frequency to show strong capacitive behavior over a wide
frequency range. The inset shows the layered structure of the sample
device (left) and control device (right). . . . . . . . . . . . . . . . . .
23
97
4-12 Absorption spectra for the four solutions used in the size series for
capacitance measurements. . . . . . . . . . . . . . . . . . . . . . . . .
99
4-13 Dielectric measurements compared with several effective-medium models. The data do not fit to these simple effective-medium models with a
PbS dielectric constant of 169, as in the bulk. The linearity of the data
suggests that some volume-weighted theory may be appropriate, but
the shallower slope implies that the effective QD dielectric constant is
smaller than that of the bulk. . . . . . . . . . . . . . . . . . . . . . .
100
A-i TGA mass-loss curves for different QD sizes and ligands. . . . . . . .
110
A-2 TGA mass-loss curves for different ligands, where the particle size is
the same for all samples. . . . . . . . . . . . . . . . . . . . . . . . . .
112
A-3 Plots of total atoms and number of surface atoms as a function of QD
diameter and first exciton peak. . . . . . . . . . . . . . . . . . . . . .
113
A-4 TGA mass-loss derivative curves for different ligands, where the particle size is the same for all samples.
. . . . . . . . . . . . . . . . . . . 115
A-5 TGA mass-loss and derivative curves for bulk PbS powder. . . . . . . 116
A-6 TGA mass-loss ion currents for different mass fragment values for a
QD sample with n-butylamine ligands. . . . . . . . . . . . . . . . . . 118
A-7 TGA mass-loss ion currents for different mass fragment values for a
QD sample with oleic acid ligands.
. . . . . . . . . . . . . . . . . . . 119
B-i Schematic drawing and relatively scaled drawing of a bottom-gated FET. 123
B-2 Cross-sectional SEM images of a top-gated QD FET. . . . . . . . . .
123
B-3 Band-bending diagram for lateral contacts to a semiconductor and a
uniform electric field resulting from an applied voltage between contacts. 125
B-4 Schematic transconductance data and interpretation.
24
. . . . . . . . .
127
B-5 Transconductance of QD FETs treated with 1,3 benzenedithiol with
gold (a) and titanium (b) source and drain contacts. The data are
shown on a linear and log scale, with the leakage current shown on the
log-scale plot in gray. The lower panels show linear fits to the data
past a threshold value in each the p-channel and n-channel. . . . . . .
129
B-6 Transconductance of QD FETs treated with tetrabutylammonium diode
with gold (a) and titanium (b) source and drain contacts. The data
are shown on a linear and log scale, with the leakage current shown on
the log-scale plot in gray. The lower panels show linear fits to the data
past a threshold value in each the p-channel and n-channel. . . . . . . 130
C-1 a) Steady-state PL spectra for a QD-PCBM device with applied voltage
showing the lack of peak shift and the increase in counts with increasing
voltage. b) Plot of the peak PL counts as a function of applied voltage.
The inset shows schematic band diagrams of a p-n junction in reverse
bias, at equilibrium, and in forward bias. . . . . . . . . . . . . . . . .
134
C-2 PL data and PL peak data as a function of applied voltage for a higher
flux of ~2.6 mW. A routine flux is ~212 uW.
. . . . . . . . . . . . .
135
C-3 Simulated QNR thickness in nm from 0 V to 0.3 V applied bias. In
this simulation the film thickness is 90 nm, the dielectric constant of
the film is 15, the built-in bias is 0.3 V and the effective doping density
is 10 7C m -3.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-4 IR microscope image of a PbS QD-PCBM device in short circuit.
. .
136
136
C-5 Intensity linecut and related image section from Figure C-4. The vertical line indicates the edge of the patterned ITO. . . . . . . . . . . .
137
C-6 Transmission (left) and reflection (right) images of the device. The
vertical line is the edge of the patterned ITO (right). The small black
box shows the portion of the image that corresponds to the intensity
im age in Figure C-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
25
C-7 Steady-state PL measurements for the stacked capacitor geometry with
(pulsed) applied bias up to -2 V and + 2 V. Integration time was 1 s.
138
C-8 Multiframe steady-state PL measurements for the stacked capacitor
geometry with (top) no applied bias (middle) continuous applied bias
from 0 to -20 V (bottom) continuous applied bias from 0 to +20 V. Integration time was 200 ps. No effect of voltage application is observable. 139
C-9 Simulated counts as a function of time for a functioning device with
increasing depletion region from 0-100 nm. In a), the short lifetime is
1 ns and the long lifetime is 10 ns and the input quantum yield of the
depleted region is 1/10th of the quantum yield of the QNR. In b) The
lifetime values used (1.7 ns and 13.2 ns) are those extracted from the
biexponential fit to the data in Chapter 3 for this same ligand exchange
treatment (10 mg/mL TBAI in methanol), and the quantum yield of
the short-lifetime region is 1/100th instead of 1/10th that of the QNR.
In b) the change in the relative lifetimes is harder to see and it shows
up more as a loss of total signal than as a change in relative lifetime
than in a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
141
C-10 Normalized raw data counts as a function of time for a range of applied
voltage from -2 V to +3 V (legend shows applied voltage). The data
were collected at 1 MHz with 200 uW flux. There is no observable
difference in the lifetimes as a function of voltage. . . . . . . . . . . . 142
C-11 Processed and normalized data from two different days and spot locations for several voltages. These curves deviate in their longer-time
components at different voltages. The left panel shows greater deviation than the right panel, but the trend is the same for both measurement sets. . . .. .. .....
.
.. ......
..........
C-12 Power-dependence at V = 0 on a functioning PV device.
26
.. . . . . 142
. . . . . . . 143
D-1
(a) Schematic of nanocrystals drop cast on an inverted FET device
(side view). (b) Scanning electron micrograph of a PbSe nanocrystal
film drop cast on an inverted FET device (top view; the gold electrodes,
which are beneath the nanocrystal film and thus obscured from view,
are outlined in orange), and (c) after annealing the film for one hour
at 400 K. (d) When the thickness of the film exceeds approximately 1
gim, cracks emerge as the film dries, namely as solvent interior to the
film evaporates and diffuses to the already dry surface. Cracking and
clustering diminish the efficiency of charge transport in nanocrystal
films and make it impossible to study the charge dynamics intrinsic to
the nanocrystals.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
151
D-2 (Left and center) An overview of the process for patterning nanoscale
films of semiconductor nanocrystals. The patterns are positioned on
the surface of the substrate with nanoscale precision. To achieve electrically conducting films without cracking the film by annealing or
exchanging the capping ligand for a smaller molecule, we exchange the
capping ligand while the nanocrystals are still in solution prior to deposition. (Right) Transmission electron micrographs of the nanocrystal
films before and after cap exchange. . . . . . . . . . . . . . . . . . . . 153
D-3 Optical micrographs of a cracked film of patterned n-butylamine-capped
PbS nanocrystals on a silicon dioxide surface.
. . . . . . . . . . . . . 158
D-4 Films made with nanocrystals from which some of the capping ligands have detached while the nanocrystals were in solution and the
nanocrystals agglomerated. . . . . . . . . . . . . . . . . . . . . . . . .
158
D-5 Optical micrographs of patterned n-butylamine-capped PbS nanocrystals on a silicon dioxide surface for patterns processed without the
sonication step. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
159
D-6 Crack-free patterns that are fabricated according to the process outlined above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
159
D-7 Nanopatterned films of CdSe nanocrystals (first and third rows) and
Zno.5 Cdo. 5 Se-Zno.5 Cdo. 5 S core-shell nanocrystals (second row). (a) Scanning electron micrograph, (b) fluorescence (actual color), and (c) AFM
im ages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
D-8 We demonstrate the flexibility in choice of nanocrystal materials by
patterning films from (a) PbSe nanocrystals capped with oleic acid,
(b) PbS nanocrystals capped with n-butylamine, and (c) Zno. 5 CdO. 5 SeZnO.5 CdO. 5 S core-shell nanocrystals capped with phosphonic acids. In
(b), the PbS nanocrystal film is patterned to a nearby transistor gate
with nanoscale precision. All of these images are scanning electron
micrographs except in (c) where we show both green fluorescence and
an electron micrograph indicating that the size of the pattern is only
about 30 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161
D-9 (a) An AFM image of a film of PbS nanocrystals capped with nbutylamine, which is 350 nm wide at its narrowest point. The film
is continuous, in contrast to those shown in Figure D-1. (b) I-V characteristic of the nanopatterned film shown in (a). (c) Conductance of
n-butylamine-capped PbS nanocrystals versus the dimensions of the
film with Vds = 0.1 V. The red circles represent the conductance of
the nanopatterned film shown in (a) and a comparable rectangular film
with nanometer dimensions. The blue circles represent the conductance of a microscopic film in a device structure shown in Figure D-1,
where the dimensions of the film are 800 pm wide, between 40 and
300 nm thick, and either 2 or 5 pm wide. The conductivity of the
nanoscopic films is higher than what is found in the microscopic films. 163
28
E-i
Overview of the fabrication process for placing QDs. (a) Schematics of
the fabrication process: PMMA was spin-coated to a thickness of 40
nm on Si, followed by EBL; Then, 6-nm-diameter CdSe QDs were spincoated or drop cast; Finally the PMMA lift off was done with acetone,
leaving clusters of CdSe QDs. (b) Top: scanning-electron micrographs
of PMMA templates with 8 nm (minimum feature size used) and 21
nm diameters. Bottom: SEM image cross-section across the PMMA
templates. (c) Left: SEM of a patterned CdSe QD cluster (dimer).
Right: SEM cross-section over one CdSe QD, with full-width at half
m aximum of 6 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
167
E-2 Scanning-electron micrographs of (a, b) 6-nm-diameter CdSe QDs and
(d, e) 5-nm-diameter CdSe/CdZnS. The fabrication was optimized to
minimize the number of QDs in each cluster. (a) QD clusters were
fabricated using templates with 15-20 nm diameter. (b) QD clusters
were fabricated using templates with 8-15 nm diameter; these were the
smallest clusters fabricated. (c) Histogram of the number of QDs in
each cluster versus the number of clusters, using the smallest fabricated
templates. We analyzed 54 sites designed for QD clusters. The QDs
were counted from the SEM micrographs. Representative SEM images
were added to the histogram. The top of (d) and (e) shows the designed
templates with 12 nm diameters for placing QDs in close proximity to
one another, with gaps of 36 nm in (d) and 12 nm in (e). The bottom
of (d) and (e) shows SEM micrograph of clusters of QDs composed of
5-nm-diameter CdSe/CdZnS (core/shell). . . . . . . . . . . . . . . . .
29
169
E-3 (a) Transmission electron micrograph of CdSe/CdZnS core/shell QDs
randomly deposited on a carbon membrane, with average diameter of
5 nm used for optical characterization. (b) Wide-field photoluminescence image of CdSe/CdZnS QD clusters placed in a rectangular array
of 2 pim x 5 pm. The peak of emission wavelength was 576 nm. (c)
SEM of QD clusters that are -10 nm to 42 nm in diameter (the top
bright clusters in (b) are 200-nm markers of QDs). (dl) Photoluminescence time trace of one QD cluster. The time trace shows intermittent
luminescence (blinking). (d2) PL intensity versus frequency. The PL
intensity presented a bi modal distribution, indicating blinking.
30
. . .
172
List of Tables
3.1
Transistor parameters for varying ligands and ligand concentrations
3.2
Photocurrent intensity dependence parameters for varying ligands and
concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
76
77
32
Chapter 1
Introduction
Semiconductor materials have played a revolutionary role in technological advances of
the past several decades: p-n-junction solar cells convert sunlight to electricity, image
sensors capture pixel information to record pictures, and transistors store information
in computers and other ubiquitous electronic accessories. The integral relationship
between material understanding and engineering capability has resulted in a series
of well defined material parameters and equations that are routinely used to create electronic and optoelectronic devices and to identify desired properties for new
materials.
The more recent capabilities to synthesize and characterize materials with nanoscale
dimensions have resulted in a new spectrum of semiconductor materials that share
some qualities and properties with bulk semiconductors, but are also subject to quantum confinement and other effects that take place at the nanoscale, which give them
qualities and properties in common with conducting polymers and molecules used
for optoelectronic applications. To fully employ these nanoscale materials in the trajectory of semiconductor electronics, their parameters and properties must be well
defined in the scope of semiconductor physics. This thesis provides quantified values and methods for important parameters and properties that are either specific to
semiconductor nanocrystal thin films, or whose behavior is distinct from bulk semiconductor films. First, some fundamentals of bulk semiconductor device physics will
be explained as a context for the nanocrystal-specific work presented in later chapters.
33
1.1
1.1.1
Energy bands and band-bending
Energy bands: the chemists approach
To introduce a bottom-up approach to band formation from a chemistry perspective,
consider the molecular orbital (MO) diagram for two hydrogen atoms (Figure 1.1.1a).
Each atom contributes one electron to the system, and there is one molecular orbital
for each contributed orbital from the component atoms (in this case, one bonding and
one antibonding). The molecular orbital diagram is similar for two sodium atomsagain each atom contributes its valence electrons and their orbitals to the molecular
system to create the relevant filled molecular orbitals. Now imagine the addition
of further atoms to the system- each contributing one valence electron and one orbital. These additional atoms also create bonding and antibonding orbitals of similar
energies, but the separation of these molecular orbitals from one another in energy
decreases as more atoms are added (Figure 1.1.1b). That is, the 51st and 52nd atoms
contribute bonding orbitals of higher energy and antibonding orbitals of lower energy
than the 1st and 2nd atoms. Of course, the location of these bonding and antibonding
orbitals in energy space and how they vary with increased orbital addition depends
on the character and contributed orbitals of the component atoms. Some combinations produce molecular orbital diagrams where the many-atom limit results in a
HOMO-LUMO gap of zero; these are metals. Other combinations produce molecular
orbital diagrams where the many-atom limit results in a HOMO-LUMO gap of a
finite nonzero value; these are semiconductors or insulators (Figure 1.1.1c).
In semiconductor physics, the HOMO-LUMO energy difference from the previous
example is called the "band gap", E9 . The word "band" refers to the series of orbitals
surrounding the band gap created from the atomic valence orbitals that are effectively
continuously distributed in energy. The band that is filled with electrons (in this
simple example, the bonding orbitals) is referred to as the "valence band" and the
band devoid of electrons is referred to as the "conduction band".
The band gap
provides information about the absorption profile. The band gap determines the
lowest-energy photon that can be absorbed: a semiconductor cannot absorb light of
34
a)
b)
C)
d)
10
---
410,
----
G
InP
Te
10,
10
102
10
200
400
600
800
1000
wavelength (nm)
1200
1400
Figure 1-1: (a) Simple MO diagram for two one-valence-electron atom. (b) The
addition of more atoms to the MO diagram creates closely spaced bonding and antibonding orbitals (c) At the many-atom limit these orbitals form a "band" (indicated
by orange box of filled orbitals and white box of empty orbitals). The distance between the two bands is referred to as the "band gap" between the "valence band"
(occupied by electrons) and the "conduction band" (devoid of electrons). (d) The
absorption spectrum of a semiconductor has an onset at the bandgap and continues
into the UV. This image is from pveducation.org.[40]
35
(a)
(c)
(b)
(d)
Figure 1-2: (a) Schematic of two molecules with simple MO diagrams where one is
shifted lower in energy. (b) The two molecules when an electron is added to the left
molecule, resulting in electron motion from the left antibonding orbital to the right
antibonding orbital. (c) The two molecules when an electron is taken away from the
right molecule, result in electron motion from the left bonding orbital to the right
bonding orbital. (d) The scenario in (c) using hole notation rather than electron
notation.
lower energy than its bandgap because there are no empty states available that energy
distance above any of the filled electron states. Because the continuum of states in
both bands allow for many combinations of states to participate in absorption events,
generally a semiconductor can absorb all photons of higher energy (at energies far
higher than the ultraviolet (UV) region, the states involved can be from bands beyond
the valence and conduction bands, so this concept does not hold rigorously true).
From a chemists perspective, it is surprising to see an absorption profile such as that
in (Figure 1.1. 1d) because molecular densities of states are generally smaller and more
confined such that there is a relatively narrow region of absorption with some peak
structure. The absorption profile of a semiconductor is particularly well suited to
solar cells and broadband photodetectors.
1.1.2
Electron and hole motion: the chemist's approach
Consider again the simplest of MO diagrams, but now adjust that picture such that
two of these molecules are so close together that an electron could feasibly move
between them and such that one of these molecules had an MO diagram shifted lower
in energy (Figure 1.1.2a). With the energy levels shown, no electron moves between
the two molecules in the ground state because there are four electrons, each electron
can hold two orbitals, and the two lowest-energy orbitals are already filled.
36
If an electron is added to the left molecule, it will occupy the antibonding orbital.
Then it will move to the antibonding orbital of the right molecule because
that molecular orbital is lower in energy (Figure 1.1.2b). This is consistent with the
atomic orbital filling understanding of general chemistry; electrons will move to a
lower-energy state if such a state is available. If an electron is taken away from the
right molecule, there is now an empty state at lower energy, so one of the electrons
from the left molecule can move to occupy that state, leaving the electron in the
HOMO of the right molecule and the vacancy in the HOMO of the left molecule
(Figure 1.1.2c). This transition can be viewed either as the electron moving down in
energy (the chemists intuitive picture) or the vacancy or "hole" moving up in energy.
The picture could also be made with notation for holes instead of electrons (Figure 1.1.2d), and the lowest energy state is the state where the holes are at the highest
energy levels. In bulk semiconductor physics, it is convenient to be able to transition
between thinking about the electron picture and the hole picture depending on the
system, so it is a valuable intuition to recognize that holes moving up in energy is
equivalent to electrons moving down in energy.
1.1.3
The Fermi level
The example in the previous section of adding or subtracting an electron to/from one
of the two molecules is analogous to what happens in a bulk semiconductor when
it is doped.
A miniscule (~10 ppm) amount of atoms of a different type in the
semiconductor introduces a small number of occupied orbitals very close (within kT)
of the conduction band edge (LUMO) (or conversely, a small number of unoccupied
orbitals very close to the valence band edge). The new electrons introduced in some
ways behave like excited electrons; they are able to traverse physical space because
there are many empty states at their energy level (in the conduction band in this
case). Because of the large numbers of contributing atoms, even small probabilities
such as the Boltzmann distribution of electrons occupying states at energies higher
than the HOMO at finite temperature can result in a substantial density of electrons
in the conduction band. More rigorously, the population of electrons in the conduction
37
EC
EV
X
Density
of States
Occupancy
Factor
-
Carrier
Density
Figure 1-3: The density of states in the band, the Boltzmann distribution, and the
temperature of the system define the electron and hole populations in the conduction
and values bands, respectively.
band (or holes in the valence band) in an undoped bulk semiconductor is derived from
the temperature, the density of states in the band, and the Boltzmann distribution
(Figure 1.1.3):
N(E) dE
nCB =
fEc B
j
p(E)f(E) dE
[2 (m7kT)
e-Eg/2kT
(11)
EOC Bh
where nCB is the number of electrons in the conduction band, N(E) is the number
of electrons at energy E, ECB is the energy of the conduction bandedge, p(E) is the
density of states in the conduction band at energy E, m is the effective mass of the
particle (electron in this case), h is Planck's constant, k is Boltzmann's constant, and
T is the absolute temperature in Kelvin.
Chemists learning about thermodynamics think about the "chemical potential"
as an important quantity that encapsulates a driving force for a reaction between
chemical species. Similarly, and even more simplistically, in general chemistry, atomic
orbital filling and molecular orbital (MO) diagrams function under the assumption
38
that electrons preferentially occupy lower energy states if those states are available.
In bulk semiconductor physics, the relevant quantity is the Fermi level,
EF.
which
expresses the relative populations of holes and electrons.
1
f (E)
=(E-EF)/kT
(12
where f(E) is the probability of an electron occupying a state at the energy
level E,
EF
is the Fermi level, k is Boltzmann's constant, and T is the absolute
temperature in Kelvin.
The Fermi level is a position or nonexistent state, usually
within the bandgap, where the probability of electron occupation (Equation 1.2)would
be 50%. Introducing extra electrons into the conduction band raises the Fermi level
from the middle of the bandgap toward the conduction band, and introducing extra
holes into the valence band lowers the Fermi level from the middle of the bandgap
toward the valence band. (Figure 1.1.3).
Semiconductors that have a significantly
higher density of electrons in the conduction band than holes in the valence band
are referred to as "n-type" (the letter "n" because the relevant charge carriers are
negative), and semiconductors that have a significantly higher density of holes in the
valence band than electron in the conduction band are referred to as "p-type" (the
letter "p" because the relevant charge carriers are positive).
These "extra" carriers
can be introduced ("doped") into a bulk semiconductor, without affecting the charge
neutrality of the semiconductor as a whole. In the simplest case, for silicon, this is
done by introducing atoms into the semiconductor lattice that have different valence
shell occupation than Si (e.g.
nitrogen or phosphorus with five valence electrons,
boron or aluminum with three valence electrons).
More generally, a dopant is an
atom that, when added to the lattice, creates an additional state in the solid state
electronic structure; if that state is a filled state near the conduction band it is an
n-dopant and if it is an empty state near the valence band it is a p-dopant.
39
1.1.4
Band bending
Figure 1.1.4 shows the steps that would take place if a p-type and n-type semiconductor were brought into close contact with one another. The electrons in the n-type
material and the holes in the p-type material suddenly have more unoccupied states
over which to spread, so by statistical or entropic forces, electrons from the n-type
material diffuse into the p-type material and holes from the p-type material diffuse
into the n-type material. Recombination between free electrons and free holes in the
newly occupied interface space would then take place, and because both semiconductors were originally charge neutral, this recombination leaves uncompensated static
charges in the lattice of each semiconductor: positive charges in the n-type material
and negative charges in the p-type material. These static charges create an electric
field between the two materials that opposes the diffusive motion of the free carriers.
The diffusion stops when a balance is reached between these two opposing forces.
It is worth noting that in the parts of the semiconductor that are far away from the
p-n interface, the density of free charges, as expressed by the Fermi level, remains the
same as if the interface did not exist. The diffusing charges are the charges near the
interface, and the corresponding uncompensated charges are also near the interface.
The depth of the p-n junctions effects (called the depletion region) depends on the
density of dopant atoms of each material, the Fermi-level difference between the two
materials, and the dielectric constant:
2co(±NA + ND) (Vbi - V
qNAND
where NA is the acceptor density in the p-type material, ND is the donor density
in the n-type material, c is the (unitless) dielectric constant of the homojunction material, co is the electric permittivity of free space, q is the absolute value of the charge
of the electron, Vi is the built-in bias between the n-type and p-type semiconductors
(difference between the two Fermi levels) , and V is the applied bias, which is zero in
equilibrium.
It is a reasonable approximation that the uncompensated charge density on each
40
e e e e e e e e e
eeee
eeee
e
a)
hhh h hhh
e
See g
b)
h h
h
h
h
hh
ee
e
h h
h
e
e
e e
e
e
h hh
h
@@e
c)
,,,
e
e
Figure 1-4: Cartoon of the series of steps that would take place if an n-type and
p-type material were brought into contact. a) Semiconductors are charge-neutral. b)
Free carriers diffuse into free states in the other material, and recombine with excess
carriers of the opposite type. c) Uncompensated atoms (red) create an electric field
across the interface in the opposite direction of the diffusion effects.
41
side of the interface is constant in the depletion region and then quickly becomes zero
(charge neutral) at points in each semiconductor that are past the depletion region
(Figure 1.1.4a). That means the electric field from these uncompensated static charges
is at its maximum at the p-n interface and decreases linearly from there to the edge
of the depletion region because the electric field is the integral of the charge density
(Figure 1.1.4b). Then because the electric potential is the integral of the electric field,
the potential follows a quadratic curve on each side of the interface (Figure 1.1.4c).
In a final step, because we tend to think of energy levels with reference to electrons
and electric potential is with respect to a positive test charge, the electronic potential
is inverted to give an energy-level (band diagram) picture (Figure 1.1.4d).
This
results in the final picture shown in Figure 1.1.4, with a flat Fermi level across both
semiconductors and their depletion regions and increasing distance between the Fermi
level and the valence/conduction band within the depletion region to indicate the
diffusion and increasing electric field and their effects to reduce the free hole/electron
populations in the bands.
The flat Fermi level makes sense intuitively because if one section of the semiconductor had a higher probability of electron occupation at a particular energy level
than the section next to it, those electrons would diffuse to equalize those probabilities. Because the flat Fermi level makes sense this way, we choose to think about
the bands, or energy levels, changing with respect to the Fermi level, rather than the
Fermi level changing (Figure 1.1.4).
To enforce the flat Fermi level in these pictures, which makes thinking about
the device physics significantly simpler, it is necessary to assume a vacuum level that
changes in energy; this can be a discomforting thought. This is a required assumption
because far away from the junction, the distance between the vacuum level and the
conduction band (electron affinity) of both semiconductors must be unaffected by the
junction, and the Fermi level of both semiconductors with respect to their valence and
conduction bands must also be unaffected far from the junction, and yet the distance
between the Fermi level and the bands change near the junction, so the distance
between the Fermi level and the vacuum level changes near the junction.
42
a)
Charge density
Distance from interface
b)
Electric field
Distance from interface
C)
Electric potential
Distance from interface
d)
Energy (electrons)
Distance from interface
e)
Figure 1-5: Plots of (a) charge density, (b) electric field, (c) electric potential, (d)
energy level, and (e) energy band diagram for a p-n homojunction.
43
b)
a)
EvacJ
Eca
..........................
