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Non-radiative energy transfer for photovoltaic solar energy conversion: lead sulfide quantum dots on silicon nanopillars

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Non-radiative energy transfer for photovoltaic solar energy conversion: lead sulfide quantum dots on silicon nanopillars

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Content 1

Non-Radiative Energy Transfer for Photovoltaic Solar Energy
Conversion: Lead Sulfide Quantum Dots on Silicon Nanopillars

by

Zachary R. Lingley

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATERIALS SCIENCE)

August 2014

Copyright 2014 Zachary R. Lingley
i

Dedication:

To my wonderful parents

ii
Acknowledgements
I am grateful for the guidance and education my advisor Prof. Anupam Madhukar has
provided. He has set a wonderful example of how scientific work should be done and has taught
me to strive for deep understanding in everything I study. Discussions with him provoked me to
improve my critical thinking and helped me grow as a scientist. I have learned lessons and
perspectives from him that simply could not have been learned anywhere else, and for that I am
grateful.
This dissertation would not exist without Siyuan Lu. It was privilege to work with him
through the entirety of this work, and the value of Siyuan’s contributions and support on every
facet of this research is immeasurable. It was simply a pleasure to work with him on a daily
basis.
I am thankful to have worked with some extremely talented colleagues during my time at
USC. I have immense respect for Tetsuya Asano and Jae Kyoo Lee, who, despite working in
different fields, demonstrated the standard for work in the Madhukar Group. Later, I was
fortunate to work with Chris Berry and Jiefei Zhang.
During my time at USC I was privileged to mentor many talented undergraduates
including Daniel Harris, Bart Stevens, Rob Rosenberg, Rohan Chalsani, Chaitanya Murthy, Luke
Bouma, Debbie Urela, Zach Gima, Juan Hernandez-Campos, Ken Hilton, and Lyssa Aruda.
Educating these students provided an additional facet of my own education that will surely serve
me well in future endeavors. Also, they were good company.
I am thankful for Prof. Stephen Cronin and Prof. Noah Malmstadt for serving on my
dissertation committee.
Additionally, I’d like to thank Krishnamurthy Mahalingham at Wright Patterson Air
Force Base for his contribution to the high resolution TEM work done for this dissertation, Larry
iii
Stewart of Prof. Dan Dapkus’s group for teaching me the basics of electron beam lithography,
John Curulli of CEMMA for maintaining the Akashi 002B and 2100F TEMs, and Dr. Chelyapov
for maintaining the USC Nanobiophysics core. I’d like to thank the Air Force Office of
Scientific Research for funding this research and acknowledge the aid of a Viterbi Graduate
Research Fellowship.
Finally I’d like to thank my parents and brothers for their support while I worked on this
dissertation.

iv
Table of Contents

Dedication……………………………………………...…………………………………..i
Acknowledgments…………………………………………………..…………………….ii
List of Figures……………………………………………………………………….….…x
Abstract……………………………………………………………...…...……………..xxii

Chapter I: Introduction……………………………………………………………….…1

I.1. Non-radiative resonant energy transfer based solar energy conversion………………1

I.2 Non-radiative resonant energy transfer………………………………………………..5

I.3 Quantum dots as light absorbers and as NRET donors and acceptors……………….12

I.3.1 Quantum confinement…………………………………………………..….12

I.3.2 Excitons in Quantum Dots………………………………………………….14

I.3.3 Realization of quantum dots: epitaxial and colloidal quantum dots……..…17

I.4. Energy Alignment considerations in Quantum dot - Nanowire NRET based
solar cell …………………………………………………………………………………19

I.5 Rationale for using Lead Sulfide Quantum Dots and Silicon Charge
transport channels………………………………………………………………………..26

I.6. The scope of this dissertation………………………………………………………..27

I.7 Chapter I references…………………………………………………………………..32

Chapter II: Experimental Details………………………………………..…………….34

II.1. Quantum dot synthesis techniques………………………….………………………34

II.1.1 PbS QD synthesis reactions and procedures………………………………37

II.1.2 Separation of nanocrystals from the growth solution………...…………… 41

II.2 Optical spectroscopy…………………………………………...……………………42

II.2.1 Time resolved photoluminescence………………….……………………..43

v
II.2.2 Time integrated photoluminescence…………………...…………………..49

II.3 Transmission electron microscopy…………………………………………………..51

II.3.1 Electron diffraction in the TEM…………………………..……………….53

II.3.2 Inelastic scattering and mass-thickness contrast…………………………..59

II.3.3 The transmission electron microscope imaging system…………...………60

II.3.4 Phase contrast imaging with diffracted beams………………………….…63

II.3.5 Specific aspects of imaging PbS QDs……………………………………..65

II.3.6 TEM sample preparation for colloidal QD specimens on amorphous
carbon support film………………………………………………………..…….66

II.4 Silicon processing techniques………………………………………...……………..67

II.4.1 Electron beam lithography…………………………………..…………….67

II.4.2 Details for specific electron beam lithography processes…………..……..71

II.4.3 Reactive ion etching……………………………………...………………..73

II.4.4 Deep reactive ion etching by the Bosch process..………………..………..74

II.5. Chapter II References…………………………………………………......………..76

Chapter III: PbS Nanocrystal quantum dot synthesis, ligand exchange, and
quantum dot solids………………………………………………………………...…....78

III.1. Colloidal quantum dots ……………………………………………………………78

III.1.1 Lead sulfide quantum dots: electronic structure...…………..……………80

III.1.2 Stokes’ shift, radiative lifetime, and mid -gap states in PbS QDs.………..85

III.2 Synthesis of PbS QDs………………………………………………………...…….89

III.2.1 Quantum efficiency of PbS QDs by PL comparison with IR125……...…90

III.2.2 Structural characterization of PbS QDs by HRTEM……………….…….92
vi

III.3. Post-synthesis manipulation: Control over QD-QD center to center spacing….. …96

III.3.1 Inorganic shell growth on PbS QDs…………………………...………….96

III.4 Quantum efficiency preserving cation - ligand exchange on PbS QDs……….......100

III.4.1 Cation-ligand exchange experimental details…….……………………..105

III.4.2 Characterization of cation-ligand exchange……………………………..107

III.4.3 QD solids: Inter-QD separation control…………… ……………...…….110

III.5. Chapter III References………………………………………..…………………..112

Chapter IV: Inter-QD NRET and competing processes………………………........117

IV.1 QD solids: Background…………… …………………………………...………….117

IV.2 Inter-QD energy and charge transfer…………………………………..………….118

IV.2.1 Inter-QD NRET…………………………………………………………118

IV.2.2 Exciton dissociation and Inter-QD charge transfer………….…….……119

IV.3 Dynamics of Competing NRET and Charge Transfer in PbS QD solids…...…….122

IV.3.1 The unique platform QD solid platform enabled by cation-ligand
exchange………………………………………………………………………..123

IV3.2 Preparation of QD dilute solutions and solids……………...……………126

IV. 4 Optical properties of PbS QD solids……………………………..……………….126

IV.4.1 Photoluminescence and the ensemble behavior of PbS QDs in
solution and in QD solids………………………… ……………………....…….127

IV.4.2 Photoluminescence decay dynamics in PbS QD Solids…………….…..130

IV.4.2.1 Control experiments: decay dynamics in dilute solution…130

IV.4.2.2 Small QDs and inter-QD NRET……….......……………..132

vii
IV.4.2.3 Large QDs and inter-QD charge transfer………………....134

IV.5 Discussion……...………………………………………………………..………..135

IV.5.1 General trends in the luminescence decay rate with temperature……....135

IV.5.2 The effect of ligand length on the effective medium dielectric
constant of the PbS QD solid………...…………………………………..…….139

IV.5.3 Inter-QD energy transfer and the influence of effective medium
dielectric constant…………………………………………………..…………..141

IV.5.4 Inter-QD charge transfer and the ligand length dependent activation
energy for change transfer………………………..………………………...…..145

IV.6 Summary of findings on Inter-QD energy and charge transfer………..………….150

IV.7 Chapter IV References…………………………………………………………….153

Chapter V: PbS QDs on Silicon: The Interface, NRET, and Charge Transfer..….158

V.1. The QD – Substrate Separation………………………………..…………………..158

V.2 An approach to imaging the QD-semiconductor interface….……………………..162

V.2.1 Our new TEM specimens……………………………….………………..164

V.2.2 Deposition of PbS QDs onto nanopillars………………………….……..167

V.3 High Resolution TEM Images of PbS QDS on Si……………..…………………..167

V.3.1 Crystallographic orientation of QDs with respect to the substrate and
preferential adsorption orientation……………………………………………...169

V.3.2 Spacing between QDs and substrate surface………………………..……172

V.4. Optical response of PbS QDs on silicon and silicon with thick SiO
2
……………..175

V.4.1 QD monolayer sample preparation by dip coating……………...……….176

V.4.2 Photoluminescence of PbS QDs on Si and on thick SiO
2
on Si…………177

V.5. Summary of PbS QDs on crystalline Si studies……………………………...……179
viii

V.6 Chapter V References…………………………….………………………………..181

Chapter VI: Quantum dot - nanostructured silicon hybrid photovoltaic devices...184

VI.1 The NRET-based solar cell…………………………………………………..……184

VI.2 Approach to silicon photovoltaic structure fabrication and the
advantages of a nanowall-based structure…………………………….………………186

VI.3 Nanowall device fabrication processing………….…………………………….…188

VI.3.1 Nanowall solar cell fabrication………………………………………….189

VI.3.2 I-V curves for nanowall solar cells……………….…………………….195

VI.4 Nanowall surfaces and sidewall recovery………....………………………………198

VI.4.1 Sidewall smoothing by thermal oxidation………………………………201

VI.4.2 Chemical approaches to surface passivation…………………………....202

VI.4.3 I-V characterization………………………………………………….….204

VI.5 Conclusions………………………………………………………………………..206

VI.6 Chapter VI References…………………………...………………………………..207

Chapter VII: Conclusions and Future Work………………………………………..209

VII.1 Conclusions………………………………………………………………………209

VII.2 Future work………………………………………………………………………213

VII.2.1 Future Work related to the synthesis and surface ligand
manipulation of PbS QDs and layer-by-layer deposition of PbS QDs………214

VII.2.2 Further Studies Related to Inter-QD energy transfer and the
temperature dependence of large QD rise times……………………………….216

ix
VII.2.3 Further studies of PbS QD to Si NRET and charge transfer…………..218

VII.2.4 Future work on silicon nanowall photovoltaic structures and
minority carrier lifetime investigations…………………………………………220

VII.3 Chapter 7 Reference………………………………………………………….…..221

x
List of Figures

Figure I.1. Schematic of non-radiative resonant energy transfer based solar
cell featuring light absorbers (green circles) dispersed around
high mobility charge transport channels.
2

Figure I.2. Schematic of the non-radiative resonance energy transfer
process. The dotted lines represent electronic transitions that
occur within the donor and acceptor and the dashed line is the
direction of the energy transfer. The separation r is defined as
the dipole center to center distance.
3

Figure I.3. Early experimental evidence of non-radiative resonant energy
transfer from Bowen and Brocklehurst [I.9]. Open circles are
fluorescence efficiency of chloroanthracene, x’s are the
fluorescence efficiency of perylene, and the open squares are
the total fluorescence efficiency. The increase in total
fluorescence efficiency with increasing concentration signifies
energy transfer from the low efficiency perylene to the high
efficiency chloroanthracene.
8

Figure I.4. Figure I.4. A schematic of single particle energy levels and the
lowest energy exciton level in a quantum dot. The bulk
conduction and valence band edges, E
CB,bulk
and E
VB,bulk,
along
with the confinement energy due to the ligands, E
conf
form the
potential well. The single particle levels are shown in grey and
the lowest energy exciton level is in black. The dashed green
arrow represents the lowest energy absorption transition that is
the excitonic gap. The exciton binding energy, E
ex
, is
illustrated.
16

Figure I.5. Energy Band diagram of an NRET based solar cell utilizing
quantum dots dispersed around inorganic charge mobility
transport channels. As described in the text, the overall
efficiency is related to the product of the efficiencies of the four
processes shown here. Brown arrows represent fast, non-
radiative relaxations and the energy barriers of confined
electrons and holes are denoted as f
b,e
and f
b,h
respectively.
Additional details are given in the text.
20

Figure II.1. Schlenk line used in synthesis and manipulation of quantum
dots.
35
xi

Figure II.2. Structures of oleic acid and hexamethyldisilathiane (TMS
2
S).
One of each type of atom is labeled and the color schemes are
the same for both molecules. The lines connecting balls
(atoms) represent single chemical bonds except as noted.
39

Figure II.3. The time resolved photoluminescence set-up. Components in
red boxes are used to create laser pulses and detect emitted
light. Components in blue boxes are timing electronics.
47

Figure II.4. Ewald’s Sphere and a representation of the possible diffracted
beams. To combinations of G and k
D
are included in the
schematic, each reciprocal lattice points enclosed by green
rectangles are those that satisfy the diffraction condition for the
crystal orientation represented here. The reciprocal lattice
points (black ovals) are elongated in the direction of the beam
because of the thin foil effect described below in the text.
56

Figure II.5. Figure II.5. Excitation errors and the diffracted intensity, I
i
(s)
for the case of a 10 nm thick foil. The excitation error is plotted
on the vertical scale on the left panel, and the diffracted
intensity I
i
(s) is relative to the maximum diffracted intensity at
s=0.
57

Figure II.6. The relationship between deviation from the optimum incident
electron orientation (red, s ≈ 0), the maximum angular deviation
(blue marked as prime) with s = s
max
and . The planar spacing
d
hkl
corresponds is 1/ | |, where is independent of the
incident electron direction.
58

Figure II.7. Contrast Transfer Function for C
s
= 1.1 mm and Df values of -
60 nm (dark blue, Scherzer) and -70 nm (dark red). The arrow
represents the spatial frequencies that correspond to a typical
spatial frequency used in TEM imaging: the Si (111) planar
spacing (3.1 Å). Circles represent the upper limit of resolution
for each defocus value. For Scherzer defocus, the greatest
range of frequencies will be transferred faithfully though the
objective lens system. The frequencies in the region of the dark
blue curve enclosed by the blue box will be faithfully
transmitted though the objective lens. Note that C
s

specification for the USC JEOL 2100F is 1.1 mm.
63

xii
Figure II.8. Coordinate Systems for the stage, substrates, and patterns used
in the Raith System. The stage coordinates are fixed. During
the set-up for each exposure, the substrate coordinates are
linked to the stage coordinates and the pattern coordinates are
linked to the substrate coordinates. Multiple pattern
coordinates can be linked to the same substrate coordinate
systems.
71

Figure III.1. PbS QD 1Se and 1Sh levels as function of QD size as
represented by absorption peak wavelength [III.18][III.19]. The
1S
e
level varies much more with size than the 1Sh level.
However, for small QDs with absorption peak marked by the
dashed line, the confinement energies for both the 1Se and 1Sh
level are significant. The upper and lower blue lines represent
the silicon conduction band and silicon valence band edges
respectively. The data in this figure is called upon in both
Chapters IV and V.
84

Figure III.2. A three level energy diagram for PbS QDs. Solid red lines
represent the 1S
e
and 1S
h
levels, which determine the energy of
the absorption peak. The dashed red lines represent excited
states involved in absorption (green arrow) of energetic
photons, and the blue line represents the energy of the mid-gap
state. The Stokes’ Shift as labeled depends on the size of the
QD. The transition corresponding to photoluminescence is
shown by the red arrow. Brown arrows represent fast non-
radiative relaxations.
87

Figure III.3. Absorption (gray) and emission spectrum (black) for small PbS
QDs illustrating the large 150 nm Stokes’ Shift. The red solid
and dashed lines are Gaussian fits.
91

Figure III.4 (a) Absorption and (b) photoluminescence of oleate capped PbS
QDS and IR 125 reference dye when excited at 700 nm. Both
the PbS QDs and IR-125 absorb 700 nm light at the same
strength, but the PbS QDs emitted much more light and thus
have much higher QE.
92

Figure III.5. HRTEM images of typical PbS QDs are shown in (a) and (b).
Panel (c) shows a high resolution image with two sets of visible
fringes due to PbS {111} planes having 3.4 Å spacing, which is
consistent with the PbS bulk lattice constant of 5.94 Å. PbS
nanocrystals become cubic as shown in (d) at sizes above 9 nm
diameter due to slow growth on {100} facets.
94
xiii

Figure III.6. Small, 2.6 nm average diameter PbS QDs, such as those used in
the majority of optical studies. This image was taken with the
aberration corrected microscope at Wright Patterson Air Force
Base, which has point-to-point resolution greater than 1 Å, but
such high resolution does not help in identification of the QD
edges due to small difference in mass-thickness contrast
between the QDs and the carbon film.
95

Figure III.7. Decreasing Quantum Efficiency of PbS QDs as a function of
exposure to dimethlycadium – TMS
2
S (blue symbols) and
diethylzinc – TMS
2
S (red symbols) solutions shell precursors.
The dotted lines are guides to the eye.
98

Figure III.8. (a) Photoluminescence spectra of PbS-core QDs with CdS
shells. These data illustrates a reduction in PbS-core diameter
as a function of increasing reaction time, as indicated by the
blue shift in emission energy. (b) Comparison of PbS QD core
diameter determined by the PL peak position and by total core-
plus-shell diameter determined from TEM images. The
invariance in total diameter before and after shell formation
shows that the mechanism of shell formation is cation-
exchange, rather than shell growth. Note that dips in PL
emission at ~1150 nm and 1200 nm are due to absorption of
light by the toluene solvent.
99

Figure III.9. Schematic diagrams of the conventional approach to ligand
exchange (a) and of the cation-ligand unit exchange (b). In both
cases, the reactive functional group of the new ligand is
generically denoted by a red X. In (a), the red dashed ellipse
represents the desired material removed (i.e. the oleate ligand
only). However, for the case of oleate-capped PbS QDs, a lead
cation will leave the surface of the as-grown QD surface during
remove of the oleate ligands as indicated by the solid red ellipse
in (b).
104

Figure III.10. Atomic structure of the ligands used to cap PbS QDs (a) as-
grown oleate ligands, (b) dodecanoate ligands (C12), and (c)
octanoate ligands (C8). In the schematics, black is carbon,
white is hydrogen, and red is oxygen. Note that only the oleate
ligand has a single double bond. The extra electron in each
structure is shared between the atoms in COO
-
group.
105

xiv
Figure III.11. Fourier Transform Infrared (FTIR) Spectroscopy (FTIR) of C8-
, C12-, C18-capped PbS QDs showing the absence of C-H
stretch at the carbon-carbon double bond after cation-ligand
exchange. The absence of a stretch peak confirms removal of
oleate groups from the surface of the QDs as a result of cation-
ligand exchange.
107

Figure III.12. PL of C8, C12, C18 normalized by absorption strength
illustrating the preservation of high QE in the post ligand
exchange QDs.
108

Figure III.13. PL of C18-as grown QDs before and after exposure to octanoic
acid without Pb cations showing a marked decrease in QE. The
reaction conditions used in this control experiment are the same
as those in the ligand exchange description for C8, except PbO
is not included in the initial solution, and thus there are octanoic
acid molecules as ligands for exchange.
109

Figure III.14. Panels (a), (b) and (c) show TEM images of arrays of C8, C12,
C18 used to determine the ligand-length dependent spacing
between QDs. Red lines illustrate the variations in QD-QD edge
to edge separation. Panel (d) show the linear relation between
edge-to-edge spacing with the carbon number of the ligands.
The dashed red line is a linear fit through three points. TEM
images were obtained in bright field at 200 kV with no
objective aperture. The QDs are supported on a ~5 nm thick
carbon film.
111

Figure IV.1. Illustrative QD size-dependent energy diagrams for PbS QD
ensembles examined. Red lines (solid and dashed) denote
intrinsic quantum confined states and blue lines midgap (MG)
states arising from defects, most likely surface states. Green,
brown, and red (solid bold) arrows represent, respectively,
absorption, fast non-radiative relaxations, and emission. The
blue arrow represents hole transfer. E
MG
is the energy of the
mid-gap state that can participate in light emission (middle
well) or even NRET (left well).
125

xv
Figure IV.2. (a) Normalized photoluminescence curves for the C8- and C18-
capped QDs in solution at 80 K and 297 K. There is the
absence of line narrowing and peak shift which is characteristic
of small PbS QDs. Arrows in panel (a) identify the
wavelengths monitored in TRPL measurements: 880 nm for
small QDs and 1080 nm for large QDS. (b) Photoluminescence
curves for C8- and C18-capped PbS QDs in dense packed QD
solids at 80° K and 297° K. Note the reduction of emission at
880nm and enhancement of emission at peak and longer
wavelengths. Note also the red-shift and line narrowing from
panel (a) to (b). Panel (c) shows the full width half max
energies for the QD is solution and in QD solids at 80° K and
297° K. These results for C18-capped QDs are consistent with
trends reported in the literature [IV.18] [IV.29].
129

Figure IV.3. (a) Time resolved photoluminescence intensity from C8 and
C18- capped QDs in dilute solution at room temperature for
1080 nm emitting (large) QDs and 880 nm emitting (small)
QDs. The four curves essentially overlap showing that neither
the ligand exchange process nor the ligand length affects the in-
solution PL decay dynamics. (b) PL decay behavior of 1080nm
emitting C8-capped QDs in solution as a function of
temperature showing the decreased decay rate with decreasing
temperature.
131