EC----
Ey
Ey
Figure 1-6: a) Illustration of vacuum level in a standard band diagram. b) Illustration
of a p-n junction band diagram if a constant vacuum level rather than constant Fermi
level were enforced.
1.1.5
Heterojunction effects
The diagrams in the previous section were indicative of a semiconductor homojunc-
tion, where the n-type and p-type material are made from the same material (e.g.
silicon) such that the electron affinity is the same for both materials. In the case
of a semiconductor heterojunction, where the p-type and n-type materials are different semiconductors, the diagrams have an important difference as a result of the
requirement that the vacuum level be continuous: at the position of the semiconductor interface, there is a discontinuity in the energy band diagram. Depending on the
electron affinities of the materials, this discontinuity can be in the same direction as
the bands are bending, or in the opposite direction (Figure 1.1.5).
The latter case
can result in a buildup of free charges at the discontinuity, and in most cases this re-
gion is quite thin such that tunneling through the region of discontinuity is a feasible
conduction mechanism.
44
a)
b)
Evac
Ec
E
V
C)
d)
Evac
EVac
E
C
Figure 1-7: Band diagrams of heterojunction architectures, showing the discontinuity
in the band levels and continuity in the vacuum level.
45
1.1.6
Common types of band diagrams
The previously detailed p-n junctions are a particularly common sort of band diagrams. They are the canonical example, particularly in the homojunction form,
though the same principles apply in a heterojunction case. Note that the two different semiconductors can have different doping densities or dielectric constants such
that the depletion region depth in the p-type semiconductor is different from the
depletion region depth in the n-type semiconductor (Equation 1.3. A higher doping
density makes the depletion region shorter because the requisite number of charges
to build up the electric field come from a smaller volume of semiconductor. A higher
dielectric constant makes the depletion region longer because the lattice atoms in
the depletion region polarize in response to the electric field, so more charges are
required to build up the same electric field across the interface. A Schottky junction (Figure 1.1.6a) is effectively a p-n junction where one of the two semiconductors
is taken to the high-carrier-density limit to become a metal. p-i-n junctions (Figure 1.1.6b) occur when a semiconductor with a very low carrier density is inserted
between the p-type and n-type semiconductors. The very low carrier density of the
middle ("insulating") layer results in the electric field extending throughout this layer
like a very long depletion region. MOS (metal-oxide-semiconductor) structures (Figure 1.1.6c) are somewhat like p-i-n structures because there is a middle "insulating"
layer across which some of the electric field extends, but in the MOS case, current
does not flow across the middle layer.
1.1.7
Electrical contacts
Electrical contacts are most often referenced as "Ohmic", "Schottky", or "blocking".
Ohmic contacts occur when the majority carrier of the semiconductor is more
strongly represented in the electrode, or equivalently, when the workfunction of the
metal is deeper than the Fermi level for p-type materials, and when the workfunction
of the metal is shallower than the Fermi level for n-type materials. In this scenario,
there is an accumulation of the majority carrier at the semiconductor-metal interface,
46
a)
b)
c)
M
O
S
Figure 1-8: Band diagram examples for some common architectures.a) Schottky
tion b) p-i-n junction c) MOS structure.
junc-
which allows for fast and effective carrier transport across this boundary when the
voltage on the contact is changed. This "accumulation region" is usually quite thin
and is much thinner than most depletion regions because it is not limited by
the
dopant concentration. Current generally flows linearly through a semiconductor when
it is symmetrically contacted by Ohmic contacts (see Chapter B for further discussion
and practicalities of Ohmic contacts)
Schottky contacts occur when the majority carrier of the semiconductor is more
strongly represented in the semiconductor than the electrode, or equivalently, when
the workfunction of the metal is shallower than the Fermi level for p-type materials
and when the workfunction of the metal is deeper than the Fermi level for n-type materials. In this scenario, a depletion region extends into the semiconductor as a result
of the Fermi level equilibration with the metal workfunction. Current generally flows
nonlinearly through a semiconductor when it is contacted by one or more Schottky
contacts.
Blocking contacts are generically any contact that does not have an accumulation
region to facilitate fast and effective carrier injection, as in Ohmic contacts. In many
47
Figure 1-9: Band diagram for an semiconductor with a Fermi level in the middle of
the bandgap that is symmetrically contacted by two deep-workfunction electrodes a)
prior to contact and b) in equilibrium.
cases, "blocking contacts" are Schottky contacts.
Because these definitions stem from bulk semiconductor physics where doping
routinely locates the Fermi levels close to the valence or conduction bands, these
definitions make less sense for electrode contact to a nearly intrinsic semiconductor,
in which the Fermi level lies infinitesimally above of or below in the middle of the
bandgap. Figure 1.1.7 illustrates a semiconductor with a Fermi level in the middle
of the bandgap that is symmetrically contacted by two deep-workfunction electrodes.
The equilibrium band diagram could be interpreted as a Schottky contact if the
semiconductor is slightly n-type, or technically Ohmic if the semiconductor is slightly
p-type. Depending on the carrier density in the semiconductor (most often low for
intrinsic semiconductors, though this same band diagram technically could result
from equally high carrier densities in the valence and conduction bands) and Fermi
level differences, the contact barrier may or may not be significant to the electrical
properties.
1.2
1.2.1
Bulk semiconductor solar cells
Photocurrent and diode current and photovoltaic metric
The diode curve in p-n or Schottky junction solar cells (Equation 1.4, Figure 1.2.1d)
is derived from the exponential tail of the occupancy factor discussed in Section 1.1.3;
when an applied voltage reduces the energetic barrier between the p and n sections
of the device ("forward bias", Figure 1.2.1c), the number of charge carriers that
overcome the barrier to flow across the junction increases exponentially. Similarly,
48
when an applied voltage increases the energetic barrier between the p and n sections of
the device ("reverse bias", Figure 1.2.1a), the number of charge carriers that overcome
the barrier to flow across the junction decreases exponentially. This current is "diodic
current" and flows from the p-type side of the p-n junction to the n-type side of the pn junction (electrons flow from n-type to p-type). Photocurrent, however, originates
from photoexcited electrons and holes that follow the energy level potential defined
by the band diagram, so photocurrent flows in the opposite direction from diodic
current, as shown in Figure 1.2.1.
Ideally for a solar cell, the photocurrent is roughly constant as a function of
voltage, effectively lowering the diode curve into the fourth quadrant.
The short-
circuit current of a solar cell is the current that flows with no load (V=O), and gives
an indicator of the "constant" value of photocurrent opposing the diodic current.
The open-circuit voltage of a solar cell is the voltage at which the diodic current and
photocurrent are equal such that there is no net current flow. The fill factor is the
ratio of the power at the maximum power point divided by the the product of the
short-circuit current and the open-circuit voltage (the area of the shaded box divided
by the area of the open box in Figure 1.2.1d).
The product of these three metrics
divided by the incident power is the solar cell efficiency.
I = IO(exp(
-_)
(1.4)
where I is the current flowing through the diode, 1o is the dark saturation current,
q is the absolute value of the charge of the electron, V is the applied voltage across
the diode, k is Boltzmann's constant, and T is the absolute temperature in Kelvin.
1.2.2
Solar cell testing as compared to solar cells in the field
Though solar cells are tested by applying a voltage and measuring the resulting current (or sourcing a current and measuring the resulting voltage), a functioning solar
cell in the field functions under a defined load. The purpose of establishing the metrics discussed in Section 1.2.1 is to choose the optimal load (voltage) for the final solar
49
a)
Reverse bias
Equilibrium
b)
Forward Bias
d)
Current
Ph)tocul rret
-----. .
-------.-.
.
.
.
.
Diodic current
.+
Voltage
-
-
.
Diodic current
Figure 1-10: Illustration of p-n junction band diagram in a) reverse bias b) equilibrium c) forward bias and d) the corresponding current-voltage curve for diodic and
photocurrent
cell to power; the voltage at the maximum power point (where the absolute value of
the product of the current and voltage is maximized in the fourth quadrant) is the
ideal load. In the field, solar cells may also be connected in series to power a larger
load, and/or in parallel to source a larger current.
1.2.3
Equivalent circuit modeling
Experimental solar cells are often non-ideal, and do not conform well to the diode
curve shown in Figure 1.2. 1d. To cursorily diagnose device-level problems an equivalentcircuit analysis can be used. The equivalent circuit model is schematically shown in
Figure 1-11 and mathematically represented in Equation 1.5. The model includes a
term for each shunt and series resistance in addition to the dark diode and the solar
photocurrent.
Ideal solar cells have high shunt resistance and low series resistance. An increase
in series resistance manifests as a decreased slope at the open-circuit voltage and
indicates that carriers are limited by their flow across regions that should be resistive
rather than diodic. This type of problem could result from low mobility in the bulk
portion of the semiconductor between the junction and the contact, or contact resistance at the semiconductor-electrode interface. An increase in the shunt resistance
manifests as an increased slope at the short-circuit current and indicates that carriers
are moving in a resistive fashion (i.e. directly proportional to the load) in regions
where they should be moving in a diodic fashion. This type of problem could result
50
R
Jac
JdarkRsh
V
RSh
decreasing
Voltage
R, increasing
Figure 1-11: Solar cells in practice can be modeled using an equivalent circuit. High
shunt resistance is beneficial for the device performance, and manifests as a shallow
slope in the current-voltage curve at the short-circuit current point. Low series resistance is beneficial for the device performance, and manifests as a steep slope at the
open-circuit voltage point.
from pinhole shorts or conductive defect pathways through the junction portion of
the film.
The equivalent circuit equation is solved iteratively, as the J term is present on
both sides of the equation. Programs can be used to fit experimental data to the
equivalent-circuit model. A reasonable estimate of Rs can be made by taking the
inverse of the slope of the experimental data curve near the open-circuit voltage, and
a reasonable estimate of RSH can be made by taking the inverse of the slope of the
experimental data curve near the short-circuit current.
J = -Jsc
+ Jo(e
q(V+JARS)
kT
- 1) +
V + JARs
RSH(1.5)
where J is the current density (current divided by device area),Jsc is the shortcircuit current density, JO is the reverse-bias saturation current in the dark, q is
the absolute value of the charge of the electron, A is the device area, Rs is the
series resistance, RSH is the shunt resistance, V is the voltage load, k is Boltzmann's
constant, and T is the absolute temperature in Kelvin.
51
1.3
QD films as semiconductor analogs: thesis overview
Because semiconductor nanocrystal quantum dots (QDs) are quantum-confined units
of a bulk semiconductor, some of their properties (e.g. broad absorption spectrum,
solid-state electronic structure and density of states, bandedge relaxation, free-carrier
density) are similar to those of bulk semiconductors.
However, because QDs are
nanoscale particles, some of the properties of individual QDs and QD films (e.g.
solution processability, quantum confinement, ligand bonding, significant surface effects) differ greatly from those of bulk semiconductors and are in some ways more
comparable to properties of small molecules.
The chapters of this thesis investigate different aspects of PbS-QD thin films
and their related optoelectronic devices to quantify aspects of QD devices that are
unique to the QD material and assess the prospects and limitations of several bulk
semiconductor physics concepts and measurements as they are applied to QDs.
Chapter 2 addresses the absorption limitation in QD thin films that results from
low conduction and/or shallow depletion widths. Chapter 3 identifies exciton quenching as the dominant loss mechanism in PbS-QD thin films as compared to recombination with trapped carriers, in addition to measuring mobilities, free-carrier densities,
and trapped-carrier densities for QDs with a series of different ligands. Chapter 4 compares QD-thin-film dielectric constants as a function of QD filling fraction (precisely
calculated using solution and film small-angle x-ray scattering measurements), and
finds that the film dielectric constant does not fit to a simple effective-medium model,
presumably due to surface effects. Appendix A quantifies the number of ligands per
QD in a thin film for several different ligands using thermogravimetric analysis. The
use and limitation of field-effect transistors for QD characterization is discussed and
demonstrated in Appendix B. Steady-state and time-dependent photoluminescence
are evaluated as metrics in functioning QD PVs in Appendix C. Finally, Appendices D and E establish a liftoff technique for nanoscale QD thin films and clusters
by adapting a bulk semiconductor processing technique.
52
Chapter 2
The QD Absorption Spectrum and
Ideal Bandgaps for Tandem Cells
2.1
Introduction
One of the major problems in quantum dot photovoltaics (QD PVs) is the tradeoff
between light absorption and conduction. As illustrated in Figure 2.1, thin films allow excited carriers to reach the edges of the film, whereas thick films often suffer
recombinative losses because the carriers do not move quickly or efficiently enough
through the film prior to their recombinative lifetime. One approach to solving this
problem is to increase the recombinative lifetime (see Chapter 3), another is to increase the electric field penetration depth into the film by increasing the built-in bias
or film dielectric constant (see Chapter 4), and another is to increase the free-carrier
mobility or exciton splitting away from the junction. Regardless, for QD PVs to be
viable, they must absorb a significant fraction of incident sunlight, particularly in the
cases where the absorption profile of QDs is touted as a key feature (e.g. tandem
cells).
53
Figure 2-1: Thin films (left) allow excited carriers to reach the edges of the film.
Thick films (right) suffer recombinative losses.
2.2
Percent absorption of the solar spectrum by a
QD thin film
To quantify the percentage of sunlight absorbed as a function of film thickness, the
OD of a series of QD films of varying thicknesses and a known absorption spectrum
were measured in a microscopic geometry to avoid the effects of scattering. Figure 2.2
shows these data and the line of best fit for QD films spun from a solution of PbS
QDs with a first excitonic feature at 1300 nm. The OD value was taken at 1300 nm,
the peak of the first absorption feature. The choice of a linear best-fit curve is based
on the assumption that Beer's law is employable in this context, which is a reasonable
assumption if scattering is not a significant contributor.
To calculate the percent absorption for the solar spectrum, first, for each film
thickness, the optical density (OD) values from the first excitonic feature were scaled
as a function of wavelength using the solution spectrum of the 1300-nm QDs (the
spectrum was normalized to the intensity at the first absorption feature and multiplied). The OD was converted to absorption percentage at each wavelength using the
logarithmic relationship of absorbance to intensity. The solar flux at each wavelength
was obtained by converting the solar irradiance[85] to photon flux. Multiplying the
percent absorption at each wavelength by the number of photons at that wavelength
produced the number of photons absorbed by the film at each wavelength. The sum
of these values across the solar spectrum yields a value for the total number of photons absorbed for a particular film thickness. Dividing this total number by the total
number of photons incident results in the total percent of photons absorbed for each
film thickness. This calculation does not include any device-level optical modeling
with a second absorption pathway or electric field maximization. The results of these
54
0.03
0.025
OD
=
1.03e-4 x thickness - 3e-7
S0.02
0.015
C)
01
0.01
0.005
0
0
50
100
150
200
250
Film thickness (nm)
Figure 2-2: Data and line of best fit for the OD of QD thin films as a function of film
thickness.
calculations are shown in the "AM 1.5" curve in Figure 2.2. For comparison, the
other curves labeled with various wavelengths show the percent of photons absorbed
if every photon in the solar spectrum were at the specified wavelength. The dashed
black line indicates a standard QD film thickness for a PV device and its related absorption percentage of ~10%. Given the absorption spectrum of the QD layer and the
solar flux, QD layers must become significantly thicker to absorb significant portions
of the solar spectrum, especially in the infrared region of the spectrum.
2.3
"Ideal" band gaps for tandem cells
The "ideal" band gaps for tandem cells[38] have been frequently quoted in the QD
literature[98] as motivation for the band-gap tunability of QDs through quantum
confinement. The calculations for these ideal band gaps, however, have been performed for bulk semiconductors, which have a much sharper absorption onset into
the UV (see Chapter 1), and for semiconducting layers that absorb a high percentage
55
100 400 nm
80 0
0100
<0
-W
nm
0
0
2 20
0
0
500
1500
1000
Film Thickness (nm)
2000
Figure 2-3: Percentage of solar spectrum absorbed as a function of film thickness.
of the incident light in given wavelength regime. For these calculations to translate
into QD cells for use in tandem cells or otherwise, QD films must be made significantly thicker, and the ideal bandgaps must be recalculated using the slower-onset
absorption spectrum of QDs.
2.4
Chapter-specific acknowledgments
Dave Strasfeld collected the Beer's Law data of OD as a function of film thickness for
PbS QDs with a first exciton feature at 1300 nm.
56
Chapter 3
The Dominant Role of Exciton
Quenching in PbS
Quantum-Dot-Based Photovoltaic
Devices
Sections of this chapter are reprinted with permission from Wanger, Correa, Dauler,
and Bawendi, Nano Lett., 2013, 13 (12), pp 59075912. Copyright 2013 American
Chemical Society.
Abstract
We present a quantitative measurement of the number of trapped carriers combined
with a measurement of exciton quenching to assess limiting mechanisms for current
losses in PbS-quantum-dot-based photovoltaic devices. We use photocurrent intensity
dependence and short-wave infrared transient photoluminescence, and correlate these
with device performance. We find that the trapped-carrier density ranges from one
in 10 to one in 10,000 quantum dots, depending on ligand treatment, and that nonradiative exciton quenching, as opposed to recombination with trapped carriers, is
likely the limiting mechanism in these devices.
57
3.1
Introduction
Surface states and disordered configurations significantly complicate the energy landscape of nanomaterials.
As these materials are further propelled and engineered
towards optoelectronic applications, their performance is limited by a set of states
assumed to exist at surfaces because of the high surface-to-volume ratio [89, 75, 43, 6].
In colloidal quantum dots (QDs), the presence or absence of ligands binding to the
surface [49], stoichiometric imbalance [52, 130, 117], and other factors can create
mid-gap states. There is limited understanding of these states and the mechanisms
and timescales by which they negatively affect QD-based photovoltaic (PV) device
performance.
In this work we present measurements of trapped carriers and exciton quenching to help identify whether non-radiative exciton quenching or recombination with
trapped carriers is currently limiting the short-circuit current in close-packed thin-film
QD-based
solar cells. The effective number of trapped carriers is determined from
an analysis of the photocurrent intensity dependence. Exciton quenching is probed
using shortwave-infrared (SWIR) photoluminescence decay. Photovoltaic device performance is assessed using a solution-processed bilayer geometry. Our results indicate
that exciton quenching, not recombination through trapped carriers, is the limiting
mechanism for current losses in this PV architecture.
3.2
Measuring the density of trapped carriers
To quantify the density of trapped carriers, we use the light-intensity dependence of
the photocurrent in steady state [97] and a lateral gold-electrode geometry (Figure 3la,b). Jarosz et al. have previously used this technique with CdSe QD films
[44]
to determine the ratio of free carriers to trapped carriers (n/Nt). This method uses
the steady-state assumption to connect the light intensity (carrier generation) with
bimolecular recombination (between two photogenerated free carriers) or unimolecular recombination (between one photogenerated free carrier and one trapped carrier).
a)
b)
0.6
Aluminum (G)
(0
C
PMMA
Au
(S)
~1)
0
AM
(D)
Glass
E
0.4 ,
C
a,
0.2 ,
0
0
O
5
0
0
50
12
Laser intensity (mW/Cm)
Figure 3-1: The intensity dependence of the photocurrent is used to determine the
ratio of free to effective trapped carriers (n/N,*). (a) Schematic of a top-gated fieldeffect transistor device, which is illuminated through the underlying glass substrate at
varying intensities with a 532-nm cw laser. Measurements of photocurrent are made
between the source and drain (IDS) under illumination. In a separate measurement
(Figure 3-2), mobilities are extracted from the slopes of the IDS curves as a function
of the gate voltage (VG) in the dark. (b) Full data set for one n/N,* measurement.
A voltage sweep is made at each light intensity. The projections (in green) show
that the current density is nonlinear as a function of light intensity, and linear as a
function of voltage.
59
We note that the generation rate is defined as the generation rate of photogenerated
free carriers (n). The sample is illuminated through the underlying glass substrate at
varying intensities with a 532-nm cw laser and a voltage sweep is made at each light
intensity. Measurements of intensity-dependent photocurrent are made between the
source and drain (IDS) with no gate voltage (VG) applied. The photocurrent density
(J) is measured as a function of laser light intensity (I) at several voltages and fit to
I
=
aj2 +/Jwith no additional parameters, where a and 3 are fitting coefficients for
the bimolecular and unimolecular terms, respectively (Figure 3-3b,c). A final value is
extracted for the ratio of the number of photogenerated free carriers to the effective
number of trapped carriers,[44] nINt* = 2Ja/
(Figure 3-3a). The parameter N*
allows for the relative inclusion of traps with different recombination cross-sections;
we define Nt* as the effective number of trapped carriers with a recombination crosssection equal to that of free carriers. We note that the values of a and 0 change as a
function of voltage, but n/Nt* remains constant as a function of voltage. To extend
this technique from a measurement of n/Nt* to a quantitative measurement of Nt*,
the value of n must be determined as a function of light intensity.
Here we complement the intensity-dependent photocurrent method with the use
of a top-gated field-effect transistor (FET) geometry [88] (Figure 3-la) to determine
both electron and hole mobilities, solve for n as a function of light intensity, and
quantitatively extract the absolute effective number of trapped carriers. The measurement of the FET mobility is performed on the same device as the measurement
of the photocurrent.
Figure 3-2 shows the lateral current (IDS) as a function of
gate voltage (VG) for three different commonly used ligand-exchange treatments on
a semilog scale and in linear sections. The gate leakage current is shown in grey in
the semilog panels, and is insignificant relative to the changes in IDS. Linear fits to
the data (sweeping away from VG= 0) in the regions used are indicated by solid lines
through the data points. The linearity of these regions is shown in the lower panels of
Figure 3-2 with the extracted hole and electron mobilities, which are extracted from
the transconductance (Equation 3.1). The high degree of linearity over an appreciable region of the scanned VG range suggests that density-dependent mobility is not a
60
10-5
105
10-5
TBACI
10- 6*.
10-7
TBABr
*r.
-6
10-7
C
10
10
-P
10
-7
M)
10-P
10
-U
eakage
101I10 -
-60-40-20
0 20 40 60
10
10
Ph
-60-40-20
cm2Ns
02
U)
2
Pe = 6.7e-06
2
cm/Ns
VG (V)
0
0
25
ph =
2.0e-03
4 m2Ns.
45
VG (V)
S10
pe = 3.7e-03
4
2
35
VG (V)
X 10-6
6x10~"
1
0
-60-40-20
-60-40-20 0 20 40 60
0 20 40 60
X1-6
10
eakage,
",4"
10 -101
VG (V)
3
70-04
7
10-9
VG (V)
6
TBAI
10-6
2
cmNs
2
0-60 -40 -20
0
0 35
2_
3 X 108.5e-04
2
Ns
cm
45
55
p = 1.5e-04
2
2
Cm
Ns
1
1
VG (V)
VG (V)
P =
0
-60 -40 -20
VG (V)
+
0 10 20 30 40
VG (V)
Figure 3-2: Quantitative determination of the FET mobility for both electrons and
holes using a top-gated transistor geometry. The IDS values over a full sweep of VG
are shown on a semilog scale (upper plots) for TBAC (VDS = 10 V), TBABr and
TBAI (VDS = 5 V), where the gate leakage (grey) is shown to be insignificant on the
order of magnitude of the signal changes. Linear fits (solid lines in both panels) to the
data sweeping away from zero (+ signs) are applied to the n-channel and p-channel
of each device (lower plots) to extract the electron and hole mobilities, respectively.
All mobility measurements were taken in the dark.
61
concern in this regime. In this VG range, the number of free carriers is of the same
order as the number of photogenerated free carriers during the Nt* measurement.
dIDs
dVG
S
W
L
PCoxVDS
(3-1)
where W is the interdigitated device width, L is the channel length (distance
between electrodes), and C0 , is the capacitance of the 465-nm-thick PMMA, which
was determined to be 5.7 nF/cm2 [88]. The derivation for this equation can be found
in Chapter B Section B.5.
All FET measurements were performed in the dark, with no photoexcitation.
Measurements were made in the linear VDS regime to match with VDS values used
for Nt* data collection. The gate voltage was pulsed to minimize bias stress effects
[88] in the sweeps away from VG = 0 that were used for mobility calculations, so that
trustable lateral FET mobilities could be obtained even in the presence of VG-related
hysteresis. We note that any bias stress or interface trapping that may take place in
the FET (though we endeavor to minimize it) will not interfere with the measurement
of Nt* because no gate voltage is applied during the photocurrent data collection.
The total number of free carriers (n = ne + nh) is related to the experimentally
measured current density:
J = nePEG* = nePe +
2
h
EG* or J = n where a = (epEG*)a
(3.2)
where e is the charge of the electron, p is the average of the electron and hole
mobilities (because ne =
nh
under illumination) (Figure 3-2), E is the electric field
across the film from source to drain (which should be constant, as evidenced by the
linear current-voltage curve- see Figure 3-1b), and G* is the gain (G* = Ah(,e/Pe(h)
when Ph(e) > Pe(h) such that G* > 1). The value of G* can have a dramatic effect on
the extracted value of n. All of the devices reported here have linear IDS-VDS curves,
consistent with an effective injection of charges, which then enables the gain to be
calculated as the ratio of mobilities. We note that the mobilities quoted here are
measured on the same device geometry as the photocurrent-intensity measurement.
62
a)
b)
x 10
180.69 0.82
.3
I
E
TBABr
120.46 0.55
I
)
7
.2
3
g
E
C:
0
TBAI
6 0.23 0.271
E
0
0
0
TBACI
JO
50
100
Laser Intensity (mW/cm 2)
.
TBAITi
1
C,
TBACI
00
TBABr
2
CO
C,
x 107
A1
10
10'
10
Laser Intensity (mW/cm 2
c)
d)
10
TBACI
*
z
4
8
18
0
8 8
8
10
17
0
0o
TBAI
E
z
TBABr
~0 0 o08
10
16
TBACI
0B
0
%Ar
ITBAr
50
100
Laser Intensity (mW/cm 2)
0 0
00
0
15
100
2
4
0o
.0
6
8 0o
8
10
Voltage (V)
Figure 3-3: Carrier data extracted from photocurrent intensity measurement and
calculations. (a) Photocurrents and free-carrier densities for a full voltage (VDs)
sweep as a function of laser intensity with a representative fit to I = aJ2 + J at a
single voltage, for three halogen-salt ligand treatments. The value of n is calculated by
multiplying the photocurrent density (left axes, matched in color to data points) by a
(of Equation 3.2).The spread of values at a given laser intensity is the variation in the
measurement made at different voltages (seen in panel (d)). (b) Free-carrier density
and a representative fit as a function of laser intensity, plotted on a logarithmic scale
in laser intensity. The logarithmic scale of the x-axis more readily shows the fit to
the data over a wide range of points. (c) Ratio of free carriers to effective trapped
carriers, n/Nt* = 2Ja/ as a function of laser intensity. The spread of values at a
given laser intensity is the variation in the measurement made at different voltages
(seen in panel (d)). (d) Trapped-carrier density as a function of voltage, calculated
at each voltage by dividing the values in panel (c) by those in panels (a) and (b).
These values are independent of voltage, which is consistent with the assumption of
linear current-voltage behavior.
63
When the mobilities (and therefore gain) can be quantitatively determined, as they
can in a top-gated field-effect-transistor structure, the value for a in Equation 3.2 can
be used to obtain values of n. The quantitative value for Nt* for a particular ligand
treatment is determined (Figure 3-3d) by dividing the value for n (Figure 3-3b,c) by
the previous calculated n/Nt* ratio (Figure 3-3a). For example, the tetrabutylammonium chloride (TBACl) device referenced in Figures 3-2 and 3-3, has mobilities
Ph
= 7.0x10- 4 cm 2 /Vs and p, = 6.7x10-6 cm 2 /Vs, resulting in a gain G* = 104.
Given the experimental current density of J = 3.33x10- 1 A/cm
2
at 10 V, and with
n/Nt*= 5.4, the resulting trapped-carrier density is Nt* = 1.1x10 15 cm-3. Figure 3-3
shows these values calculated for TBAC, TBABr, and TBAI curves at each voltage,
which are averaged to report the N* value for each ligand. The value of Nt* is not a
function of light intensity. The Nt* values in Figure 3-3d are independent of voltage,
which is consistent with the assumption of linear current-voltage behavior. We note
that Nt* is the density of trapped carriersrather than the density of trap states. The
trapped-carrier density is particularly relevant because it contributes to the location
of the dark equilibrium Fermi level.
We performed similar measurements on PbS QD films treated with a variety of
commonly used ligands (Figure 3-4) and find that the effective number of trapped
carriers ranges from 1x10
15 -
1x10 18 cm-3.
These values are similar to the values
extracted from previous device-scale simulations for the number of traps [136, 137].
Each value reported is the result of measurements of multiple devices and found to be
consistent across a range of voltages (Figure 3-3d). The mobilities used for each device
are the mobilities measured on that same device and found to be consistent with other
films with that treatment condition (see Table 3.1). The much lower number of free
carriers in the dark (1x10 13 - 1x10
carriers (1x10 15
-
1x10
18
16
cm-3) relative to the effective number of trapped
cm- 3 ) (Figure 3-4) indicates that the filled trapped states
are not effective dopant states. We note also that the two bromine salts (CTAB and
TBABr) result in different trapped-carrier densities, indicating that the counterion
may control the efficacy of the ligand exchange process and/or residually be present
in the conducting film.
64
101
10
SH
H C
118
Trapped
SH
Carriers
ce)
HS
E 1017 - (Effective
Density, NO*)
C
16
C>
10
C,)
U)
H3 C
0
0oH1
CH
H3C(H 2C) 5
3
Br
-CH3
8
Cr
8
151 Dark Free
10 F Carriers
H3C-\
H3C
Ia
O_/H
3
102
CH,
g
10
10
101-5
1013
I
13BDT
MPA
CTAB
TBACI
I
TBABr
I
10~
TBAI
Figure 3-4: Ligands affect the effective density of trapped carriers and density of dark
free carriers, though all Nt* values remain significantly below one trapped carrier per
QD. Dark free-carrier values (pink diamonds) are lower than trapped-carrier values
(blue circles). Values for free carriers in the dark are not calculated for the high-gain
ligand (TBACl) because the average mobility assumption does not hold. 13BDT is 1,3
benzenedithiol, MPA is mercaptopropionic acid, and CTAB is cetyltrimethylammonium bromide (see Table 3.1 and 3.7 for all ligand concentrations and solvents). Dark
free-carrier densities are extracted from the lateral current using Equation 3.2 and
trapped-carrier densities are extracted from the photocurrent intensity dependence.
65
-20
10 3
~
CH 3
H3C
11
-CH 3
0
OH
0
CH 3
N '-N
1175 nm PbS with TBAI
10
3
10
100 mg/mL
4_j
4-J
mg/mL
10
2
C
10
1
6
4
5
3
2
d spacing in nm
Figure 3-5: Small-Angle X-ray Scattering (SAXS) to determine inter-dot spacing.
Integrated counts over a cone of signal (excluding surface reflection) for films of PbS
QDs deposited as for photovoltaic devices but on crystalline Si substrates with no
surrounding layers show no appreciable change in inter-dot distance as a function of
ligand-exchange solution concentration. The inter-dot spacing as determined from
the peak is 4.5 nm. Extracting the pair-distribution function for a QD film of the
same size particles (see Chapter 4) yields a larger spacing of -5.3 nm.
66
b)
a)
C)
Voltage (V)
0.2
0.1
/.0
10 8
10 0
Trapped Carriers
100 mg/mL
0
=3~
8
-5
E 1016
10
4)
E
mg/mL2:
NC
E
"2,
10gm
0
10
--
0
50
Time (ns)
1
Dark Free Carriers
10 144
100
A
0B
1
10
100
TBAI Concentration (mg/mL)
Figure 3-6: Increasing TBAI concentration results in higher PL lifetimes and an
increase in short-circuit currents without changing the density ofeffective trapped
carriers. (a) SWIR-PL decay traces for encapsulated QD films on glass, as treated
with TBAI ligand-exchange solutions of three different concentrations. (b) Trappedcarrier densities (blue/black circles) and dark free-carrier densities (pink diamonds)
plotted as a function of TBAI concentration. (c) Current-voltage curves for the three
TBAI concentrations under AM1.5 solar illumination. Inset shows device architecture. Shading shows standard deviation.
Using the center-to-center dot spacing determined from small-angle x-ray scattering (Figure 3-5), we translate these numbers into a unit of "trapped carriers per
QD" and find that it ranges from one in 10 to one in 10,000 QDs, depending on
the ligand treatment, which is a surprising result given the general assumption that
trap states originate from the many unpassivated surface sites on each individual QD
[89, 75, 43, 6].
Although the effective number of trapped carriers is quite low for all of the ligands studied here, the number of mid-gap states may be much higher.
Mid-gap
states could serve to quench excitons prior to their dissociation, thus reducing the
short-circuit current of the PV device. Exciton quenching through fast non-radiative
recombination pathways can be probed by measuring the PL decays of the QD films;
photoluminescence primarily takes place when an exciton recombines, so a reduction
in PL emission implicates either quenching or dissociation.
Non-radiative exciton
quenching reduces both the PL lifetime and the number of photocarriers available for
67
0.3
extraction in a solar cell, whereas dissociation reduces the PL lifetime and increases
the number of photocarriers available for extraction. To probe non-radiative losses in
the bulk of the film, thin films of QDs were spun on glass and encapsulated in a nitrogen environment, so the lifetime should be limited only by film-related phenomena
such as exciton quenching or spontaneous exciton dissociation. This measurement
of the thin-film lifetime is therefore not affected by device-specific effects such as
electric-field-induced dissociation or device-layer-interface quenching.
3.3
Measuring non-radiative exciton quenching
Non-radiative exciton quenching was probed in films as a function of the concentration
of the ligand-exchange solution by measuring PL decays. Films of QDs were deposited
onto glass and treated with different concentrations (1 mg/mL, 10 mg/mL and 100
mg/mL) of tetrabutylammonium iodide (TBAI). Figure 3-6a shows a clear trend in
the PL lifetime on glass with ligand concentration, where increasing ligand-exchangesolution concentration results in longer lifetimes, or equivalently, lower non-radiative
recombination rates. We note that the lifetime data do not include deep-trap emission
because the optical fiber used cannot transmit photons with wavelengths longer than
1600 nm (and the steady-state emission peak is at ~1330 nm). In contrast to the
PL lifetime trend, the trapped-carrier density measured for these same treatments
(Figure 3-6b) is unchanged (within the statistical variation of different chips in this
experiment).
To directly assess the effects of TBAI treatment concentrations on photovoltaic
devices, we fabricated bilayer architectures [133] (inset of Figure 3-6c) with the ligandexchange-solution concentrations used in the PL experiment. The results are shown
in Figure 3-6c, where the shaded regions indicate the standard deviation for 5-10
devices on each of three chips fabricated on two different days. With the increase
of TBAI concentration, a significant change is observed in the short-circuit current
density, which correlates with the increased photoluminescence lifetime measured and
not with the static trapped-carrier density.
68
TBAI 100 mg
0
TBAI 10 mg
0
C
Methanol
Oleic Acid
3500
3000
2500
Wavenumber cm-1
2000
1500
Figure 3-7: Increasing TBAI concentration changes the peaks in FTIR from the native
oleic acid ligand peaks.
3.4
Discussion
We have quantified the effective density of trapped carriers and measured the photoluminescence decays to assess the degree of exciton quenching in PbS QD thin films.
We find that the trapped-carrier density ranges from one in 10 to one in 10,000 quantum dots, depending on ligand treatment, and that the occupied trap states do not
act as effective-dopant states. The general assumption has been that there is a high
density of surface states in QD films and that these surface states primarily serve to
trap carriers[137, 133, 34, 67, 32, 136]. Our results call that assumption into question
because the value for the effective density of trapped carriers is low. This low value
of effective trapped carriers per QD may support a claim that carrier trapping is not
a property of the QD surface as much as a property of the ligand solution used for
treatment, impurities in the chemicals used for ligand exchange, or a result of "dark"
QDs interspersed throughout the film. This low value also suggests that attempts at
improving the passivation of long-lived carrier traps on the QDs may not be likely
69
to have a significant effect on device efficiency because they exist on such a small
fraction of the QDs.
A study of the concentration dependence of the ligand-treatment solution was performed to quantify the trapped-carrier densities and exciton quenching, and correlate
these to device performance.
Higher TBAI concentrations result in higher short-
circuit current densities, correlating with an increase in photoluminescence lifetimes,
and show no dependence on trapped-carrier densities, which remain constant over
the range of treatment concentrations. The increasing PL lifetimes with increasing
ligand exchange concentration are consistent with better passivation of non-radiative
recombination pathways that compete with emission and current extraction.
We
note that the QD spacing, mobility, and free-carrier density in the dark are not affected beyond chip-to-chip sample variations by the change in the concentration of
the ligand-exchange solution (Table 3.1 and Figure 3-6b), so the change in PL lifetime cannot be attributed to changes in energy transfer rates between QDs or exciton
quenching by free carriers in the dark. The improvement in short-circuit current
with increasing PL lifetime excludes the possibility that the increase in short-circuit
current is due to faster exciton dissociation into free carriers. This result clearly attributes the device improvement to decreased exciton quenching in the film, which
happens prior to any exciton dissociation that may occur.
3.5
Conclusion
Although different ligand treatments can have widely different trapped-carrier densities, our analysis suggests that carrier trapping is not the limiting mechanism for
current losses in QD-based solar cells, but rather that non-radiative exciton quenching limits the extent to which photocurrent is extracted from these devices.
We
therefore encourage future materials efforts to maintain similar mobilities while focusing on minimizing non-radiative exciton quenching as a specific target for device
improvement.
70
3.6
3.6.1
Experimental Methods
PbS QD Synthesis
Quantum dot synthesis was carried out using the procedure from Zhao et al. [133]
using 75 mL of oleic acid and 225 mL of octadecene in the three-necked flask. The
particles were kept air-free via cannula transfer to a nitrogen-flushed flask, pumped
into a nitrogen glovebox, precipitated with anhydrous butanol and methanol, and
stored in anhydrous hexanes. Two additional, similar precipitations were performed
prior to weighing and redissolving in octane at 50 mg/mL for device fabrication (no
solution-phase ligand exchange was performed).
3.6.2
Top-gated lateral geometry device fabrication
Glass substrates with pre-patterned gold electrodes (2-3 nm of Cr and 40-50 nm
Au, ordered from Thin Film Devices in Anaheim, CA) were cleaned by sonicating
sequentially in deionized water with Alconox detergent, deionized water, acetone, and
isopropanol. The substrates were then blow-dried with dry nitrogen or pressurized
air (filtered), and pumped into a nitrogen glovebox. One layer of QDs (50 mg/mL
in octane) was spun at 1000 rpm onto the substrates. Following the deposition of
the QD layer, a solid-state ligand exchange solution was deposited onto the QD
layer, allowed to remain there for 30 seconds, and removed by spinning at 1300 rpm.
Finally, several drops of the solvent used for ligand exchange (methanol or acetonitrile)
were deposited onto the ligand-exchanged film and spun off at 1300 rpm. The gold
contact pads were exposed by lightly scraping the QD film away with metal tweezers.
Polymethylmethacrylate (PMMA, 950PMMA A4 in anisole from MicroChem) was
spun at 1000 rpm to yield a 465-nm-thick film. The devices were transferred in an
air-free container to a glovebox containing a thermal evaporator, where they were
unloaded and left under vacuum overnight at < 1x10-
6
mbar prior to evaporation
of 25-50 nm of aluminum through a shadow mask. The gold contact pads were reexposed prior to testing by scraping away the PMMA with metal tweezers.
71
The
interdigitated electrodes have a channel length of 10 pm and a W/L value of 1150
(except for one MPA data point at 6 [im with a W/L of 3250). For the 30-nm films
used, this results in an area of 3.45x10- 6 cm 2 for the 10-pm channel devices (this
value was used to convert current to current density).
3.6.3
Photoluminescent film preparation
Three layers of QDs (50 mg/mL in octane) were spun at 1000 rpm onto glass substrates and treated as described in the lateral geometry fabrication section. The
spun films were placed face-down on a microscope coverglass slide and the edges were
coated with two-part epoxy (Parbond 5105 from McMaster-Carr) and left for several
hours to cure in the glovebox prior to removal and measurement.
3.6.4
Photovoltaic device fabrication
Patterned indium tin oxide (ITO) substrates (Thin Film Devices) were cleaned by
sonicating sequentially in deionized water with Alconox detergent, deionized water,
acetone, and isopropanol, and then treated for five minutes in an oxygen-plasma
chamber (Harrick Plasma Cleaner Company PDC-32G) on the "low" setting. A 20-30nm layer of poly (3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS,
Aldrich 1.3 wt% aqueous, conductive grade) was spun onto the substrates at 5000 rpm
with no filtering, and baked in air on a temperature-controlled hotplate at 150 C for 20
minutes prior to pumping them into a nitrogen glovebox for QD film deposition. Films
of QDs were deposited using the procedure detailed in the lateral geometry fabrication
section above, though photovoltaic device films consisted of three sequential layer
depositions (each treated and rinsed as described above).
A ~50-nm-thick film of
PCBM was spun (10 mg/mL in chloroform, Aldrich >99% pure) on top of the final QD
layer. The devices were transferred in an air-free container to a glovebox containing
a thermal evaporator.
A small area of the QD/PCBM film above the ITO was
scraped off with metal tweezers to ensure good electrical contact to the ITO during
testing. The devices were subjected to evaporator pressures of < 1x1072
6
mbar prior
to evaporation of 50-100 nm of aluminum.
3.6.5
Top-gated lateral geometry device testing
All electronic measurements were performed in a nitrogen glovebox. A three-channel
semiconductor parameter analyzer (Agilent 4156C) or Keithley 2636A was used to
simultaneously measure source-drain and source-gate (leakage) currents. The gate
voltage was pulsed and the source-drain voltage was held constant at 5 V unless
otherwise specified.
Intensity-dependent measurements were made on devices illuminated with a 532nm cw laser coupled through a multi-mode optical fiber into the glovebox. Different
intensities were created by passing the beam through ND filters (two sequential sixposition filter wheels) prior to fiber coupling. A Newport reference solar cell masked to
one quarter of the active area was used to measure the laser intensity (as a fraction of
AM1.5 intensity, then converted to mW/cm 2 ) at each filter wheel position. The beam
was centered on the substrate at a low laser intensity and remained there throughout
all intensities and voltage sweeps. Between intensity points, the sample was exposed
to the highest laser intensity used (see Pmax column in Table 3.7) for 10 s. Neither the
length of this high-intensity exposure time nor the intensity of the exposure between
voltage sweeps affected the photocurrent or its intensity dependence.
Automated
data analysis was performed using a Matlab script; voltages with artifact signals and
consequent poor fits were eliminated from analysis, but no final values were accepted
without many acceptable fits at different voltages on at least two different devices.
3.6.6
Photoluminescence lifetime measurement
Measurements were taken using a system like that described in Correa et al. [18] with
a superconducting nanowire detector at MIT Lincoln Laboratory. The sample was
illuminated with a 633-nm laser through the thin coverglass and measured at several
places on the film. The illuminating laser power was 5 puW at a 1-MHz repetition
rate. Background levels determined by averaging the counts in a range of time prior
73
to the illumination pulse for each film. The background level for each sample was
subtracted prior to peak-intensity normalization.
3.6.7
Photovoltaic device testing
All measurements were taken on a Keithley 6487 picoammeter through a Keithley
7001 switch box in a nitrogen glovebox. The devices were illuminated with a Newport
(67005) solar lamp with AM1.5 filter and a diffuser to equalize illumination across the
substrate. A Newport-calibrated Oriel reference cell (91150v), masked to one quarter
of its active area, was checked to assure accurate illumination intensity. All devices
were measured in the dark and then illuminated. Shorted or otherwise non-diodic
devices (which were a significant minority and not reproducible) were eliminated
from further analysis. Reported curves are from the voltage sweep in the negative
direction from 1 V.
3.7
Data tables for all ligands and concentrations
The tables below show the data and parameters used for transistor and photocurrent
calculations for the ligands and concentrations referenced in the text. All 13BDT
and MPA data points were ligand-exchanged using acetonitrile as the solvent, while
all other ligands shown used methanol as the solvent. The acronyms are as follows:
13BDT is 1,3 benzenedithiol, CTAB is cetyltrimethylammoniumbromide, MPA is
mercaptopropionic acid, TBABr is tetrabutylammonium bromide, TBAC is tetrabutylammonium chloride, and TBAI is tetrabutylammonium iodide.
The channel
length, L, is given in microns, and is 10 pm for all samples except one MPA sample,
for which the channel length is 6 pm. The value for n in the dark (Table 3.1) is
found by measuring the current as a function of voltage (corresponding Vmax values
are given in Table 3.2) with a step size of 1/10 the value of Vmax and solving for n as
in the main text. The n value obtained is not exact because in the dark the number of
electrons and the number of holes have no constrained equivalence, and no values are
computed for the high-gain cases because this degree of uncertainty varies too widely
74
(because the average mobility is not a reasonable approximation for either carrier).
In Table 3.7, P,,,
is the highest power (in mW/cm2 ) at which the photocurrent
was measured (the maximum power used, up to a value of 250 mW/cm 2 did not
dramatically affect the final value extracted for Nt*). Regardless of the Pmax value,
the photocurrent was measured at 23 light intensities, two of which were duplicates,
so there are 21 unique light intensity values. The values recorded for nI/N* at Pmax,
n at Pmax and N* at Pmax are a linear average of the values at each voltage (note
that n varies with light intensity but not with voltage and N* varies with neither
light intensity or voltage).
Any voltage for which the current-power plot did not
adequately ( R 2 > 0.98) fit the functional form (usually due to electronic instrument
artifacts) was excluded from this average. Final values were only accepted for devices
with many valid points with minimal variation as a function of voltage. All data
shown here are from linear current-voltage curves; because non-linearity indicates a
non-uniform electric field across the film and negates the assumptions made about
the relation between free carrier density and current density, any devices tested with
clearly non-linear current-voltage characteristics were not analyzed using this method.
75
Table 3.1: Transistor parameters for varying ligands and ligand concentrations
Ligand Exchange
Treatment
Solution
Concentration
13BDT
13BDT
13BDT
Channel
Length (pm)
Pe
(cm 2 /Vs)
Gain
(cm 2 /Vs)
n (dark)
(cm-- 3 )
0.1 % vol = 8.2 mM
0.1 % vol = 8.2 mM
0.1 % vol = 8.2 mM
10
10
10
2.OE-05
2.4E-05
2.1E-05
6.5E-06
1.2E-05
1.OE-05
3.1
2.0
2.1
7E+14
2E+15
1E+15
MPA
MPA
0.01 % vol = 1.2 mM
0.01 % vol = 1.2 mM
10
6
1.9E-03
1.4E-03
1.3E-03
1.7E-03
1.5
1.2
7E+13
3E+13
CTAB
CTAB
CTAB
10 mg/mL = 27.4 mM
10 mg/mL = 27.4 mM
10 mg/mL = 27.4 mM
10
10
10
1.5E-03
2.2E-03
1.2E-03
7.6E-03
1.2E-02
5.OE-03
5.1
5.5
4.2
4E+13
2E+13
3E+ 14
TBABr
TBABr
TBABr
TBABr
TBABr
TBABr
8.7
8.7
8.7
8.7
8.7
8.7
mM
mM
mM
mM
mM
mM
10
10
10
10
10
10
1.5E-03
1.5E-03
2.OE-03
2.OE-03
1.6E-03
1.6E-03
1.6E-03
1.6E-03
3.7E-03
3.7E-03
1.4E-03
1.4E-03
1.1
1.1
1.9
1.9
1.1
1.1
1E+15
1E+15
8E+14
9E+14
1E+16
4E+15
7.5 mg/mL = 27 mM
10
7.OE-04
6.7E-06
104.5
mM
mM
10
10
10
10
10
10
10
7.OE-04
5.OE-04
5.OE-04
4.4E-04
4.4E-04
4.3E-04
4.3E-04
6.7E-06
6.5E-06
6.5E-06
1.2E-05
1.2E-05
8.4E-06
8.4E-06
104.5
76.9
76.9
36.7
36.7
51.2
51.2
TBAC1
(10 V FET VDS)
TBACI
(10 V FET VDs)
TBACI
TBACI
TBACI
TBAC
TBACI
TBACI
7.5
7.5
7.5
7.5
7.5
7.5
7.5
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
27
27
27
27
27
27
=
=
=
=
=
=
=
27
27
27
27
27
27
27
mM
mM
mM
mM
mM
Ph
TBAI
TBAI
TBAI
1 mg/mL = 2.7 mM
1 mg/mL = 2.7 mM
1 mg/mL = 2.7 mM
10
10
10
3.6E-03
2.8E-03
5.4E-04
4.8E-03
2.4E-03
7.8E-04
1.3
1.2
1.4
2E+ 15
5E+15
2E+15
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6.1E-04
9.5E-04
7.9E-04
9.2E-04
6.5E-04
6.5E-04
9.1E-04
9.1E-04
6.9E-04
6.9E-04
8.OE-04
8.OE-04
9.3E-04
9.3E-04
7.2E-04
8.3E-04
5.8E-04
2.4E-04
1.9E-03
1.9E-03
9.3E-04
9.3E-04
2.2E-04
2.2E-04
6.7E-04
6.7E-04
1.OE-03
1.OE-03
1.2
1.1
1.4
3.8
2.9
2.9
1.0
1.0
3.1
3.1
1.2
1.2
1.1
1.1
1E+15
1E+15
4E+15
7E+15
1E+15
1E+15
3E+15
1E+15
2E+15
7E+14
6E+14
7E+14
9E+14
2E+15
TBAI
TBAI
TBAI
100 mg/mL = 270 mM
100 mg/mL = 270 mM
100 mg/mL = 270 mM
10
10
10
8.8E-05
8.8E-05
1.6E-04
1.7E-05
1.7E-05
7.2E-04
5.2
5.2
4.5
4E+15
2E+ 15
7E+13
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
=
=
=
=
=
=
=
=
=
=
=
=
=
=
27
27
27
27
27
27
27
27
27
27
27
27
27
27
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
76
Table 3.2: Photocurrent intensity dependence parameters for varying ligands and
concentrations
Vmax(V)
Pmax
(mW/cm 2 )
n/Nt*
at Pmax
n (cm- 3 )
at Pmax
Nt* (cm- 3 )
1
1
1
40
40
40
0.49
0.49
0.31
2.30E+17
3.40E+17
2.40E+ 17
4.80E+17
7.60E+17
7.80E+17
0.01 % vol = 1.2 mM
0.01 % vol = 1.2 mM
1
1
40
40
0.20
0.10
2.80E+16
3.OOE+16
1.30E+17
2.20E+17
CTAB
CTAB
CTAB
10 mg/mL:
10 mg/mL:
10 mg/mL:
10
1
10
40
40
40
0.48
0.35
1.47
8.60E+15
6.80E+15
2.OOE+16
1.80E+16
2.OOE+16
1.40E+16
TBABr
TBABr
TBABr
TBABr
TBABr
TBABr
8.7
8.7
8.7
8.7
8.7
8.7
mg/mL 27 mM
mg/mL 27 mM
mg/mL
27 mM
mg/mL : 27 mM
mg/mL
27 mM
mg/mL
27 mM
1
10
1
10
10
10
100
100
100
100
100
100
0.07
0.05
0.21
0.30
0.94
0.44
1.OOE+17
1.10E+17
2.70E+16
3.70E+ 16
2.OOE+17
2.10E+17
1.80E+18
4.OOE+18
1.30E+17
1.30E+17
2.20E+17
5.20E+17
7.5 mg/mL = 27 mM
10
100
1.77
5.70E+ 15
3.60E+15
7.5
7.5
7.5
7.5
7.5
7.5
7.5
10
1
10
1
10
1
10
100
100
100
100
100
100
100
2.00
2.69
2.61
1.71
4.54
2.32
6.26
7.90E+ 15
1. 10E+ 16
1.40E+16
9.90E+15
1. 20E+ 16
1. 1OE+ 16
1. 1OE+ 16
4.OOE+15
4.20E+15
5.60E+15
6.OOE+15
3.10E+15
5.OOE+15
2.40E+ 15
Ligand Exchange
Treatment
Solution
Concentration
13BDT
13BDT
13BDT
0.1 % vol
0.1 % vol
0.1 % vol
MPA
MPA
TBAC
(10 V FET VDS)
TBAC1
(10 V FET VDS)
TBACI
TBACI
TBAC1
TBACI
TBAC
TBACI
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
mg/mL
8.2 mM
8.2 mM
8.2 mM
27.4 mM
27.4 mM
27.4 mM
27
27
27
27
27
27
27
mM
mM
mM
mM
mM
mM
miM
TBAI
TBAI
TBAI
1 mg/mL = 2.7 mM
1 mg/mL = 2.7 mM
1 mg/mL = 2.7 mM
1
10
1
100
100
100
3.28
3.86
0.80
3.10E+16
2.OOE+16
2.70E+ 16
9.45E+15
5.18E+15
3.38E+16
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
TBAI
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1
1
1
1
10
1
10
1
10
1
10
1
10
30
30
30
100
100
100
100
100
100
100
100
100
100
100
2.16
2.20
2.62
4.52
0.58
2.36
3.72
1.96
1.78
1.58
1.50
2.28
1.66
2.00
9.90E+ 16
1.20E+17
9.90E+ 16
4.90E+ 16
8.20E+15
1.60E+16
4.40E+16
4.70E+16
5.80E+16
5.20E+16
6.80E+ 16
7.10E+16
6.OOE+16
3.50E+16
4.58E+16
5.45E+16
3.78E+16
1.08E+16
1.41E+16
6.78E+15
1.18E+16
2.40E+ 16
3.26E+16
3.29E+16
4.53E+16
3.11E+16
3.61E+16
1.75E+16
TBAI
TBAI
TBAI
100 mg/mL = 270 mM
100 mg/mL = 270 mM
100 mg/mL = 270 mM
1
10
1
100
100
100
3.76
4.16
0.24
1.50E+17
1.40E+17
2.40E+15
3.99E+16
3.37E+16
1.OOE+16
mg/mL = 27
mg/mL= = 27
mg/mL
27
mg/mL = 27
mg/mL ==27
mg/mL =- 27
mg/mL == 27
mg/mL == 27
mg/mL == 27
mg/mL =* 27
mg/mL == 27
mg/mL = 27
mg/mL = 27
mg/mL == 27
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
77
3
(N0
E
2-
E
0
0
0
o
z0
0
0
0
00
Bare Glass
Silated
Surface Treatment
Figure 3-8: Surface trapping control experiment using ungated films. The n/N*
values are within the same range for bare glass and silated (octadecyltrimethoxysilane)
glass surfaces. The device architecture used to make these measurements uses the
same glass substrates as top-gated devices used for the Nt* measurements, but the
fabrication ends after the deposition of the QD layer. If surface trapping at the glass
interface contributed significantly to the values measured for Nt*, one would expect
the value for n to be higher and the value of Nt* to be lower for the silated glass,
making the n/Nt ratio significantly larger for the silated surface.