Figure IV.4. (a) Influence of QD size on temperature dependence of in-
solution decay rate. Summary of in-solution decay rates as a
function of temperature. In panel (b) closed triangles are
measurements on C18-capped QDs, open symbols are
measurements on C8-capped QDs. In-solution decay for C12-
capped QDs (closed stars) was measured only at 297K and
consistent with the C8- and C18-capped QD behavior at that
temperature.
132

Figure IV.5. (a) PL intensity decay behavior for 880 nm emitting QDs with
C8, C12, and C18 ligands. The light green lines are the fits to
equation (IV.4). Note the clear increase in decay rate with
reduction of ligand length. Panels (b) and (c) show the decay
behavior of the C8-capped and C-18 capped PbS QDs
respectively. They clearly show an increase in decay rate as
temperature is reduced.
133

xvi
Figure IV.6. Summary of 1080 nm decay in a QD-solid: (a) shows the
increasing decay rate with decreasing ligand length. The thin
green lines are fits to eq (IV.6) and clearly show a rise in PL
intensity at short times. Panels (b) and (c) shows the decrease in
decay rate with reduction of temperature for C8-capped and
C18-capped QDs respectively. For all 1080 nm decay curves
with C8, C12, and C18 ligands for the temperature range
covered here, there is a detectable rise in the initial PL intensity
which is characteristic of excitons being fed by NRET from
smaller, adjacent QDs.
136

Figure IV.7. Trends in photoluminescence decay rates for both small and
large QDs for C8-, C12-, and C18-cappings with temperature.
The small and large QDs show the opposite general behavior,
but in both cases the decay rate is largely temperature invariant
below 150K. For all cases, the both the large and small QDs,
the decay rates increase with decreasing ligand lengths at all
temperatures.
138

Figure IV.8. Schematic illustrating the effect of ligand length on volume
fraction of the lead sulfide crystalline cores (blue circles) in the
QD solid for the case of overlapping ligands (rendered in grey)
on adjacent QDs. The ligands are approximately equal to or
greater than the QD diameter, so the volume fraction of PbS
changes considerably with ligand length. The schematic is
drawn with realistic proportions assuming 2.6 nm diameter and
d values from TEM images.
140

Figure IV.9. (a) Summary of NRET rates for C8-, C12-, and C18-capped
QDs as a function of 1/r
6
. Although at room temperature there
is a near-zero intercept that is expected from the Förster
expression, there is clearly a deviation at lower temperatures.
142

Figure IV.10. NRET rates normalized by the fourth power of the effective
medium index of refraction with fitted lines that pass near the
origin as expected from equation (IV.1) and thus suggesting
that NRET is the dominant decay mechanism.
143

xvii
Figure IV.11. (a) Illustrative TRPL curves showing the enhancement in
1080nm decay rate for QDs in QD solid (bold lines) over the
same sized QDs in solution (thin lines). Panel (b) shows the
quantitative values of enhancement in decay rate of the 1080nm
emitting QDs in the QD-solid over the same sized QDs in dilute
solution as a function of QD edge-to-edge separation, d,
determined from TEM measurements. The lines are guides to
the eye and show a clear change in slope with temperature.
145

Figure IV.12. Arrhenius plot showing the ligand length dependent activation
energy for charge transfer.
147

Figure IV.13. After accounting for the ligand-length dependent activation
energy we find that the distance dependence due to the
tunneling parameter is nominally the same for temperatures in
the range from 150K to 297K. The line is a best fit and we
find that the temperature independent value of the tunneling
parameter is 3.1 nm
-1
.
148

Figure V.1. Band diagram for PbS QDs on Si for the case of 2.6 nm average
diameter (with absorption peak at 810 nm). In addition to the
alignment of energy levels in the PbS QD and silicon with
respect to each other, the separation between the QD and silicon
surface is of key importance. In general, the separation is
determined by the ligands on the QD and the surface chemical
layer (native oxide, for example) that are present on the silicon
surface with surface density of states schematically shown by
the green line. Electron affinities and ionization potential of the
QD are from Refs [V.15] [V.16].
160

Figure V.2. Schematic of the arrangement of QDs on a substrate surface
oriented to allow imaging of the cross-sectional interface. For
QDs sitting on the top surface, it is possible to image the QD-
semiconductor interface in cross section. The patterns on the
nanopillar side surface are drawn to indicate the characteristic
shape of sidewalls created by Bosch etching as described in
section V.2.1 below.
163

xviii
Figure V.3. Scanning electron microscope images of a TEM specimen as
prepared using procedures described in the text. Panel (a)
shows an as-etched pillar. Panels (b), (c), and (d) show the
same TEM specimen at different magnifications. The circled
region in (b) and (c) is enlarged in (c) and (d) respectively. In
(b), the circular 3 mm diameter gold coated slotted grid is
shown. In (c) the thickness of the wafer in the direction of the
beam of approximately 100 mm. Panel (d) shows a high
magnification view of a part of one nanopillar. The red arrows
in (a) and (d) indicate the direction ([110]) of impinging
electrons in the TEM.
166

Figure V.4. (a) High resolution image of a PbS QD on a silicon nanopillar
with (001) top surface. The beam is oriented along the Si [110]
zone axis as determined from the inset diffraction pattern of the
silicon nanopillar in a region away from any QDs. The visible
planes and their spacings are identified, and the spacing
between the PbS QD crystalline surface as indicated by the
lowest point visible on the {111} plane indicated by the white
arrow and the silicon crystalline lattice as indicated by the red
lines is ~0.6 nm. This image is from sample number 092512-
14b.
168

Figure V.5. Variations in PbS QD shape and orientation with respect to the
silicon substrate. All three images were taken under the same
conditions and with the incident electrons in the same
orientation with respect to the silicon nanopillar. In (a) and (b)
the angle between the PbS {111} planes and the (001) silicon
top surface is 19+2°, same angle observed for the QD in Fig.
V.4, suggesting a preferential adsorption by the {112} plane
adjacent to the silicon. Panel (c) shows that the PbS {002}
planes are 3+1° from the (001) silicon top surface, suggesting
that other orientations are possible. These images are from
sample number 092512-14b.
171

Figure V.6. TEM images of silicon nanopillars Pillars without PbS (a)
before removal of HSQ by HF etching and (b) after removal of
the HSQ. In (a), the near atomic level smoothness on the Si
top surface is observed. The HSQ is amorphous. Clearly there
are only two phases: crystalline silicon and HSQ. In (b), the
amorphous native oxide is observed after HF etching but before
the PbS QDs were deposited. These phase contrast images were
taken with the electron beam along the [110] zone axis with no
objective aperture in the JEOL 2100F at USC.
173
xix

Figure V.7. Fourier filtered images. (a) and (b) show the TEM image and
Fourier filtered images respectively of the of the QD in Figure
V.4. The filtered image was created using the points in the
Fourier transform circled in (c) that include the PbS (111) and
(222) (blue circles) and the Si (002) (red circles) to highlight
the edge of the crystalline silicon and the crystalline PbS QDs.
Red arrows in (a) and (b) point to the same lattice plane, and
two {111} planes are visible in (b) (as indicated with blue
arrows). These {111} planes are not visible in (a) suggesting
that the separation due to the native oxide and ligands can be
much less than observed in the TEM images. However, for the
QD shown in images (d) and (e) that correspond to the QD in
Figure V.5(a), the separation appears to be approximately
equal.
175

Figure V.8. AFM images of sub ML coverage of PbS QDs on Si (a) and Si
with 20 nm of SiO
2
(b) that show approximately the same
coverage of QDs. The color scale bar inset in each image is 10
nm.
177

Figure V.9. Photoluminescence from sub-monolayer coverage of PbS QDs
on 20nm SiO
2
on Si and on Si with ~2 nm native oxide showing
significant quenching of emission from the QDs in the latter
case. The background PL signal from substrates without PbS
QDs is subtracted from each curve. Error bars represent the
standard deviation of three PL measurements at different
locations on the same substrate.
178

Figure VI.1. Cross section schematic of silicon-nanowall solar cell
architecture. This geometry allows the entirety of the structure
to be connected electrically to the metallic top contact while
still allowing the QDs to be deposited into the open trenches as
a final step. To emphasize the silicon architecture, only one QD
is shown here Note that the nanowalls have aspect ratio of 10-
20. The nanowalls and QD are not to scale.
185

xx
Figure VI.2. A schematic showing the geometry and key features of the solar
cell device. (a) shows the full 1 mm
2
device. The region in the
dotted box in (a) is enlarged and shown in panel (b). The black
squares in (a) represents the area of nanowall arrays and in (b)
the black bars represent trenches. The trenches are actually 200
nm wide and not drawn to scale in panel (b). In both panels, the
yellow represents the contact bars that wrap around the regions
with the nanowall arrays, the blue represents the isolation
trench and the pink is the top surface of the silicon wafer. The
purpose of the isolation trench is to define the total area of the
solar cell as described in the text.
191

Figure VI.3. Process steps involved in fabrication of nanowalls using deep
reactive ion etching.
192

Figure VI.4. Process steps to create the top and bottom metallic contacts.
Step numbers continue from those in Figure VI.3.
194

Figure VI.5. SEM images of trenches created by Bosch etching, the isolation
trench and the contacts in the complete device. Panel (a) shows
cross section of typical deep etched trenches and resulting
nanowalls. The pitch is 400 nm and the nanowall aspect ratio is
17. Panel (b) shows a cross section of the deep etched
nanotrenches and the much larger and deeper isolation trench.
Note that this image was taken in a sample that did not have
the top contact, which would be present on the surface between
the isolation trench and the nanowalls. Panel (c) shows a top
view of a device after deep reactive ion etching and top-contact
fabrication with PtSi – Cr – Au.
196

Figure VI.6. Laser illumination I-V curves for solar cells without (a) and
with (b) trenches. For both, curves were created with laser
excitation at 850 nm and 100 mW/cm
2
(the equivalent power to
sun light at AM1.5). Note the voltage and current scales; the
device without trenches is substantially more efficient. The
device without trenches (a) was from lot #031010 and device in
(b) is part of lot #042210.
197

xxi
Figure VI.7. Reduction in sidewall scallop amplitude by thermal oxidation
and etching as determined by AFM. Panel (a) is sidewall
roughness of as-etched sidewalls. Panels (b) and (c) show the
sidewall after one and two oxidation-etch cycles, respectively.
(d) Shows profiles of the scalloping in (a-black), (b-red) and (c-
blue). The dashed line represents the wafer surface and the
curves are offset vertically for clarity and the scale is relative.
Note that the color scale bar on the left applies to all three
images, and the image size is 2.5 mm
2
for each.
202

Figure VI.8. (a) Contact angle measurements of samples with fully
functionalized methylation and control substrates (i.e., before
and after passivation with CH
3
groups). (b) I-V Curves for
solar cells with as-DRIE sidewalls, after CH
3
passivation, and
after sidewall smoothing and CH
3
passivation. The I-V curves
in (b) are from cells from lot #092611.
205

Figure VII.1. HRTEM of QD edges without the obstruction of amorphous
carbon film or other support. The oleate ligands (~2 nm long)
are not distinguished in these imaging conditions, but the edges
of the QDs are clearly distinguished against the vacuum.
215

Figure VII.2. TRPL curves illustrating the opposite trends with change in
temperature for the short wavelength decay rate and long
wavelength rise rate for the case of C8-capped QD solid. In
panel (a) at 297K the 880nm decay and 1080nm rise occur on
similar time scales, but in panel (b) the same QD solid at 80K
shows 880 nm decay that is occurs much faster than the
1080nm rise.
217

Figure VII.3. PL behavior for two sizes of PbS QDs on silicon and silicon
with thick, 140 nm SiO
2
. PL emission from Size 1 (average
diameter 2.5 nm) overlaps with the silicon absorption spectra
shown in pink thus making the Size 1 – Si pair a potential
donor-acceptor pair for NRET. The emission from the larger
Size 2 (average diameter of 4 nm) does not overlap with the Si
absorption spectra meaning NRET from Size 2 to silicon does
not occur. However, we still observe significant quenching in
the Size 2 QDs on Si. This suggests that the quenching of PL
from Size 2 QDs on Si can be attributed to be primarily a
consequence of charge transfer.
219

xxii
Abstract:
This dissertation comprises a study aimed at understanding the competing
dynamics of energy and charge transfer in quantum dot (QD) solids and from QDs to
crystalline semiconductor substrates to assess a new type of hybrid solar cell that is based
on non-radiative resonant energy transfer (NRET) from light absorbers such as
nanocrystal QDs to high mobility charge carrier transport channels such as silicon
nanopillars. The NRET-based solar cell offers the potential to bypass the limitations of
the so-called hybrid excitonic solar cells arising from the large exciton binding energy
and poor charge (electron and hole) transport following exciton break at the
heterojunction of the light absorbers (such as organic dyes and QDs) and the substrate to
which these are attached (such as polymers and inorganic nanowires). Use of NRET
places both the electron and hole generated following exciton break-up in the same
medium for transport unlike the excitonic solar cells studied so far which result in only
one type of charge transferring to another medium.
As a platform to investigate a NRET solar cell we employed lead sulfide
nanocrystal QDs as light absorbers and silicon as the acceptor transport channel for the
NRET generated electrons and holes. Given NRET as the basic physical process at the
core of the new type of solar cell the dissertation focused on examining: (1) synthesis of
and surface ligand exchange for high quantum efficiency lead sulfide quantum dots, (2)
studies of inter-QD NRET and competing inter-QD charge transfer as a function of inter-
QD average separation and temperature, (3) structural and optical characteristics of lead
sulfide quantum dots adsorbed on crystalline silicon surfaces, and (4) fabrication and
examination of prototype colloidal PbS QD - silicon nanopillar array solar cell.
The work in these four areas has each provided insights into and new results for
the field of quantum dots, QD-based solids, and QD based opto-electronic devices that
are of generic value. The need for maintaining the high quantum efficiency (QE) of the
as-synthesized PbS QDs while exchanging the surface ligands with new ones better
suited for the device lead us to introduce a new approach to ligand exchange that employs
pre-conjugated lead cation – ligand complexes as units that replace the lead cations
xxiii
bound to their as-grown ligand, thus maintaining the Pb-rich stoichiometry that
suppresses defect formation while gaining the ability to control the length of the ligands.
The ability to control the length of the ligands allowed control over the QD-QD
separation in densely packed films referred to as QD-solids. These QD solids of
controlled and experimentally determined average inter-QD separation enabled the first
systematic study of exciton decay dynamics involving competition between separation-
dependent QD to QD NRET and QD to QD charge transfer as a function of temperature
and quantum dot size. Our principal findings are : (1) the NRET rate from smaller to
larger QDs increases with decreasing QD-QD average separation as the inverse sixth
power, as expected; (2) reduction in temperature enhances the inter-QD NRET rate (3)
exciton decay in the largest QDs is dominated by thermally activated tunneling of charge
and (4) a consistent understanding of both inter QD energy and charge transfer is
obtained by accounting for the ligand-length dependent effective medium nature of QD
solid dielectric constant and postulating the presence of gap states.
As transfer of energy from the QDs adjacent to the acceptor channels is an
integral step in the NRET-based photovoltaic solar cell paradigm we under took
examination of the structural nature of the PbS QD- crystalline Si interface as formed
upon deposition of PbS QDs on Si. To directly image the QD-substrate interface in a
transmission electron microscope (TEM) we introduced a new approach to TEM
specimen preparation that enabled the first simultaneous high resolution imaging of a
silicon nanopillar with thickness less than 100 nm and PbS QDs adsorbed on it, and thus
the interfacial region as well. The separation between the crystalline core of the PbS QD
and the crystalline silicon was found to be substantially less than the length of the ligands
that coat the PbS QD.
The dissertation concludes with a report on progress towards fabricating and
characterizing PbS QD - silicon nanowall solar cell devices. Prototype devices were
made by etching high aspect ratio and high density of trenches in silicon having an
existing p-n junction. The walls of silicon between the trenches thus act as the charge
transport channels for the electrons and holes generated by the NRET from QD absorbers
in the trenches. This approach has two primary advantages: (1) the doping profile
xxiv
within the silicon channels is already in place in the wafer and (2) the PbS QDs can be
deposited into the trenches after the formation of contacts. The nanowalls devices
created for this dissertation have low power conversion efficiency of less than 1% which
is primary limited by high surface recombination at the nanowalls surfaces. Thus the
greatest challenge in fabricating efficient silicon nanowall-based devices is establish an
effective surface passivation scheme to reduce surface state density on the silicon
nanowalls to ~1E10/cm
2
without introducing steric hindrance between the QDs and the
silicon nanowalls transport channels. In the last part of this dissertation, progress toward
surface state density reduction by chemical passivation with methyl groups is presented.
This chemical passivation resulted in 60% increase in short circuit current over devices
with as-etched nanowalls.

1
Chapter I: Introduction

I.1. Non-radiative resonant energy transfer based solar energy conversion
The work and ideas that form this dissertation are motivated by understanding a
new type of hybrid solar cell proposed by Lu and Madhukar [I.1] that consists of efficient
and tailorable light absorbers such as inorganic nanocrystal quantum dots that are
dispersed around an array of inorganic charge transport channels to efficiently transfer
the absorbed energy carried as excitons to the channels as electron and hole, as shown
schematically in Figure I.1. The objective of this research is to explore this novel way of
utilizing two distinct materials for light absorption and charge transport, each designed
and required to do only one task efficiently, by coupling the two tasks by the process of
non-radiative resonant energy transfer (NRET). This unique approach and its
implementation can be understood by following the sequential processes involved in
conversion of the absorbed photon energy to electricity as outlined below. The details
related to understanding and implementing these processes constitute the bulk of this
dissertation.
The proposed solar cell functions as follows. First, solar photons are absorbed in
the absorber material, here inorganic QDs depicted as green spheres in Figure I.1, and
create an excited electron - hole pair that is confined within the QD and bound by
coulomb attraction between the two. This bound electron-hole pair, the exciton, has an
associated exciton binding energy which is the energy required to overcome the coulomb
attraction and in inorganic QDs is typically ≥ 0.2 eV. The bound electron -hole pair acts
as a dipole which can couple to the charges in an adjacent light absorber, here another
2
QD or the charge transport channel in Figure I.1, and result in non-radiative resonant
energy transfer (NRET) arising from dipole-dipole interactions.

Figure I.1. Schematic of non-radiative resonant energy transfer based solar cell featuring
light absorbers (green circles) dispersed around high mobility charge transport channels.

The NRET process involves the exciton in the first absorber, called the donor,
relaxing to its ground state by exciting an exciton in the adjacent absorber, called the
acceptor. The process requires that the initial and final states are of the same energy.
The probability of NRET between the donor and acceptor depends upon the degree of
spatial confinement of their electronic states: for 3D confined to 3D confined, such as
between two QDs, it depends inversely as the sixth power of the separation between the
donor and acceptor, r (Figure I.2). For transfer from the 3D confined state of a QD to
the adjacent inorganic acceptor channel (wall) with unconfined electronic states such as
indicated in Figure I.1, the NRET transfer probability is inversely proportional to the
3
third power of separation. The use of NRET is largely what separates the proposed device
here from all other approaches to photovoltaic energy conversion, and because of its
central importance, NRET is discussed in detail in section I.2.

Following absorption of a photon by a QD, the second step involves sequential
NRET events between adjacent QDS that can allow, in circumstances discussed next, the
energy of absorbed light to migrate from the absorbing QDs to absorbers adjacent to the
inorganic acceptor channels – the nanowalls or nanowires – where exciton separation into
unbound electron and hole will occur and for transport. Migration of energy by NRET
from the QD in which a photon is absorbed to the QDs that are adjacent to the transport
channels can occur either by a random process involving transfer to successively larger
QDs in all directions at equal probabilities, or by a directed process that involves QDs
arranged in layers that are structured by QD size to guide NRET towards the transport
channels. The latter is desirable as it will require, on average, fewer NRET events for the
energy of absorbed light to reach the absorbers adjacent to the transport channels.
Figure I.2. Schematic of the non-
radiative resonance energy
transfer process. The dotted lines
represent electronic transitions
that occur within the donor and
acceptor and the dashed line is
the direction of the energy
transfer. The separation r is
defined as the dipole center to
center distance.