78
3.8
Chapter-specific acknowledgments
This work was primarily supported by Samsung SAIT. The fast SWIR-PL decays were
measured by Raoul Correa, who is supported by the Center for Excitonics, a Department of Energy EFRC (Award No. DE-SC0001088).
At MIT Lincoln Laboratory,
the work was sponsored by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract #FA8721-05-C-0002.
Opinions, interpretations,
recommendations and conclusions are those of the authors and are not necessarily
endorsed by the United States Government.
Jennifer Scherer, Joel Jean, Patrick Brown, Dr. Andrea Maurano, Dr. Gautham
Nair, Dr. Alexie Kolpak, Jian Cui, and Dr. Scott Speakman provided helpful discussions and comments during the experimentation and preparation of this work.
79
80
Chapter 4
Quantum Dot Size and Thin-Film
Dielectric Constant: Precision
Measurement and Dielectric
Constant Reduction
Abstract
We study of the dielectric constant of lead sulfide quantum dot (QD) films as a
function of the volume fraction of QDs by varing the size and keeping the ligand
constant. We create a reliable QD sizing curve using small-angle x-ray scattering
(SAXS), thin-film SAXS to extract a pair-distribution function for QD spacing, and
a stacked-capacitor geometry to measure the capacitance of the thin film. Our data
support a reduction in dielectric constant for nanoparticles.
4.1
Introduction
In quantum dot (QD) photovoltaics and light-emitting diodes, the dielectric constant is an important parameter in device design, but is not well measured. In this
work we perform a thorough study of the dielectric constant of lead sulfide (PbS)
QD
films as a function of the volume fraction of QDs by measuring the size, spac-
ing, and dielectric constant of a size series of QDs. We use a capillary small-angle
81
x-ray scattering (SAXS) technique to create a reliable QD sizing curve, SAXS measurements of thin films to extract a pair-distribution function for QD spacing, and a
stacked-capacitor geometry to measure the capacitance and determine the film dielectric constant. Generally, the dielectric constant of a composite film is estimated by
a volume-fraction-weighted average of the component materials or another effectivemedium theory (Maxwell-Garnett, Bruggeman) [15]. Because bulk PbS has a high
static dielectric constant of 169[22], there is a large contrast between component
dielectric constants in PbS QD thin films. This high bulk dielectric constant also
suggests that increasing the volume fraction of QDs, for example by shortening the
spacing between QDs by attaching a shorter ligand or using larger QDs in the films,
could result in a large increase in film dielectric constant. This change in QD density
would then permit longer depletion regions and enable increased thin-film absorption
and photovoltaic efficiency. Device design relies on an accurate dielectric constant
calculation; errors in this value can result in errors in device architecture, for example to determine pillar spacing in a lateral heterojunction architecture[62]. Most
literature reports of QD thin-film dielectric constants are estimated using an effectivemedium theory[25, 70, 110]. Two reports of PbS-QD film dielectric constants have
been derived using the real and imaginary components of the absorption[74, 60], and
few experimental measurements of the dielectric constant of a single PbS thin film
have been reported[16, 9] using CELIV or Schottky devices in reverse bias. In this
work, we use a stacked-capacitor geometry to measure the dielectric constant of a
size series of QDs using tetrabutylammonium iodide, a ligand that is commonly used
in QD photovoltaic devices. The advantage of this capacitor technique is that it is
not sensitive to electronic interface effects such as Fermi-level pinning and depletion
regions. In our method, the QD film is deposited onto an HfO 2 insulating oxide and
covered by a film of parylene, with an ITO or Al electrode on either side of the insulating materials. We measure the capacitance of the stack and model it as three
capacitors in series. We isolate the capacitance of the QD film by subtracting the
effects of the capacitance of the HfO 2/parylene control device. Our experiments yield
values of dielectric constants as a function of the volume fraction of QDs in the thin
82
films. We find that our data do not fit within any simple model that applies the
bulk dielectric constant of PbS. We suggest that surface and other size effects play a
role in altering the dielectric constant of the individual QDs, as has been observed in
the nanoscale Si/SiO 2 system[13, 68, 81] and supported by previous theoretical and
computational studies[118, 119, 114, 113, 104, 11, 23].
4.2
QD sizing curve
The first step in calculating the volume fraction of QDs in the thin film is to precisely
determine the size of the QDs themselves. To do this, we use a small-angle x-ray
scattering (SAXS) method where a concentrated QD solution in octane is placed
air-free into a capillary tube. We match the experimental low-angle signals with
computed scattering of a simulated PbS QD that takes into account the lattice and
individual atomic scattering factors[78].
Because this measurement takes place in
solution such that the inter-particle spacing is both variable and outside of the region
probed, this sizing method only measures x-ray scattering of individual QDs rather
than inter-particle interactions. The analysis method is the same as that used for
QD self-scattering of x-rays in Murray et al.[78].
We note that a high degree of
monodispersity in the QD samples is necessary for this measurement to assure a
high quality of fit between the experimental and simulated scattering. We chose this
sizing method over the more common transmission-electron-microscope (TEM) sizing
method because it requires no user input or thresholding, is not sensitive to systematic
TEM magnification or tilt calibrations, and demonstrates a higher precision. We
used this sizing technique on QDs with a range of first-exciton peak wavelengths
from 844 nm to 1425 nm (Figure 4-la), where the samples remained air-free from
synthesis to absorption measurement.
Figure 4-1b shows the x-ray intensity as a
function of angle (20) and the matching simulation curve for each of ten differently
sized samples. The location of the first exciton peak
(APL)
(Aabs)
and the emission peak
from the experimental data are shown to the right of the curve, in addition to
the average diameter of the corresponding simulation curve. We find these average
83
diameters to range from 2.97 nm to 5.69 (+/- 0.15) nm. We use these data to establish
a sizing curve with a second-order polynomial fit, such that the (average) size of
future samples can be determined using only the location of the first exciton peak.
Figure 4-2 shows this sizing curve alongside other literature values for sizing. This
solution-SAXS sizing method maps a given diameter to a larger bandgap than other
methods[51, 120, 76, 46, 10, 50], or a given peak location to a larger diameter. This
result suggests that other methods may underestimate the size of the QD particles,
which is consistent with previous observations of a poorly resolved surface layer in
TEM images of CdSe QDs that is resolved in x-ray analysis[77].
4.3
4.3.1
Solution SAXS simulations
Single-size simulation of scattering intensity
The PbS QD was simulated with a MATLAB script that utilized the PbS rocksalt structure to map the position of Pb and S atoms onto positions in a threedimensional matrix. Figure 4-3 shows the simulated QD at a particular radius, in
units of lattice spacings (apbs= 5.94A). The blue and green points indicate Pb and
S atoms, respectively. We note that faceting is not included in this model; atoms are
only located on points within the radius input for any particular particle size.
Figure 4-4 shows the simulated scattering intensity due to Pb-Pb scattering (blue),
S-S scattering (green), and Pb-S scattering (red). The higher scattering factor of Pb
as compared to S is readily apparent and is due to the higher Z value of Pb.
Figure 4-5 shows the simulated small-angle region in the left panel and the wideangle region in the right panel. The small-angle region shows the expected oscillatory
shape that comes from spherical particle scattering. The slight broadening of the
peaks and the fact that the intensity values do not reach zero between oscillations is
an important result of the lattice of atoms within the particle. If the particle were
a uniform sphere of electron density, the oscillations would have greater definition;
the lattice of scattering atoms is an important and accurate representation of the
84
I
2abs
APL
dfit
1425 nmn14 9 5 nm .
5 7 0 nm
750
75-
1370 nm14 2 2 nm
5 5 0 nm
U
?%abs
APL
dfit
1274 nm13 3 6 nm 14 nm
5
20C
abs
APL
dfit
12 5 2 n1328nm
19 n
05()
0
1
M,
X 15
Aabs
~155
V
0
kE
1a0
APIL
nmn12 87
d fit
m4 0
m
Aabs
APIL
dfit
147 nm12
6 2 nm4 4 8 nm
_15
0.
10-
Aabs
10
0:
151
10-
APL
1033 nm1 1 4 6
dfit
1
=m387 nrn
Aabs
APIL
dfit
1023 nm1, 1 4 3 nm 3 .83 nmn
015
Aabs
APL
dfit
853 nmn 1004 nm3 .00 nmn
0~
abS
20800
1200 1600
Wavelength
APIL
d fit
846 nm 995 nm 2.97 nmj
3
4
5
6
20
Figure 4-1: Development of the PbS QD sizing curve. (a) Absorption and photoluminescence spectra for all sizing samples. (b) Solution SAXS data and simulated fits
for all sizing samples. Absorption and photoluminescence peak positions are noted
in addition to the matching simulated diameter.
85
1.6
(D
0
0K
1.5
0
0
0L
C
0
-o
U)
1.4k
1.3
0
Fit to PL
p
4
1.2 F-
0%
0
1.1k
*S.
1
&
LU
*
Kang and Wise
K> Wang
Moreels Calculation
+
Moreels Expt
Watkins
Cademartiri
S
Kane
K>
*0
0
.60
This work, PL
Fit to Abs
4-'
t-
This work, Abs.
K>
40,
K>?
,~
0.9k
0. I8
3
ft
3.5
4
4.5
Diameter in nm
5
5.5
6
Figure 4-2: Sizing curve plotted with literature sizing values. This solution-SAXS
sizing method maps a given diameter to a larger bandgap than other methods[51, 120,
76, 46, 10, 50], or a given peak location to a larger diameter. This result suggests that
other methods may underestimate the size of the QD particles, which is consistent
with previous observations of a poorly resolved surface layer in TEM images of CdSe
QDs that is resolved in x-ray analysis[77].
86
20
Pb
" 15,
5,
20
-i--o-. .
.
5.
--
0
122
10
10
0 0
Figure 4-3: Simulated PbS QD at a particular radius, in units of lattice spacings.
Blue and green points represent Pb and S atoms, respectively. We note that faceting
is not included in this model; atoms are only located on points within the radius
input for any particular particle size.
87
x
10 7
32
Pb-Pb
4-d
0
-1
20
40
20
60
Figure 4-4: Simulated scattering intensity due to Pb-Pb scattering (blue), S-S scattering (green), and Pb-S scattering (red). These are the scattering values prior to the
addition of the (constant) atomic scattering factors; the negative value of the Pb-Pb
baseline does not result in a simulated negative scattering value.
88
25 F
3
20
x
10
C
C)
CM
C
15
C
0)
W
U)
00
10
5 10 1520
A
20
I
40
2E in degrees
I
I
60
2E in degrees
Figure 4-5: Simulated x-ray scattering in both the small-angle and wide-angle regions.
89
PbS QD, and including this lattice in the simulation avoids an overestimation of
the polydispersity, which could also affect the extracted peak position and therefore
particle size. The simulation is verified by its agreement with the literature values
for bulk PbS peak positions (black bars) in the wide-angle region. Oscillations near
the baseline in the wide-angle region are a result of the Fourier transform of the
scattering, and vary as a function of distance between 20 data points simulated.
4.3.2
Signal variation with particle size and polydispersity
To accurately represent the experimental samples, we created a library of scattering
intensity profiles with single-unit-cell increments that spanned the size range of QDs
and simulated sample curves assuming a normal distribution of radii surrounding
an average value, and adding the intensities of the single-size curves together with
number-weighting for that distribution. Figure 4-6 shows the change in the simulated
sample curves for different diameters (from 12
A to 66 A where the standard
deviation
of the normal distribution is set at 5% of the particle size, which is a regularly achieved
value of particle-size dispersion for QDs, and is similar to a dispersion extracted from
the full-width-half-maximum of an absorption or emission spectrum for our QDs.
Figure 4-7 shows the effects of increased polydispersity on the simulated curve for
an unchanging average particle size. The higher polydispersity curves have significantly less peak definition.
4.4
4.4.1
SAXS measurements
Solution SAXS data
Figure 4-8 shows images of the 2D-detector intensity for the solution-SAXS measurement for a size series of QDs. These data were circularly integrated to generate a 1D
data plot as a function of 20, and these curves were used for matching to simulated
curves.
90
10
10
A Increasing size
4I-J
10
5
0
5
10
2E
Figure 4-6: Simulated x-ray scattering with increasing diameters from 12 Ato 66 A
where the standard deviation of the normal distribution is set at 5% of the particle
size.
91
10
10
A
Increasing polydispersity
4~D
(j~
C
U)
C
10
10
0 1
0
5
10
20
Figure 4-7: Simulated x-ray scattering with increasing polydispersity from 0% to 6%
for an unchanging average particle size of 50 A.
Figure 4-8: 2D-detector intensity for the solution-SAXS measurement for a size series
of QDs.
92
4.4.2
Matching simulations with experimental data
The matching between simulation and experiment was performed by iterative looping
of the simulation function, for which the input values were the average QD size and the
standard deviation of the normal distribution of sizes. The function performs scaling
and flat baseline addition for each input set using a binary tree algorithm to minimize
the mean of the absolute difference between the simulated curve and the experimental
curve for all 20 values. A chi-squared value is calculated for each set of input values
using the sum of the squares of the residuals divided by the simulated value at each
20 point. The input parameters with the lowest chi-squared value were used as the
function seed for a finer-grade matrix of sizes and standard deviations, and the inputs
that yielded the lowest chi-squared value were identified as the matching simulation
parameters. The 95% confidence error bar on the fit was determined by identifying
the value for the average size that resulted in an increase of 2 in the chi-squared value.
The 95% confidence error bar for the standard deviation was determined in the same
manner as for the average size.
4.5
4.5.1
QD spacing in a film
Spacing determined from pair-distribution function
The second step to measuring the volume fraction of QDs in a close-packed film is to
measure the center-to-center distance between particles. We performed SAXS measurements on spin-cast thin films of QDs of a range of sizes, which had all undergone
a solid-state ligand exchange with tetrabutylammonium iodide (TBAI), a process
commonly employed for photovoltaic QD applications[135]. The SAXS data for the
TBAI-treated films are shown in Figure 4-9a. The most prominent peak of the SAXS
data shifts to shorter 20 angles with larger QD size. The smaller peak at higher 20
angles in each of the four curves matches the location of the solution-SAXS peaks
for the corresponding QD size. Though it is tempting to apply a standard Bragg
conversion of 20 to distance and identify the peak d-position as the nearest neighbor
93
dspace= 6.4 nm
Aabs
1407 nm
Z
d space =5.3 nm
abs
d
1155nm
dspace=
4 .6
nm
CC
kabs
966 nn
j
dspace=' 4.5 nm
Aabs
841 11nm
1
2
3
4
29 in degrees
5
0
2
4
6
8
Distance in nm
Figure 4-9: a) Raw film SAXS data (open data points) and GNOM fit (solid black
line). The minor peaks at larger 20 values are self-scatter peaks like those shown
in Figure 4-1. b) Extracted pair-distribution function for fits in (a) using GNOM.
Error bars are calculated by GNOM. The peaks of the P(r) curves are the center-tocenter spacings for nearest neighbors and other features of the curves are a result of
self-scattering and limited measurement range.
94
distance, correct determination of the nearest-neighbor distance requires extracting
the pair-distribution function[78] because the particles are not arranged in a crystalline lattice. The calculation of the pair-distribution function takes into account
the particle geometry and form factor. The pair-distribution function was calculated
from these data using the program GNOM[105].
Figure 4-9a shows the SAXS data
(open circles) and their GNOM fits (solid lines) of four samples ranging in size (2.92
nm, 3.58 nm, 4.49 nm, and 5.78 nm, with first exciton peaks at 841 nm, 966 nm, 1155
nm, and 1407 nm in solution), as determined using the solution-SAXS sizing curve
from the previous section. The minor peaks at larger 20 values are self-scatter peaks
like those shown in Figure 4-1.
Figure 4-9b shows the pair-distribution functions,
P(r), as determined by GNOM, as labeled by their
Aabs.
The P(r) values are normal-
ized and offset on the y axis for clarity. The peaks of the P(r) curves in Figure 4-9a
are the center-to-center spacings for nearest neighbors and other features of the curves
are a result of self-scattering and limited measurement range. The center-to-center
spacings extracted from the pair-distribution function (4.5 nm, 4.6 nm, 5.3 nm, and
6.4 nm) are consistently larger than the size of the particles determined from the
sizing curve.
4.5.2
Film SAXS data
Figure 4-10 shows images of the 2D-detector intensity for the film-SAXS measurement
for the four film samples in the text. These data were semi-circularly integrated in
the section of the detector with signal to generate a ID data plot as a function of
20. To confirm that the horizontal and vertical scattering were the same, conical
sections were also integrated and their peak positions were found to match that of
the full semicircular integration. The lower half of the image shows only scattered
beam counts and no signal counts because the film sample blocks the path of the
beam. The central feature (small semicircle with central dot) is the scattered intensity
surrounding the beam block and the hole in the center of the beam block, and is not
a feature of the sample. The pointed nature of this semicircle in some of the data is
due to an x-ray beam reflection; the position of this feature can be moved with slight
95
Figure 4-10: Images of the 2D-detector intensity for the film-SAXS measurement for
the four film samples in the text.
sample tilt without affecting the 20 values of the data, and is not a feature of the
sample.
4.6
Dielectric measurement using stacked architecture
The capacitance of the QD film was measured by AC impedance spectroscopy using
a stacked-capacitor geometry so that
1
1
1
COt
CHfQ2
CQDfilm
1
dH fo2
Cparylene
ACHfo
4
2
dQD film
dparylene
AEQDfilm
AEparylene
(4.1)
where C is a capacitance, d is a film thickness, A is the device area, E is a material
dielectric constant, and the subscripts denote the material to which these values
belong.
This architecture was engineered to have a high-dielectric oxide and thin insulating layers (~25-50 nm) to maximize the relative contribution of the QD film layer to
the total capacitance. A control device with only HfO 2 and parylene was also mea96
40
C
030
1407 nm
0
nmn
Ol1155
S20
E
966 nm
841 nm
10210 2
10 410
10 3
5
Frequency (Hz)
90
C
a) 85
-C
80
CT
a
neene
-0
1 75
T
702
10 2
10 4
10 3
a
10 5
Frequency (Hz)
Figure 4-11: Measurement and evaluation of the film dielectric constant. (a) Dielectric
measurements as converted from capacitance as a function of frequency, after control
subtraction. (b) Impedance phase angle as a function of frequency to show strong
capacitive behavior over a wide frequency range. The inset shows the layered structure
of the sample device (left) and control device (right).
97
sured and the inverse of its capacitance was subtracted from the inverse of the total
capacitance to yield the inverse of the QD film capacitance. The thickness (in the
range of 100-200 nm) of the QD film is measured using a profilometer and the device
area (4.86 mm 2 ) was known from the mask geometry and confirmed via optical microscopy and profilometry. By incorporating the known QD film thickness and device
area, and subtracting the contributions of the Hf0
2
and parylene layers, the capac-
itance of a sample yields the dielectric constant of its QD film. Figure 4-11a shows
the dielectric constants as a function of frequency for the size series of QDs. The
bands each color denote measurements of different chips with the same size of QDs
used in fabrication. The width of the color band indicates the deviation of calculated
dielectric constants based on the thickness variation of the QD film for each chip.
The capacitance (and therefore also the extracted dielectric constant for a given film
thickness) is constant across several orders of magnitude of frequency. Figure 4-11b
shows the impedance phase angle of the stack containing the QD layer as a function
of frequency, which is relatively constant at frequencies lower than 104 Hz and very
near to the pure capacitive phase angle of 90 degrees.
4.7
Detailed values for samples used in stackedcapacitor measurements
4.7.1
Absorption spectra
Figure 4-12 shows the absorption spectra for the four solutions used in the size series
for capacitance measurements.
4.7.2
Random close packing
Random close-packing was chosen as the model packing type because the SAXS
signal showed no higher-order rings or concentrated points of signal along the ring
of intensity. We used Finney's report of a packing fraction of 0.64 for a randomly
close-packed system[30], where the close-packed units are the QDs with ligand "shell".
98
0d
CL
0
CI)
C
600
1000
1400
Wavelength (nm)
Figure 4-12: Absorption spectra for the four solutions used in the size series for
capacitance measurements.
4.8
Discussion
To convert the QD size and spacing data into volume fraction, we assume that the
QD-ligand units are randomly close packed. Mathematically:
47
Volume fraction q = packing fraction *
3
WQc D
SQD-QDspacing
(4.2)
where r7is the QD volume fraction and rQD is the QD radius determined from the
sizing curve in Figure 4-1.
The value for the dielectric constant of the QD film is found by averaging the values
between 1000 Hz and 10,000 Hz because the phase angle is consistently flat and less
noisy in this frequency range. We note that the experimental uncertainty is dominated
by chip-to-chip variations rather than frequency or thickness variations within a single
chip. Figure 4-13 compares the dielectric constant data from our stacked capacitor
method against three simple models using the bulk dielectric constant of PbS, 6 =
99
60 -
Volume-Weighted
50
Bruggerman
E
w~ 40Q
This work
030
-20
-
Maxwell Garnett
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Volume Fraction
Figure 4-13: Dielectric measurements cornpared with several effective- medium models. The data do not fit to these simple effect ive-medium models with a PbS dielectric
constant of 169, as in the bulk. The linearity of the data suggests that some volumeweighted theory may be appropriate, but the shallower slope implies that the effective
QD dielectric constant is smaller than that of the bulk.
169 and a matrix dielectric constant of 2, which is a reasonable approximation for
a combination of air and any residual organic solvent.
Volume-weighted effective-
medium theory predicts a linear relationship between the volume fraction occupied
by
QDs, a higher slope (comparable to the value of the PbS static dielectric constant
of 169 at 300K[22]), and a small y intercept set by the static dielectric constant of
the matrix surrounding the
QDs:
Etotal
etotal
= EQD *
(EQD
77QD + Ematrix
~-
Cmatrix ) *
QD-~(4.D)
*
9IQD
+
Ematrix
Maxwell-Garnett effective-medium theory is frequently referenced for nanoparticle
100
film dielectric calculations[25, 81, 109, 70]. Its functional form weights the dielectric
constant of the surrounding medium more heavily than the dielectric constant of the
inclusion material:
S-i 1
ei-l
C+1=
c +2
c±C
E
(4.4)
+ 2
where c is the dielectric constant of the composite,
of the inclusion material, and
m1
6i
is the dielectric constant
is the volume fraction of the inclusion material.
Maxwell-Garnett effective-medium theory significantly underpredicts the dielectric
constant, which is not surprising because it is optimized for very dilute solutions of
particles or inclusions[15].
Bruggeman effective-medium theory is better suited for high volume fractions
because it incorporates a threshold volume fraction and material parity, and reaches
the bulk value at a volume fraction of unity[15], but this theory also clearly does not
match the shape or values of the measured dielectric constants. The characteristic
equations of Bruggeman effective-medium theory are:
r(
C)
C
c1 +2c
+
62
62 +
2E
)
=
(4.5)
0
1
c =
(0 +
(37 1 - 1)c +
V32
+
(3rq2 -
1)62
where c is the dielectric constant of the composite,
the inclusion material,
62
-
T1
6i
is the dielectric constant of
is the dielectric constant of the matrix,
fraction of the inclusion material, and
1
(4.6)
86E62)
712
m1
is the volume
is the volume fraction of the matrix
(q)2
for the two-component case considered here).
Each of these simple effective-medium models is predicated on the local field
being the same throughout the sample[15].
This may be an incorrect assumption
for close-packed QD films on the scale of the relevant polarizations because the
high surface-to-volume ratio results in a much higher relative number of polarized
101
QD-ligand bonds at the surface than in conventional theories. The linearity of the
data suggests that some volume-weighted theory may be appropriate, but the shallower slope implies that the effective QD dielectric constant is smaller than that
of the bulk.
The deviation from simple models is an indicator of an effectively
lower dielectric constant of PbS when it is in nanoscale structures instead of in the
bulk. This size-dependent dielectric constant of the particles in the film is expected
based on experimental measurements[13, 68, 81] and theoretical and computational
studies[118, 119, 114, 113, 104, 11, 23] primarily in the nanoscale Si/SiO 2 system,
for which both the of band-gap expansion and of surface reconstruction have been
discussed as explanations for the dielectric constant reduction.
4.9
Conclusion
We have provided a reliable measure of QD size using solution SAXS, QD-QD spacing
using the pair-distribution function from thin-film SAXS data, and QD-film dielectric
constant using a stacked capacitor geometry, and have found that the dielectric constant is not accurately predicted by the simple effective-medium theories. We propose
that the dielectric constant of a QD film is strongly affected by the nanoscale nature
of the material due to surface and other size effects. We conclude that no simple
effective-medium theory model can be employed for these nanoscale films using the
bulk PbS dielectric constant, and that a size-dependent dielectric constant like those
in observed and discussed in Si/SiO 2 work is supported by this experimental study.
This conclusion has implications in device architecture design; higher film dielectric
constants allow for increased depletion region depth. Because the intrinsic dielectric
constant of QDs is limited by the nanoscale nature of the material, higher-dielectric
ligand matrices may enable higher film dielectric constants and consequently deeper
depletion regions. By identifying the inadequacy of common effective-medium models
for the dielectric constant and providing a method to empirically determine a film dielectric constant, we hope to aid both theorists and experimentalists in understanding
the nanoscale physics and engineering and improving QD optoelectronic devices.
102
4.10
Experimental Methods
4.10.1
PbS QD synthesis and purification
PbS QDs were synthesized according to a previously published procedure[133]. The
relative amount of oleic acid and octadecene in the initial four-necked flask was varied
to create different QD sizes. For the smallest particle sizes, the injection temperature was lowered from 150'C to 120'C or 90'C. Air-free cannula-transfer techniques
were used to transport the crude solution into a N2 glovebox without exposure to air.
Within one hour from synthesis, the crude solution was purified by adding either a butanol/methanol mixture or acetone, and centrifuged at 3.9 krpm for 3 minutes. The
supernatant was discarded and the precipitate was dissolved in a minimal amount
of hexane for storage (in the glovebox and with anhydrous solvents).
Further pu-
rification was performed more immediately prior to the various measurements. For
the solution SAXS measurements, a very careful size-selective precipitation was performed in a glovebox using butanol, and in some cases a butanol/methanol mixture.
The supernatant of the first size-selective crash out of storage was precipitated separately, such that there are two solutions of similar size obtained from each synthetic
batch. Two total precipitations were performed on each initially stored solution and
the final precipitate was dissolved in a minimal amount of octane for solution measurements.
For the dielectric devices and film SAXS measurements, the solutions
were precipitated from the storage solution in a volumetric ratio of 4:2:1 QD solution:butanol:methanol.
Two precipitations were performed on each initially stored
solution and the final precipitate was dissolved in octane at a concentration of ~50
mg/mL for deposition.
4.10.2
SAXS sample preparation
All sample preparation was performed in a nitrogen glovebox. For each solution SAXS
sample, a capillary (0.5 mm, glass number 50 from Hampton Research) was snapped
toward one end in the thin section, and the thin end of the capillary was dipped in a
103
concentrated QD solution (in octane). The capillary was removed from the solution
before the meniscus reached the widened portion of the capillary, and was tipped
horizontally to leave a gas bubble at either end of the capillary. The thin end of the
capillary, while still held horizontally, was pressed into a slab of Critoseal and twisted
to seal the thin end of the capillary. A small fragment of Critoseal was packed into
the wide, top end of the capillary using tweezers; the press-and-twist method was
deemed ineffective because it induced a pressure in the capillary that dislodged the
sealant of the thin end. The sealed capillary tubes were removed from the glovebox
and the SAXS measurement was performed within several hours. For each film SAXS
sample, six layers of QDs were deposited using the following procedure for each layer:
deposit 10 pL QD solution on silicon wafer fragment (blow-dried with nitrogen prior
to use), spin at 1000 rpm for 10 s, deposit ~100 pL solution of 10 mg/mL TBAI in
methanol, wait 30 s, spin at 1300 rpm for 5 s to remove treatment solution, deposit
~100 pL methanol, spin at 1300 rpm for 5 s to remove methanol rinse solution. Film
samples were removed from the glovebox and measured within several hours.
4.10.3
Stacked capacitor device fabrication
Patterned ITO was purchased from Thin Film Devices in Anaheim, CA. The ITO
was cleaned by sequential sonication in water/detergent, DI water, acetone, and isopropanol and blow dried with nitrogen. Hf0
2
(25 nm) was deposited via sputtering.
Six layers of QDs were deposited as described for SAXS film sample preparation in
a glovebox using TBAI ligand treatment. The samples were transferred without air
exposure to the parylene deposition system, where 25 nm of parylene was deposited
via chemical vapor deposition. An aluminum electrode was deposited by thermal
evaporation.
4.10.4
SAXS measurement
Small-angle x-ray scattering measurements were made on a Bruker D8 with GADDS
and 2D detector SAXS attachment and 0.05-mm monocap, with copper K, radiation.
104
The detector distance was set at > 40 cm and the precise distance value was calibrated
using a silver-behenate standard in relevant geometry (a powder on a glass surface for
film samples and powder coating a glass capillary for solution samples) and matching
its circularly integrated peak positions to standard values. After loading each QD
sample, the position was adjusted to optimize the amount of signal, and data was then
collected for 30 minutes. The GADDS program was used to perform chi integration
(circular for solution samples and semicircular for film samples).
4.10.5
Capacitor measurement
AC impedance spectroscopy was performed using a Solartron 1260 impedance analyzer. No DC voltage was applied, the AC voltage was 10 mV, and the frequency
was varied. The system was nulled using an evaporated gold film for the short-circuit
current and without a chip in the setup for the open-circuit voltage. The impedance
testing setup is housed in a dark box with low-noise cables in a glovebox.
4.11
Chapter-specific acknowledgments
This work was primarily supported by Samsung SAIT. Pearl Donohoo-Vallett assisted with the iterative algorithm and wrote a portion of the MATLAB code for the
solution sizing background and scaling to match simulated and experimental curves.
Dave Strasfeld was a part of the idea conception for the measurement of QD film
dielectric constants. Ankit Rohatgi, the author of WebPlotDigitizer[96] greatly eased
the collection of literature data for sizing curve comparison. Scott Speakman provided valuable discussion and experimental assistance for both the solution and film
SAXS measurements.
105
106
Appendix A
Ligand Quantification using
Thermogravimetric Analysis
(TGA)
A.1
Introduction
For QD electronic devices, where ligand exchange is an important aspect of device
design, the number of ligands per QD and their propensity to leave or remain in the
film are valuable metrics. To roughly quantify the number of ligands per particle,
thermogravimetric analysis (TGA) was used: QD samples were precisely heated and
the mass loss was tracked as a function of temperature. Controlling for PbS mass
loss (see Section A.5.2) allows the number of ligands per QD to be calculated. This
measurement is performed for four different ligands for one size of QD and on an
additional QD size with oleic acid ligands. Mass spectrometry is performed in addition
to TGA (TGA-MS) to measure the molecular mass of the species released from the
QD
film as a function of temperature.
107
A.2
QD
Sample preparation
samples were prepared for analysis by deposition into a platinum pan. Prior to
deposition, the pan was cleaned with first a solvent rinse and then a butane torch until
the point of glowing (several seconds). The pan was allowed to cool and was tared
in the instrument, and then the QD solution was deposited in air into the pan. For
solution deposition, several drops of QD solution in hexane or octane were placed into
the pan and the solvent was allowed to evaporate. For low solution concentrations,
this process took place several times to build up a substantial enough weight of QDs
to get instrument signal (several mg). For solid deposition using n-butylamine (NBA)
or oleic acid (OA) ligands, previously dropcast films of QDs were scraped off of their
silicon or glass substrates using a metal spatula and the solid was transferred to
the platinum pan. For deposition using thiol ligands (ethanedithiol, EDT, and 1,3
benzenedithiol, BDT), one or two drops of QD solution with OA ligands was deposited
into the pan, and the solvent was allowed to evaporate, as in the solution-deposition
method. Then an acetonitrile solution of the thiol ligand (0.02% by volume) was
deposited into the pan, left to sit for 30 seconds, and removed from the pan. The pan
was then rinsed with acetonitrile and allowed to dry for several seconds. These steps
were performed three times (QDs, thiol solution, acetonitrile rinse).
A.3
TGA method
Thermogravimetric analysis (TGA) was performed on a TGA Q50 from TA instruments. A platinum pan was used with 10 mL/minute of helium balance gas and 90
mL/minute of nitrogen sample gas. After sample preparation and pan loading, the
programmed step sequence performed was (the first two steps can be switched in
order with no apparent effect):
1. Isothermal for 10-20 minutes
2. Equilibrate at 30'C or 100 0 C
3. Ramp 10C/minute to 600'C
108
4. Isothermal for 5 minutes
5. Air cool
The percentage mass loss and the derivative of the mass loss as a function of
temperature are extracted from the data file, which has a timestamp, temperature,
mass, and derivative output.
A.4
A.4.1
Mass loss and ligand quantification
Size variation
Figure A.4.1 shows the higher mass loss from smaller QDs (OA QDs with a first
absorption feature at 837 nm have a lower mass % at 600'C than OA QDs with a first
absorption feature at 1250 nm). This is an expected result because smaller particles
have a higher surface-to-volume ratio, so for a given extent of ligand coverage, the
ligands should account for a higher proportion of the total QD-ligand mass.
A.4.2
Ligand variation
Figure A.4.1 also shows the mass % as a function of temperature for several samples.
The slight rise of mass % in the 1250 OA sample does not occur in all OA samples.
Both the OA and NBA ligands resulted in a minimum QD mass of 72% of the starting
mass for QDs with a first exciton feature at 1250 nm, regardless of the deposition
method. This is a surprising result because the oleic acid molecule has a molecular
weight of 282 g/mol and n-butylamine has a molecular weight of 73 g/mol, so if
the ligand exchange from OA to NBA is a one-to-one binding-site ligand exchange,
the mass loss of the OA ligand should be much greater than the NBA ligand. This
result of roughly equal mass loss percentages for these two ligands is an indicator that
either there are many (-4x) more NBA molecules in the sample than OA molecules,
or that the NBA ligand exchange is incomplete. The latter scenario is unlikely given
the disappearance of the oleic acid signature in the FTIR measurements performed
by the initiators of the NBA ligand exchange procedure
109
[57].
It should be noted
1
0.95k
0.9
0
4
-D
0.85k
0.8
1250 OA_
0.750.7
-
1250 NBA
0.65837 OA
0
100
200
400
300
Temperature in C
500
600
Figure A-1: TGA mass-loss curves for different QD sizes and ligands.
110
that having more NBA molecules in the sample does not necessarily require that
these molecules be bound to the surface of the QD. Although the smaller size of the
NBA molecules may allow for a higher packing density on the surface of the QD,
it is also possible that there are unbound NBA molecules that are associated with
individual QDs due to Van der Waals forces from bound NBA ligands or unbound
charging interactions like those discussed in Fafarman et al.[28]. Liquid-deposition
samples have flat curves at lower temperatures, while solid-deposition samples have
more constant mass loss at lower temperatures. Solid-deposition samples consistently
have a mass loss at ~110 C (see later section on species lost). Thiol ligand-exchanged
curves behave more like solid-deposition samples in the low-temperature region.
Figure A.4.2 shows the mass-loss curves for different ligands, where the particle
size is the same for all samples. The EDT sample shows the largest percentage mass
loss as a function of temperature; the EDT molecules account for more than half of
the mass of the sample. Given the small molecular weight of EDT (94 g/mol), this
translates to a very large number of EDT molecules per QD. The BDT, OA, and
NBA ligands all result in roughly the same fraction of the total sample mass, which
is surprising given the large differences in their molecular weights.
A.4.3
Ligand quantification
A simulation of spherical QDs enables easy quantification of both the total number of
atoms in a QD of a certain size and the number of surface atoms in that QD. These
plots and their second-order polynomial fits are shown in Figure A.4.3. It should be
noted that the allowed QD diameters are discretized by the lattice constant of PbS,
and the calculation of total atoms is based only on the radius and does not include
faceting. For the particle size shown in Figure A.4.2 with first excitonic feature at
1250 nm, these simulations yield an average diameter of 4.94 nm, and -2100 total
atoms, ~370 of which are surface atoms.
Using the atomic mass of Pb and S and attributing the full mass loss in TGA to
ligand loss such that remaining mass % at 600 C is the mass of the bare QD core, the
mass of a single QD and its ligands can be independently calculated. Dividing the
111
------------------- ------------------ -------
0.9
--------------------
------ ----------
E 0.8
--------------------
:-------
0.7
------------------
Cb
0
0
t5 0.6
0.5
------------------------- -------------------------------------------------
OA
------ ----------- --------------------------------------: ----------- ----BDT
EDT
------------------------------------------ ----------------------- -------------------------NBA
--------------- -------------------------------------
------
--------------------
-------- ------------------------------------
----------------- ------ ---------------------
------
----------- -------------------------------
--------------------- ----------------
-------------------------
0.4
0
100
200
300
400
Temperature in C
500
600
Figure A-2: TGA mass-loss curves for different ligands, where the particle size is the
same for all samples.
112
E
5000 Total atoms= 7.3e-03x2 -11.1 x + 4666
a 700 Surface atoms
4000
c00
3000
500
8400
4!
2000
0 300
1000
0
0
E
200
800
1000
0
1200
1400
First Exciton Peak
Total atoms = 193 x2- 652 x + 570
a
E
z3
5.51 e-04 x2- 0.51 x + 146
600
E
E
0
=
E 100L
160 0 Z
800
0
1400
1200
First Exciton Peak
1(
600
2
Surface atoms = 11.4 x + 45.5 x -141
E 600
0
E 500
40003000-
400
0
300
2000Cu
Z
1000
0-
7UU
1000
200
100
2
3
4
5
6
QD diameter (nm)
z
0 22
3
4
5
6
QD diameter (nm)
7
Figure A-3: Plots of total atoms and number of surface atoms as a function of QD
diameter and first exciton peak.
single-particle ligand mass by the molecular weight of the ligand yields the number
of ligands per QD: 348 OA, 1480 NBA, 3227 EDT, 624 BDT.
Given that the number of surface atoms for this particle size is only -370, the
calculated numbers of ligands per QD are far to high to be bound to the particle.
This large disparity in values suggests that either the mass loss is not an indicator
of the ligand mass, or that the mass loss from the sample is not only from bound
ligands. In the latter case, the mass loss may be due to unbound ligands, residual
solvent, and/or oxidation products that are created at room temperature prior to the
beginning of the measurement.
113
A.5
Species lost at each temperature
A.5.1
Mass-loss derivative analysis
The derivative data shown in Figure A.5.1 show effectively no mass loss peaks before
the onset of a peak at ~200'C, with the exception of a small loss sometimes present
at ~11 0 'C. Regardless of the ligand, there appears to be one very significant peak
between 250-300'C, and in the case of BDT, NBA, and OA, there is another smaller
peak between 300-350'C. The initial small peak at 110 0 C may be residual solvent
evaporation. The boiling point of octane is -125'C, but it is worth noting that the
boiling point of a molecule is a statement of the forces between many molecules of
the same type, and may not be a direct indicator of an octane molecule interspersed
among QD ligands or another molecular species. It is possible that the major peak
in each sample is due to the detachment of the respective ligands from the QD,
though the binding strength interpretation is not easy to reconcile. A higher peak
temperature would be expected for ligands with stronger bonds to the QD surface,
and in these experiments the two thiol ligands have the most drastically different
peak positions, suggesting that either the binding group is not the defining factor for
the binding strength, or that the peak is not associated with the binding strength of
the ligand to the QD.
A.5.2
Bulk study to probe Pb evaporation
To determine whether a portion of the mass loss could be attributed to mass loss of
the PbS itself, rather than the ligands or associated molecules, a TGA sample with
bulk PbS powder was measured in two immediately sequential runs (Figure A.5.2).
The extent of mass loss in both runs was very small, and there were no peaks that
were present in the first run but not in the second run. It is therefore unlikely that
any Pb evaporation or other inorganic mass loss is occurring over this temperature
range. The bulk PbS data also show a dip and rise above 450'C that may be the
same feature as the observed dip in the 1250 OA data.
114
BDT
EDT
QA
C>
U)
0
-j
Cfl
Ca
NBA
0
100
200
300
400
Temperature in C
500
600
Figure A-4: TGA mass-loss derivative curves for different ligands, where the particle
size is the same for all samples.
115
CD1.008
I
I
I
I
-
CO 1.006
E
1.004
1.002
40 1.000
C
0 0.998
0.996
I
50
I
100
I
150 200 250 300 350 400 450
Temperature in C
500
550
---------- -----------
---------- -------
----------
----------- ---------- ---------- ---------------------
---------- ----------- ------------------
---------- I-------------
------- ------ ------------- ---------- ----------- ---------- ----------------- _ --------- ----------------- ---------- --- ---- --------------- ---------- ----------- ---------- ---------- I----------
------
------------------------------------------------------------------------------- -----------
150 200 250
300 350 400 450
Temperature in C
500
Figure A-5: TGA mass-loss and derivative curves for bulk PbS powder.
116
A.5.3
TGA-MS
In an attempt to gain more specific information about the molecular species lost at
each temperature for these different samples, TGA-MS (thermogravimetric analysis
with mass spectrometry) was used. In these measurements, shown in Figure A.5.3,
the mass fragment values that would be associated with the NBA ligand did not show
a defined signal. The observed signals were largely from mass fragments associated
with an OH radical, water, CO 2 , and SO 2. In particular, temperatures above 400'C
result in a high output of sulfur dioxide, and there is some output of sulfur dioxide
between 200-250'C as well.
Given the large carbon dioxide signal, it is likely that the ligands are effectively
burning off rather than detaching from the QD surface and evaporating at these
temperatures. The peak position of the mass-loss derivative for the different ligands,
then, would be more indicative as a metric of the burning process than the binding
energy to the QD surface.
The OH radical and water signals are a reminder that humidity and water vapor,
even for short ambient exposure times, can have a significant presence in QD films.
In explorations of the electronic properties of patterned QD thin films with members
of the Kastner group, we have found humidity to have an effect on QD substrate
adhesion as well as, importantly, in electronic signals.
A.6
Conclusions
In general, QD films can be heated under nitrogen to -200'C
without significant
mass loss, regardless of their size or ligand. Heating the film to -11
0
'C may be an
effective way to remove solvent from the film without altering the ligands or QDs.
Higher temperatures do result in a loss of mass, but this mass loss is not strictly
the evaporation or detaching of ligands from the QD surface, but rather a burning
mechanism.
TGA-MS does not permit detailed study of the ligand species on the
surface of the QDs.
The mass loss due to inorganic losses from the PbS core is
insignificant. Rough quantification of ligands per QD yields 300-3000, for 4.94-nm-
117
a
0.1.
>
0.06
3 0.04
0.0
50
100
150
200
250
300
350 400
in C
450
500
550
Temperature
1013
1.1
1.05
n-butylamine
0.9
100
150
200
250
300
350
400
450
500
550
150
200
250
300
350
400
450
500
550
12
11
water
10
3
9
0
81
50
100
x 1071
3 --
-- --
-
-
2.5
OH radical
2
5
-
1.50
100
150-200
250
300
350
400
450
-250-
300
350
400
450
250
300
0
400
450
500
550
X ull
carbon dioxide
2
1'
005
100
150
200
-650
-50
50
13
x 107
0
C
1
4
sulfur dioxide
3
2
50
100
150
200
500
550
Temperature in C
Figure A-6: TGA mass-loss ion currents for different mass fragment values for a QD
sample with n-butylamine ligands.
118
)
0.4
$
0.3
0.2
.0
-
0.1
0
0
a
-0.1
0
100
150
200
250
x 10-13
1.55
300
350
400
450
500
550
Temperature in C
oleic acid
1.5
C
1.45-o
C.)
C
0
h
141
1.4
6
50
100
(.V,
9
150
200
250
300
350
400
450
500
550
150
200
250
300
350
400
450
500
550
x 1010
2
water
C
a)
C.)
C
0
1
0.5
50
100
x 10-11
6
C
5
OH radical
C
a)
4
C-)
C
0
3
9
'
uum!C6,
V
50
100
150
200
250
300
350
400
450
500
550
250 300 350 400
Temperature in C
450
500
550
x 10.1y
81
C
6
carbon dioxide
C
a)
U
C
0
4
2
UTIZG WCu 1-110
01
50
100
150
200
Figure A-7: TGA mass-loss ion currents for different mass fragment values for a QD
sample with oleic acid ligands.
119
diameter particles, depending on the ligand. Only the lowest end of this range of
ligands per QD is lower than the calculated number of surface atoms, which suggests
that there are many ligands in the thin film that are not directly bound to the QD.
A.7
Chapter-specific acknowledgments
Donghun Kim of the Grossman group performed the simulation calculations for the
number of surface atoms as a function of total atoms in the QD.
120
Appendix B
QD
Films in Transistor Geometries
B.1
Introduction
Deducing the position of the Fermi level in semiconductor nanoparticle films is an
important and ongoing challenge in the field of nanoscale devices. The knowledge
of Fermi level position and its consequent engineering would enable the creation of
many classic semiconductor architectures at the nanoscale including p-n junctions,
definitively Ohmic contacts, and other more complicated structures.
More simply,
the identification of a material as "p-type"or "n-type" would allow for significant
progress in the field.
Unlike in silicon, where the deliberate and externally controlled introduction of
dopants determines the designation of p- or n-type (with holes or electrons, respectively, as the majority carrier), semiconductor nanoparticle films are understood to
be n- or p-type as a consequence of the energetic position of surface states. Only as
a result of the high surface-to-volume ratio do these surface states exist in significant
enough quantities to have a strong effect on the electronic material properties.
Transistor measurements have been frequently used to determine the n- or pcharacter of nanoparticle films [24, 36, 35, 71, 54, 56, 106, 110, 135, 116, 128, 1291,
but because these devices function by carrier injection into the nanoparticle film[122],
these measurements are not able to determine the inherent carrier type or density.
121
B.2
Length scales and electric-field boundaries
The top panel of Figure B-1 shows the common schematic of a field-effect transistor
(FET). The application of negative gate bias (minus signs at the gate/oxide interface)
induces a channel of positive charges in the semiconductor (plus signs at semiconductor/oxide interface) that then flow from drain to source. The reverse takes place with
positive gate bias: a channel of negative charges is induced and those charges flow
from source to drain. While this cartoon captures much of the correct FET behavior,
like many cartoons, its length scale is misleading. A more accurately scaled picture,
for QD FETs in particular, is shown in the bottom panel of Figure B-1. In this more
accurate picture, the distance between source and drain is large (-
10 Pim), and the
semiconducting film is thinner. When a gate voltage is applied, the gate acts as one
plate of a capacitor, and the opposite plate of the capacitor forms when charges move
to compensate for the induced field, which resides initially between the source and the
gate, and between the drain and the gate. The thickness of the semiconducting film
and short distance between the source and drain in the inaccurate-distance picture
(Figure B-1 top) make it feel intuitive that already-present positive charges in the
semiconducting film move to create the channel, but this is not correct; in most cases,
the charges in the channel are injected by the contacts, in response to the field from
the gate, to compensate for the capacitive charge. Figure B-2 shows a cross-sectional
SEM image of a top-gated FET (experimental details in Chapter 3), which shows the
relatively large distance between the source and drain electrode as compared to the
film thickness.