4
The third step in the energy conversion process involves the excitons in the
absorbers adjacent to the transport channels transferring their energy by NRET to the
charge transport semiconductor channels by exciting an electron-hole pair. In the
materials used for transport channels such as silicon, however, the electron-hole pair is
typically not bound to a hole at room temperature due to the small exciton binding energy
of less than 10 meV. Thus the large exciton binding energy in most light absorbing
materials such as organic dyes, small molecules, or inorganic nanocrystal QDs does not
need to be overcome as in the so-called bulk-heterojunction solar cells because charge
separation ultimately occurs in the very low exciton binding energy transport channels.
Fourth and finally, both the unbound electron and hole in the charge transport channel are
transported and collected at the ohmic metallic contacts that connect to an external
circuit. In our proposed structure, the transport channels contain a p-n junction, as in a
traditional p-n junction solar cell, that allows for the electrons and holes created by
energy transfer to be collected as photocurrent and used for electrical power.
The potential benefits of the NRET approach are numerous, but in general the
main advantage is that two different materials can be chosen for light absorption and
charge transport without the need for charge transport or exciton separation in the light
absorbing material or light absorption in the charge transport channels. This can
potentially open doors to allow for use of a wide range of materials such as inexpensive
organic materials or inorganic quantum dots to be used as light absorbers. These
materials typically have large exciton binding energy (0.1 to 1 eV) [I.2] and very low
charge carrier mobility ( 1 cm
2
/Vs) [I.3] and therefore are difficult to utilize
5
effectively in energy conversion schemes that require break-up of the excitons in the light
absorbing material and subsequent charge transport within the same material. In such a
structure, the device thickness and therefore required length of the charge transport
channels is determined by the thickness of the light absorbing material needed to absorb
most of the incident solar photons, which is typically on the scale of one micron or less
for light absorbers such as quantum dots or organic dyes. Therefore, a second important
benefit of the NRET approach is that the volume of the typically expensive charge
transport channel material needed is much less than is required in solar cells that feature
direct photon absorption in the material used for charge transport. For example,
compared to crystalline silicon solar cell that are typically ~300 m thick [I.4], a 1 m
thick NRET based device silicon transport channels with 50% transport channel filling
factor (and 50% light absorbers) requires 600 times less silicon per unit area.
As the NRET process is of central importance to the solar cell contemplated here
and as its use imposes certain limitations on the geometry of the solar cell architecture a
brief description of the NRET mechanism is given next.
I.2 Non-radiative resonant energy transfer (NRET)
NRET is a process by which an excited electron in a donor particle relaxes
without the emission of a photon and excites an electron in an adjacent acceptor particle.
The origin of this interaction is the coulomb interaction between the electrons in the
donor and the electrons in the acceptor. The length scales over which the coulomb
interactions can be substantial are on the scale of ~10 nm [I.5] which is very long
compared the length scales for electron transfer that typically rely on wavefunction
6
overlap between the initial and final states and are thus confined to length scales of ~2
nm or less [I.6]. The quantum mechanical origins of the NRET process are elaborated
upon below, but first it is useful to note some qualitative aspects of NRET to provide a
physical understanding of the process. Because NRET results in the creation of an
exciton in the acceptor at the expense of the exciton in the donor, and since excitons in
both have finite probability of recombining radiatively as a competing process, most
experimental investigations of NRET rely on photoluminescence measurements to detect
the light emitted from the acceptor or investigate the quenching of light from the donor.
Useful introduction to the NRET process in general and the history of the subject have
been written by Förster [I.7] and Clegg [I.8], respectively.
The NRET process was first observed by Cario and Franck in 1922 in an
experiment monitoring luminescence from a mixture of mercury and thallium atoms in a
vapor [I.8]. When exposing the mixed vapor to exciting light at a wavelength that can
only be absorbed by mercury atoms, luminescence from both species of atoms was
observed. Because light emitted by mercury atoms cannot be absorbed by thallium, the
emission from thallium suggested that it had been excited by receiving energy in a
different fashion, though it was not clear whether coupling between the mercury and
thallium lead to an intermediate coupled state that allowed transfer. Briefly, their
observations showed that light was absorbed by mercury and light was emitted by
thallium. Further studies of the luminescence of liquid solutions of 1–chloroanthracene
and perylene by Bowen and Brocklehurst shown in Figure I.3 [I.9] yielded conclusive
evidence of energy transfer by a non-radiative mechanism. In their studies,
7
chloroanthracene is the donor and has low fluorescence quantum efficiency and perylene
is the acceptor and has high fluorescence quantum efficiency. At a constant ratio of five
chloroanthracene to one perylene, measurements of the fluorescence efficiency of each
component were made as a function of increasing concentration and the following three
observations were made
1. The fluorescence efficiency of the perylene increases with increasing concentration.
2. The fluorescence efficiency of the chloroanthracene decreases and its fluorescence
lifetime decreased with increasing concentration.
3. The total fluorescence efficiency of mixture increases with increasing concentration.
The fluorescence efficiency of perylene could increase by absorption of emitted
light from the chloroanthracene and the measured fluorescence efficiency of
chloroanthracene would decrease if the emitted photons from it were absorbed by the
perylene and thus not detected. However, the fluorescence lifetime would not change if
the energy transfer was by trivial emission and absorption. Additionally, the overall
increase in quantum efficiency of the combined system could not increase if the transfer
mechanism was due to trivial light emission from chloranthacene and absorption by
perylene. At the highest concentrations, the average donor-acceptor separation was
estimated to be four nm and at all concentrations the absorption spectra of the donor and
acceptor were similar thus rejecting the possibility of a coupled state facilitating transfer.
Because NRET is based on coulomb interaction and not direct exchange
interactions that require wavefunction overlap, it can be substantial on relatively long
8
length scales compared to electron transfer reactions. This quality has enabled biologists
to utilized NRET as molecular rulers to study the structure and conformations of
biological molecules that have size scales between 1 and 10 nm [I.5].

Figure I.3. Early experimental evidence of non-radiative resonant energy transfer from
Bowen and Brocklehurst [I.9]. Open circles are fluorescence efficiency of
chloroanthracene, x’s are the fluorescence efficiency of perylene, and the open squares
are the total fluorescence efficiency. The increase in total fluorescence efficiency with
increasing concentration signifies energy transfer from the low efficiency perylene to the
high efficiency chloroanthracene.

For example, if a large protein is labeled with a NRET donor and a NRET
acceptor and the average spacing between the donor and acceptor changes when the
protein changes conformation, changes in the nature (i.e. intensity) of emission of light
from the acceptor can thus indicate that the protein has changed conformation [I.5]. The
coulomb interaction energy,

between the donor electrons and the acceptor electrons
9
can be approximated assuming that the separation between dipoles is greater than the
length of either dipole as [I.10],

[

̂

̂

̂

̂

] (I.1)
Here

and

are the charge on the acceptor and donor,

is the center-to-center
separation between the donor and acceptor dipoles,

and

respectively (that depend
on the positions of all the electrons in the donor and acceptor),

is the dielectric
constant of the medium that contains the two dipoles, and ̂ is the unit vector connecting
the donor and acceptor. The first three terms are zero if the donor and acceptor are
uncharged, and thus for the common case of uncharged donors and acceptors the
interaction is dominated by the dipole term and can be approximated [I.10] as

̂

̂

(I.2)
The interaction depends strongly on the orientation of the dipoles with respect to each
other and the magnitude of the dipoles.
The NRET rate can be calculated in the framework of Fermi’s Golden rule usi ng
the dipole-dipole interaction energy and transition from an excited donor to ground state
acceptor state. Considering the initial state to be the product of the excited donor
wavefunction,

⃗

and ground state acceptor wavefunction

⃗

, and the final
state to be the product of the excited acceptor

⃗

and ground state donor

⃗

10
where ⃗

and ⃗

are the positions of the electrons involved in the transition in the
acceptor and donor respectively and the interaction between the initial and final to be the
dipole-dipole Hamiltonian [I.11], V
DD
, the transition rate is given by,

|∫

⃗

⃗

⃗

⃗

|

(

) (I.3)

where

is the energy of the transition in the donor, and

is the energy of the transition
in the acceptor, and the integral is over all space. From eqs. (I.2) and (I.3) it can be
shown that, k
NRET
, is proportional to the inverse sixth power of separation between
dipoles [I.11] [I.12]. It is necessary to recognize that the matrix elements in eq. (I.3) are
the same as those that are involved for the optical transitions of light absorption and
emission. Theodor Förster expressed the NRET rate in terms of the emission and
absorption spectra of the donor and acceptor respectively. Förster’s achievement was to
show that NRET rate can be written in terms of quantities that can be measured. The
simplified and useful expression for the energy transfer rate was obtained by Förster [I.7]
is

(

)

∫

(I.4)
in which

is the radiative recombination rate of the donor in the absence of the
acceptor,  is the factor that contains information on the relative orientation of the two
dipoles,

is the index of refraction of the medium containing the dipoles, N
A
is
Avogadro’s Number,

is the normalized donor emission spectrum with the
11
quality ∫

,

is the molar absorptivity of the acceptor, and is the
wavelength of light associated with optical transition. The magnitude of the integral in
eq. I.4 depends on the overlap of the donor emission and acceptor absorption spectra and
captures both the need for energy conservation (i.e. resonance) and the oscillator strength
of optical transitions in the acceptor which is captured by the magnitude of the molar
absorptivity coefficient. This integral is usually called the overlap integral. The
radiative recombination rate,

, is related to the photoluminescence lifetime,

, and
the photoluminescence quantum efficiency, , (also abbreviated as QE) by

. The quantities and

can be determined experimentally, so all the
experimentally measureable quantities can be captured into one constant called the
Förster Radius, R
0
, that captures all the relevant characteristics of the system and is given
as

∫

(I.5)
and the NRET rate is expressed in the operational formula as

(

)

(I.6)

Clearly, for efficient NRET, the donor-acceptor separation must be less than

In order
to give credit to Förster for his contribution, NRET is often referred to as Förster resonant
energy transfer and abbreviated as FRET. Eqs. (I.5) and (I.6) are valid at any given
temperature so long as the absorption and emission spectra are representative of the
donor and acceptor at that temperature [I.11]. The temperature dependence of the NRET
12
rate therefore depends specifically on temperature dependence of the donor emission and
acceptor absorption spectra, and the NRET rate can either increase or decrease with
increasing temperature [I.11]. Eqs. (I.5) and (I.6) are useful for making estimates related
to NRET rates and understanding design criteria for the NRET based solar cell. Indeed in
chapter IV we will show that the NRET rate is not only dependent on the inverse sixth
power of donor-acceptor separation, but also on the temperature.
The historic literature on NRET focused on understanding transfer between
molecules in solution or between impurity atoms in a host crystal [I.11], both which have
emission and absorption spectra that are intrinsic properties of the particles involved in
energy transfer. In principle, however, there can be numerous donor-acceptor pairs that
can exhibit NRET. The development of nanocrystal quantum dots provides another more
flexible materials platform to study and utilize NRET. As described below, quantum dots
have absorption and emission spectra that are controlled by the extrinsic property of
particle size. This unique property allows for the flexibility to control the magnitude of
the overlap integral eq. I.4 by controlling the size of the donor and acceptor quantum
dots.

I.3 Quantum dots as light absorbers and NRET donors and acceptors
I.3.1 Quantum confinement
Quantum dots are a unique class of small particle that exhibit one essential
characteristic: the physical size of the small particle in all three spatial dimensions are
smaller than the de Broglie Wavelength for that material. For a particle of this size
13
regime, the discontinuity of atomic potentials at the boundaries of the particle arising
from either a second material or vacuum at the particle boundary can act as potential
barriers and thereby influence the motion of electrons in the particles. For quantum dots,
extended Bloch functions of the corresponding bulk material are not appropriate and a
different representation of electronic states is needed. When the quantum dot is
significantly larger than the inter-atomic spacing, the bulk band edges of the quantum dot
material and the surrounding materials can be treated as defining the effective potential
[I.12], [I.13] to confine the electrons and holes within the quantum dot. When confining
energy arising from the discontinuity in energy between the bulk band edge energy of the
particle and the surrounding material (that is, the ligands), E
conf
, is large, the simplest
description of the quantum dots potential energy is to approximate the confinement
energy as being infinite. In this case the potential can be represented as [I.13]

{
| |

| |

(I.7)

where

is the radius of the quantum dot, is the position inside the QD, and the zero
in energy is the bulk band edge. The solutions to the Schrodinger equation for this
potential are Bessel functions and the energies of the available electron states are given as
[I.13]

(I 8)
14
where

is the n
th
zero of the l
th
spherical Bessel function [I.13] and

is the effective
mass of the electron or hole. The energies

are with respect to the bulk band edge
energies which are taken as zero in eq I.7. The solutions in eq. I.8 show that only
discrete energies levels are available for single particle (electron) states. Due to the
similarities between the solution for this potential and the hydrogen atom, quantum dots
are frequently called artificial atoms. The values of n are usually written as 1,2,3… and
values of l are written as s,p,d ... to follow the standard notation in atomic physics. For
the case of the QD, the lowest two energy levels are the 1S and 1P levels.

I.3.2 Excitons in Quantum Dots
A second size effect that is important for understanding optical properties of
quantum dots is enhanced coulomb attraction between excited electrons and holes in
quantum dots. When the quantum dot smaller to than the bulk exciton Bohr radius, the
spatial confinement of electrons and holes acts so to enhance the coulomb attraction
between the two and increase the exciton binding energy [I.13]. The bulk exciton Bohr
radius, a
ex
, is given [I.14]

⁄
{

}

⁄
{ } (I.9)

where is the dielectric constant of the material,

and

are the electron rest mass
and electron-hole reduced mass respectively,

is the permittivity of free space, is the
reduced Planck’s constant, and is the elementary charge. The bracketed part in the
15
middle term is the well-known expression for the hydrogen Bohr radius with value of
0.53 Å. The exciton Bohr radius in a semiconductor represents the average separation
between an excited electron and hole in a particle with size that is much larger than the
separation. When the particle is smaller than the exciton Bohr radius the energy barrier
at the boundary will force the average separation between the electron and hole to
become smaller than the bulk exciton radius. The confinement acts to increase the
coulomb attraction between the electron and hole (i.e. increase the exciton binding
energy) and partially counteracts the increased kinetic energy due to quantum
confinement. The simplest expression to capture the confinement energy of the electron
and hole and the effects and give the energy of the lowest energy exciton energy, which
is also called the excitonic gap

[I.15] is

(

)

(

)

(I.10)

where

is the bulk band gap of the material,

is the optical dielectric constant of
the quantum dot, and

and

are the electron and hole effective mass respectively.
The third term in eq. I.10 represents the exciton binding energy, E
ex
. The single particle
states and the excitonic gap is illustrated schematically in Figure I.4. The exciton gap is
significant because it is the lowest energy optical transition in a quantum dot and
therefore can be monitored and easily identified in absorption and photoluminescence
experiments. This lowest energy exciton is also called the band-edge exciton and the
16
1S
e
-1S
h
exciton. Because the excitonic gap depends on the QD radius, optical studies can
and are frequently used to investigate the size of nanocrystal QDs.

Finally, because the emission and absorption spectra for quantum dots are depend on
size, therefore control over QD size allows for control over the absorption and emission
spectra and thus how the QDs will behave as NRET donors and acceptors.

Figure I.4. A schematic of single
particle energy levels and the lowest
energy exciton level in a quantum
dot. The bulk conduction and
valence band edges, E
CB,bulk
and
E
VB,bulk,
along with the confinement
energy due to the ligands, E
conf
form
the potential well. The single
particle levels are shown in grey and
the lowest energy exciton level is in
black. The dashed green arrow
represents the lowest energy
absorption transition that is the
excitonic gap. The exciton binding
energy, E
ex
, is illustrated.

17
I.3.3 Realization of quantum dots: epitaxial and colloidal quantum dots
For most semiconductors of technological interest the de Broglie wavelength
ranges from about 3 to 50 nm and correspondingly most quantum dots of this size or
below have between 1,000 and 100,000 atoms. From a practical standpoint, in order to
create materials with dimensions on this scale there are two main approaches: (1) to use
lattice mismatch and accompanying strain in vapor phase epitaxy to create self-assembled
defect-free small islands that act as quantum dots [I.16] and (2) to use chemical
techniques to synthesize sufficiently small nanocrystals in solution by nucleation and
growth [I.17]. The former has the advantage of being synthesized with epitaxial
confining barriers that provide very low defect density surfaces in an ultra-clean
environment that is conducive for fabrication of electronic devices. The latter has the
advantage that it allows for greater flexibility of chemical species used to create the QDs
and greater ranges of achievable QD sizes for a given material, but is limited by growth
conditions that inevitably contain high concentrations of chemical impurities by the
standard of purities required for most electronic devices. Colloidal quantum dots also
have advantage in terms of the range of post-synthesis manipulation possibilities owing
to their discrete existence in solution that allows for deposition of the colloidal quantum
dots into macroscopic quantum dot films or further growth of inorganic shells or organic
chemical groups onto their surfaces. For the present work, the benefits of flexibility and
possibility of post-growth manipulations out-weigh the disadvantages related to
impurities and thus colloidal quantum dots are used as light absorbers and NRET donors
and acceptors. Colloidal quantum dots are the subject of much of this dissertation and
18
are discussed in detail in chapters III, IV, and V, but first, some of their generic
characteristics are introduced for the purpose of explaining the function of a quantum dot
based NRET based solar cell in section I.4 next.
All colloidal quantum dots consist of a crystalline core with dimensions smaller
than the de Broglie wavelength and the material that provides the energy barrier for
confinement is typically organic ligands that bind to the QD surface. In addition to
providing the confinement energy, the ligands also prevent agglomeration when in
solution by passivating dangling orbitals of atoms on the surface of the quantum dot as
well as providing steric repulsion between the QDs and their environment – neighboring
quantum dots or otherwise. Due to the small size, and thus high surface to volume ration
compared to bulk materials, the absence of organic ligands would allow multiple
quantum dots in contact to chemically bind and agglomerate and change the essential size
dependent characteristics. In order for the colloidal QDs to be used for NRET there must
be resonance between the emission energy in the donor and absorption transition energy
in the acceptor. Therefore inter-QD NRET between QDs of the same chemical species
can occur from relatively small donors (with relatively large energy gap) to larger
acceptors (will smaller energy gap), but not the other way around. This is a key point for
the work in this dissertation and the proposed solar cell. Asymmetry of NRET from small
QDs to large QDs can in principle allow directed flow of energy from the site at which
photons are absorbed to the charge transport channels when many different sizes of QDs
are used and they are graded so the largest QDs are adjacent to the transport channels.
19
For comparison, achieving directed energy transfer over large distances with organic
molecules would require many layers with each being a distinctly different chemical.

I.4. Energy Alignment considerations in Quantum dot - Nanowire NRET based
solar cell
Given the above discussed this understanding of the NRET process and colloidal
quantum dots electronic structure, next the considerations for implementing an NRET
based solar cell with quantum dots as light absorbers and nanowires as charge transport
channels can be discussed. This section thus provides the background information
required to guide discussion of the specific problems that are addressed in this
dissertation in as discussed in section I.5.
The steps in the energy conversion process are shown in the energy band diagram
in Figure I.5 below. The overall efficiency of the NRET solar cell depends on the
product of the individual efficiencies of the sequential processes involved in energy
conversion as listed below [I.1] and described thereafter:
1. The probability that a solar photon impinging on solar cell will be absorbed by a QD,
f
ab
.
2. The probability that an exciton generated in any QD i, (i=1,m) away from the QD
adjacent to the transport channel (labeled QD
0
) reaches QD
0
by sequential QD-to-
QD NRET events,

.
3. The probability of NRET from an adjacent QD to the inorganic charge transport
channel,

.
20
4. The probability of transport of excited electron and hole create by NRET in the
transport channels to the external contacts, 
trans.

Figure I.5. Energy Band diagram of an NRET based solar cell utilizing quantum dots
dispersed around inorganic charge mobility transport channels. As described in the text,
the overall efficiency is related to the product of the efficiencies of the four processes
shown here. Brown arrows represent fast, non-radiative relaxations and the energy
barriers of confined electrons and holes are denoted as 
b,e
and
b,h
respectively.
Additional details are given in the text.

Under the reasonable assumption that the electrons and holes in the transport channels
can be separated with unity efficiency due to the small exciton binding energy transport
channels, the overall energy conversion efficiency from incident optical energy per unit
area to electrical energy per unit area, 
PCE
, of this device is given as

21

(I.11)

where 
0
is the maximum efficiency for a solar cell created from a single p-n junction
and depends on the band gap of the material used for the transport channel that contains
the built-in electric field, given by Shockley and Queisser [I.18]. Note the quantity 
PCE
does not account for the contribution to photocurrent due to charge carriers excited by
light absorbed directly in the high mobility channels, which will also occur to some
extent. Thus the actual efficiency of an NRET based solar cell will be greater than 
PCE
because of the contribution due to direct photon absorption in the transport channels.
For the first step of light absorption, the efficiency f
ab
, can be made close to unity
by making the solar cell sufficiently thick. For most densely packed QDs, using Beer’s
Law [I.5], the expression for

is

(

), where for the QD
absorption cross section is

, the packing of QDs is P, is the thickness of the QD
layer, and

is the radius of the QD including the contribution from the ligands. The
absorption cross section,

for the 1S
e
-1S
h
absorption peak in 3 nm diameter PbS QD
is about 0.025 nm
2
[I.19]. Assuming the QDs are arranged in close packed arrangement,
P = 0.74. Two microns will absorb 80% of the incident light at 800 nm. Thus, little
emphasis is placed on absorption in the QDs.
As in all solar cells, geminate recombination pathways that allow for relaxation of
the excited charge carriers before they reach the external load, compete with the desired
processes result in energy loss and must be minimized [I.4]. Therefore the focus is to
22
maximize the efficiency of each individual step by understanding the processes
competing with each.
The efficiency of migration of energy by NRET from where light is absorbed to
the QDs adjacent to the transport channels depends on the efficiency of the inter-QD
NRET process,

, and the number of NRET events, m, required for the energy to
reach the adjacent QDs. The inter-QD NRET efficiency is the probability that an exciton
on a donor QD will relax by NRET to an adjacent (nearest neighbor) acceptor QD.

is given as the NRET rate divided by the total decay rate, k
tot
, which is the sum of
decay by all pathways including NRET, radiative recombination (k
rad
), and non-radiative
recombination (k
non-rad
):

(I.12)

The radiative decay rate is largely an intrinsic property of the QD donor, so to increase

the objective is to minimize the non-radiative decay rates and maximize the NRET
rate. Non-radiative recombination acts to waste energy from absorbed light and is
primarily mediated by energy states in the intrinsic band gap that arise from defects due
to impurity atoms or the dangling orbitals at the surface. As discussed above in section
I.3.3, since most QDs have between 1,000 and 100,000

atoms, having just one impurity
atom per QD is the equivalent to very high bulk impurity concentrations of 1E17/cm
3
to

1E19/cm
3
. To put this in perspective, for the example of point defects such as gold or
nickel in silicon solar cells the typical level of acceptable impurity concentrations at
23
which there is an onset of impurity caused degradation by non-radiative recombination is
in the range from 1E13/cm
3
to 1E16/cm
3
[I.20]. Thus for the presence of a small number
of defects in the QDs we can expect a large effect on the non-radiative recombination
rate. Additionally, for all nanostructures, including colloidal quantum dots, the small
size leads to large surface to volume ratio, and thus the increased propensity for surface
related defects. Therefore the use of colloidal quantum dots requires control of synthesis
environment to reduce impurities and control of surface chemistry to reduce the number
of reactive dangling orbitals to ultimately minimize

and maximize

The quantity of interest,

, is the average probability that an exciton
created by absorption of photon in a QD between the transport channels will successfully
undergo sequential NRET events to reach the QDs adjacent to the channels.

depends on

and the number of NRET events needed for the given separation
between transport channels. For the case of size-ordered structures as shown in Figure
I.5 where the NRET processes are directed towards the transport channels the average
probability of energy transfer from excitons from m QDs in a row is,

[ ∑

] (I.13)

where m is number of QDs that spans half the gap between adjacent transport channels
trenches and the index i refers to the layer of QD where i = 1 identifies the first QD layer
adjacent to QDs in direct contact with the transport channels. The first term in the
bracket in the ride hand side of eq. I.13 represents the contribution due to direct
24
absorption in the QDs adjacent to the transport channels. For example, for 100 nm
spacing between transport channels and QDs center-to-center spaced 5 nm apart, m is
equal to 10. Equation I.13 shows that m should be minimized in order to maximize

. This, in turn, means that the spacing between transport channels must be
minimized.
The need for closely spaced transport channels also means that the transport
channels must be thin (to realize high fill factor for the QDs) and thus have high surface
area to volume ratio. The structural and chemical nature of the transport channel surfaces
will thus play an important role in determining the electronic properties. In the case of
the NRET solar cell of interest here, the transport channel surface chemical and structural
characteristics influence both

and

.
The efficiency

depends on the NRET rate from the QDs to the transport
channels and the sum of all relaxation pathways.

(I.14)

The NRET rate between a quantum dot and an adjacent charge transport channel is
proportional to the inverse third power of separation between the QD and the
semiconductor surface [I.21]. The difference in dimensionality (sixth vs third power) of
the rate law is due to the substrate electronic states extending in three dimensions.
The transport efficiency,

, is the ratio of generated carriers collected in the
external circuit to the carriers brought by NRET into the transport channels. Under the
25
reasonable assumption that the contact resistance between the semiconductor and the
metal contacts is negligible, the transport efficiency depends on the probability that a
minority carrier will diffuse from where it is excited to the region of the p-n junction that
contains a static electric field. This probability depends on the ratio of the average time
for a carrier to diffuse to the p-n junction region to the average time a carrier will exist in
an excited state before it relaxes by one of many possible pathways including radiative
recombination, defect mediated Shockley-Read-Hall recombination by point defects in
the bulk, or by surface states. For a nanostructured solar cell with high surface area to
volume ratio, such as the one depicted in Figure I.1, carrier recombination at the surface
is usually the primary cause of energy loss. Therefore much effort must be spent to
reduce the surface state density by controlling the chemistry of the transport channel
surface layer, depicted in red in Figure I.5, and thus increase carrier lifetime by reducing
the surface recombination rate. For the specific case of interest here, however,
approaches to reduce surface state density that also add a substantially thick physical
barrier of more than 1-2 nm (e.g. thick thermal oxide passivation) would have the
detrimental effect of hindering quantum dot to transport channel NRET and reducing

and thus would be unacceptable.
As in the majority of single-junction solar cells, the largest unavoidable sources of
energy loss are (1) losses due to the heat created when a hot electron or hole created by
absorption of photons with energy greater than the band gap relaxes to the band edge and
(2) losses due to transmission of photons with energy below the absorption edge of the
semiconductor. These are factors largely determining the values of 
0
, which depend on
26
the band gap of the solar cell. As noted above, the values of 
0
are commonly credited to
Shockly-Queisser [I.18] and called the Shockley-Queisser limit. For many
semiconductors used in traditional solar cells such as Si, GaAs, and CdTe, the 
0
values
fall in the range of 0.25 to 0.30.
Although Figure I.5 is drawn with quantum dots and inorganic, bulk
semiconductor transport channels in mind, this conceptual picture is applicable to a
variety of materials for each component. Next we discuss of how we chose a suitable
light absorber – transport channel pair for implantation and study.

I.5 Rationale for using Lead Sulfide Quantum Dots and Silicon Charge transport
channels
There are numerous possible combinations of absorbers that can acts as NRET
donors and transport channels that can act as NRET acceptors and satisfy the primary
requirement of donor emission – acceptor absorption spectra overlap as per eq. I.4. We
chose silicon as charge transport channels as the best choice for proof-of-concept work
because (1) there are a variety of well-developed growth and processing techniques for
silicon, (2) it has a band gap that is suitable for efficient single junction solar cells ( 
0
~
30% for silicon), and (3) high purity silicon that is suitable for photovoltaics is relatively
inexpensive and readily available. Silicon has a band gap (i.e. absorption edge) of 1.1
eV, and thus compatible absorbers should have emission energy that is slightly larger, in
the range of ~1.2 to 1.4 eV. Emission energies greater than this will result in substantial
energy losses due to thermalization of excited electrons and holes generated by NRET in
27
the silicon, and QDs with emission energies lower than this will not be able to donate
energy to silicon at all. The two species of inorganic quantum dots that can be
synthesized to emit in the range of 1.2 to 1.4 eV are lead sulfide and indium arsenide.
Indium arsenide quantum dots are relatively difficult to synthesize because of the lack of
available arsenic precursors and the toxicity of those that are used, so we decided to use
lead sulfide quantum dots as the light absorbers and NRET donors.

I.6. The Scope of this dissertation
The breadth of topics that must be addressed to understand such an NRET based
lead sulfide quantum dot – silicon transport channel hybrid solar cell is truly vast. This
work spans the fields of inorganic chemistry, crystal growth, and microelectronics
fabrication that are necessary to create the components and requires structural and optical
characterization to understand the processes involved in energy conversion. Most of the
experimental aspects related to synthesis, fabrication, and characterization techniques
used in this research are presented in Chapter II. After having established an
experimental foundation, the remainder of this dissertation is aimed at understanding, for
the case of PbS QDs and silicon transport channels, the physical processes involved in
photovoltaic energy conversion as expressed in eq. I.11 above. To this end, the focus of
this dissertation is on four main areas:
(1) Synthesis of lead sulfide quantum dots and introduction of a new approach to
photoluminescence quantum efficiency preserving ligand exchange.
28
(2) Time resolved photoluminescence dynamics studies of inter-QD NRET and
competing processes such as charge transfer in QD solids.
(3) High resolution transmission electron microscopy study and optical characteristics of
lead sulfide quantum dots on crystalline silicon and their photoluminescence.
(4) Progress toward fabrication of photovoltaic devices
Although each of these specific areas is ultimately aimed at understanding the
NRET based solar cell, each study is of value beyond the scope of this dissertation. Area
(1) is the topic of Chapter III. Lead sulfide quantum dots (PbS QDs) are the primary
building block for this device and the first step was to develop capabilities to synthesize
and manipulate them. All colloid quantum dots have two main characteristics that
govern their behavior: the size and chemical composition of the crystalline core and the
size and electronic properties of chemical species (ligand) bound to the outside surface of
the crystalline core. The former determines the energy band gap of the nanocrystal and
the latter determines (a) how the QDs interact with their environment and (b) the role that
defects, intended or otherwise, play in relaxation of excited carriers. Both of these
characteristics are addressed for the case of PbS QDs.
Bulk lead sulfide has a band gap of 0.41 eV and a relatively large exciton Bohr
radius of ~20 nm [I.22]. Because quantum dots have size dependent electronic structure
and exciton energy levels, the first step is to gain control over the synthesis to control
their size. In order to reach the emission energies of 1.2 to 1.4 eV as required for NRET
to silicon as an acceptor, the PbS QDs must be on average between 2.5 and 3 nm in
diameter.
29
Lead sulfide quantum dots are typically created with carboxylate ligands bound to
the lead cations at the crystalline core surface. Our principal addition to the current
literature, discussed in Chapter III, is our idea of using conjugated lead cation-ligands as
exchange units. By understanding that carboxylate ligands typically leave the QD
surface bound to a Pb cation and that exposed sulfur ions at the surface can oxidize to
form deep traps, we developed a new method of exchanging the carboxylate ligands on
as-grown PbS QDs by using lead-cation-ligand exchange units. The benefits of this
approach to ligand exchange are (1) the quantum efficiency is approximately the same
before and after ligand exchange and (2) the size distribution of QDs doesn’t change as a
result of ligand exchange. Thus we have the ability to create many ensembles of PbS
QDs in which the only major difference is the length of the ligand used to cap them and
thus the average inter-QD separation when in QD solids.
To proceed beyond studies of individual quantum dots we studied the interactions
between closely packed quantum dots including inter-QD NRET and its competing
processes. The focus of Chapter IV is the presentation of our results of an extensive
study of exciton decay dynamics in densely packed PbS QDs. This study is enabled by
the success of cation-ligand exchange that allows for control over spacing between
quantum dots when in densely packed arrangements called quantum dot solids.
Additionally, by monitoring the temperature-dependent photoluminescence decay at
different emission wavelengths that correspond to different portions of the QD size
distribution, we can distinguish between characteristics of the relatively large and
relatively small quantum dots within the ensemble size distribution. Thus, our systematic
30
study spans the parameter space of inter-QD separation, relative QD size, and
temperature. We find that the exciton decay in largest quantum dots, that do not have
any nearest neighbor energy acceptors, provides insight into charge transfer processes
and that NRET is dominant in the smallest quantum dots that have many nearest neighbor
NRET acceptors.
Following the energy flow in our photovoltaic device, the next step after study of
inter-QD energy transfer is study of the characteristics of lead sulfide quantum dots on
silicon surfaces, which is the topic of Chapter V. Our work on this subject consists of
structural studies enabled by a new approach to imaging the QD-crystalline
semiconductor interface by cross sectional transmission electron microscopy and
complementary optical characterization to investigate charge and energy transfer
processes. We present the first near atomic scale resolution cross-sectional simultaneous
images of the crystalline silicon nanopillar with a QD adsorbed onto it and thus the
interface as well.
Chapter VI covers progress toward fabrication of photovoltaic devices. Therein is
a presentation of preliminary work on fabricating nanostructure silicon solar cell
architectures to use as platform to study the entire power conversion process. Because of
the need to create high surface area structures, the primary obstacle in fabricating silicon
solar cell architectures is establishing suitable surface passivation approaches that will
reduce the surface trap density without introducing a thick surface layer that would
ultimately separate the quantum dots from the silicon surface and reduce

.
Methodology used to fabricate solar cells is aimed towards understanding the processes
31
involved in photovoltaic energy conversion, rather than creating the highest power
conversion efficiencies.
Finally in Chapter VII the overall work is summarized and directions for future
research are presented.

32
I.7 Chapter I References
I.1. S. Lu and A. Madhukar, Nonradiative Resonant Excitation Transfer from
Nanocrystal Quantum Dots to Adjacent Quantum Channels. Nano Lett., 7 (2007)
3443.

I.2. H. Hoppe and N.S. Sariciftci, Organic Solar Cells: An Overview. Journal of
Materials Research, 19 (2004).

I.3. S. Gunes, H. Neugebauer and N.S. Sariciftci, Conjugated Polymer-based Organic
Solar Cells. Chemical Reviews, 107 (2007) 1324-1338.

I.4. A. Goetzberger, J. Knoblach and B. Voss, Crystalline Silicon Solar Cells1998:
Wiley.

I.5. J.R. Lakowicz, Principles of Fluorescent Spectroscopy. 2nd ed1999, New York:
Klumew Academic/Plenum Publishers.

I.6. K.V. Mikkelsen and M.A. Ratner, Electron Tunneling in Solid-State Electon-
Transfer Reactions. Chemical Reviews 87 (1987) 113-153.
I.7. T. Förster, 10th Spiers Memorial Lecture. Transfer mechanisms of electronic
excitation. Discussions of the Faraday Society, 27 (1959) 7-17.
I.8. R. Clegg, The History of FRET Reviews in Fluorescence 2006, C. Geddes and J.
Lakowicz, Editors. 2006, Springer US. p. 1-45.
I.9. E.J. Bowen and B. Brocklehurst, Energy Transfer in Hydrocarbon Solutions.
Transactions of the Faraday Society, 49 (1953) 1131-1133.

I.10. L. Novotny and B. Hecht, Principles of Nano-Optics2012, New York: Cambridge
University Press.

I.11. D.L. Dexter, A Theory of Sensitized Luminescence in Solids. The Journal of
Chemical Physics, 21 (1953) 836-850.

I.12. A.L. Rogach, ed. Semiconductor Nanocrystal Quantum Dots. 2008, Springer:
New York.

I.13. V.I. Klimov, ed. Semiconductor and Metal Nanocrystals. 2004, Marcel Dekker,
Inc.: New York. 484.

I.14. P. Bhattacharya, Semiconductor Optoelectronic Devices. 2nd ed1997, Singapore:
Pearson Education.

33
I.15. M.G. Bawendi, M.L. Steigerwald and L.E. Brus, The Quantum Mechanics of
Larger Semiconductor Clusters ("Quantum Dots"). Annual Review of Physical
Chemistry, 41 (1990) 477-496.

I.16. S. Guha, A. Madhukar and K.C. Rajkumar, Onset of incoherency and defect
introduction in the initial stages of molecular beam epitaxical growth of highly
strained In
x
Ga
1-x
As on GaAs(100). Appl. Phys. Lett., 57 (1990) 2110-2112.

I.17. C.B. Murray, D.J. Norris and M.G. Bawendi, Synthesis and characterization of
nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor
nanocrystallites. J. Am. Chem. Soc., 115 (1993) 8706-8715.

I.18. W. Shockley and H.J. Queisser, Detailed Balance Limit of Efficiency of p-n
Junction Solar Cells. Journal of Applied Physics, 32 (1961) 510-519.

I.19. L. Cademartiri, E. Montanari, G. Calestani, A. Migliori, A. Guagliardi and G.A.
Ozin, Size-Dependent Extinction Coefficients of PbS Quantum Dots. J. Am.
Chem. Soc., 128 (2006) 10337-10346.

I.20. A.A. Istratov and E.R. Weber, Electrical properties and recombination activity of
copper, nickel and cobalt in silicon. Applied Physics A: Materials Science &
Processing, 66 (1998) 123-136.

I.21. R.R. Chance, A. Prock and R. Silbey, Molecular Fluorescence and Energy
Transfer Near Interfaces, I. Prigogine and S. Rice, Editors. 1976.

I.22. E.H. Sargent, Infrared Quantum Dots. Adv. Mater., 17 (2005) 515-522.

34
Chapter II: Experimental Details

The major experimental techniques used for this research fall into four categories
that encompass material synthesis and characterization. In the order corresponding to the
progression of work and ideas of this dissertation, these four techniques are (a)
nanocrystal quantum dot synthesis by nucleation and growth, (b) optical characterization
by photoluminescence and time-resolved photoluminescence, (c) structural
characterization by transmission electron microscopy, and (d) nanostructure fabrication
by electron beam lithography and reactive ion etching.

II.1. Quantum dot synthesis: apparatus, reactions, and procedures
Most colloidal nanocrystal quantum dots, such as those consisting of binary II-IV,
III-V, IV-VI compounds, are most often synthesized by nucleation and growth by
thermolysis of metallorganic precursors [II.1]. This is the process by which complex
organic molecules that contain the metal atoms that will be the cations in the QDs and
other molecules that contain atoms that will be anions in the QD react to form inorganic
single nanocrystals. Typically the nature of the reactions that lead from discrete precursor
molecules to nanocrystal quantum dots are unknown and only the initial state (i.e. the
precursors) and final state (i.e. the stable quantum dots after growth) are observed.
Synthesis of binary colloidal QDs consists of three primary steps: (i) preparation of
precursors, (ii) initiation of nucleation, and (iii) nanocrystal growth. Each synthesis
requires four chemical components: cation precursors, anion precursors, ligands, and a
solvent. Although the experimental conditions used in colloidal nanocrystal quantum
35
dot synthesis (i.e. solution chemistry) are always inherently high in impurity
concentration compared to high vacuum vapor phase synthesis, many steps are taken to
minimize the level of impurities present. The two main pieces of equipment used in QD
synthesis are the Schlenk line and the glove box, and they primarily are meant to reduce
the effects of impurities in the QDs. The former, however, is where all chemical
reactions are carried out, and some discussion is necessary to understand how it is
maintained and used. The latter simply provides an argon environment for weighing
chemicals, etc., so only a short description is included at the end of this sub section.
The Schlenk Line, shown in Figure II.1, creates a controlled and relatively inert
environment. It consists of an enclosed glass system with a heater and temperature
controller that can be connected to either an argon gas source or a rough vacuum pump.

Figure II.1. Schlenk line used in synthesis and manipulation of quantum dots.

three neck
flask
thermo-
couple
finger
Vacuum
Line
cold trap
flask heater
argon
line
36
The most important measurable parameter used to control the synthesis of QDs is
temperature. We control the temperature with a PID controller, heat source, and
thermocouple. To measure the temperature, we use a glass thermocouple finger inserted
into one of the three necks of the reaction vessel. The thermocouple is separated from the
solvent and chemical reactions by a thin layer of glass. The temperature that is measured
by the thermocouple depends on the length of the thermocouple, the size of the three neck
flask, and the volume of solvent in the flask. Therefore, for temperature sensitive
experiments such as synthesis of small (<4 nm diameter) QDs, it is crucial to use the
same glassware each time. The heat setting on the PID temperature controller for
volumes between 50 and 500 mL should be used to avoid overshooting the temperature
set point without unnecessarily slow heating rates. This point is not trivial because if the
temperature is changing at the time of injection the final size will not be what is expected
based on the thermocouple reading.
The vacuum system consists of a roughing pump (Kinetic Thermal System, model
VP100A) and a Varian thermocouple vacuum gauge (type 0531). The Schlenk line has
many glass-to-glass fittings sealed by vacuum grease that are relatively leaky and thus
not able to reach high vacuum. The baseline vacuum with a liquid nitrogen cooled trap
was typically between 40 and 110 mtorr for experiments done for this dissertation, and if
the pressure did not reach this range the fittings were detached, cleaned using lint-free
wipes, toluene and acetone, re-greased and re-attached. Cleaning the glass to glass
fittings must be done about once per year. Note that the large fitting for the cold trap
37
shown in Figure II.1 needs to be cleaned and re-greased about every three months and is
typically the first point to leak.
Most of the procedures for synthesizing nanocrystal QDs are aimed at creating an
environment with minimal chemical impurities that negatively impact some desired
property of the QDs. The glove box consists of a circuit of circulating argon that passes
through an activated carbon and a copper purification system. The activated carbon
(charcoal) removes volatile organic chemicals such as toluene from the environment.
Over time it becomes saturated and must be replaced about once a year. The copper
removes oxygen and water from the environment by reacting to form copper oxide. In
typical operation, the water level should be less than 1 ppm and the oxygen should be less
than 5 ppm. As the copper saturates, the efficiency of removing oxygen and water
decreases and the copper catalyst must be regenerated by extended heating in a reducing
environment consisting of 5% H
2
in N
2
forming gas.

In general, the amount of organic
vapors allowed into the circulation system should be minimized, and alcohols and amines
are particularly damaging to the copper catalyst. The circulation must be stopped when
these substances are used and the glove box should be purged afterwards.