B.3
Charge injection
The application of a gate bias is performed with reference to a common ground or
with reference to a grounded source electrode. In either case, the gate forms one plate
of an effective capacitor, while the semiconductor is left to perform the role of the
other capacitor plate (with opposite charge). A normal gate voltage of 10 V with an
122
oxide
300 nm
0.7 mm
Figure B-1: Schematic drawing and relatively scaled drawing of a bottom-gated FET.
......
. .......
Figure B-2: Cross-sectional SEM images of a top-gated QD FET.
123
oxide capacitance of -3x10-8 F/cm
2
(SiO2) requires a charge of 3x10-
7
cm- 2 , which
equates to ~2x10 12 electrons or holes per square centimeter on each "plate". These
carriers accumulate next to the oxide and can come either from the semiconductor film
itself or from the electrodes. This latter case is crucial to take into consideration; if
this were not the case, no thin film would be able to produce an "ambipolar" transfer
curve because there cannot exist enough free carriers of both types to compensate
for both VG = +10 V and VG
-10 V; in a 10-nm-thick film with a standard
order of magnitude carrier density of 1x10 16 cm- 3 holes, there are 1x10 10 holes/cm
and far fewer electrons- nowhere near the required 2x10
12
/cm-2,
2
,
and higher gate
voltages are routinely applied. Therefore, when a gate voltage is applied the "n"
value for free carrier density is largely due to free carriers injected into the film from
the contacts. When a positive gate voltage is applied, electrons are injected into (or
holes are extracted from) the semiconductor film. When a negative gate voltage is
applied, holes are injected into (or electrons are extracted from) the semiconductor
film. The existence of a current between the source and drain (or lack thereof) with
a gate bias application is therefore not an indication of the inherent carrier type of
the semiconductor film. Rather, the slope of the transfer curve assumes capacitive
compensation through carrier injection so that field effect mobilities can be extracted
from either channel.
B.4
Importance of Ohmic contacts
Provided the source and drain electrodes make Ohmic contact with the semiconductor
film to assure charge injection, a transistor measurement can provide a trusted fieldeffect mobility value for each channel (n or p depending on the sign of the gate
voltage past the threshold). Prior to any voltage application, the Fermi levels of the
(semiconductor) nanoparticle layer and the source and drain electrode equilibrate.
These should be Ohmic contacts for any further standard analysis to be performed, in
which case there is a thin accumulation region at the semiconductor/contact interface
where there is a high concentration of holes (p-type semiconductor) or electrons (n124
.--.
--
equilibrium -
-------
-
V applied
-
Figure B-3: Band-bending diagram for lateral contacts to a semiconductor and a
uniform electric field resulting from an applied voltage between contacts.
type semiconductor).
Subsequent voltage application can then directly define the
charge density and (uniform) electric field in the semiconductor.
The application of a drain bias with no gate bias should result in a uniform electric
field across the channel (Figure B-3) because the semiconductor should be dramatically more resistive than the contact resistance (assuming good Ohmic contacts).
This is intuitive for the accurate-distance image in Figure B-1; the distance between
source and drain is so large that a semiconductor spanning that distance should dominate the resistance in comparison to the contacts. The current between the source
and drain is linear with source-drain voltage (VDS) at low voltages, and the limiting
aspect of the current is the resistivity of the semiconductor film. At a higher drain
bias, the current saturates as the region next to the drain depletes of carriers and the
depleted region's resistivity limits the current.
B.5
Mobility measurements using FETs
Mobility measurements in FETs are fairly straightforward, provided good Ohmic
contact is made to the semiconducting material. The source-drain current (IDS) is
then:
IDS
+
sWt
(B.1)
where nh is the number of free holes, ne is the number of free electrons, #h is the
hole mobility, p, is the electron mobility, e is the fundamental charge of the electron,
VDS
is the source-drain voltage, W is the device width (the full extended width of the
interdigitated electrodes in the relevant experimental case), t is the film thickness,
125
and L is the channel length (the distance between the two electrodes).
In a particular channel (n or p) past the threshold, the number of free electrons
or free holes, respectively, dominates the current, so the current equation can be
simplified to:
IDS
Wt
=
(B.2)
TtIUCDS LZ
The slope of the source-drain current (see Figure B-4) as a function of gate voltage
(transconductance) is then:
'B -
VGB
'A
__ /1n(B -
VGB -
VGA
eV DSWt
VGA
(B.3)
L
The premise of the mobility measurement is that (past the threshold), the number
of charge carriers in the channel is directly proportional to the gate voltage (VG), as
in a capacitor
(Q
= CV so n = COXVG), where C0 , is the capacitance of the oxide or
dielectric medium separating the gate and the semiconductor, such that:
IB
-
VGB -
IA
VGA
_
LCox(VGB -
VGA)
eVDSWt
Wt
L
L_= MCoxeDS-
VGB - VGA
( B.4)
This result is the transconductance equation referenced in Chapter 3 Equation 3.1.
B.6
B.6.1
Carrier-type characterization
Misinterpretation of FET measurements
The growth of the slope of one channel or the decrease in slope of the other (Figure B-4b), as discussed in Section B.5, is not an indicator of a Fermi level shift in the
semiconductor; as long as the contacts remain Ohmic, this behavior is solely due to
a change in the hole and electron mobilities, not their relative populations. Furthermore, the lack of an n-channel does not translate to the semiconductor being p-type,
or vice versa, but is rather an indicator that current is unable to flow at positive gate
bias. There are many reasons that current could be unable to flow at positive gate
bias including low electron mobility, inability to inject electrons or extract holes from
126
B
Source-Drain
A
Current
Source-Drain
Current
++
+4
**-.,
,
++
*-.,
VG=4
Gaevotg
Source-Drain
Current
Figure B-4: Schematic transconductance data and interpretation.
the contacts, or a large threshold voltage.
A shift in the threshold voltage (Figure B-4c) also cannot be used to determine an
absolute Fermi level because there are too many complicating experimental factors
(e.g. gate work function, gate charging effects, etc.), but some qualitative determinations may potentially be made if great care is taken in the measurement to avoid
gate charging and only relative results are considered.[86]
B.6.2
QD FET mobility variation as a function of contact
metal
As an example of the FET measurements that are incongruous with the concept of
FET carrier typing (a single material cannot be both n-type and p-type), Figure B-5
shows FET transconductance measurements performed on QD thin films treated with
127
0.1% 1,3 benzenedithiol (BDT) in acetonitrile with each gold and titanium source and
drain contacts. When deposited on gold contacts, the QD film has a higher hole mobility than electron mobility, and when deposited on titanium contacts, the QD film has
a higher electron mobility than hole mobility. In both cases the transconductance is
linear in both the n-channel and p-channel, indicating effective charge injection from
both contacts, which is surprising given their dramatically different workfunctions.
All device-geometry and other processing steps are identical (detailed in Chapter 3)
for devices with each electrode type, and gate-source leakage in both cases is at least
an order of magnitude lower than the source-drain current. For the BDT ligand exchange treatment, slightly higher currents flow with titanium electrodes than with
gold electrodes. These behaviors are not fully understood, but may be an indicator
that QD FETs are subject to somewhat different device physics than bulk semiconductor device physics, or perhaps the Fermi level in the QDs is far from either band
edge such that both electrodes have some injection barrier for one carrier.
In QD FETs treated with 10 mg/mL tetrabutylammonium iodide (TBAI) in
methanol, as shown in Figure B-6, both channels have higher source-drain currents
in the gold-electrode device than in the titanium-electrode device. Additionally, the
channels of the TBAI transconductance curves with titanium contacts are definitively less linear than with gold contacts. This is consistent with a picture where the
injection barrier created by gold contacts is smaller than that created by titanium
contacts, whereas in the BDT case the injection barrier may be comparable for the
two electrode types.
B.6.3
Accurate carrier-type characterization
Accurate carrier-type characterization is nontrivial. Hall-Effect measurements[86] can
be accurate provided that the material's carrier mobilities are high enough to provide
electronic signal on the instrument selected with the available magnetic field at the
length scales between electrodes, and that the contacts are Ohmic. Thermopower
measurements[55] can also be accurate, but are notorious for their experimental difficulty, and also require Ohmic contacts.
128
Ultraviolet Photoelectron Spectroscopy
BDT treaatment on Auelectrod sQ
10-6
A
to8 x1
cuu4
010-8
2
0
=-2
5
*
*
0
1F0
*
0
-50
x
LO -
10-8
10-12 -50
50
Linear fit
410
p (hole) = 2 x 10-5
cm 2Ns
19
x
U)
47,
50
p (electron) = 8 x 10-6
cm 2Ns
8
-I
0
Vg
Linear fit
4
-60
-50
-40
Vg
-30
2 11
35
-20
45
Vg
40
50
55
BDT treatment on Ti electrodes
3
x10
10-6
32
1*
0
0
Vg
Linear fit
-50
x
10-8
10712 -50
50
6
p (hole) = 6 x 10~
40 +
cm2Ns
_3.5
2.5
10"7
11
p (electron) = 1 x 10
-
cm2Ns
-o
++
-60
50
x
1.5
+
3
0
Va
Linear fit
LO
I2
+
4.5
+
.8
C
=0.5
-+
-40
-20
0
00
20
40
60
Vg
Vg
Figure B-5: Transconductance of QD FETs treated with 1,3 benzenedithiol with gold
(a) and titanium (b) source and drain contacts. The data are shown on a linear and
log scale, with the leakage current shown on the log-scale plot in gray. The lower
panels show linear fits to the data past a threshold value in each the p-channel and
n-channel.
129
1-
x
LO
TBAI treatment on Au electrodes
6
i
105
1.5.
CA,
*1
cc
*
0.5*
*
0Lo
+
II
U)
-50
0
Vg
Linear fit
10-6
x
*
0-10
10-50
0
-7
Vg
Linear fit
10~
6.
p (electron) = 1 x 10cm 2Ns
4
50
p (hole) = 1 x 10-
1.5
2A
0
30
-
-40
3
0
-20
Vg
0 '
10
40
0
0
50
Vg
=1
I
tO
2
n
0.5
50
TBAI treatment on Ti electrodes
7
10-
x
10- 6
C
210
-8
*0
10-
*
.
22
0)
-50
S i01 2
0
Vg
Line ar fit
x 10~
-50
0
Vg
LO
x 10 7
Linear fit
-L 2
1
p (electron) = 1 x 10~c1.5
m2Ns
p (hole) = 5, (10cm 2Ns
M0. 5
+
W
++
+
-60
50
-50
-4
-30
O.5
*0
-20
Vg
020
+
30
40
50
Vg
Figure B-6: Transconductance of QD FETs treated with tetrabutylammonium diode
with gold (a) and titanium (b) source and drain contacts. The data are shown on a
linear and log scale, with the leakage current shown on the log-scale plot in gray. The
lower panels show linear fits to the data past a threshold value in each the p-channel
and n-channel.
130
(UPS) measurements are also experimentally challenging, but can provide accurate
information about the position of the Fermi level in QD samples[8]. It is not clear
whether the Fermi level obtained from UPS measurements translates directly into
solid-state device physics with electronic contacts. Rigorously functioning Schottky
devices can also provide Fermi-level information if the workfunction of the metal is
well characterized and the absence of Fermi-level pinning or other interface effects
can be guaranteed.
B.6.4
Evaluating Ohmic contacts
It is generally assumed that gold metal (Au) makes Ohmic contact with PbS QDs[47,
103, 127, 16]. There is some logic to this assumption theoretically because the valence
band edge of PbS QDs has been recorded at ~ 5.2 eV[42], which is at the same level as
the gold workfunction, so if the PbS QDs are p-type, the electrode should be deeper
than the Fermi level and form an Ohmic contact. If the PbS QDs are n-type, a poor
contact would be expected from this reported band alignment. Additionally, there
have been several reports of linear current-voltage behavior of PbS QDs between gold
electrodes[16, 121]. These assumptions cannot be universally applied; the linearity of
the current-voltage behavior between gold electrodes is ligand-dependent, the position
of the bands and Fermi level may change as a function of ligand, size, or other
treatment[46, 8], and a Schottky barrier between PbS QDs and gold has also been
reported[70, 33].
Generally the current-voltage behavior of the QD material can be measured in
a lateral architecture, and if the behavior is highly linear in a voltage regime far
surrounding the voltage regime relevant for the final device, it is likely that the
contact can be considered effectively Ohmic.
For this measurement, it is crucial
that the film deposited on the lateral device be deposited and treated as similarly as
possible to the film used in the final device, and if the final device is deposited in a
sufficiently different geometry, it must be assumed that neither the surfaces of the
lateral measurement nor the different electrode deposition in the lateral device have
an effect on the current-voltage behavior[103].
131
Ohmic contacts in lateral architectures at high voltages can produce superlinear
current-voltage behavior in situations where the carrier density of the semiconductor
is low enough that the majority of the carrier density in the material is both injected
and moved by the electric field induced by the electrodes (e.g. space-charge-limited
current). In this case, linear current-voltage behavior is not necessarily requisite for
Ohmic contacts. In the opposite regime, at very low voltages, interface effects may
create a barrier to injection that manifests as a threshold voltage after which there is a
current onset, though after that onset the current-voltage behavior may be linear. For
this reason, it is important to evaluate the linearity of the current-voltage behavior
in the regimes surrounding that relevant for the device function. More ideal would be
a more rigorous test for Ohmic contacts, but the existence of a linear current-voltage
curve is more informative than an assumption alone.
B.7
Chapter-specific acknowledgments
Patrick Brown provided expertise on UPS measurements.
Joel Jean contributed
knowledge of bulk semiconductor FET functionality and performed cross-sectional
SEM imaging for Figure B-2.
132
Appendix C
Photoluminensce as a Metric for
Functioning Electronic QD Devices
C1
Introduction
Measuring important electronic quantities in QD devices often requires separate device architectures (e.g. interdigitated electrodes for conductivity, FET structures for
mobility measurements), and very few measurements can be performed in a meaningful way on the finished device architecture. One of the reasons for this limitation
is the presence of many components or layers in a full device, such that it is difficult to distinguish properties of the QD material from properties of the interfaces
or a particular combination of components. In this chapter, a full-functioning-device
photoluminescence-based characterization method is performed and the results are
analyzed.
C.2
Steady-state photoluminescence
C.2.1
Increased PL with voltage in PV architecture
The steady-state photoluminescence (PL) of a simple device architecture (ITO-PbS
QDs-PCBM-Al, where PCBM is phenyl-C61-butyric acid methyl ester) was observed
133
a)
b)
1200
1000
Reverse bias
positve
100More
Forward Bias
Equilibrium
-V
-=
voltage
=V
000
4001
0)
20 0 2,
6
40020
W g
N 0.4
0
*00
30.1
0
)g
0
m
900
1000
1100 1200 1300 1400
Wavelength (nm)
1500
1600
in
-2
= 0.67, offset
rSlope
-1.5
-1
-0.5
Voltage (V)
0
a0.79
0.5
1
Figure C-i: a) Steady-state PL spectra for a QD-PCBM device with applied voltage
showing the lack of peak shift and the increase in counts with increasing voltage.
b) Plot of the peak PL counts as a function of applied voltage. The inset shows
schematic band diagrams of a p-n junction in reverse bias, at equilibrium, and in
forward bias.
as a function of applied voltage. Applying a positive bias to bring the device in
the direction of forward diodic current resulted in a higher number of PL counts,
and applying a negative bias resulted in a lower number of PL counts. In neither
case did the peak location shift, and the simultaneously measured current did not
deviate from the previously measured current-voltage (IV) data acquired without
PL measurement. Figure C-ia shows the steady-state PL spectra for a QD-PCBM
device with applied voltage. If the counts at the PL peak are plotted as a function
of applied voltage (Figure C-1b), there are three distinct slopes. These slopes were
hypothesized to correspond to the electric field penetration into the film in three key
regimes, illustrated in schematic band diagrams in Figure C-1c.
The application of negative voltage in a p-n junction extends the electric field
further into the semiconducting film, and the opposite is true for positive voltage
(forward bias). The trends in these data are not significantly affected by increased
flux (Figure C-2).
In the case where the presence of an electric field in the semiconducting film
makes exciton splitting more likely, thereby reducing the probability of radiative
recombination of that exciton, one would expect a decrease in PL counts as the
134
3.5
3.5 x 106
-
Applied voltage
3
0
3
2.-2
0
o
0.3
0
2
0
a'
M-1
2.5
-0.5!
-1.51.
010
0.5
800
900
1000 1100 1200 1300 1400 1500 1600 1700
Wavelength (nm)
-2
1.5
-1
0
-0.5
Voltage (V)
0.5
1
Figure C-2: PL data and PL peak data as a function of applied voltage for a higher
flux of ~2.6 mW. A routine flux is ~212 uW.
voltage becomes more negative and the electric field penetrates further into the film
and the quasi-neutral region (QNR) gets smaller. A simulation of the QNR thickness
from 0 V to 0.3 V is shown in Figure C-3.
To further this hypothesis, at a large positive bias, the PL signal should saturate
because the depletion width should be small and unchanging. In high forward bias
where there is significant charge injection, the PL counts may be expected to increase
if injected carriers recombine at the band edge and yield a PL signal in addition to
excitonic recombination.
At a large negative bias, the PL signal should reach zero because the electric field
should extend throughout the film to maximize exciton splitting.
Given the latter portion of the hypothesis, it is surprising that the peak PL intensity of the reverse-biased devices is only -1/3 of the peak PL intensity in forward bias.
This suggests that either the depletion/QNR hypothesis is incorrect, or that there
are "dead regions" in the QD film that are somehow electronically isolated from the
field in the QD film. In an attempt to observe dead regions on a microscopic length
scale, a functioning device was observed with an IR microscope.
The microscope image (Figure C-4) of a section of the device at short circuit does
show variation in PL intensity across the film. The intensity linecut (Figure C-5)
across the image, however, shows that this intensity variation is too small to account
135
100
90
80
E
C
70
0
60
0
50
z 40
a
30
20
10
U
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
Applied Voltage
Figure C-3: Simulated QNR thickness in nm from 0 V to 0.3 V applied bias. In this
simulation the film thickness is 90 nm, the dielectric constant of the film is 15, the
built-in bias is 0.3 V and the effective doping density is 10
17
cm-3.
Figure C-4: IR microscope image of a PbS QD-PCBM device in short circuit.
136
70,000
C
0
U
w
C
w
U
50,000
0 -
w
C
0
S.
.1
%
30,000
*
5
5
4
.%~I
,
S
1.
W
*04 0 0 04%
set
eve r0
%J160e
4.2
00 00
0 0
0
0
%
41%
0 000
V-0- A.A-
0
0
0
I
0
0
0~
*
qb
0
Figure C-5: Intensity linecut and related image section from Figure C-4. The vertical
line indicates the edge of the patterned ITO.
Figure C-6: Transmission (left) and reflection (right) images of the device. The
vertical line is the edge of the patterned ITO (right). The small black box shows the
portion of the image that corresponds to the intensity image in Figure C-4.
137
9000
8000
7000
6000
5000
CL
4000
0-
3000
2000
1000
0
-3
-2
0
-1
1
2
Voltage (V)
Figure C-7: Steady-state PL measurements for the stacked capacitor geometry with
(pulsed) applied bias up to -2 V and + 2 V. Integration time was 1 s.
for the hypothesized 1/3 "dark" portion of the film at least to the resolution of the
pixels in the microscope. The intensity variation is also insignificant over the border
from glass to ITO substrate (vertical line in Figure C-5), and does not appear to
correlate with physical "spots" or features on the film, as measured by reflection and
transmission imaging (Figure C-6).
C.2.2
Consistent PL with voltage in capacitive architecture
To more directly probe the PL effects of an electric field, the PL was measured during
voltage application for a stacked capacitor (ITO-HfO 2 -PbS QDs-parylene-Al). With
pulsed applications of voltages up to 2 V (translating to a voltage drop of solar-cell
magnitude across the QD film), no PL increase or decrease was observed (Figure C-7).
Furthermore, no changes were observed in the continuous application of voltages up
to -20 V and + 20 V (Figure C-8). This result suggests that the PL changes are not
due to an electric field across the film.
138
2000
1500
1000
500
0
>~
-505
100
600
50
400
200
Scan
0 0
Pixel
-20 V
2000
1500
1000
I0,
500
I
0
';
I
''
-500.
100
'V
600
50
400
200
Scan
0 0
Pixel
+20 V
2009
1500
100
oV
500,
V
-50Q
100
600
400
200
Scan
0 0
Pixel
Figure C-8: Multiframe steady-state PL measurements for the stacked capacitor geometry with (top) no applied bias (middle) continuous applied bias from 0 to -20 V
(bottom) continuous applied bias from 0 to +20 V. Integration time was 200 ps. No
effect of voltage application is observable.
139
C.3
Lifetime invariance with voltage
The previously stated hypothesis of electric field penetration splitting excitons is that
there are two radiative lifetimes: one short (in the depleted region) and one long (in
the QNR). To further test this hypothesis, the time-dependent PL was measured on
the functioning PV device as a function of voltage. Two simulations of the expected
signal are shown in Figure C-9. Figure C-9a shows the expected counts as a function
of time for an increasing depletion width from 0-100 nm where the short lifetime is 1
ns and the long lifetime is 10 ns. This 10-ns value is much shorter than the observed
1-ps lifetime of PbS QDs in solution, and it is estimated from the lifetimes of PbS QD
films on glass measured and discussed in Chapter 3. The input quantum yield (QY)
of the depleted region is 1/10th of the quantum yield of the QNR (the same as the
ratio of their lifetimes), which results in the t=0 counts being equal, but this is not
true for all input QY values. Using the two lifetime values (1.7 ns and 13.2 ns) from
a biexponential fit of the data in Chapter 3 for this same ligand exchange treatment
(10 mg/mL TBAI in methanol), and if the quantum yield of the short-lifetime region
is 1/100th instead of 1/10th that of the QNR, the change in the relative lifetimes
is harder to see and it shows up more as a loss of total signal than as a change in
relative lifetime, as seen in Figure C-9b. It is worth noting that this simulation applies
a single short lifetime throughout the entire depletion region, which is not necessarily
accurate because the lifetime may be a function of electric field and the electric field
in the depletion region is not constant (see Chapter 1 Section 1.1.4).
Time-dependent PL measurements were taken using a system like that described
in Correa et al. [18] with a superconducting nanowire detector at MIT Lincoln Laboratory. The normalized raw data are shown in Figure C-10. There is no observable
difference in the lifetimes as a function of voltage, which is counter to the expectation
formed by the hypothesis and shown in Figure C-9.
Processing these raw data with 4-channel averaging and background subtraction,
which is feasible because the noise is flat at long times, extends the observable signal
to longer times. Figure C-11 shows processed and normalized data from two devices
140
1) 9
b) 109r
b) io~
a) ~
0
0-
0 1
10 7
5
Time (ns)
10
10 8
1071.
0
5
5
lime (ns)
10
15
Figure C-9: Simulated counts as a function of time for a functioning device with
increasing depletion region from 0-100 nm. In a), the short lifetime is 1 ns and the
long lifetime is 10 ns and the input quantum yield of the depleted region is 1/10th of
the quantum yield of the QNR. In b) The lifetime values used (1.7 ns and 13.2 ns)
are those extracted from the biexponential fit to the data in Chapter 3 for this same
ligand exchange treatment (10 mg/mL TBAI in methanol), and the quantum yield
of the short-lifetime region is 1/100th instead of 1/10th that of the QNR. In b) the
change in the relative lifetimes is harder to see and it shows up more as a loss of total
signal than as a change in relative lifetime than in a).
on two different days (left panels and right panels) at OV, -2 V, and +2 V. These
curves deviate in their longer-time components at different voltages. The left panel
shows greater deviation than the right panel, but the trend is the same for both
measurement sets. To view the curve deviation more clearly as a function of voltage,
the normalized PL intensity is plotted at each voltage for a series of different time
points (Figure C-11 lower panels). A larger negative voltage does reduce the PL decay
time, as predicted, and a larger positive voltage does increase the PL decay time, if
only slightly. The extent of deviation is far less significant than predicted, and not
consistent enough to report quantitatively.
The variation in PL intensity at V=0 suggests that performing the measurement
might have an effect on the lifetimes measured; a "burn-in" process may occur such
that the lifetime changes initially upon exposure to the pulsed laser and then becomes
stable, or the excitation flux may irreversibly affect the film. A power-dependence
was performed at 0 V (Figure C-12) to evaluate the effect of excitation flux. These
141
Applied voltage (V)
100
__-2
0
0.1
0.25
0.5
W,
N 10-1
2
__2.5
C
-_
3
0
10-2
C
J
I II
10- 3
0
|. .
,
, |II[IiIIU
2
6
8
10
12
Time (ns)
4
14
16
I
I[
18
Figure C-10: Normalized raw data counts as a function of time for a range of applied
voltage from -2 V to +3 V (legend shows applied voltage). The data were collected
at 1 MHz with 200 uW flux. There is no observable difference in the lifetimes as a
function of voltage.
100
k
100
N.
0
C
0
2
O0 V
lv
hkWL_
4C
Ca
-J
+2 V
0V
.2
2V
0
I
I.
+2V
1
0
5
10
15
20
Time (ns)
25
30
0
5
10
20
15
Time (ns)
25
Figure C-11: Processed and normalized data from two different days and spot locations for several voltages. These curves deviate in their longer-time components at
different voltages. The left panel shows greater deviation than the right panel, but
the trend is the same for both measurement sets.
142
100
UW
M1
10-1
102
3 uW
10
-3
uW
10
10 Uvv
10
10
1-5
102 uW
10 -
0
50
Time (ns)
Figure C-12: Power-dependence at V
100
150
0 on a functioning PV device.
results show a faster PL decay for the 102 pW flux than for flux values at or below 10
puW, and may implicate multiexciton behavior in the early-time regime, but should
not extend to the voltage-dependent differences at -20 ns.
C.4
Device encapsulation and testing experimental details
PV cells were fabricated as detailed in Chapter 3 with 10 mg/mL TBAI in methanol
for the ligand exchange. The devices were pretested prior to external electrode application. External electrodes consisted of thin strips of copper tape adhered to the
ITO and aluminum pads with two-part silver epoxy (Epotek EE129). The device with
attached external electrodes was heated in a ceramic oven in a glovebox at ~70'C for
30-60 minutes to cure the epoxy, after which the device was retested to assure that the
attachment of external electrodes did not affect its performance. The device was then
placed electrode-side down onto a 1"x3" microscope slide and the edges were coated
with a viscous, partially cured two-part epoxy (Parbond 5105 from McMaster-Carr).
143
The sealant epoxy was afforded several minutes to cure, and the device was again
retested to assure no device performance change. The mounting microscope slide
was clamped into an optical NIR-spectrometer setup, and brought into focus. The
excitation source was a 532-nm cw laser passed through filters to reach the power
levels specified in the text. The detector was an InGaAs array detector cooled by
liquid nitrogen. Bias was applied to the device using a Keithley 2636A or Keithley
2400 multimeter. To collect data, the bias level was manually "pulsed", meaning that
the bias level was set on the multimeter but not applied, then in quick succession,
the button was pressed to apply the bias, data collection was initiated (with an integration time of 2 s or less), and after data collection finished the bias was removed.
This process took place for each voltage, except where indicated that the voltage
was "continuously applied", in which case the application of bias was not removed
between measurements and the value of the applied bias was changed continuously.
C.5
Conclusions
The steady-state photoluminescence of a functioning PbS-QD device varies as a function of applied voltage; increasing positive bias results in a higher PL signal and
increasing negative bias results in a lower PL signal, and neither the shape nor location of the PL peak varies with voltage. The intensity varies with three distinct
slopes, which are potentially correlated to regimes of device functionality. The relatively high value of PL counts at high negative bias shows that the PL process is
not terminated at high fields in the device, whether because of sections of the film
isolated from the field, or otherwise. IR-PL microscope imaging of the device in short
circuit does not identify bright patches on the 10s-of-pm scale that explain this high
PL at negative voltage.
Photoluminescence of a functioning PbS-QD device does not correspond with variation of depletion width with voltage using time-dependent fluorescence as a metric.
Though some deviation between positive and negative bias is seen, the deviation is
small compared with the expected amount, and the results are not consistent enough
144
to report quantitative values. It is possible that the PL-relevant device physics take
place only at much lower flux values, that the exciton dissociation is not strongly
affected by electric field, or that the quantum yields of the radiative processes are so
drastically different that these measurements only observe one process.
C.6
Chapter-specific acknowledgments
Thomas Bischof was instrumental in the collection of the time-dependent PL measurements at Lincoln Labs. Mark Wilson contributed the MATLAB code for timedependent PL 4-channel averaging, background subtracting, and smoothing, which
enable long-time signals to be seen because the noise is flat.
145
146
Appendix D
Nanopatterned Electrically
Conductive Films of
Semiconductor Nanocrystals
Sections of this chapter are reprinted with permission from Mentzel, Wanger, Ray,
Walker, Strasfeld, Bawendi, and Kastner, Nano Lett., 2012, 12 (8), pp 4404-4408.
Copyright 2013 American Chemical Society.1
Abstract
We present the first semiconductor nanocrystal films of nanoscale dimensions that
are electrically conductive and crack-free. These films make it possible to study the
electrical properties intrinsic to the nanocrystals unimpeded by defects such as cracking and clustering that typically exist in larger-scale films. We find that the electrical
conductivity of the nanoscale films is significantly higher than that of drop-cast, microscopic films made of the same type of nanocrystal. Our technique for forming
the nanoscale films is based on electron beam lithography and a lift-off process. The
patterns have dimensions as small as 30 nm and are positioned on a surface with
30-nm precision. The method is flexible in the choice of nanocrystal core-shell materials and ligands. We demonstrate patterns with PbS, PbSe, and CdSe cores and
Zno.5 Cdo.5 Se-Zno.5 Cdo.5 S core-shell nanocrystals with a variety of ligands. We achieve
unprecedented versatility in integrating semiconductor nanocrystal films into device
structures both for studying the intrinsic electrical properties of the nanocrystals and
'This work was performed in close collaboration with Tamar Mentzel, Nirat Ray, Brian Walker,
Dave Strasfeld, Moungi Bawendi, and Marc Kastner.
147
for nanoscale optoelectronic applications.
D.1
Introduction
The tunable electronic and optical properties of semiconductor nanocrystals and their
low-cost solution processing make them attractive building blocks for designer solids
and for various optoelectronic applications. However, it is only with nanoscale control of their assembly and placement on a surface that nanocrystal solids can be used
for nanoelectronic and nanophotonic circuits,[87] LED nanodisplays, [53, 7] diffraction
gratings,[99] and the capture and detection of individual biomolecules. [91, 20] Moreover, crack- and cluster-free nanocrystal films that are integrated into devices with
nanoscale precision open the possibility of studying the nanoscopic electronic dynamics of these artificial solids. Investigating charge transport in the localized states of
the nanocrystals is important for their application in optoelectronic devices and more
generally for acquiring a deeper understanding of charge transport in localized electronic states, which arise in technologically important materials such as amorphous
semiconductors, organic materials, and semiconductor nanostructures. Finally, eliminating structural defects in the films, such as cracks and clustering, and their effect on
charge transport is an essential step toward realizing a nanocrystal solid that exhibits
the predicted charge correlations. [83] Prior methods for assembling nanocrystals into
patterned structures on a substrate fall into three main categories.
The first en-
tails functionalizing the nanocrystals with a ligand to control the interaction between
the nanocrystals and a surface. For example, nanocrystals can be photopatterned
by functionalizing them with a photosensitive ligand that renders them insoluble
when exposed to ultraviolet light. [48, 69, 90] Another example is by Tsuruoka et al.
who immobilized nanocrystals on a surface by functionalizing the nanocrystal with
a ligand that binds to the substrate.[115] These techniques do not form close-packed
films, and the patterns are limited to microscale resolution. A second method uses
a nanopatterned template that guides the assembly of the nanocrystals. Son et al.
nanopatterned a block copolymer thin film and assembled nanocrystals in the grooves
148
on the surface of the polymer film.[101] Another related technique takes advantage
of capillary forces to drive nanocrystals into trenches etched into a substrate[19] or
in a polymer film.[29] These techniques attain nanoscale control over the formation
and placement of the nanocrystals on a specialized surface but do not allow the integrated device fabrication necessary for the aforementioned applications. A third
class of patterning techniques is printing: microcontact printing,[53, 99, 37] inkjet
printing, [111] and nanoimprint lithography of a nanocrystal-polymer composite. [108]
Microcontact printing achieves nanoscale patterns, but it is highly sensitive to the
chemical compatibility of the nanocrystal solution, the stamp, and the substrate; the
nanocrystals must preferentially adhere to the substrate over the polymer stamp,
which tends to exclude prevalent device surfaces like silicon dioxide ostensibly because its hydrophilicity is incompatible with hydrophobic ligands. Moreover, stamps
offer only limited control over the placement of the pattern onto the surface. Inkjet
printing eliminates the constraints on chemical compatibility that exist with a stamp
but at the cost of pattern resolution because droplets are 50-100 pm in size. The
challenge remains to form nanoscale films of semiconductor nanocrystals that can
be integrated into a device structure with nanoscale precision.
An additional re-
quirement of nanocrystal films for many of the aforementioned applications is that
they be electrically conductive and free of structural defects such as cracks and clusters. When nanocrystals are drop-cast onto a surface, they tend to form clusters as
shown in Figure D-1b. Experiments by Mics et al.[73] indicate that when clustering
is present, the measured conductivity of nanocrystal films differs from the intrinsic conductivity of the nanocrystals. As such, clustering diminishes the efficiency of
charge transport in nanocrystal films in optoelectronic and other device applications.
It also makes it impossible to study the charge dynamics intrinsic to the nanocrystals
and is thus a barrier to realizing nanocrystal-based designer solids. In addition to
clustering, cracks in the films can be a compounding problem. The electrical current
in drop-cast nanocrystal films is typically immeasurably small because the electronic
coupling between nanocrystals, as determined by the size of the native capping ligand,
is weak.[71, 25, 107, 128] To increase the coupling strength of the nanocrystals, either
149
the film is annealed[71, 64, 123] or the native capping ligand on the nanocrystal is
exchanged for a smaller molecule by immersing the film in a solution containing the
smaller molecule.[107, 94, 45] In both of these approaches, there is a strong driving
force that creates cracks in the film, adding to the structural defects. (Figure D-1c
shows an annealed film.) Despite the clusters and cracks, it has been possible to study
charge-transport in these films because current may flow through a continuous pathway that connects the clusters; or, a second layer of nanocrystals can be deposited
to fill in the voids between clusters.[107] All studies of charge transport that we are
aware of have been performed on films of micrometer dimensions or larger and involve annealing or a ligand exchange, which makes it likely that structural defects are
influencing the transport properties. Eliminating structural defects is important for
investigating the intrinsic charge transport properties and for optimizing the transport efficiency in micrometer-scale films or larger. When voids of the order of tens
or hundreds of nanometers arise in nanopatterned films, a complete break in the film
can make it impossible for charge to flow at all. In this work, we present semiconductor nanocrystal films of nanoscale dimensions that are electrically conductive without
clustering or cracks.
D.2
Technique
To assemble the nanocrystals into nanoscale patterns, we use electron-beam lithography followed by nanocrystal deposition and lift-off. The technique uniquely combines
the following characteristics: nanocrystal films with features as small as 30 nm; controlled placement of nanocrystal films onto a surface or into a device structure with
nanoscale precision
(~
30 nm); flexibility in choice of nanocrystal core material, lig-
and, and solvent; flexibility in the choice of substrate; and structurally continuous
films with a measurable electrical current. We perform electrical measurements of
these nanopatterned films comprised of PbS nanocrystals and find that the electrical conductivity is significantly higher than what is found in larger-scale films. The
nanoscale size of the film is essential to eliminating defects so that we can measure
150
(a)
Nanocrystals
(b)
2 pm
(d)
(c)
2pim
2 im
Figure D-1: (a) Schematic of nanocrystals drop cast on an inverted FET device
(side view). (b) Scanning electron micrograph of a PbSe nanocrystal film drop cast
on an inverted FET device (top view; the gold electrodes, which are beneath the
nanocrystal film and thus obscured from view, are outlined in orange), and (c) after
annealing the film for one hour at 400 K. (d) When the thickness of the film exceeds
approximately 1 pm, cracks emerge as the film dries, namely as solvent interior to
the film evaporates and diffuses to the already dry surface. Cracking and clustering
diminish the efficiency of charge transport in nanocrystal films and make it impossible
to study the charge dynamics intrinsic to the nanocrystals.
151
the intrinsic electronic properties of the nanocrystals.
The following describes the process for forming electrically conductive, crackfree nanocrystal films of nanoscale dimensions. Here we discuss the preparation of
PbS nanocrystal films, (Figure D-2) and the same approach holds for films of other
types of nanocrystal. We choose silicon dioxide as a substrate on which to pattern
the films because of its prevalence in a variety of device applications. On a substrate approximately 5 mm x 5 mm, we spin coat a 100-nm thick layer of positive
resist, poly(methyl methacrylate) (PMMA), for electron-beam lithography. We pattern nanoscale trenches in the PMMA of arbitrary shape and size as small as 30
nm. The next step is to drop cast nanocrystals into the nanopatterned trenches. PbS
nanocrystals are prepared by high-temperature pyrolysis of Pb and S precursors in an
oleic acid/octadecene mixture.[102, 133] Before drop-casting, we process the growth
solution to remove remaining salts and byproducts and to exchange the native capping
ligand for a smaller molecule. Exchanging the capping ligand while the nanocrystals
are still in solution is critical for making films with a measurable current and free of
the cracks caused by annealing or by exchanging the ligand once the film is formed.
Processing occurs in the nitrogen environment of a glovebox according to a modified version of a previously reported method. [94] A mixture of methanol and butanol
is added to the solution to precipitate the nanocrystals. The sample is centrifuged
to collect the nanocrystals and the supernatant is discarded. The nanocrystals are
redissolved in hexane and are precipitated a second time in a mixture of methanol
and butanol and redissolved in a solution of n-butylamine. After stirring the solution
for approximately 72 h, the native oleic acid ligand (~
replaced with n-butylamine
(~
1.8 nm long) is completely
0.6 nm long).[57, 103] The nanocrystals are precipi-
tated a third time with isopropanol, redissolved in a 9:1 hexane/octane mixture, and
passed through a 0.1 am filter. In Figure D-2, transmission electron micrographs
(TEM) of a monolayer of PbS nanocrystals before and after exchanging the ligand
reveal decreased inter-nanocrystal spacing with the n-butylamine cap, as expected.
Drop-casting the nanocrystals into the trenches and lift-off are performed in the
glovebox. We tune the concentration of nanocrystals in solution to -2-85 pmol per
152
I
7 nm Long native
Electron
Beam
Lithography
ligand is
replaced
with a shorter
Immerse
liaand
in solution
with ligand
at 100 C
Dropcast
7 nm
Nanocrystals
Liftoff
and
Sonication
Figure D-2: (Left and center) An overview of the process for patterning nanoscale
films of semiconductor nanocrystals. The patterns are positioned on the surface of the
substrate with nanoscale precision. To achieve electrically conducting films without
cracking the film by annealing or exchanging the capping ligand for a smaller molecule,
we exchange the capping ligand while the nanocrystals are still in solution prior to
deposition. (Right) Transmission electron micrographs of the nanocrystal films before
and after cap exchange.
153
liter. We drop cast 1 puL of this solution on the surface and allow it to dry for 10
min. For lift-off, we put the substrate into a vial of acetone to dissolve the remaining
PMMA, leaving a 50-nm thick film of nanocrystals on the substrate whose shape is
defined by the pattern in the PMMA. In traditional lift-off processes, care is taken to
avoid depositing the film on the sidewalls of the PMMA. In contrast, in our process
the hydrophobic ligands on the surface of the nanocrystals have an affinity for the
PMMA and coat the sidewalls of the trenches patterned in the PMMA. To ensure
that the nanocrystal film tears cleanly at the boundary of the patterns, we sonicate
the substrate in the vial of acetone for three seconds. Longer sonication times may
cause tears in nanoscale features of the film.
The resulting films are robust and remain bound to the surface even when immersed in nonpolar solvents like hexane or octane in which the nanocrystals are
normally soluble. We hypothesize that during the lift-off process, acetone removes
the ligands from the surface of the nanocrystals on the outermost layer of the film
rendering the film insoluble. We speculate that the ligand is being removed from only
the top layer because the nanopatterned films fluoresce (as shown in Figures D-7 and
D-8), which would not be the case if the ligands were absent.
D.3
Detailed patterning process
The following is a detailed description of the process for forming electrically conductive, nanoscopic films of n-butylamine-capped PbS nanocrystals that are approximately 50-nm thick. This process is flexible and can be used to make films from a
variety of nanocrystal core materials, shell materials and ligands. For example, we
have demonstrated patterns with PbSe, CdSe and Zno. 5 Cdo.5 Se-Zno. 5 Cdo.5 S core-shell
nanocrystals, capped with ligands including n-butylamine, oleic acid, and phosphonic
acids. We can also tune the process to produce films that range from 20- to 150-nm
thick with lateral dimensions 30 nm to 1 mm, primarily by changing the solution
concentration and resist thickness.
154
1. A silicon dioxide wafer 5 mm x 5 mm is cleaned by soaking it in acetone for 10
minutes, rinsing it with methanol and DI water, and blowing it dry with nitrogen.
2. To remove water from the surface of the wafer, it is placed on hotplate set to
180'C with a glass lid on the wafer to ensure thermal equilibration between the wafer
and the hotplate.
3. We spin a resist for electron-beam lithography on the wafer. We use MicroChem's poly(methyl methacrylate) (PMMA) 950A2 (2% of a 950,000 molecularweight resin dissolved in anisole).
We spin the resist at 6000 rpm for 1 minute,
and postbake the wafer on a hotplate set to 180'C for 90 seconds while covered with
a glass lid. We spin a second layer of PMMA 950A2 at 6000 rpm for 1 minute, and
postbake it on a hotplate for 2 minutes. The resulting PMMA stack is approximately
100-nm thick.
4. With electron-beam lithography, we pattern trenches in the resist with features
as small as 30 nm. We write with the electron beam set to 30 keV, the aperture set
to 30 mm, and a dose that varies depending on the feature size. After writing the
pattern with the electron beam, we develop the wafer in 1:3 MIBK:IPA for 1 minute,
rinse with IPA, and blow dry with nitrogen.
5.
We synthesize and process PbS nanocrystals according to the method de-
scribed previously. The nanocrystals are precipitated once quickly after synthesis
and are stored in hexane until prior to experimentation. After the ligand-exchange
treatment is performed and the ligand-exchanged nanocrystals are purified with the
isopropanol precipitation, we redissolve them in hexane. We dropeast the nanocrystals to form the patterns as soon as possible after passing them through a filter in
the final step of the processing, and ideally within the same day. If the n-butylaminecapped nanocrystals are stored in solution for an extended period, the ligands will
detach from the nanocrystals and the nanocrystals will agglomerate.
155
When drop
casting agglomerated nanocrystals, either clumps appear in the in the resulting film
(Figure D-3) or the patterns may wash off of the substrate during the lift-off process.
To slow the rate at which the n-butylamine ligands detach from the nanocrystals,
make the solution as concentrated with nanocrystals as possible (about 30-60 mg of
nanocrystals per mL of a 9:1 hexane:octane mixture) and pass it through a 0.1-mm
filter before drop-casting. These conditions may enable storing the solution for more
than one day. On the other hand, the most flexibility with timing exists in the step
prior to the third precipitation; the nanocrystal solution can be left stirring in nbutylamine for longer than 72 hours if necessary (up to at least several weeks if no
solvent loss takes place).
6. Drop-casting the nanocrystals is performed as described previously. To measure the concentration of nanocrystals in solution, we take a sample of the nanocrystal
solution out of the glovebox and measure its optical absorption. We tune the concentration to ~ 85 mmol/L and use a micropipette to drop cast 1 mL of solution on the
5 mm x 5 mm substrate to form a 50-nm-thick film. The thickness of the film approximately scales with the concentration of nanocrystals in solution. The thickness
of the film can vary slightly for patterns that have differing lateral dimensions even
though they are made with an identical nanocrystal solution. Specifically, the film
tends to be thicker as the pattern is made smaller. (We find a 10-20% variation in
thickness among features that vary in size from 30 nm to 1 mm .) We postulate that
when the drop-casted nanocrystals coat the sidewalls of the trenches in the PMMA,
the film tends to be thicker along the edges of the pattern compared to the center (as
seen in the AFM images in D-7(c)). As the pattern is made smaller, the edge effect
becomes more pronounced, thereby forming a thicker pattern.
7. Lift-off is performed as described in the text. Sonication during lift-off ensures
that the films tear cleanly at the edges of the patterns.
D-5(a) shows the results
without this sonication step. On the other hand, even minimal sonication can tear
some delicate features in the patterned film. Squirting the film with acetone is a
156
gentler alternative to sonication.
8. After lift-off, the substrate is soaked in a vial of isopropanol to clean off the
acetone residue and then left to dry in the nitrogen environment of the glovebox.
Allowing the isopropanol to evaporate while the substrate sits flat on a surface can
also leave a residue. Instead, we hold the substrate with tweezers so that the isopropanol runs to the edge of the substrate before evaporating. A kimwipe can be
used to wick the solvent from the edge of the substrate. When we make patterns in
PMMA less than 50-nm thick, a residue of nanocrystal aggregates tends to remain on
the surface surrounding the pattern after lift-off. In this case, squirting the substrate
with acetone and isopropanol after lift-off and blowing the surface dry with nitrogen
can eliminate the residue. When possible, we avoid using a nitrogen gun because its
force can tear the edges of the patterns.
9. If performing electrical measurements on the patterns, the substrate is mounted
onto a chip carrier with silver epoxy that cures at room temperature in the glovebox.
After the epoxy dries (24 h), the patterns are exposed to air for wire bonding. We
aim to limit the air exposure to ten to fifteen minutes while wire bonding, and then
load the chip carrier into a crysostat for measurement.
D.4
Patterns and their properties
In Figures D-6, D-7 and D-8, we show films made from PbS nanocrystals with nbutylamine ligands, PbSe nanocrystals with oleic acid ligands, CdSe nanocrystals
with phosphonic acid ligands, and Zno.5 Cdo.5 Se-Zno.5 Cd0 .5 S core-shell nanocrystals
with phosphonic acid ligands. In Figure D-8b, the nanoscale pattern of nanocrystals
is placed with nanoscale precision relative to a nearby transistor gate. Our patterns
are as small as 30 nm in size (Figure D-8c).
By adjusting the concentration of
nanocrystals in solution, we are able to tune the thickness of the nanocrystal pattern
from 20 to 150 nm thick.
157
Figure D-3: Optical micrographs of a cracked film of patterned n-butylamine-capped
PbS nanocrystals on a silicon dioxide surface.
Figure D-4: Films made with nanocrystals from which some of the capping ligands
have detached while the nanocrystals were in solution and the nanocrystals agglomerated.
158
Figure D-5: Optical micrographs of patterned n-butylamine-capped PbS nanocrystals
on a silicon dioxide surface for patterns processed without the sonication step.
Figure D-6: Crack-free patterns that are fabricated according to the process outlined
above.
159
200 nm
100nm
0 nm
1000
nm
60 nm
30 nm
0 nm
250 nm
125 nm
Onm
Figure D-7: Nanopatterned films of CdSe nanocrystals (first and third rows) and
Zno. 5 Cdo.5 Se-Zno
0 5 Cdo.5 S core-shell nanocrystals (second row). (a) Scanning electron
micrograph, (b) fluorescence (actual color), and (c) AFM images.
160
(a)
(b)
Transistor
Gate
PbS Nanocrystals
380 nm
(C)
380 nm
200 nm
CdSe Nanocrystals
30 nm
Figure D-8: We demonstrate the flexibility in choice of nanocrystal materials by patterning films from (a) PbSe nanocrystals capped with oleic acid, (b) PbS nanocrystals
capped with n-butylamine, and (c) Zno. 5 Cdo. 5Se-Zno. 5 CdO.5 S core-shell nanocrystals
capped with phosphonic acids. In (b), the PbS nanocrystal film is patterned to a
nearby transistor gate with nanoscale precision. All of these images are scanning
electron micrographs except in (c) where we show both green fluorescence and an
electron micrograph indicating that the size of the pattern is only about 30 nm.
161
To measure the electrical conductance of the films, we pattern a nanocrystal film
approximately 130 nm thick (~ 22 monolayers) between two gold electrodes, as shown
in Figure D-9a. The pattern is 350 nm wide at its narrowest point, and from the
current-voltage characteristic, which is fairly linear and assumed to be Ohmic at low
voltages (Figure D-9b), we find the zero-bias conductivity to be 17 pS/cm. We pattern
a second film that is rectangular with dimensions 50 nm thick, 2 pm wide, and 1 pm
long and find that the conductivity is equal to that of the first film. To compare the
conductivity of the patterned films with drop-cast, microscopic films, we fabricate
device structures of the kind illustrated in Figure D-la and drop cast on them the
same PbS nanocrystals with an n-butylamine capping ligand. The morphology of the
resulting films is as shown in Figure D-lb. We measure one film that is 300 nm thick,
800 pm wide, and 2 pm long and two that are 40 nm thick, 800 pm wide, and 2 or
5 pm long. We plot the conductance versus the dimensions of the films in Figure D9c. The conductivity o- is calculated from the relationship G = or
where G is the
conductance, I is the length, t is the thickness, and w is the width of the film. The
plot illustrates that the conductivity of the crack-free, nanopatterned films is higher
than the conductivity of the unpatterned, drop-cast films, which exhibit structural
disorder.[73] The conductivity of the unpatterned, microscopic films is approximately
0.09 pS/cm, which is lower than in the nanoscopic films. By eliminating the clustering,
the conductivity in semiconductor nanocrystal films is significantly higher.
Another technological benefit of our method for forming nanoscale films is that we
are able to remove the patterned films from the substrate and to recycle the substrate
if necessary. By submerging the substrate with the film in a solution of 19:1 octane/nbutylamine and heating it to 100 'C overnight, the films dissolve into the solution. We
chose octane as a solvent because its boiling point (125 'C) is higher than that of other
commonly used solvents like hexane (boiling point of 68 0C), and the solution does
not evaporate when we raise the temperature for a prolonged period. We believe that
when we immerse the film in a heated solution containing the n-butylamine ligand,
Le Chatelier concentration pressure increases the ligand coverage on the surface of
the outermost layer of nanocrystals, first enabling the outermost layer of nanocrystals
162
(a)
(b)
1 im
2.0 -
I
I
1
5
10
I
I
1.5 -
1.0
0.5 -
0.0
0
I'
20
I
15
Vd, [V]
25
(C)
I
10-9
I
I
Patterned
10-10
Unpatterned
C
10
C
0
0-12
10
1
1
10
10
10-13
10
Thickness
1
104
10
Width /Length [nm /
t
1
Figure D-9: (a) An AFM image of a film of PbS nanocrystals capped with nbutylamine, which is 350 nm wide at its narrowest point. The film is continuous,
in contrast to those shown in Figure D-1. (b) I-V characteristic of the nanopatterned
film shown in (a). (c) Conductance of n-butylamine-capped PbS nanocrystals versus
the dimensions of the film with Vds = 0.1 V. The red circles represent the conductance of the nanopatterned film shown in (a) and a comparable rectangular film with
nanometer dimensions. The blue circles represent the conductance of a microscopic
film in a device structure shown in Figure D-1, where the dimensions of the film
are 800 pm wide, between 40 and 300 nm thick, and either 2 or 5 pm wide. The
conductivity of the nanoscopic films is higher than what is found in the microscopic
films.