II.1.1 PbS QD synthesis reactions and procedures
The approach we used for lead sulfide QD synthesis is a modified version of the
method of Hines and Scholes [II.2]. Lead sulfide QDs are synthesized by combining
lead-oleate (the cation precursor) and hexamethyldisilathiane (the anion precursor) in an
octadecene solvent. Hexamethyldisilathiane has the formula ((CH
3
)
3
Si)
2
S, is also called
38
bis(trimethylsilyl)sulfide, and is abbreviated as TMS
2
S. The oleate groups that are
attached to the lead cations in lead oleate ultimately become the ligands bonded to Pb on
as-grown PbS QDs. Octadecene is a long chained, non-polar alkane with one double
bond and high boiling point of 315° C. The high boiling point allows for reactions to
occur at elevated temperatures without the solvent evaporating significantly over the
course of an experiment. Use of octadecene also requires that all precursors be dissolved
in non-polar solvents that will mix well with octadecene.
To prepare the lead-oleate, lead oxide (99.9% metal basic, Sigma Aldrich) and
oleic acid (CH
3
(CH
2
)
7
HC=CH(CH
2
)
7
COOH, 99%, Sigma Aldrich) in octadecene (90%
technical grade, Sigma Aldrich) are weighed in a 25 mL three neck flask in the glove box
and transferred to the Schlenk Line. The structures of the oleic acid and
hexamethyldisilathiane are shown in Figure II.2.
These three chemical are exposed to air for less than one minute during transfer
between the glove box and the Schlenk line. Next, air in the flask is removed using a
vacuum pump. The octadecene bubbles profusely as it degasses during the first vacuum
exposure. Then, the flask is refilled with argon (ultra-high purity, 99.999%) and again
exposed to vacuum. This process is repeated three times and the third vacuum step is
allowed to proceed for about 10 minutes until an acceptable base pressure is achieved
(also, typically between 40 and 100 mTorr).
Next, the three neck flask is heated to roughly 85° C to allow for step 1 to occur.
The completion of the reaction is indicated by the transition from a diffuse yellow, the
39
appearance of the yellow lead oxide powder – octadecene solution, to a completely clear
and colorless solution of lead oleate in octadecene.

Figure II.2. Structures of oleic acid and hexamethyldisilathiane (TMS
2
S). One of each
type of atom is labeled and the color schemes are the same for both molecules. The lines
connecting balls (atoms) represent single chemical bonds except as noted.

Step 1: Oleic Acid and lead oxide yield lead oleate and water
2 CH
3
(CH
2
)
7
HC=CH(CH
2
)
7
COOH + PbO  (CH
3
(CH
2
)
7
HC=CH(CH
2
)
7
COO)
2
Pb + H
2
O

The lead-oleate solution is then degassed while at 85° C for 10 minutes to remove the
water created in step 1. The solution bubbles profusely for the first two or three minutes.
carbon
oxygen
sulfur
silicon
hexamethyldisilathiane
oleic acid
carbon – carbon
double bond

hydrogen

40
The system typically reaches base pressure within five minutes. Note that if the solution
is kept at elevated temperatures for an extended period of time (approximately two hours
or longer), it will become yellow, which is possibly an indication of small lead or lead
oxide precipitates forming. This should be avoided by keeping the degassing times short.
TMS
2
S is commercially available. To prepare for use, it is dissolved in
trioctylphosphine (TOP, 97%, STREM) in the glove box in a septum capped vial and not
exposed to air. The TOP is used to carry the TMS
2
S; typically only 40-200 L of TMS
2
S
is used, and this small volume is difficult to handle by itself. Octadecene can also be
used as a solvent for the TMS
2
S. Note that TMS
2
S has a powerful odor and it should
never be exposed to the working environment: only use in the glove box or fume hood.
After degassing, the lead oleate in octadecene solution is heated to the desired
injection temperature. After the solution stabilizes at the desired injection temperature
for roughly five minutes and while the lead oleate – octadecene is stirred vigorously, the
hexamethyldisilathiane -TOP solution is rapidly injected to induce step 2

Step 2:
Pb(CH
3
(CH
2
)
7
HC=CH(CH
2
)
7
COO)
2
+ (CH
3
)
3
Si S Si(CH
3
)
3
 oleate capped PbS QDs

After injection the solution is observed to go from clear to black. This change in
color indicates the formation of QDs that are large enough to absorb light in the visible
spectrum (i.e > 2 nm diameter) [II.3]. Typically after injection and during the growth
process, small aliquots (~ 10 L) of solution containing the QDs can be extracted to
41
monitor the progress of growth. The extraction process quickly reduces the temperature
of extracted material to room temperature (i.e. the temperature of the metal needle used in
extraction) and effectively stops QD growth. Thus these QDs can be analyzed to
investigate the progression of the growth. After the desired growth time, typically one to
ten minutes, the reaction flask with growth solution lifted from the heating mantle to
quickly to cool to room temperature. The grown solution is extracted from the reaction
flask without exposure to air.

II.1.2 Separation of nanocrystals from the growth solution
Extraction of the as-grown QDs from the growth solution to separate the QDs
from excess precursors is an important step in each QD synthesis. To separate the QDs
from the rest of the growth solution, the QDs must be precipitated and then dissolved in a
pure solvent for storage and subsequent use. In the glove box, the PbS QDs are
precipitated by slow addition of a polar solvent to the growth solution (that contains
mostly non-polar octadecene). The polar solvent must mix well with the growth solution
and not inadvertently affect the QDs or introduce defects. For PbS QDs, we typically use
acetone as the polar solvent, though dimethyl sulfoxide also works. Acetone is added
slowly until the solution becomes cloudy. The cloudy appearance indicates the first stage
of QD precipitation, which is the presence of larger agglomerated clusters of many QDs.
The amount of acetone necessary to induce precipitation depends on the size of the QDs
(i.e. larger QDs require less acetone). After addition of acetone, the cloudy solution is
centrifuged for five minutes at 5000 rpm. After centrifuging, the supernatant should be
42
colorless and the QDs should be in a precipitated pellet at the bottom of the vial. Next,
the supernatant is decanted and the precipitated PbS QDs are dissolved in toluene. Note
that if the supernatant is not colorless, some QDs remain in solution and more non-
solvent must be added. Next, the solution is further cleaned by adding acetone to the
toluene solution to allow for the QDs to precipitate in the centrifuge. The final solution
is dissolved in toluene and stored in the glove box in the dark. This entire process is
also referred to as the cleaning process.

II.2. Optical spectroscopy
In this dissertation the major techniques employed to examine the electronic
response of the synthesized PbS QDs are photoluminescence (PL) and time-resolved PL
in the optical regime. This section focuses on the instrumentation used for these studies
Optical characteristics of lead sulfide quantum dots are discussed in detail in chapters III
and IV. The lead sulfide quantum dots studied for this dissertation typically have
emission wavelengths in the range of 800 to 1200 nm, and each batch has a line width on
the scale of about 100 to 200 nm reflective of the variations in the QD size in the sampled
ensemble. In PbS QDs, PL decay occurs on a time scale between 10 ns and 10,000 ns,
which is relatively slow compared to the spontaneous decay in most other semiconductor
quantum dots. The time scale of processes in PbS QDs dictate many aspects of the
optical systems used to characterize them and guide the decisions related to the
experimental set-ups and measurements. The large line widths mean high wavelength
resolution is not necessary and therefore makes spectral detection relatively
43
straightforward. The long time scales of PL decay and the processes of interest such as
NRET dictate the time resolution of the electronics that are used in the time-resolved
measurements as described below.
Optical characterization is used in this work to extract information on a wide
variety of processes such as inter-QD energy and charge transfer that occur in the
quantum dots, and three optical set-ups were used in this thesis: (1) a set up to measure
temperature-dependent time resolved photoluminescence (TRPL) (2), a set up to measure
temperature-dependent time integrated photoluminescence (PL), and (3) a user facility
set-up in the NanoBio Core Facilities to measure PL of QDs in solution at room
temperature.

II.2.1 Time resolved photoluminescence
Time resolved photoluminescence (TRPL) measurements determine how the
intensity of emitted light from a luminescent sample, I
PL
(t), changes as a function of time
after excitation with a light pulse of short duration. Useful information on this technique
can be found in the textbook by Lakowicz [II.4]. The excitation pulse creates excitons
within the sample, all of which will eventually relax back to the ground state. Some will
relax by the process of radiative recombination and emit a photon that can be collected
and counted. The intensity of emitted light after a time t is therefore effectively a
measure of the remaining excitons in the sample at that time. Because the number of
remaining excitons after time t depends on the rates of all the processes by which
44
excitons can recombine or dissociate, the measurement of emitted photons can provide
information about all the mechanisms and rates.
An exciton in a quantum dot will have multiple channels by which it can relax,
and the relaxation rate,

, is the sum of the radiative recombination rate (

and the
total non-radiative decay rate (

), which is the sum of all possible non-radiative
decay mechanisms:

(II.1)

Note that the latter can correspond to multiple physical mechanisms such as Auger
recombination and Shockley-Read-Hall recombination. Non-radiative recombination and
exciton dissociation both act to reduce the number of excitons that can potentially emit
light and are therefore indistinguishable in TRPL measurements. Frequently in this work
we perform wavelength selective time-resolved measurements that probe the decay of a
subset decaying excitons that emit at a certain wavelength upon radiative recombination.
For the case that each exciton created by an excitation pulse has the same set of available
decay pathways, the rate law can be expressed as

(II.2)

that leads to a simple single exponential decay rate. The photoluminescence intensity
I
PL
(t) is proportional to the number of excitons, N, at that time and can thus be written as
45

(II.3)

where A is a constant. Additional degrees of complexity will arise if different parts of
the decaying population being examined have different decay pathways. As we will see
in chapter IV, the potential decay mechanisms for a given exciton can depend on the
exciton energy and local environment and require more complex analysis.
To measure I
PL
(t), we use the time correlated single photon counting technique.
In this technique, an incident excitation pulse creates many excitons, but on average one
photon per 50 incident pulses is detected. For each detected photon, the difference in
time between the excitation pulse and the detection is determined and marks a single
count. Therefore, in order to collect sufficient data to determine I
PL
(t), the process of
delivering an incident pulse and detecting a single photon must be repeated thousands of
times, and the time between incident pulses must be sufficiently long to allow for the
system to fully relax.
The time resolved photoluminescence set-up consists of a light source, timing
electronics, and light detection system as shown in Figure II.3. A detailed description of
the Madhukar group TRPL system used for the studies undertaken here can be found in
reference [II.5]. The light source consists of an Innova 310 argon ion laser that pumps a
mode-locked Coherent Mira 900D titanium sapphire (Ti:S) laser. The argon laser is
specified to output 8 W at 60 Amp, but we typically operate with a target power of 4.5 W
at 45 Amps. The Ti:S lasing medium can be tuned to lase between 750 nm and 850 nm,
but is typically operated at 800 nm. The pulse duration for this mode-locked cavity is
46
less than 1 ps and has a frequency of 54 MHz (18 ns between pulses). Because the time
scale of the physical processes that are of interest for work in this dissertation are many
orders of magnitude slower than 1 ps the duration of the pulse time does not influence the
measurements and the excitation time is considered infinitesimally small. However, the
frequency of pulses is too fast to allow for the QDs to fully relax between pulses.
Therefore we use a ‘pulse switch’ to deliver pulses to the sample at lower frequency. The
pulse switch uses an oscillating quartz crystal that deflects a fraction of the pulses out of
the cavity. In addition to determining the frequency of delivered pulses, the pulse switch
also triggers the delay electronics (Ortec 425A) that determines the time of the “STOP”
signal. The trigger from the pulse switch is delayed electronically for a time that can be
set to be slightly longer than both the laser pulse interval and the physical process of
interest. Typical values of delay range from 4 s to 80 s. For all experiments here, the
time for a hot electron or hole that has been excited to a state above the band edge to
relax to form a “band ed ge” exciton is much faster (~ 1 ps [II.6]) than any process of
interest in this dissertation and is thus ignored. Therefore the time that the radiative and
non-radiative decay processes are initiated, t = 0, is considered to be the time at which the
pulses impinge upon the sample.
Emitted light is collected by a lens and focused into a monochromator (CVI
Instruments Digikrom 242, wavelength resolution of 3 nm at 1 mm slit). The photons
passing through the monochromator are directed toward a micro-channel plate photo-
multiplier tube (PMT, model Hamamatsu R3809-U) and counted. The PMT is designed
47
for temporal measurements and the multiplication process creates a small spread in time
(which contributes to temporal uncertainty in the measurements) of about 25 ps.

Figure II.3. The time resolved photoluminescence set-up. Components in red boxes are
used to create laser pulses and detect emitted light. Components in blue boxes are timing
electronics.

Note that the PMT can be damaged if (1) the voltage to the multiplier tube is applied
without having cooled it by the thermoelectric cooler or (2) the PMT is exposed to room
48
light or other strong sources (flashlight or lamp light directed towards the entrance slit,
for example) when the voltage is on. Therefore it is common practice to reduce the PMT
voltage at any break in the experiment.
The signal from the PMT after the detection of a photon is amplified and
delivered to the PICO timing discriminator to trigger the ‘START’ signal. The action of
triggering the ‘START’ signal prompts the electronic request for the ‘STOP’ from the
time discriminator which is the delayed signal from the pulse switch. The difference in
time between the ‘START’ and ‘STOP’ signals is thus the difference between the delay
time set by the user and the exciton lifetime that leads to the emission of the photon that
was collected.
Errors can arise if the system cannot correctly match the detected photon to its
corresponding incident pulse or if multiple photons reach the PMT per incident pulse. In
the case that each pulse creates multiple photons that reach the PMT, only the first
detected photon will signal the ‘ START’ cue and thus the second photon will be ignored.
This will artificially skew the data to higher I
PL
(t) at short times. Therefore it is
necessary to ensure that each incident pulse will lead to much less than one collected
photon. In order to ensure that each pulse leads to on average much less than one
collected photon we monitor the total photon count rate with a photon counter. As a rule
of thumb, the total counts per second should be less than [54E6/DR]*0.02 where DR is
the pulse selection factor from the pulse switch and therefore [54E6/DR] is laser pulse
repetition rate for the system with a natural frequency of 54 mHz. This rule of thumb
means one photon is collected per 50 pulses. The number of detected photons per
49
second can be controlled by opening or closing the slits at the entrance to the
monochromator or inserting ND filters before the monochromator. Furthermore, the
count rates are monitored prior to every acquisition to ensure the proper rate.
The accuracy of the time resolved measurements can be determined by measuring
the light intensity as a function of time for photons that are reflected or diffusely scattered
from the sample. The measurement of the reflected photons is called the instrument
response function (IRF), and its width is a measure of the accuracy of the system. In our
set-up the primary limitation on the measurement accuracy is the uncertainty in delay
time. The width of the IRF increases with increasing delay time, and we find that the
width of the IRF ranges from ~2 ns to 30 ns for delay times from 4 s to 80 s.
Fortunately, the long delay times (with relatively wide IRF functions) are only used when
physical processes of interest occur on long time scales, so for all measurements the
width of the IRF is much shorter than the time scale of the physical processes of interest.
Practically, the IRF is measured by setting the monochromator to collect photons
of the same wavelength as the excitation pulses. Typically, the intensity of measured
photons at this wavelength is very high so ND filters of 3.0 or greater must be used at the
excitation or collection.

II.2.2 Time integrated photoluminescence
The NMDL time-integrated PL set-up can utilize a variety of light sources but
always uses a Spex 1404 0.85m monochromator and a Ge detector. The light sources
include the Ar+ laser, the Ti:S laser, and a low power 532 nm diode laser (120 mW).
50
Emitted light is collected by a lens and delivered to the monochromator. The wavelength
resolution of this monochromator is ~1 Å, but this resolution is not utilized. We typically
used 5 nm wavelength steps during our PL measurements because the spectral line widths
are greater than 100 nm. The Ge detector must be cooled by liquid nitrogen for 30
minutes prior to the first measurement. A chopper is always used to modulate the
excitation, and the output from the Ge detector is amplified by a Stanford Lock-In
Amplifier.
Additionally, basic in-solution PL measurements of QDs were frequently
performed at the USC NanoBio Physics core facilities. The system there consists of a Xe
arc lamp (65 W) and an InGaAs detector. The excitation wavelengths range from 400nm
to 1000 nm and the detection can range from 700 nm to 1600 nm. The manufacturers of
the instrument, PTI, supply a calibration file to account for system (monochromator and
InGaAs detector) detectivity and collection efficiency.
For both TRPL measurements and PL measurements we use a Janis variable
temperature cold finger cryostat that can work with either liquid nitrogen or liquid
helium. All PbS QD samples for PL and TRPL are prepared and loaded into the cryostat
in the argon environment of the glove box. The sealed cryostat is transferred from the
glove box to the optical set up and immediately pumped to low pressure (<1E-5 torr)
without exposure to air. Additionally, we use an Oxford bath cryostat that operates
between 78K and room temperature at ambient pressure. Operating at ambient pressure
allows us to use quartz cuvets without vacuum seal to hold solutions of QDs at low
51
temperature, therefore TRPL measurements of QDs in-solution at low temperature are
done with the Oxford cryostat.

II.3 Transmission electron microscopy
Structural characterization of the quantum dots was primarily carried out using
transmission electron microscopy (TEM). In TEM, high energy collimated electrons
impinge upon a specimen that is sufficiently thin to allow for transmission of the most of
the incident electrons. The high energy (~ 200 keV) electrons have very short
wavelengths on the scale of a few picometers that enable diffraction-based structural
information and typically provide energy loss based chemical information on an atomic
scale. Successful use of TEM demands command on: (1) the physics of the interactions
between the electrons and the specimens that allows for information to be extracted and
(2) the instrumentation, its operation, and its limitations in order to perform the
experiments. Useful text books on TEM have been written by Reimer [II.7] and Carter
and Williams [II.8]. The former is a good source for understanding the physics involved
in TEM and the latter is a useful source of practical information in all aspects of TEM.
Although present day TEMs can be used in a variety of imaging modes, such as
scanning transmission mode, and collect information from such sources as emitted x-rays
from a sample or energy loss due to inelastically scattered electrons, the TEM work done
for this dissertation employed mainly broad beam, phase contrast high resolution
transmission electron microscopy. In this mode, the most basic experimental condition
consists of a uniform and collimated electron beam with electron energy between 100 and
52
300 keV that impinges on a thin crystalline sample between 0 and 200 nm thick, and
utilizes interference between diffracted electrons and directly transmitted electrons to
create useful images. The objectives are to understand how the electron – specimen
interactions determine the exiting electron wavefunctions, both in terms of spatial
variations in intensity and in direction, and how the instrument can collect the exiting
electrons to form an image. Electron - specimen interactions can be classified into two
major categories: inelastic scattering and elastic scattering. The former is the most basic
and occurs in all types of imaging. It gives rise to mass-thickness contrast. The latter is
most important in crystalline specimens and can be used to create high resolution phase
contrast lattice images. This section describes first the basic electron-specimen
interactions and then the instrumentation.

II.3.1 Electron diffraction in the TEM
For crystalline specimens, it is possible to use diffracted beams to extract useful
information about the atomic scale structure of the specimen. This section will describe
electron diffraction and the next section will show how the diffracted beams can be used
to create lattice images. The physical origin of electron diffraction is interactions between
the incident electrons and the electrons in the crystals and is proportional to the electron
density in the specimen. For a crystalline specimen with the set of reciprocal lattice
vectors, , the electron density ⃗ at position ⃗ can be represented by the sum over
all reciprocal lattice vectors [II.9] as

(II.4)
53
⃗

∑

( ⃗

)

where

are Fourier coefficients. Note that vectors are written in bold text and the
symbol ⃗ is used to distinguish the position vector from the Förster Radius, r, as
described in chapter I. The periodicity of the electron density has implications for how
an incident plane wave can scatter from the crystal. The total elastic scattering
amplitude, , of an incident plane wave with wavevector

and wavefunction ⃗

⃗
into a scattered plane wave with wavevector

and wavefunction ⃗

⃗
is given as,

∫ ∑

( ⃗

)

⃗

∑

(

)

where the integral is over the crystal volume. Therefore for every reciprocal lattice
vector, there will be one allowed value of

, and the diffraction condition is thus
written

(II.6)

This is another form of the well-known Bragg Law:

, where

is
the spacing between planes with indices h,k,and l, is the wavelength of the diffracted
(II.5)
54
particle (electron),

is the angle between the incident and diffracted beams, and is an
integer.
To determine the scattering amplitude for a given diffracted beam in an actual
TEM specimen, we must consider two additional factors about the crystal: the atomic
basic within a unit cell and the actual size of the crystalline specimen. To account for
the atoms in the basis, we consider that the electron density ⃗

within a unit cell can
be expressed as the sum of the electron densities for each individual atom, indexed ,
which depends only on the distance from the position of the ion core, ⃗

, within the unit
cell. Thus ⃗

∑

⃗ ⃗

, where

is an atomic property. For a crystal with
unit cells, the integral over the crystal volume in eq. II.5 can be approximated as times
the integral over of a single unit cell. The scattering amplitude for the diffraction
condition for

is

∫ ∑

(II.7)

If we assume that the total electron density in the unit cell can be decomposed into the
sum of the electron densities due to each atom, the integral over the unit cell can be
written as the sum of the electron densities for the A atoms in a unit cell,

∑

⃗

(II.8)

55
where

is the atomic scattering factor for the j
th
atom which depends on both

and

.
Thus the intensity of

depends on the species and positions of the atoms in the basis.
For most crystals of interest, there are only a few atoms per unit cell (a few values of

and ⃗

). Therefore eq. (II.8) is usually written as a set of rules that relate specific
reciprocal lattice vector to the expected scatting amplitude for a given structure.
In determining the right had side of eq. II.5, use of a delta function is only strictly valid
for the case on an infinite crystal. Because TEM imaging requires transmission of
electrons through the sample and hence specimen thicknesses of less than about 200 nm,
an actual TEM specimen can never be considered as an infinite crystal. For any TEM
specimen, it is important to recognize that small deviations from the diffraction condition

can still allow for substantial diffracted intensity, and that the diffracted
intensity decreases with increasing deviation from the precise diffraction condition. The
deviation from the exact diffraction condition is given by the parameter , called the
excitation error that is defined by the expression,

. (II.9)

The scattering amplitude for diffracted electrons depends strongly on the excitation error,
and

is reduced by a factor

[II.7] where

is the excitation error for the
diffracted beam with corresponding vector

, L is the thickness of the sample in the
direction of the incident beam, and a is the crystal lattice parameter. At = 0 the
scattering amplitude is maximum. As the crystal thickness is reduced, the diffracted
56
intensity will have less dependence on excitation error. In other words, reduction of
diffraction intensity with increasing excitation error (i.e deviation from the exact
diffraction condition) is more pronounced for thick specimens. This phenomenon is
called the thin foil effect.
For a collimated electron beam impinging on a crystalline TEM specimen, there
are usually many combinations of and

vectors that satisfy the diffraction condition.
To visualize which reciprocal lattice points will satisfy the diffraction condition for a
given incident beam orientation with respect to the sample and the influence of excitation
error on scattering amplitude, it is useful to use Ewald’s sphere construction in the
reciprocal space as shown in Figure II.4. There will be a diffracted beam each time the
Ewald’s sphere crosses a reciprocal lattice spot.

Figure II.4. Ewald’s Sphere and a repr esentation of the possible diffracted beams. Two
combinations of G and k
D
are included in the schematic, each reciprocal lattice points
enclosed by green rectangles are those that satisfy the diffraction condition for the crystal
orientation represented here. The reciprocal lattice points (black ovals) are elongated in
the direction of the beam because of the thin foil effect described in the text.

57
The effect of excitation error on diffracted intensity,

|

|

, is visualized in Figure
II.5. The horizontal axis on the plot on the right hand side of the Figure II.4 shows the
diffraction intensity relative to the maximum intensity at s = 0. This shows that the first
zero in diffraction intensity occurs when the excitation error has magnitude of 1/L.

Figure II.5. Excitation errors and the diffracted intensity, I
i
(s) for the case of a 10 nm
thick foil. The excitation error is plotted on the vertical scale on the left panel, and the
diffracted intensity I
i
(s) is relative to the maximum diffracted intensity at s=0.

When the incident beam is oriented along a zone axis, as is the case in Figure II.4, the
excitation error for the closest points in reciprocal space is typically small. However, if
the incident beam is oriented away from a zone axis, the excitation error will depend on
how far the beam is oriented from the zone axis. For a sample with thickness L, the size
of the reciprocal lattice spots which represents the magnitude of the upper limit of
deviation in reciprocal space from the Bragg Condition that can allow for diffraction is
1/L. Accordingly, for diffraction from a set of planes with spacing d
hkl
, the upper limit
58
for angular departure of the incident beam from the precise diffraction condition (at s=0),
 
max
, that can still allow for diffraction is  
max
=Sin
-1
[d
hkl
/L] [II.10]. This is illustrated
in Figure II.6.

Figure II.6. The relationship between deviation from the optimum incident electron
orientation (red, s ≈ 0), the maximum angular deviation (blue, marked as prime) with s =
s
max
and . The planar spacing d
hkl
corresponds to 1/ | |, where is independent of the
incident electron direction.

With this understanding of the diffraction condition and how characteristics of the
crystalline sample affect the intensity of diffracted beams for a given crystalline


s
max

𝑮
k
0

k'
0

k
D

k'
D

59
orientation, the next step is to understand how the diffracted beams can be used to create
useful images. This requires understanding of the lenses in the TEM and their
limitations.

II.3.2 Inelastic scattering and mass-thickness contrast
The impinging electrons can interact with the atoms in the sample because of
electron-electron repulsion and electron-nucleus interactions (i.e. Rutherford scattering).
Mass-thickness contrast relies on the latter. Mass-thickness contrast imaging is the most
basic form of imaging and will occur for all types of samples, crystalline or otherwise.
Inelactistic scattering is proportional to atomic number of the atoms interacting with the
electron beam and higher Z elements will scatter a larger fraction of incident electrons
than will lighter elements. Mass thickness contrast in a TEM can be understood by
examining which electrons will be deflected and unable to contribute to the image. The
cross section for scattering to an angle greater than is [II.7]

∫
|

|

(II.10)

and

is the Rutherford scattering factor that increases with atomic number Z and
sample thickness and decreases with increasing incident electron energy [II.8]. In
general these interactions act to deflect the trajectory of the incident electrons.
Practically, the minimum angle, , is determined by the collection angle determined by
the objective aperture; electrons that are scattered at angles greater than are blocked
60
and thus unable to contribute to the image. The values of vary with position
across the sample as the thickness and atomic composition changes. Therefore, mass-
thickness contrast is useful in determining the location of particle edges, and is primarily
used in this dissertation to estimate QD diameter. Mass-thickness contrast in TEM,
however, cannot provide information about the atomic structure of the specimen.

II.3.3 The transmission electron microscope imaging system
A TEM consists of four main parts: (1) an electron source and accelerating
system, (2) a condenser lens system to deliver the electrons to the specimen (i.e. control
the incident electron directions), (3) an objective lens system to collect and magnify the
exiting electrons from the specimen, and (4) a projector lens system to further magnify
the image. Details of these systems are discussed in Carter and Williams [II.8]. TEMs
use the Lorentz force from magnetic lenses to control the trajectory of the electrons
impinging upon the specimen and the electrons that have been transmitted through or
scattered by the specimen. The most important lens for phase contrast imaging is the
objective lens that deflects the diffracted beams back towards the optic axis and allows
for interference between the diffracted and direct beams. Magnetic lenses are typically
far from ideal and deviations from ideality tend to increase with lateral distance from the
optic axis. Rather than focusing a collimated beam to a single point, in a standard TEM
the electrons impinging far from the optic axis are overly deflected and focused to a point
above the ideal focal plane. This is spherical aberration. The need to limit the problems
arising from spherical aberrations also motivates microscopists to use high energy
61
electrons for phase contrast imaging. From Bragg’s Law

it’s clear that
high energy electrons, and hence those with relatively short wavelength,  will lead to
smaller diffracted angles for a given planar spacing. Diffracted beams with smaller
values of

will thus deviate less distance from the optic axis in the space between the
specimen and the objective lens, and therefore are subjected to less spherical aberration
than diffracted beams with large values of .
A key to understanding TEM phase contrast imaging is understanding the
objective lens spherical aberrations. To describe the imaging properties of the objective
lens system independently from the sample, in the simplest sense, we must understand
how to counteract problems arising from spherical aberration of the objective lens by
adjusting the focus of the objective lens [II.8]. Spherical aberration has the effect of
focusing electrons at greater distances from the optic axis to higher focal planes.
Therefore changing the focal strength of the objective lens can bring into focus the
electrons at different distances from the optic axis. To predict which diffracted beams
will be faithfully transmitted though the objective lens system of the TEM and be capable
of being used for phase contrast imaging (as described below), a useful expression called
the contrast transfer function given by eq. (II.11) [II.8] relates the coefficient of spherical
aberration (C
s
) and the defocus value ( ) for spatial frequencies corresponding to the
inverse planar spacing ( ), as

[

] (II.11)

62
where is the wavelength of the electron. For values of of 1 or -1, the TEM
objective lens system can transmit information for the corresponding values strongly
and these frequencies will appear in the image. As the values depart trend from 1
and approach 0 the information for spatial transmitted progressively weaker and for
= 0 information is lost [II.8]. Therefore small negative values of will balance the
effect of spherical aberrations. This expression provides information regarding the extend
in which spherical aberrations will limit the resolution that can be achieved in contrast
imaging and shows that, to some extent, adjusting the defocus can counteract the
detrimental effects of spherical aberrations. The optimum defocus value to balance the
effects of spherical aberrations is called the Scherzer defocus,

and is given as

√

(II.12)

Plots of for two different values of are shown in Figure II.7 for the C
s
of 1.1 mm
operative in the JEOL 2100F TEM at USC employed for most of the studies. In
practice, a crystalline sample will have only a few key discrete spatial frequencies
corresponding to spacing of low index planes that are near the diffraction condition for a
given orientation. Thus, the when operating the TEM the objective focus is simply
adjusted to maximize the clarity for the frequencies that are visible.
Note that for TEMs with aberration correction for the objective lens system, C
s

values below 1 m can be obtained. For these cases, the expression for contrast transfer
function given in eq. II.11 above is no longer relevant because the chromatic aberrations
63
that result from energy variations (and thus velocity variations) in the electrons emitted
from the source limit the information transfer through the TEM.

Figure II.7. Contrast Transfer Function for C
s
= 1.1 mm and f values of -60 nm (dark
blue, Scherzer) and -70 nm (dark red). The arrow represents the spatial frequencies that
correspond to a typical spatial frequency used in TEM imaging: the Si (111) planar
spacing (3.1 Å). Circles represent the upper limit of resolution for each defocus value.
For Scherzer defocus, the greatest range of frequencies will be transferred faithfully
though the objective lens system. The frequencies in the region of the dark blue curve
enclosed by the blue box will be faithfully transmitted though the objective lens. Note
that C
s
specification for the USC JEOL 2100F is 1.1 mm.

II.3.4 Phase contrast imaging with diffracted beams
Ewald’s sphere shows that, for a given orientation of a crystalline specimen with
respect to the incident beam, there will be many diffracted beams, and equation II.11 and
Figure II.6 show that only the diffracted beams that correspond to the smallest spatial
frequencies (greatest planar spacing) will be faithfully transmitted though the TEM
imaging system. For these diffracted beams, it is possible to use phase contrast between
64
the diffracted and transmitted (not scattered) beams and utilize their superposition and
interference between the two beams to create useful images [II.8]. The total
wavefunction, ⃗ that includes both the direct and diffracted components is [II.8]

⃗

⃗

⃗

(II.13)

where

and

are the amplitudes of the direct and diffracted beams respectively.
Using the diffraction conditions we have,

⃗

⃗
[

⃗

] (II.14)

The intensity as a function of position in the image plane of the objective lens, ⃗ is the
modulus square of the total wavefunction:

⃗

⃗ ⃗

⃗ (II.15)

Thus we expect that the intensity of the image will have periodicity of 1/ | |, or so called
lattice fringes, that correspond to planar spacing 1/ | |. Utilizing phase contrast for
lattice imaging is typically referred to as high resolution TEM imaging. For a specimen
that is oriented so multiple diffracted beams are used for phase contrast the image will
appear as an interference pattern with summed periodic intensity of each of the
diffraction conditions contributing to phase contrast. This condition is commonly met by
65
imaging along a zone axis that allows multiple sets of planes from the same family to be
used for phase contrast.

II.3.5 Specific aspects of imaging PbS QDs
In this dissertation, TEM samples generally consist of the rock salt structure lead
sulfide nanocrystals dispersed on amorphous carbon of the typical TEM Cu grid
specimen holder. The rock salt structure is two interpenetrating face centered cubic
lattices, one of cations, and one of anions, that are shifted by a vector [1/2,0,0]. For the
eight atoms in the unit cell, the structure factor follows the rules for rock salt written for
the case of PbS for the scattering amplitudes following eq. (II.8) as,

|

| if h,k, and l are all even
|

| if h,k, and l are all odd
if h,k, and l are mixed,

where

and

are the atomic scattering factors for lead and sulfur respectively. For
PbS QDs , the {111}, {002}, and {220} planes with spacing of 3.42 Å, 2.97 Å, and 2.09
Å, respectively, are most commonly observed in high resolution images.
Many different TEM instruments were used in this dissertation work as listed
below, and all are capable of producing high resolution lattice images of PbS QDs.
1. Akashi OO2-B with LaB
6
thermionic emission source at the Center for
Electron Microscopy and MicroAnalysis (CEMMA).
66
2. JEOL 2100 with LaB
6
thermionic emission source and C
s
of 1.1 mm at the
USC Health Science Campus in the group of Dr. David Hinton.
3. JEOL 2100F with tungsten field emission source and C
s
of 1.1 mm at
CEMMA.
4. FEI Titan 300 kV with tungsten field emission source and objective lens
aberration corrector at Wright Patterson Air Force Base.

The images reported in Chapter III were taken with the Akashi and the JEOL 2100 with
LaB
6
and the images reported in Chapter V were taken on the aberration corrected
microscope at Wright Patterson Air Force Base.

II.3.6 TEM sample preparation for colloidal QD specimens on amorphous carbon
support films
Specimen preparation for imaging colloidal QDs in a TEM is very simple: two or
three drops of dilute solutions of 0.1 to 2 mg/mL are dropped onto TEM grid with
amorphous carbon support film. We prefer to use Ted Pella lacey carbon with ultra-thin
amorphous (~ 5 nm thick) carbon grids (product number 01824) to maximize contrast.
Additionally, well-ordered 2D arrays of QDs can be created by slow evaporation of the
solvent that contains the QDs. Following the work of Ryan et. al. [II.11] we find that
well-ordered 2D arrays of spherical QDs can be obtained by slow evaporation of a
solvent confined between parallel plates.
67
Finally, I note that details of the new approach to specimen preparation and TEM
imaging of QDs on crystalline substrates, as for PbS QDs on c-Si, introduced in this
dissertation, are given in Chapter V.

II.4. Silicon processing techniques
In this dissertation, silicon processing techniques are used to fabricate nanopillars
that are used as a platform for (i) cross sectional TEM studies of the silicon – nanocrystal
quantum dot interface (the subject of Chapter V) and (ii) fabricated solar cell
architectures (the subject of Chapter VI). Both classes of silicon structures consist of
features with lateral dimensions on the scale of 100 nm and etch depths between 500 and
2000 nm. Outlines of the processes used to create silicon structures for each application
are included in the corresponding chapters but included here are the details of the two
major techniques employed: electron beam lithography and deep reactive ion etching.

II.4.1 Electron beam lithography
Briefly, electron beam lithography can be described as the process of using a
focused electron beam to expose certain areas of a polymer film (also called resist) that
will undergo some change as a result of electron exposure, which then can allow for
preferential wet chemical etching (developing) of the exposed or unexposed resist. The
main advantage of electron beam lithography is the ability to focus the electron beam
onto a very small area (~2 nm diameter spot) and thus has the potential to define very
small features. Changes in the resist due to electron exposure result a change in the
68
solubility of the exposed polymer in special solvents (i.e. the developer) with respect to
the unexposed polymer. For positive tone resists, the electron beam acts to severe the
polymer chains into subunits with average molecular weights that are much smaller than
the average of that in the original polymer chain. The smaller subunits have increased
solubility in certain solvents called developers, and thus the exposed region can be
removed in the developer. For negative toned resists, the electron exposure acts to cross-
link adjacent polymer chains. The cross-linked regions have decreased solubility and
thus remain after exposure to a suitable developer. Each resist requires a characteristic
amount of charge per unit area, or dose, to create sufficient change in the resist structure
to allow for high contrast during development.
In most EBL processes, the limiting factor that determines the minimum size
features that can be created is the interaction volume of the impinging electrons within
the polymer resist. The impinging electrons have kinetic energy on the scale of 10 to 100
keV but the bonds in the polymer only require roughly 5 eV to break. Therefore, each
impinging electron can scatter inelastically many times within the resist and break many
bonds. The minimum feature size is thus the interaction volume which is determined by
the lateral (perpendicular to the beam) extent of the scattering within the resist rather than
the spot size of the focused electrons.
In addition to the capability to create features that are very small, the most
important benefit of EBL for research applications is the ability to change exposure
patterns easily without the need to create a new mask, as is needed for photolithography
and many other techniques such as nanoimprint lithography. The primary drawback of
69
EBL is the fact that exposure of the resist is done serially, and therefore is relatively slow
compared to parallel processes such as photolithography or nanoimprint lithography.
Because of the serial nature of EBL the total exposure time (also called the write time)
for a given experiment must always be taken into consideration.
In order to carry out an EBL experiment, each exposure requires the following
steps: creation of an electronic pattern, preparation of the substrate with resist, and
exposure set-up and execution. The electronic pattern defines the features that will be
written and is created by software that is specific for each EBL system. The electronic
pattern contains all information regarding the features, such as size and placement, and
allows for a dose factor to be defined for each feature. The dose factor scales a nominal
dose as described below and allows for different features to be subject to different doses.
Substrates with resists are typically prepared by spin coating.
The exposure set-up consists of three steps: defining the coordinate systems,
focusing the electron beam, and defining the exposure parameters. The Raith EBL
system used for these experiments at USC uses three coordinate systems: the (X,Y)
coordinates that define locations on the sample holder, the (U,V) coordinate system to
define locations on the sample substrate, and the (u,v) coordinate system to define
locations and dimensions of the features in the electronic exposure pattern. The
coordinate systems are depicted in Figure II.7. The substrate coordinates are defined by
defining the (X,Y) coordinates of point 1 as the (U,V) origin and defining the U axis as
the line that connects points 1 and 2. Point 2 can be at any location along the substrate
edge and is only necessary to define the direction of the U axis. Each electronic pattern
70
has its own (u,v) coordinates so many patterns can be written on the same substrate. The
positions in each electron pattern that correspond to the center of the lower left write field
is linked to a specific (U,V) position.
Focusing the beam is crucial for creating well defined features. Small, 20 nm
diameter gold nanocrystals are used to aid in focusing. Gold nanocrystals that are
suspended in water are commercially available (from Ted Pella, for examples) and are
deposited onto the substrate in a region away from where the patterns are to be written.
Proper focus is achieved when facets on individual 20 nm diameter nanocrystals can be
resolved.
When the beam is focused, the next step is to define how both the beam and stage
will move during the exposure. The electronic pattern is divided into segments called
write fields. Each write field represents the region of the pattern that is exposed when the
stage is stationary at a single location. Write fields are typically (25 m)
2
or (100 m)
2
.
The features within each write field divide the patterns into arrays of points and the
points are exposed sequentially by allowing the beam to dwell on the points for a defined
time depending on the desired dose and step size. For each pattern, the step size, write
field size, and dose can be defined.
The USC Raith instrument links the (U,V) coordinates of the substrate to the (u,v)
coordinates of the pattern by assigning a specific (U,V) point as the center of the lower
left write field of each pattern. The key parameter related to exposure is the charge per
unit area, or dose, and beam step size. The required dose to create the desired change in
the resist mainly depends on the characteristics of the resist and its thickness. The total
71
exposure time for given pattern depends on the dose required to sufficiently change the
resist and the total area to be exposed. However, the greater influence on exposure time
is the beam settling time and the stage settling time. The former is the time it takes for
the beam to move between exposure points and the latter is the time it takes for the stage
to move between write fields. Thus large step sizes and large write fields are at times
necessary to have manageable write times.

Figure II.8. Coordinate Systems for the stage, substrates, and patterns used in the Raith
System. The stage coordinates are fixed. During the set-up for each exposure, the
substrate coordinates are linked to the stage coordinates and the pattern coordinates are
linked to the substrate coordinates. Multiple pattern coordinates can be linked to the
same substrate coordinate systems.

II.4.2 Details for specific electron beam lithography processes
Two resists are used in this work – one positive and one negative. The positive
resist is poly-methyl methacrylate (PMMA) with average molecular weight of 950,000
72
Daltons at 4% concentration by mass in Anisole. This product is referred to as PMMA
950K A4. The negative resist is hydrogen silsesquioxane (HSQ) (Dow Chemical Corp,
product number XR-1541, 6% in methyl isobutyl ketone). For both resists, 20 kV is
used with the 30 m condenser aperture which leads to a beam current of ~320 pA.
For the PMMA recipe, sample preparation consists of two steps. First, the
substrates are degreased with trichloroethylene, acetone, methanol, and deionized water.
Next, the 950 A4 resist is spun on for 40 seconds at 4000 rpm and baked for two minutes
at 200C. The PMMA is about 200 nm thick after this preparation. The exposure uses 20
nm steps and 100 m write fields. The dose for strip features on the scale of 100-200 nm
wide is 240 C/cm
2
. For a 1 mm
2
pattern with densely packed strip features, the write
time is about one hour. After exposure, the patterns are developed in 3 methyl isobutyl
ketone (MIBK): 1 isopropanol (IPA) for 40 seconds to remove the exposed PMMA. The
post developing rinse is done with IPA only.
For the HSQ recipe, the substrates are degreased and etched in 49% HF for 15 s to
remove the native oxide. The HSQ is spun onto the substrates for 40 seconds at 6000
rpm and baked for one minute at 120C. The HSQ layer is about 60 nm thick. In the EBL
tool, the exposure parameters are 10 nm step size and 25 m write fields. The dose for
strip features on the scale of 100 nm wide is 6000 C/cm
2
. The dose for HSQ is
significantly greater than for PMMA, but because the patterns typically used with HSQ
have sparse features the write time for a 1 mm
2
pattern is also typically about one hour.
After exposure the patterns are developed in an aqueous solution containing 1% NaOH
73
and 4% NaCl by weight following the work of Yang and Berggren [II.12] for 40 seconds
and rinsed in DI water.