163
to redissolve in the solution and subsequently the remaining nanocrystals to do so as
well.
D.5
Conclusion
We have demonstrated the ability to form nanoscale patterns of semiconductor nanocrystals that are electrically conductive and structurally continuous. Using electron-beam
lithography and lift-off, we achieve patterns with 30 nm resolution that can be integrated into a device structure with 30 nm precision. The process allows for flexibility
in the choice of nanocrystal core material, ligand, and solvent without constraints on
the choice or design of the substrate. We have performed the first electrical measurements of nanocrystal films of nanoscale dimensions that are free of the clustering
and cracks typically found in films of micrometer dimensions or larger. The electrical
conductivity of the patterned, nanoscale films is notably higher than the conductivity of larger, drop-cast films where the nanocrystals form clusters. This technique for
pattering nanocrystal films opens the possibility of studying the nanoscopic charge
dynamics in the localized states of the nanocrystals. Finally, the ability to control
the formation of nanocrystal films with nanoscale resolution makes it possible to
use nanocrystal films in applications such as nanoelectronics, nanophotonics, LED
nanodisplays, and nanoscale detection of biomolecules.
D.6
Chapter-specific acknowledgments
Mark Mondol and the RLE SEBL facility provided experimental help with electronbeam lithography. This work was supported by the U.S. Army Research Office under contract W911 NF-07-D-0004 (patterning and electrical measurements of PbS
nanocrystals), by the Department of Energy under award number DE-FG02-08ER46515
(patterning and imaging of PbSe, CdSe, and CdSe/ZnS nanocrystals), and by Samsung SAIT.
164
Appendix E
Controlled Placement of Colloidal
Quantum Dots in Sub-15 nm
Clusters
Sections of this chapter are reprinted with permission from Manfrinato, Wanger,
Strasfeld, Han, Marsili, Arrieta, Mentzel, Bawendi, and Berggren, Nanotechnology
2013 24, 125302.'
Abstract
We demonstrated a technique to control the placement of 6-nm-diameter CdSe and
5-nm-diameter CdSe/CdZnS colloidal quantum dots (QDs) through electron-beam
lithography. This QD-placement technique resulted in an average of three QDs in
each cluster, and 87% of the templated sites were occupied by at least one QD. These
QD clusters could be in close proximity to one another, with a minimum separation
of 12 nm. Photoluminescence measurements of the fabricated QD clusters showed
intermittent photoluminescence, which indicates that the QDs were optically active
after the fabrication process. This optimized top-down lithographic process is a step
towards the integration of individual QDs in optoelectronic and nano-optical systems.
'This work was performed in close collaboration with Vitor Manfrinato, Dave Strasfeld, Hee-Sun
Han, Francesco Marsili, Jose Arrieta, Tamar Mentzel, Moungi Bawendi, and Karl Berggren.
165
E.1
Introduction
Semiconductor colloidal quantum dots (QDs) are important building blocks for nanoscience. [4]
One key aspect of this system is the fine synthetic control of its electronic and optical properties[4, 27].
For convenience, many optical and electronic studies use a
thin film of QDs deposited by spin casting, dip coating or drop casting. This ensemble configuration is extensively used to investigate the fundamental properties
of QDs, such as band-gap engineering,[27] energy transfer,[58, 131, 14] and multiexciton generation,[80] which are relevant to the future applications of QDs in solar
cells[80] and light-emitting diodes.[5] However, properties such as exciton lifetime
and photoluminescence intermittency are obscured by ensemble measurements and
can be better understood at the single-QD or few-QD-cluster level.[27, 26] Most
single-dot and cluster studies are performed on films spun from very dilute solutions, which results in a random distribution of quantum dots on a substrate. Some
of these measurements would benefit immensely from accurate position control of
sub-10-nm QDs, which has not previously been possible. Single-QD patterning is
one of the challenges in designing a system that takes advantage of the single-dot
properties of QDs.[84] In addition, systematic investigation of single QDs, dimers
(clusters of two QDs), and trimers (clusters of three QDs) is limited by complex,
or non-reproducible fabrication processes. Hence, placement of sub-10-nm QDs at
desired positions is expected to be a powerful tool to quantitatively investigate this
system. Previous reports have demonstrated template-directed self assembly of colloids at the 100-nm scale.[112, 2, 12, 125, 126, 132] In the sub-100-nm scale, there
are reports of template-directed placement of sub-20-nm-diameter clusters of gold
colloidal QDs,[63, 19, 65, 124, 41] and sub-50-nm-diameter clusters of semiconductor colloidal QDs[132, 59, 92, 134, 72, 1] using electron-beam lithography, dip-pen
lithography, scanning-probe lithography, and block-copolymer self assembly. However, for semiconductor QDs smaller than 10 nm in diameter, sub-20-nm patterning
has not previously been possible and is crucial to permit placement of single QDs and
small QD clusters. This letter presents a simple and effective patterning technique
166
(a)
(b)
PMMA
Si
EBL
PMMA
Si
6 nm CdSe
000
ee
90
80
Ui
U)40 0
99
00
C
CD
PMMA
...... . .r....n..
70
e.e
100
200
0
image cross-section (nm)
(c)
lFU110
C
acetone lift-off I,
ese
21 nm
Si
LU
L)
6 nm
L2
60
0
9=250
image cross-section (nm)
Figure E-1: Overview of the fabrication process for placing QDs. (a) Schematics
of the fabrication process: PMMA was spin-coated to a thickness of 40 nm on Si,
followed by EBL; Then, 6-nm-diameter CdSe QDs were spin-coated or drop cast;
Finally the PMMA lift off was done with acetone, leaving clusters of CdSe QDs.
(b) Top: scanning-electron micrographs of PMMA templates with 8 nm (minimum
feature size used) and 21 nm diameters. Bottom: SEM image cross-section across the
PMMA templates. (c) Left: SEM of a patterned CdSe QD cluster (dimer). Right:
SEM cross-section over one CdSe QD, with full-width at half maximum of 6 nm.
to control the position of individual QDs by using sub-10-nm electron-beam lithography (EBL). We show that the placed QDs are luminescent and present intermittent
photoluminescence (PL), known as blinking, which indicates the presence of single
QDs.[58, 131, 14] Applications that may emerge through the use of this technique are
the fabrication of single-photon emitters,[84, 21] excitonic circuits,[39, 93, 95] and a
large variety of nano-optical devices.[3, 31]
E.2
Results and discussion
The fabrication process for QD placement is illustrated in Figure E-1.
A poly-
(methylmethacrylate) (PMMA) resist was spin coated on a silicon substrate to a
thickness of 40 nm, and baked at 200 0 C for 2 minutes on a hotplate. Then, a design
167
with single-pixel exposures (doses from 10 to 200 fC/dot) and 10- to 20-nm-diameter
areal exposures (doses from 400 to 4,000 pC/cm 2 ) were exposed on PMMA by EBL.
This exposure was used to obtain an array of templates, PMMA holes, with varying
diameters. EBL was carried out at an electron energy of 30 keV on a Raith 150 EBL
system. The QD deposition was carried out at a relative humidity lower than 38%.
In particular, working in a nitrogen glove box improved QD assembly uniformity[72].
The QD solution (6-nm-diameter CdSe or 5-nm-diameter CdSe/CdZnS) was spin cast
or drop cast on top of the PMMA templates, and the remaining resist was removed
by dissolution in acetone for 3 min. This process resulted in QD clusters attached
to the substrate. Figure E-1b shows the patterned PMMA with templates from 8
to 21 nm in diameter. The placed QDs were analyzed in a Zeiss scanning electron
microscope (SEM), as shown in Figure E-1c. In order to minimize the number of
QDs
in each cluster and increase the patterning yield, defined here as the percent-
age of the templated sites that were occupied by at least one QD, the QD solution
concentration, the QD solution purification[27], the resist thickness, and the feature
size were systematically optimized. We found that 1-2 layers of QDs were obtained
by spin casting a 2-pM QD solution or by drop casting a 2-4 piM solution of QDs
(as determined by the absorption at 350 nm).[61] We maximized the QD adhesion on
the substrate by purifying the QDs three times[79] to reduce the number of ligands
on the QD surface and to reduce the number of free ligands in solution. To achieve
the smallest QD clusters, the EBL development was optimized to obtain the smallest
templates. PMMA development was done at 7'C [41, 17] for 30 s in 3:1 (isopropyl
alcohol: methyl isobutyl ketone), without any subsequent rinse, and blow dried with a
nitrogen gun for 1 min. The resist thickness was also minimized to 12 nm to decrease
the number of QDs that could fit inside each template hole in the resist.
Figure E-2 shows the results of the optimized process, achieved by using 12nm-thick PMMA as the mask, a development temperature of 70 C, and a 2-pM QD
concentration. We achieved placement of a few QDs in each cluster for the smallest
templates, as shown in Figure E-2b. We also observed a few QDs present outside
the patterned area; we suspect that these QDs were re-deposited during the lift-off
168
(c)
16
CU
E
S12
4'
0-M
I
F
1
2
3
4
5
other
number of quantum dots in each cluster (36%)
(d)
(e)
0O
S.
Figure E-2: Scanning-electron micrographs of (a, b) 6-nm-diameter CdSe QDs and
(d, e) 5-nm-diameter CdSe/CdZnS. The fabrication was optimized to minimize the
number of QDs in each cluster. (a) QD clusters were fabricated using templates with
15-20 nm diameter. (b) QD clusters were fabricated using templates with 8-15 nm
diameter; these were the smallest clusters fabricated. (c) Histogram of the number
of QDs in each cluster versus the number of clusters, using the smallest fabricated
templates. We analyzed 54 sites designed for QD clusters. The QDs were counted
from the SEM micrographs. Representative SEM images were added to the histogram.
The top of (d) and (e) shows the designed templates with 12 nm diameters for placing
QDs in close proximity to one another, with gaps of 36 nm in (d) and 12 nm in (e).
The bottom of (d) and (e) shows SEM micrograph of clusters of QDs composed of
5-nm-diameter CdSe/CdZnS (core/shell).
169
process. In order to quantify the statistical distribution of this process, a histogram
of the fabricated structures in Figure E-2b is shown in Figure E-2c. The QDs in each
cluster were counted from SEM micrographs. The pattern yield (percentage of the
templated sites occupied by at least one QD) was 87%. An average of three QDs
in each site was observed. For this average value, only clusters with an identifiable
number of QDs (64% of total) were considered.
QD clusters with undetermined
number of QDs were 36%. From these undetermined clusters, 24% (8% of total) had
area smaller than 12x12 nm (2x2 dots), so they were expected to have less than 5
QDs in each cluster. 76% of the undetermined clusters (27% of total) had area larger
than 12x12 nm, so they were expected to have more than 5 QDs in each cluster. The
difficulty in counting QDs is due to the SEM resolution limits, residues of PMMA and
solvents (i.e., acetone, hexane) from the fabrication process, and possible QD vertical
stacking. This technique allows QDs to be placed with the accuracy and resolution of
EBL. Figure E-2d shows placement of pairs of QD clusters with ~36-nm separation.
We also defined the dimer placement yield, which is the percentage of two adjacent
templated sites occupied by at least one QD in each site.
The dimer placement
had 55% yield (the placement yield of each QD cluster was 78%). Figure E-2e shows
placement of pairs of QD clusters with -12 nm separation. The dimer placement here
had a 36% yield (the placement yield of each QD cluster was 66%). We hypothesize
that the placement yield was significantly smaller for 12-nm gaps due to two factors:
(1) reduced template uniformity; and
(2) the template size was close to the hydrodynamic radius of the QDs (~10 nm).
We hypothesize that the variation in the number of QDs placed in each site came
in part by a non-chemical-equilibrium deposition of the hydrophobic QDs on the
hydrophilic SiO 2 substrate. Because of this non-equilibrium, the QDs were forced to
deposit on the SiO 2 surface during solvent drying. Nevertheless, this process presented
high resolution and simplicity, and does not require a pre-treatment of the substrate.
For the application of patterned QDs in excitonic or nano-optical devices, optical
characterization is required. We investigated the resilience of the photoluminescence
(PL) following the patterning process. By generating small QD clusters, we expected
170
to be able to observe intermittent PL, i.e., "blinking" [82]
The CdSe QDs (or core QDs) are not ideal for spectroscopic techniques that
require high quantum yield because numerous non-radiative pathways are available
in these QDs. For this reason, we used core/shell dots (CdSe/CdZnS) to maximize
the PL signal. We generated samples using CdSe/CdZnS core/shell (5-nm diameter)
QDs deposited on 300-nm-thick SiO 2 on a silicon substrate. The sample fabrication
follows the same procedure previously described. We stored the samples in a nitrogen
glove box before the PL measurements to prevent QD oxidation. The samples were
observed with wide-field and confocal scanning microscopy, as shown in Figure E-3.
Figure E-3a shows a TEM micrograph of the 5-nm CdSe/CdZnS QDs used for optical
characterization. In Figure E-3b, the QD clusters were placed in a rectangular grid
with 2 pum x 5 prm spacing to easily resolve their position in the PL microscope. We
obtained significant PL signal of the QD patterns, with ~10 to 200-nm dimensions.
We also observed a few QDs present outside the patterned area. These QDs may
have moved and re-deposited during the lift-off process. The top row in Figure E3b had 200-nm-QD clusters with constant PL. The PL signal was also constant for
micrometer size clusters. The two lower rows of QDs in Figure E-3b are made of
QD
clusters from -10 to 20 nm. We chose one QD cluster at the bottom row (~ 15
nm diameter) and measured the PL time trace for 160 s, as shown in Figure E3d.
We notice significant PL intermittency. This behavior was also observed for
sub-40-nm QD clusters. Figure E-3d2 is the histogram of the PL counts. This PL
intermittency shows that we generated small enough QD clusters so that we can
resolve PL fluctuation caused by QD blinking; thus, the placed QD clusters may be
used for further experiments and applications.
E.3
Conclusion
In summary, we demonstrated a technique to control the placement of few-QD clusters through EBL. This QD placement allows QD clusters of one to five QDs to be
fabricated. The process was developed by optimizing QD solution, resist thickness,
171
(a)
(b)
(c) cluster diameter
(dl)
5000-
(d2)
--
4000
0
3000
2000
S1000
50
time (s) 100
150
frequency
Figure E-3: (a) Transmission electron micrograph of CdSe/CdZnS core/shell QDs
randomly deposited on a carbon membrane, with average diameter of 5 nm used
for optical characterization. (b) Wide-field photoluminescence image of CdSe/CdZnS
QD clusters placed in a rectangular array of 2 pam x 5 pm. The peak of emission wavelength was 576 nm. (c) SEM of QD clusters that are -10 nm to 42 nm in diameter
(the top bright clusters in (b) are 200-nm markers of QDs). (dl) Photoluminescence
time trace of one QD cluster. The time trace shows intermittent luminescence (blinking). (d2) PL intensity versus frequency. The PL intensity presented a bi modal
distribution, indicating blinking.
172
and template size. One figure of merit in this process is the pattern yield, defined
here as the percentage of templated sites occupied by at least one QD. A pattern yield
of 87% was achieved with an average of three QDs in each cluster. We performed
PL of the fabricated QD clusters, showing that the QDs are optically active after the
fabrication process, presenting blinking in the photoluminescence. This optimized
top-down lithographic process is a step towards the integration of individual QDs in
optoelectronic systems.
E.4
E.4.1
Experimental
Synthesis of CdSe(ZnxCdl-xS) core(shell) QDs
CdSe cores were synthesized according to previously reported procedures.[79, 100]
Overcoating with an alloyed shell was carried out via modifications to previously reported procedures.[66] Briefly, CdSe cores precipitated from the growth solution by
the addition of methanol were redispersed in hexane and injected into a degassed
solution of 6 g of 99% trioctylphosphine oxide (TOPO) and 0.4 g n-hexylphosphonic
acid. After removing the hexane under reduced pressure at 50 0 C, the flask was backfilled with dry N2 and the temperature increased to 170'C before adding 0.25 mL
of decylamine and stirring for 30 min. Precursor solutions of diethylzine (ZnEt 2 ),
dimethylcadmium (CdMe 2 ), and hexamethyldisilathiane ((TMS) 2 S) were prepared
by dissolving the appropriate amounts of each in 4 mL of TOP and loading them into
two separate syringes for metal and sulfur under an inert atmosphere. The molar
quantity of ZnEt 2 required to achieve the desired shell thickness (typically 5 monolayers) was calculated according to the methods of Leatherdale.[61] For an alloyed
shell, an appropriate mole fraction ZnEt 2 was replaced by CdMe 2 . A 1.5-fold molar
excess of (TMS) 2 S was used. The precursor solutions were injected simultaneously
into the 170 C bath at a rate of 4 mL/h. The QDs were stored in the growth solution
under ambient conditions and centrifuged once more before use.
173
E.4.2
Electron-beam Lithography (EBL)
EBL was carried out at an electron energy of 30 keV on a Raith 150 EBL system
with a thermal-field-emitter source operating at 1800 K
(
0.5 eV energy spread), a
20-jim aperture, 50-pm field size, a working distance of 6 mm and a beam current of
150 pA.
E.4.3
Scanning Electron Microscopy
The colloidal quantum dots were placed on Si and 300-nm-thick SiO 2 on Si substrates
(using the described fabrication method), and imaged in a thermal-field-emitter source
Zeiss scanning electron microscope (the same used for lithography) at 10 keV, using inlens secondary-electron detector, with electron-beam current of ~250 pA, and 6-mm
working distance. No contrast enhancement techniques (such as metal deposition)
were used.
E.4.4
Transmission Electron Microscopy
The TEM sample was prepared by dropping a dilute hexane solution of QDs onto a
TEM grid (Ted Pella, Ultrathin Carbon Type-A, 400 mesh, Copper) resting on filter
paper. TEM imaging was performed on a JEOL 200CX in bright field mode, with an
accelerating voltage of 120 kV onto a 1.3-Mpix AMT digital camera. Only standard
condenser and objective apertures were used.
E.4.5
Optical Chracterization
The samples were observed with wide-field and confocal scanning microscopy using
an air microscope objective (100x, 0.7 NA) and a 514-nm CW argon ion laser for
excitation. The collected emission was detected by an avalanche-photodiode-based
single-photon detector. The background from the laser was removed using a 514-nm
filter.
174
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187
DARCY D. WANGER
EDUCATION
Massachusetts Institute of Technology Advisor: Moungi Bawendi
2014
Ph.D. in Physical Chemistry - GPA: 4.8/5.0
Thesis: TranslatingSemiconductor Device Physics into Nanoparticle Films for Electronic Applications
University of California- Los Angeles Advisor: Benjamin Schwartz
2008
M.S. in Physical Chemistry - concurrent M.S./B.S. GPA: 3.84/4.0
Thesis: Morphology Explorations for Improvement of Polymer-Based Photovoltaic Devices
University of California- Los Angeles Advisors: Yves Rubin, Benjamin Schwartz
B.S. in Chemistry/Materials Science with an Organic Emphasis - GPA: 3.84/4.0
Magna Cum Laude, College Honors, Departmental Highest Honors
2008
EXPERIENCE
Massachusetts Institute of Technology
Graduate Research Fellow
2008-2014
Cambridge, MA
o Identified pivotal scientific problems and organized a 10-member interdisciplinary group of experimentalists and theorists to create a complementary set of experiments and simulations to propose innovative
materials and devices.
o Collaborated with electrical engineers, physicists, chemists, chemical engineers, and materials scientists
to identify and pursue creative solutions to key problems in nano-scale solar cells and patterning.
o Formulated, carried out, and critiqued a variety of projects including the synthesis, characterization,
and applications of new materials and solar cell architectures, experimentally determining the dielectric
constant of a nanoparticle film, comparing carrier trapping and exciton quenching as limiting mechanisms in solar cells, and nano-scale patterning of solution-processed materials.
o Experimentally measured and characterized nanoparticles and optoelectronic devices using electron microscopy, x-ray diffraction (including small-angle), elemental analysis, time-resolved photoluminescence,
current, voltage, and impedance measurements, and optical absorption and emission.
o Developed MATLAB programming capabilities to manipulate and analyze data from a variety of ex-
periments and produce evaluative figures of merit.
o Wrote a simulator of x-ray diffraction of nano-scale particles from first principles to deduce particle size
and size distribution from experimental measurements.
o Taught undergraduate general chemistry and physical chemistry laboratory, presented in public outreach demonstrations, workshops, and educational videos, resulting in MIT Chemistry Teaching Assistant Award.
University of California- Los Angeles
Undergraduate and Masters Student Researcher
2005-2008
Los Angeles, CA
o Designed experiments to measure electronic effects of polymer/fullerene morphology.
O
Performed electronic and optical characterization experiments to probe polymer solar cell limitations.
O Synthesized, purified, and characterized fullerene compounds for solar cells.
O Taught 6 terms of lectures and lab to sections of 12-30 undergraduates.
HONORS AND AWARDS
Hertz Foundation Graduate Fellowship (2009-2014)
MIT Chemistry Teaching Assistant Award (2009)
MIT DuPont Presidential Fellowship (2008-2009)
A. Furst Undergraduate Research Award (2008)
UCLA Graduate Award for Teaching (2007)
Goldwater Scholarship (2007)
SKILLS AND TRAINING
Computer: MATLAB, LabVIEW, Adobe Illustrator, Premiere Pro, Photoshop, LaTeX.
Characterization: Transmission Electron Microscopy (TEM) including high-resolution TEM, Scanning Electron Microscopy (SEM), Field-effect Transistors, Keithley Sourcemeters (1- and 2-channel,
pulsed and static), X-ray Diffraction (powder, SAXS), Optical Absorption and Photoluminescence
(UV, Visible, IR), Profilometry, Optics (multimode fiber coupling, filters and alignment, confocal microscopy), Semiconductor Parameter Analyzer, Thermogravimetric Analyzer, Impedance Analyzer, Elemental Analysis, 4-Point Probe, Contact Angle Wetting Analysis, Potentiostat.
ACTIVITIES AND MEMBERSHIPS
Bassoon (orchestral, chamber music, musical theatre), Club Volleyball (player, officer, team organizer),
Chembites author, MIT Science Policy Bootcamp.
SELECTED PUBLICATIONS AND PRESENTATIONS
Wanger DD, Correa RE, Dauler EA, Bawendi MG. The Dominant Role of Exciton Quenching in PbS
Quantum-Dot-Based Photovoltaic Devices. Nano Letters 2013, 13, 5907-5912.
Cui J, Beyler AP, Marshall LF, Chen 0, Harris DK, Wanger DD, Brokmann X, Bawendi MG. Direct
probe of spectral inhomogeneity reveals synthetic tunability of single-nanocrystal spectral linewidths.
Nature Chemistry 2013, 5: 602-606.
Manfrinato VR, Wanger DD, Strasfeld DB, Han HS, Marsili F, Arrieta JP, Mentzel TS, Bawendi MG,
Berggren KK. Controlled placement of colloidal quantum dots in sub-15 nm clusters. Nanotechnology
2013, 24: 125302.
Wanger DD, Bawendi MG. Trapped-Carrier Density Measurement and Exciton Quenching in PbS
Nanocrystal Films. Contributed Talk. Materials Research Society Conference, San Francisco, CA. 2013.
Mentzel TS., Wanger DD, Ray N, Walker BJ, Strasfeld D, Bawendi MG, Kastner MA. Nanopatterned
Electrically Conductive Films of Semiconductor Nanocrystals. Nano Letters 2012, 12: 44044408.
Osedach TP, Zhao N, Andrew TL, Brown PR, Wanger DD, Strasfeld DB, Chang L-Y, Bawendi MG,
Bulovic V. Bias-Stress Effect in 1,2-Ethanedithiol-Treated PbS Quantum Dot Field-Effect Transistors.
ACS Nano 2012, 6: 3121-3127.
Strasfeld DB, Dorn A, Wanger DD, Bawendi MG. Imaging Schottky Barriers and Ohmic Contacts in
PbS Quantum Dot Devices. Nano Letters 2012, 12: 569-575.
Wanger DD. Quantum Dots and Solar Cells: Understanding Materials to Maximize Awesomeness.
Invited Physics Seminar. Mt. Holyoke College, South Hadley, MA. 2011.
Zhao N, Osedach TP, Chang LY, Geyer SM, Wanger DD, Binda MT, Arango AC, Bawendi MG,
Bulovic V. Colloidal PbS Quantum Dot Solar Cells with High Fill Factor. ACS Nano 2010, 4: 3743-
3752.
Ayzner A, Wanger DD, Tassone C, Tolbert S, Schwartz BJ. Room to Improve Conjugated PolymerBased Solar Cells: Understanding How Thermal Annealing Affects the Fullerene Component of a Bulk
Heterojunction Photovoltaic Device. J. Phys. Chem. C. 2008, 112: 18711-18716.
Kennedy R, Ayzner A, Wanger DD, Day C, Halim M, Khan S, Tolbert S, Schwartz BJ, Rubin Y.
Self-Assembling Fullerenes for Improved Bulk-Heterojunction Photovoltaic Devices. J. Am. Chem.
Soc. 2008, 130: 17290-17292.