II.4.3 Reactive ion etching
Reactive ion etching (RIE) is used to create prototype photovoltaic devices and to
create the TEM specimens used in the studies of the quantum dot – semiconductor
interface. Reactive ion etching employs an external energy source (typically an
oscillating electric field) to create a vapor-phase plasma that contains ions and radicals.
RIE has many advantages over wet chemical etching, including the flexibility to use the
increased chemical reactivity of the ions and radicals over ground state neutral molecules
to achieve high etch rates, and also the ability to impart significant kinetic energy to the
ions to etch by sputtering material. The latter ultimately allows for anisotropic etching
which is conducive for fabrication of high aspect ratio and nanoscale features. In this
work we use standard RIE with CF
4
based plasmas to etch SiO
2
and a more elaborate
technique based on a two-step process to etch Si.
Standard RIE uses a RF frequency power source to decompose CF
4
-based
plasmas into a variety of neutral species and ions including F
+
ions and CF
X
+
ions where
X = 1,2, or 3. The RF power source acts to accelerate both electrons and ions in the
plasma. Additionally, increasing the RF power acts to increase both the density and
energy of the ions. The etching process has two key aspects. One is that the F+ ions
react with the silicon or silicon dioxide material to form SiF
4
and SiOF respectively.
Formation of either product, both of which are volatile, allows for removal of material.
74
The other is that CF
X
+
ions have a large sticking coefficient on silicon and during etching
these ions will deposit on the surface to form a (CF
2
)
N
polymer layer. This type of
polymer can also be removed by energetic F+ ions, but its presence will act to reduce and
in some cases even stop the etching of the underneath silicon or silicon dioxide. To
combat the problems related to the deposition of (CF
2
)
N
and the resulting reduction in
silicon or SiO2 etch rate, usually oxygen is added to the plasma to rapidly remove the
deposited polymer and thus allow for unobstructed etching of the underneath SiO
2
or Si.

II.4.4 Deep reactive ion etching by the Bosch process
To create the trenches for the silicon solar cell structure and the silicon
nanopillars used in the TEM studies, we employ a specific two-step etching process in an
inductively coupled plasma (ICP) referred to as the Bosch process [II.13]. ICP etching
has the benefit over standard RIE instruments in that the density of the reactive ions in
the plasma and the ion energy can be controlled separately and that the minimum
pressure needed to maintain the plasma is much lower than in RIE. In an ICP plasma, the
region of the chamber that has the highest density of ions and radicals is a separated from
the sample being etched. Thus, ICP is considered a remote plasma. As described below,
this process uses the deposition of (CF
2
)
N
polymer

to enhance the anisotropy of etching.
The two steps in this process are, first, an etch step with SF
6
based plasma and, second, a
deposition step with C
4
F
8
based plasma. In the first step, the SF
6
gas decomposes into
SF
5
+ and F+ ions and utilizes physical etching mainly by energetic F+ ions to etch the
silicon. In this step, the gas pressure is typically low (~ 10 mTorr) to allow for a
75
relatively long mean free path of the F+ ions. Because the ICP plasma is remote and the
pressure is relatively low, the F+ ions impinge nearly perpendicular to the sample
surface.
The second step in the cycle is deposition of hydrofluorocarbons. The
hydrofluorocarbon ions and radicals in the C
4
F
8
based plasma have high sticking
coefficients on Si at room temperature and will act to coat the surfaces that were freshly
etched in the prior etch step. Because of the cyclic nature of the etching, each etch-
deposition cycle will result in a characteristic undulation. Each period of undulation
corresponds to one cycle of the two-step process.
The DRIE done for this dissertation used an Oxford PlasmaLab 100 ICP etch tool.
Ten parameters are used in the Bosch process including five for the etch step and five for
the deposition step. These are ICP power, RF power, inlet gas content (C
4
F
8
or SF
6
) and
flow, gas pressure, and etch/deposition time. We used the following two sets of
parameters for Si etching and polymer deposition to protect the etched sidewalls
respectively: (1) etch step time of 4 seconds, 30 standard cubic centimeters per minute
(sccm) of SF
6
, 500 W ICP power, 40 W RF power, and 10 mTorr of SF
6
and (2)
deposition step of 5 seconds, 80 sccm of C
4
F
8
, 500 W ICP power, 10W RF power, and 18
mTorr of C
4
F
8
.

76
II.5. Chapter II References
II.1 V.I. Klimov, ed. Semiconductor and Metal Nanocrystals. 2004, Marcel Dekker,
Inc.: New York. 484.

II.2. M.A. Hines and G.D. Scholes, Colloidal PbS Nanocrystals with Size-Tunable
Near-Infrared Emission: Observation of Post-Synthesis Self-Narrowing of the
Particle Size Distribution. Adv. Mater., 15 (2003) 1844-1849.

II.3. I. Moreels, K. Lambert, D. Smeets, D. De Muynck, T. Nollet, J.C. Martins, F.
Vanhaecke, A. Vantomme, C. Delerue, G. Allan and Z. Hens, Size-Dependent
Optical Properties of Colloidal PbS Quantum Dots. ACS Nano, 3 (2009) 3023-
3030.

II.4. J.R. Lakowicz, Principles of Fluorescent Spectroscopy. 2nd ed1999, New York:
Klumew Academic/Plenum Publishers.

II.5. S. Lu, Some studies of nanocrystal quantum dots on chemically functionalized
substrates (semiconductors) for novel biological sensing, Ph.D. Dissertation,
University of Southern California (2006)..

II.6 A.J. Nozik, Spectroscopy and Hot Electron Relaxation Dynamics in
Semiconductor Quantum Wells and Quantum Dots, Annual Review of Physical
Chemistry, 52 (2001) 193-231

II.7. L. Reimer, Transmission Electron Microscopy: Physics of Image Formation and
Microanalysis. 4th ed1997, Heidelberg: Springer. 584.

II.8. D.B. Williams and C.B. Carter, Transmission Electron Microscopy: A Textbook
for Materials Science1996, New York: Springer.

II.9 C. Kittel, Introduction to Solid State Physics. Seventh ed1996: John Wiley & Sons,
Inc. 673.

II.10. P. Fraundorf, W. Qin, P. Moeck and E. Mandell, Making sense of nanocrystal
lattice fringes. Journal of Applied Physics, 98 (2005) 114308-114308-10.

II.11. K.M. Ryan, A. Mastroianni, K.A. Stancil, H. Liu and A.P. Alivisatos, Electric-
Field-Assisted Assembly of Perpendicularly Oriented Nanorod Superlattices.
Nano Letters, 6 (2006) 1479-1482.

II.12. J.K.W. Yang and K.K. Berggren. Using high-contrast salty development of
hydrogen silsesquioxane for sub-10-nm half-pitch lithography. 2007. AVS.
77

II.13. F. Laerner and A. Schilp, Method of anisotropically etching silicon, 1996, Robert
Bosch: United States of America.

78
Chapter III: PbS Nanocrystal quantum dot synthesis, ligand
exchange, and quantum dot solids

This chapter covers our investigations relating to individual PbS quantum dots
including composition, physical characteristics, and electronic structure as well as work
relating to PbS QD synthesis and post-growth manipulation using cation-ligand
exchange. Several important, yet subtle details of PbS QDs are described with emphasis
on the important relations among surface chemistry and those properties central to
controlling QD design QDs for various applications.

III.1. Colloidal quantum dots
Colloidal nanocrystal quantum dots are a subject of immense interest in the past
20 years and a key component of the field of nanoscience. Interest in this subject
accelerated following pioneering work by Brus et. al. in the early 1980’s [III.1], which
pointed out fundamental aspects of semiconductor nanocrystals and experimentally
verified relations between nanocrystal quantum dot size and absorption edge energy, thus
demonstrating the quantum confinement effect in nanocrystal QDs. Two key
developments further propelled the subject in the 1990’s and allowed for wide spread use
and investigation of colloidal quantum dots: (1) Experiments by Murray and Bawendi
[III.2] precisely controlled QD sizes and achieved narrow size distributions for Cd-based
QDs and (2) Hines and Guyot-Sionnest and Dabbousi et al. [III.3] [III.4] created
epitaxial shell layers on quantum dots that provide well-passivated surfaces, which
79
dramatically increase the efficiency of light emission (i.e., reduction of non-radiative
recombination rates) in Cd-based II-VI QDs. The ability to form inorganic shells
protecting the core quantum dots marks the earliest major development in post-synthesis
manipulation. Creating these shells allows greater flexibility in controlling the chemistry
of the organic ligands (that are still necessarily on the surface of the inorganic shell)
without introduction of defects, which can affect the QD core and its luminescence
properties. In particular, the ability to grow epitaxial shells allowed for further organic
functionalization that allows for high QE QDs to be used in aqueous environments and in
conjunction with biological molecules that bind as fluorescent tags to specific proteins
and thus act as cellular probes [III.5] [III.6]. Beyond the first successful application of
QDs as biological markers, more recently has the community turned to quantum dots as a
platform for optoelectronic devices such as photodetectors [III.7], light emitting diodes
[III.8], Schottky-type solar cells [III.9], and solar cells based on the junction between n-
type and p-type QD-solids [III.10]. QD based optoelectronic devices typically require
macroscopic quantities of densely packed and electronically coupled quantum dots called
QD solids. The properties of the QD solids depend on the both the characteristics of
individual quantum dots such as chemical species and stoichiometry, the organic ligands
that cap them when in solution, possible extrinsic defects, and size distribution of the
QDs that comprise the solid and the degree of coupling between the QDs. Therefore, the
all of these factors must be considered when creating QDs that are to be used in
optoelectronic devices.

80
III.1.1 Lead sulfide quantum dots: electronic structure
During the past ten years, interest in lead salt nanocrystal quantum dots has
increased tremendously, due in part to their potential as light absorbers in photovoltaics.
Lead sulfide QDs have numerous interesting properties that make them stand out against
other major classes of QDs such as II-VI colloidal quantum dots of CdSe or III-V self-
assembled quantum dots of InAs. Although all quantum dots share the common size-
dependent electronic structure, there are details that stem from the bulk properties of the
material that also play an important role in how these QDs will behave. For example,
investigating lead sulfide quantum dots with a particle-in-a-box model is insufficient
because this model loses much information regarding the surface chemistry and subtle
details of the electronic structure that ultimately play a significant role in how the QDs
function. In order to understand the properties of lead sulfide quantum dots, one must
first understand the properties of bulk lead sulfide.
Lead (II) sulfide is a rock salt crystal with lattice parameter of 5.94 Å and bulk
band gap of 0.41 eV at room temperature. Lead sulfide has high dielectric optical
constant (17.2) and small effective mass for both the electrons and holes (0.105 m
0
),
which lead to large exciton Bohr radius of 20 nm. The bulk valence band maxima and
conduction band minima are both at the L point of the Brillouin zone. There are four
equivalent L-Points in the Brillioun zone for both the valence band edge and the
conduction band edge. Therefore, the band edge states are 8-fold degenerate (including
spin). The conduction band edge states are mainly Pb p-like and the valence band states
are mainly Se p-like at the band edges [III.11]. The Pb 6s orbitals are many eV below the
valence band edge and thus chemically inactive. Also note that though lead sulfide
81
quantum dots are the subject of interest here, they have a close cousin in lead selenide
quantum dots. Studies of PbS and PbSe QDs have many similarities, so briefly, it’s
important to note that both have rock salt structure and conduction band and valence band
edges at the L-point of the Brillioun Zone, but PbSe has a slightly higher dielectric
constant (optical dielectric constant of 23 for PbSe compared to 17.2 for PbS), a larger
exciton Bohr radius (46 nm for PbSe compared to 20 nm for PbS), and PbSe is more
susceptible to oxidation than PbS.
Both the electron and hole levels in PbS QDs are strongly confined because of the
large exciton Bohr Radius for PbS QDs with diameters in the range of interest in this
dissertation of less than 4 nm [III.12]. The absorption edge for PbS QDs of the size
range used in most of our optical studies ranges from 1.3 to 1.7 eV, which is three to four
times greater than the bulk band gap. For all colloidal quantum dots, the electronic
structure depends on both the effects of quantum confinement and the inevitable surface
defects which can result from foreign impurities or the intrinsic characteristics of the
dangling bonds of atoms at the QD surface. Because of these complexities, there is yet
to be consensus regarding the electronic structure of PbS QDs in terms of the nature and
origin of electronic states. As in all electronic devices, the energy structure is of critical
importance so it behooves us to survey the current understanding of the electronic
structure of individual PbS QDs, the effects of surface chemistry and stoichiometry, and
the trends in electronic structure with relation to PbS QD size are of critical importance,.
Although it is well known that quantum confined energy levels depend strongly on the
82
QD size in the size regime below the exciton Bohr radius, other size-dependent
characteristics that effect their surface chemistry and photoluminescence behavior.
All colloidal quantum dots require a surface layer that creates an energy barrier
for quantum confinement. Most colloidal QDs consist of crystalline cores of binary
compounds and have surface layers of binary inorganic material or organic ligands.
When the surface layer is a binary compound with a larger bandgap that is grown
epitaxially around the core, (e.g. CdSe cores with with ZnS shells), dangling orbitals on
both the core cation and core anion are passivated. In such cases, the density of surface
states is typically much lower than a bare surface. The most common alternative to using
epitaxial binary shells is to use a single type of organic ligand to cap the QDs. Typically
ligands bind to either the cations or the anions, thus leaving the dangling orbitals on the
opposing species unpassivated. The implications of having ligands that only bind to one
type of atom can be explained using a specific example; the most common approach to
synthesis uses lead oleate as the lead precursor and results in oleate ligands on the surface
of the QDs. These oleate ligands are anions with a charge of approximately negative one
and bind to lead cations at the surface. The density of oleate anions on the surface is
estimated to be three per nm
2
[III.13], which corresponds to approximately one oleate
anion per two surface lead cations suggesting that some Pb atoms on the surface are not
passivated by ligands. Also, because these ligands are negatively charged, there must be
excess Pb cations on the QD surface to balance the negative charge and thus the
stoichiometry of the oleate capped QD is biased towards Pb cation rich. As the size of
the QD decreases, the surface to volume ratio increases and the oleate ligands to
83
inorganic atoms ratio also increases. Consequently, as QD size decreases, the overall
ratio of lead to sulfur in the QD increases [III.14]. Fortunately, there are two related
characteristics of PbS QDs that suggest excess lead is beneficial for high quantum
efficiency: First, it is known that sulfur atoms on the surface of PbS QDs can oxidize to
form deep traps that can allow for non-radiative recombination [III.15], and second, for
oleate-capped PbS QDs with varying sizes prepared under the same conditions, the
quantum efficiency increases with decreasing size and increasing Pb to S ratio [III.13]
[III.16]. These observations suggest maintaining a Pb-rich stoichiometry is critical to
forming PbS QDs with high quantum efficiency. The density of states (DOS) is
considerably higher in the bulk valence band than the bulk conduction band.
Calculations suggest that variations in 1S
e
levels with size are much greater than
variations in 1S
h
levels with size [III.17] and that the 1S
e
levels are more sparse in energy
than the 1Sh levels. Experimental studies of trends in energy of the highest occupied
quantum dot energy states by photoelectron emission [III.18] and of trends in energy
conduction band states by cyclic voltammetry both conclude that variation in electron
levels with size are much greater than variation in low unoccupied quantum dot energy
level with size [III.19]. Data from Jasieniak et al. [III.18] and Hyun et al. [III.19] show
the relations of the absolute energies at 1S
e
and 1S
h
levels as functions of absorption
peak wavelength (which is analogous to QD size) are shown in Figure III.1. Similarities
in the trends from both data sets are remarkable given the two different approaches
(photoelectron emission v. cyclic voltammetry). Additionally, both photoelectron and
cyclic voltammetry measurements are consistent with trends predicted from calculation
84
[III.20]. Figure III.1 also shows the energies of the Silicon conduction band edge and
valence band edge with the upper and lower blue lines respectively. This information
regarding the size dependence of PbS QD energy levels is called upon in both Chapters
IV and V.

700 800 900 1000 1100 1200 1300 1400
-5.2
-5.0
-4.8
-4.6
-4.4
-4.2
-4.0
-3.8
-3.6
-3.4
Silicon Valence Band Edge
Silicon Conduction Band Edge
1Sh
1Se
SMALL QD
Absorption Peak
Jasieniak 2011
Hyun 2008
Energy (eV)
1st Exciton Absorption Peak Wavelength (nm)

Figure III.1. PbS QD 1Se and 1Sh levels as function of QD size as represented by
absorption peak wavelength [III.18][III.19]. The 1S
e
level varies much more with size
than the 1Sh level. However, for small QDs with absorption peak marked by the dashed
line, the confinement energies for both the 1Se and 1Sh level are significant. The upper
and lower blue lines represent the silicon conduction band and silicon valence band edges
respectively. The data in this figure is called upon in both Chapters IV and V.

Several reports investigators assume that energy levels in the electron manifold are
symmetric to the levels in the hole manifold because electron and effective hole effective
masses are equal. Work relying on the assumption that the confinement energy affects
electron levels within the same as hole level are listed in [III.17]. However, data
85
presented in Figure III.1 shows that this assumption is incorrect for PbS QDs and show
that effective mass approximations are insufficient for PbS QDs.

III.1.2 Stokes’ shift, radiative lifetime, and mid-gap states in PbS QDs
Optical studies of PbS QDs show two additional and key trends as functions of
decreasing QD size: (1) A large difference in energy between the first absorption peak
and the emission peak (which is generically referred to as the Stokes’ shift) that increases
with decreasing quantum dot size and (2) long radiative lifetime that increases with
decreasing size [III.21]. Both of these factors point to the presence of a mid-gap state
between the 1Se and 1Sh level as explained below.
The two typical contributions to the Stokes shift in QDs that originate in their
intrinsic electronic structure are the Frank-Condon shift and the difference in energy
between the strongly absorbing exciton states and the lowest emitting exciton state. The
Frank-Condon shift is due to changes in lattice vibrational modes, which accompany
changes in electronic charge distribution. This shift results from formation of an exciton
and changes in lattice vibration modes, which typically act to rearrange electronic states
in ways that reduce the energy of the transition between the 1Se and 1Sh levels.
The difference in energy between the strongly-absorbing exciton and the lowest
emitting states is related to the fact that the lowest energy exciton levels will split into
multiple levels due to exchange interactions [III.20]. The difference also occurs because
higher energy exciton states typically have greater oscillator strength, which determines
absorption-peak energy, but the lowest energy level will dominate in light emission and
86
determine the emission peak position. The theoretical underpinnings of origin of the
Stokes’ shift on PbS QDs have not been investigated. However, calculations for PbSe
QDs suggest that the contribution due to the Frank-Condon shift for 2.5 nm diameter
PbSe QDs is 30 meV [III.22]. Contributions to the Stokes’ shi ft in PbSe QDs resulting
frome difference in the highly-absorbing exciton levels and the lowest eneregy-emitting
exciton level is 80 meV for 2.6 nm diameter QDs [III.20]. Oleate-capped PbS QDs 2.6
nm in diameter have absorption peak at 805 nm and emission peaks at 950 nm and a
corresponding Stokes Shift is of 230 meV. Thus the experimentally observed Stokes
Shift is much greater than expected sum of the two intrinsic contributions described
above.
Another revealing characteristic of small PbS QDs, and of lead salt QDs in
general, is their long radiative lifetime (>2 s at room temperature) as contrasted against
CdSe QDs which have radiative lifetime on the order of some tens of nanoseconds at
room temperature [III.23]. Both the Stokes’ Shift and the radiative lifetime decrease
dramatically with increasing PbS QD size; for PbS QDs larger than ~6 nm the Stokes’
Shift is approximately zero and the radiative lifetime is ~500 ns [III.21]. The drastic
change in exciton lifetime with size suggests a fundamentally different transition larger
and smaller QDs. This relationship between the lifetime and the Stokes shift suggests the
presence of an additional, mid-gap energy level that is active in light emission for small
QDs but not for large QDs. A three level system can capture the observed experimental
behavior, and the basic band diagram for PbS QDs is shown in Figure III.2.
87
The two key experimental observations described above as well as the shapes of
the absorption and emission spectra can be captured in this model assuming that
oscillator strength for optical transitions between the 1S
e
and 1S
h
level is much greater
than for optical transitions between the mid-gap state and the 1S
e
level. For small QDs,
the Stokes’ Shift E
Stokes
is much greater than room temperature thermal energy and the
charge is trapped in long-lifetime mid gap state. As the QD size increases, E
Stokes
falls
below the thermal energy and light emission from the 1S
e
state dominates and thus larger
PbS QDs have very small Stokes’ shift. Additional evidence for the presence of mid -gap
states are indicated by photo-induced absorption measurements [III.24].

Other explanations proposed for this long radiative lifetime include: (1)
Screening between the electron and hole due to the high dielectric constant of the PbS
Figure III.2. A three level energy
diagram for PbS QDs. Solid red
lines represent the 1S
e
and 1S
h
levels,
which determine the energy of the
absorption peak. The dashed red
lines represent excited states involved
in absorption (green arrow) of
energetic photons, and the blue line
represents the energy of the mid-gap
state. The Stokes’ Shift as labeled
depends on the size of the QD. The
transition corresponding to
photoluminescence is shown by the
red arrow. Brown arrows represent
fast non-radiative relaxations.

88
QDs [III.25] [III.26], and (2) The presence of a lowest-energy exciton state that is dark
and therefore requires thermal activation to reach the bright state required for emission
[III.20] [III.27]. The former cannot account for the large variations in radiative lifetime
as a function of QD size and the latter is contradicted by studies that suggest that the
bright exciton – dark exciton splitting energy is some tens of eV and thus does not
significantly affect radiative lifetimes [III.28].
Although it’s crucial to account for the presence of the mid -gap states, their origin
remains unknown. Presumably the mid-gap states are unrelated to the oleate ligands
because long radiative lifetime at room temperature (>1 s), which is indicative of the
mid-gap state, is observed in two systems without oleate ligands: small PbSe core - CdSe
shell QDs [III.29] [III.30] and small three nm diameter PbS QDs encapsulated in glass
without organic ligands [III.27]. Additionally, studies of electronic transport in films of
small three nm diameter anion-rich PbS QDs have also identified mid-gap states at 400
meV below the 1Se level [III.31].
Understanding these aspects of the electronic structure of PbS QDs is necessary
for understanding the inter-QD energy and charge transfer presented in Chapter IV. This
chapter contains details of PbS QD synthesis and characterization based on optical
measurements and TEM analysis and on our new approach to ligand exchange using lead
cation-ligand complexes.

89
III.2 Synthesis and characterization of PbS QD
The primary objective in synthesizing PbS QDs is to make suitable NRET donors
for silicon as an acceptor. QDs that emit light in the energy range of 1.2 to 1.4 eV with
high QE ensures spectral overlap with Si with absorption threshold of 1.1 eV.
Additionally, we grow larger quantum dots for other studies related to the structure of
QD solids and studies of QDs on silicon substrates. For all these purposes, lead
sulfide quantum do ts are grown using lead oleate and hexamethydisiylthiane as lead and
sulfur precursors, respectively. Sulfur is the limiting reactant, which ensures that oleate
groups terminate the surfaces of the as-grown PbS QD s. Lead terminated surfaces are
desirable for reasons discussed above.
Two growth recipes were commonly used to create PbS QDs for optical and
structural studies respectively. Small (~2.6 nm diameter) PbS QDs for optical studies
were created as follows. Ninety milligrams of PbO and 220 mg of oleic acid (99%) were
dissolved in octadecene (90%) at 90 C. After degassing, the lead oleate-octadecene
solution was heated in argon to 120 C and 35.5 mg of hexamethyldisilythiane in 2 ml of
trioctylphoshine at 4°C was rapidly injected. The overall lead-sulfur ratio in the growth
solution is 2:1. At these growth conditions, the final PbS QD size is reached about one
minute after injection:samples taken after one minute of growth and after 10 minutes of
growth show the same absorption spectra and thus size distribution.
Large (~6 nm diameter) PbS QDs for structural studies were synthesized by
dissolving 180 mg of PbO in 1.4 grams of oleic acid and 2.6 grams of octadecene. This
solution is degassed at 100° C for 10 minutes. The solution is heated to 150 C and 35.5
90
mg of hexamethyldisilythiane in 2 ml of trioctylphoshine at room temperature is rapidly
injected. After 10 minutes, another 35.5 mg of hexamethyldisilythiane in 2 ml of
trioctylphoshine is slowly added drop-wise over about 10 minutes (one drop per three to
four seconds). Slow addition allows continued growth without nucleation of additional
particles. After the drop-wise additions, the QDs are allowed to grow for an additional
10 minutes at 100 C. The Pb-oleate content present in the solution prior to the first
injection is sufficiently large that lead will be in excess after the initial injection and
throughout the drop-by drop injection of an additional TMS
2
S precursor. This ensures
that lead-oleate is the limiting reactant and that the large PbS QDs are lead terminated.

III.2.1 Quantum efficiency of PbS QDs by comparison to IR125
The most basic and essential characterizations of as-grown ensemble of small
QDs are the absorption and emission spectra when in solution as shown in Figure III.3.
The peaks in both the absorption spectra and emission spectra fit well to a single
Gaussian distribution as shown by the red lines on Figure III.3. Gaussian absorption and
emission distributions for QDs indicate that the spectra comes from single type of optical
transition within a population of QDs having a single size distribution [1III.21]. The
absorption full-width-at-half-maximum intensity (FWHM) is 270 meV and the emission
FWHM is 220 meV. The emission FWHM is less than the absorption FWHM because of
the size-dependent Stokes’s shift in PbS QDs. Within a single ensemble, the smallest
QDs that have 1Se to 1Sh transitions at the highest energy will experience larger Stokes’
Shifts than the largest QDs with the smallest 1Se to 1Se transition energy which results in
line narrowing of the PL spectra with respect to the absorption spectra.
91

Figure III.3. Absorption (gray) and emission spectrum (black) for small PbS QDs
illustrating the large 150 nm Stokes’ Shift. The red solid and dashed line s are Gaussian
fits.

The absorption peak wavelength is a measure of the 1Se to 1Sh transition energy
and can be used to estimate QD size. The emission spectra are used to determine the
quantum efficiency (QE). A Reference Dyewith known QE, IR-125, is used to estimate
the QE of the QDs. This dye has a QE of 13% in dimethylsulfoxide at 700 nm excitation,
and has the benefit that its QE does not degrade significantly over time when stored in an
inert environment such as the argon glove box.
QE is estimated by comparing the ratio of total emission intensity from an IR-125
solution with the total emission intensity of a solution of QDs when both solutions have
the same absorption strength at the excitation wavelength. The QE is estimated from the
ratio of the total emission intensity of the same two solutions and the known QE of the
IR-125. Figure III.4 shows sample absorption and emission spectra for IR-125 and PbS
92
QDs used to estimate QE. Panel (a) shows that both solutions have approximately the
same optical density at 700 nm and that the total emission intensity for the PbS QDs is
about 4.5 times greater than the total emission intensity of the IR-125. Note that the PbS
QD must not be exposed to air at any time; even brief exposure will result in substantial
degradation of QE.
We find that the small PbS QDs as-grown have QE in the range of 55+10%.

Figure III.4. (a) Absorption and (b) photoluminescence of oleate capped PbS QDS and IR
125 reference dye when excited at 700 nm. Both the PbS QDs and IR-125 absorb 700
nm light at the same strength, but the PbS QDs emitted much more light and thus have
much higher QE.

III.2.2 Structural characterization of PbS QDs by HRTEM
To identify QD size, shape, and structure, we use high resolution transmission
electron microscopy (TEM). Figure III.5 (a) and (b) show typical images of spherical, 6
nm diameter PbS QDs. Variations in the lattice fringes visible in different QDs in Figure
III.5 (a) and (b) result from variations in orientation of the individual QDs with respect to
800 900 1000 1100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Photoluminescence (a.u.)
Wavelength (nm)
IR 125
PbS QDs, as-grown (60% QE)
600 700 800 900 1000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
IR 125
PbS QD - as grown
Absorbance (a.u.)
Wavelength (nm)
(a) (b)
93
the incident beam. In order for fringes to be visible, a set of low index planes with
diffraction angles sufficiently small to allow phase contrast must be aligned nearly
parallel to the incident beam. (Recall that the concept of ‘nearly-parallel’ can be
described by equation II.9.) Figure III.5 (c) shows high resolution images of a single, PbS
QDs showing two sets of {111} planes with spacing of 3.4 Å consistent with the bulk
lattice parameter for PbS. For larger PbS QDs shown in Figure III.5(d), we observe a
transition from spherical to cubic geometries at approximately 9 nm, which is consistent
with previous work [III.32]. Note that these large QDs were synthesized under the same
conditions as described for the small QDs except that: (1) The injection temperature was
150° C and 2) the growth solution consisted of 4 gr of oleic acid with no octadecene,
which also illustrates the drastic effects of oleic acid concentration in the growth
environment on the final size of the QDs.
For the small PbS QDs used in optical studies, TEM imaging by phase contrast is
inappropriate for determining QD sizes and shapes, because of the low contrast between
the QDs and the amorphous carbon film (~ 5 nm thick) used as support. Figure III.6
shows a TEM image of small PbS QDs using the aberration- corrected TEM at Wright
Patterson Air Force Base and illustrates phase contrast and lattice imaging, but the QD
edges, and therefore diameter, cannot be determined by this method.

94

Figure III.5. H RTEM images of typical PbS QDs are shown in (a) and (b). Panel (c)
shows a high resolution image of a PbS QD with two sets of visible fringes due to PbS
{111} planes with 3.4 Å spacing, which is consistent with the PbS bulk lattice constant of
5.94 Å. Pb S nanocrystals become cubic as shown in (d) at sizes above 9 nm diameter
due to slow growth on {100} facets.

95

Figure III.6. Small, 2.6 nm average diameter PbS QDs, such as those used in the majority
of optical studies. This image was taken with the aberration corrected microscope at
Wright Patterson Air Force Base, which has point-to-point resolution greater than 1 Å,
but such high resolution does not help in identification of the QD edges due to small
difference in mass-thickness contrast between the QDs and the carbon film.

Contrast between the PbS QDs and the carbon support film is not high enough to
allow accurate QD size measurement. In this case, we can only estimate that QD size in
in the range of 2 to 3 nm. In order to estimate PbS QD size in the regime below 4 nm,
we used the data compilations of Moreels et al. to relate absorption peak, which is easily
measured, to PbS QD diameter [III.25]. For the QDs with absorption peaks at 810 nm,
we estimate that the average diameter is 2.6 nm.

96

III.3. Post-synthesis manipulation: Control over QD-QD center to center spacing
As described in chapter I, it is desirable to reduce the inter-QD spacing in densely
packed QD solids to enhance the inter-QD NRET rate. The relatively long oleate ligands
(~2 nm) on as-grown PbS QDs provide steric repulsion between QDs and ultimately
determine the separation between adjacent as-grown QDs. In order to decrease inter-
QD spacing between QDs in a QD solid, the oleate ligands must be replaced with a
capping layer of lesser thickness: either shorter organic ligands or a thin inorganic shell.
Core-shell structures require organic ligands to prevent agglomeration in solution, so use
of shell growth to reduce QD-QD separation when in films would require the removal of
the organic ligands, which can be accomplished by exposure to solvents such as pyridine.

III.3.1 Inorganic Shell Growth on PbS QDs
The general approach to using inorganic shells for passivation is to grow epitaxial
inorganic crystal shells with band gap greater than the 1S
e
-1S
h
energy of the core. For II-
VI QDs, this approach has been successful in increasing the photoluminescence quantum
efficiency of the QDs with respect to the core-only II-VI QDs [III.4]. In this case, shell
growth is typically achieved by exposing as-grown core-only QDs to solutions that
contain both the anion and cation precursors of the shell material at sufficiently low
concentrations to suppress nucleation of crystals of the shell species. To follow the
standard approach for PbS QDs, a wide band-gap material suitable for the shell must be
identified. Unfortunately for PbS QDs, wide band-gap materials having rock salt
97
structure and similar lattice constants as lead sulfide, such as calcium sulfide for example,
(which has a 4% smaller lattice parameter than PbS) but features cations (calcium) for
which suitable organometallic precursors are not readily available.
Because of the lack of suitable rock salt shell candidates, we decided to pursue
growth of cadmium sulfide shells. CdS is a tetrahedrally bonded semiconductor, but
previous studies have illustrated growth of shells with different crystal structures than the
cores, including CdX shells on PbX cores where X is S, Se, or Te [III.33], [III.34].
We attempted to create CdS shells on PbS QDs by: (1) shell growth by addition of
both Cd and S precursors to a PbS QDs solution, and (2) by cation exchange to replace
Pb cations on as-grown PbS QDs with Cd cations, and thus form a CdS shell. We used
the standard approach of exposing as-grown PbS cores to low concentrations of the
cation precursor dimethyl cadmium and low concentrations of anion precursors (TMS
2
S)
in the presence of a suitable ligand (trioctyphospine oxide (TOPO)). Exposing PbS QDs
to small amounts of cadmium cation precursor and sulfur anion precursor resulted in QDs
exhibiting a significant drop in QE. Figure III.7 shows the quantum efficiency for PbS
QDs as a function of addition of Cd precursor along with TMS
2
S in toluene at room
temperature. Similar behavior was observed when Zn precursors (diethyl zinc) were
used, as also shown in Figure III.7.
Each QD has approximately1,000 total Pb and S atoms. The onset of QE
degradation occurs before formation of even a single layer of shell. Thus it is expected
that one of the precursors alone is creates a defect state that allows for radiative
recombination rather than a defect related to the presence of a CdS shell such as lattice
98
structure mismatch or strain. This QE degradation is unacceptably high and therefore the
standard two-precursor approach was not pursued. This degradation of QE resulting
from exposure to shell growth precursors, forced us to seek different approach.

Figure III.7. Decreasing Quantum Efficiency of PbS QDs as a function of exposure to
dimethlycadium – TMS
2
S (blue symbols) and diethylzinc – TMS
2
S (red symbols)
solutions shell precursors. The dotted lines are guides to the eye.

Next, we experimented with forming inorganic shells of CdS by exposure of PbS
QDs to high concentrations of Cd-oleate and rely on diffusion of Cd cations into the PbS
QDs to form the shells. This seemed to be a favorable approach owing to shared sulfur
anion in both PbS and CdS and the previous demonstration of cation exchange in
colloidal nanostructures [III.34]. This approach is also attractive in that the QDs will
0%
10%
20%
30%
40%
50%
60%
70%
0.0 50.0 100.0 150.0 200.0
Quantum Efficiency
Molar Ratio of Shell Precursor Molecules to PbS QDs
99
remain capped by oleate ligands during the exchange process, just as in the synthesis of
the PbS QDs.
To form CdS shells, we exposed as-grown PbS QDs to high concentrations of Cd-
oleate at elevated temperatures for an extended period of time. By monitoring the
luminescence from the core-shell structures that depends primarily on the size of the PbS
QD core, we can indirectly measure the size of the PbS core. Additionally,
complimentary TEM measurements allow us to determine the total diameter of the core-
shell structure. As shown in Figure III.8, we find that the growth of CdS shells by cation-
exchange successfully allowed for reduction of PbS core diameter without changing the
size or size distribution of the as-grown QDs.

Figure III.8. (a) Photoluminescence spectra of PbS-core QDs with CdS shells. These data
illustrates a reduction in PbS-core diameter as a function of increasing reaction time, as
indicated by the blue shift in emission energy. (b) Comparison of PbS QD core diameter
determined by the PL peak position and by total core-plus-shell diameter determined
from TEM images. The invariance in total diameter before and after shell formation
shows that the mechanism of shell formation is cation-exchange, rather than shell growth.
Note that dips in PL emission at ~1150 nm and 1200 nm are due to absorption of light by
the toluene solvent used to suspend the QDs during PL measurement.

100
Despite the successful demonstration of CdS shell growth by cation exchange, a
practical problem with this method stems from difficulty in extracting post shell-growth
QDs from the growth solution. At room temperature, the Cd-oleate solution forms a
viscous gel. Separating the QDs from this gel is inefficient and yields few core-shell
QDs. The problem of low yields of PbS core – CdS shell QDs led us to to investigate an
alternative approach to reducing inter-QD separation. Thus, we developed a new
approach to ligand exchange utilizing lead-ligand complexes as explained below.

III.4 Quantum efficiency preserving cation - ligand exchange on PbS QDs
Our new approach to reducing inter-QD spacing is based on exchanging
organic ligands on as-grown QDs with ligands of shorter length. Efforts to manipulate
ligands on as-grown colloidal QDs have been an integral part of the development of
nanocrystal QDs and the progression of the field. The earliest experiments in this area
showed that trioctylphosphine oxide (TOPO) ligands on CdSe QDs could be replaced by
pyridine [III.35] as well as a variety of other ligands [III.36]. Typically, ligand exchange
is facilitated by exposing as-grown QDs to solutions containing many times more new
ligands in solution than bound ligands of the as-grown type. For new ligands that can
bind to the QD surface with similar or greater binding energy than the as-grown ligands,
the expectation is that thermal fluctuations will eventually allow for the new, highly
concentrated ligands to replace the as-grown ligands. This expectation is commonly
realized. This general approach of exposure to high concentration of new ligands
Solution phase exchange has become the standard approach to ligand exchange and is
101
illustrated in Figure III.9 (a). The standard approach to solution-phase ligand exchange
has been applied to PbS QDs in order to replace oleate ligands with octadecylamine,
dodecylamine, or octylamine in solution, but the influences of such ligand exchange on
the QE or emission spectrum have not been reported [III.37].
Ligand exchange that results in a fundamental change in surface chemistry from
non-polar ligands to polar ligands typically requires ligand exchange induced
precipitation from the initial organic solvent and subsequent dissolution of the post-
exchange QDs into a polar solvent. Because QDs synthesized in organic solvents
typically have higher QE than QDs synthesized in aqueous solvents, ligand exchange to
introduce chemical moieties that impart water solubility and permit binding to specific
biological receptors has been a significant achievement [III.5][III.6][III.38].
Additionally, if very short ligands of any type are used maintaining solubility is not
necessarily possible in any solvent because of the lack of steric repulsion between QDs.
To traverse the issue of post-ligand exchange solubility when using very short ligands, a
variation of the standard approach to ligand exchange is commonly used in the literature
is to expose a solid-film of as-grown QDs on a substrate to a solution that contains the
new ligands but will not dissolve the deposited QDs [III.39]. This approach has the
advantage that solubility of the post-exchange QDs is not required, and therefore very
short ligands can be used. This approach is particularly convenient when the objective is
to create a densely packed QD-solid on a solid substrate. This solid-phase approach was
originally developed for II-VI QDs [III.40], but has been used successfully for a variety
of new ligands on lead chalcogenide QDs [III.9][III.41][III.42]. In particular,
102
ethanedithiol is the most common ligand used for lead salt QDs in the solid-phase
approach. Although this ligand exchange approach has provided a way to control QD-QD
spacing and thus manipulate the electrical characteristics of the QD film (such as carrier
mobility [III.43]), the fact that the post-ligand exchange QDs are necessarily deposited on
a substrate makes it infeasible to evaluate the effects of ligand exchange on QE which is
of critical importance for understanding exciton relation mechanisms in light energy
harvesting applications. Therefore the lack of a solution based, high QE preserving ligand
exchange method for lead chalcogenides QDs in the literature motivated us to develop
one.
The nature of the surface chemistry of oleate ligand capped PbS QDs suggests
that the standard approach to ligand exchange will have detrimental effect on the QE of
these QDs as described below. As noted above, high QE PbS QDs are expected to be
terminated

by Pb atoms bonded by oleate ligands III.15]. Furthermore, the binding energy
between a Pb atom and a typical carboxylate ligand is estimated to be ~1.7 eV (~168
kJ/mol) [III.44]. This energy is on the same order of magnitude as the binding energy
between a Pb atom and nearby S atoms on a highly curved PbS QD surface. We estimate
that the binding energy associated with a Pb atom with one of its S neighbors in a PbS
crystal is ~ 1 eV using the known PbS enthalpy of formation of 98.12 kJ/mol (1.02 eV
per Pb-S pair) [III.45] , the cohesive energy of Pb (2.03eV/atom) and S (2.85 eV/atom)
[III.46], and the coordination number (6). Thus surface Pb atoms are bound to oleate
ligands with strength comparable to that of Pb atoms bound to neighboring S atoms. For
this reason, we predict that heating as-grown oleate-capped PbS QDs together with high-
103
concentrations of the new ligands (either dispersed in solution or on a solid film
substrate) should result in dissociation of ligands from surficial Pb atoms concomitant
with dissociation of Pb-ligand units from the QD. This heating process should leave a
sulfur-terminated surface, which in turn leads to deep level surface traps and degradation
of the QE [III.15]
.
This prediction is supported by observations that (1) Oxidization of
PbS QDs is accompanied by the loss of the oleate ligands and their bonded-surface Pb
atoms together into the solution [III.47][III.48], and (2) The presence of oleic acid in PbS
QD solution significantly accelerates the removal of Pb atoms from the QDs surface
[III.48]. Thus, the expectation in the standard approach that the as-grown ligands can be
removed without removal of removing core atoms is not valid for the case of oleate-
capped PbS QDs. To combat problems related to unwanted removal of Pb atoms with
their as-grown ligand, we introduce an alternative approach to ligand exchange, as
illustrated in Figure III.9 (b). In this approach, the desired new ligands are first
conjugated to Pb cations to form cation-ligand units for exchange to which the as-grown
QDs are then exposed.
As exchange conjugates, we use Pb cations bound to carboxylate anion ligands of
varying length. The different carboxylates including the as-grown oleate ligand are
shown in Figure III.10. Because each carboxylate is terminated by a methyl group, we
expect that the as-grown QDs and post-exchange QDs will both be soluble in non-polar
solvents and thus allow for optical characterization of the post-ligand exchange QDs in
solution to allow us to determine the QE of post-exchange PbS QDs. The conjugated
cation-ligands are synthesized by reacting PbO and carboxylic acid at ratios that are kept
104
just below the stoichiometric ratio of 1:2 (typically ~1:1.9) so that the presence of free
carboxylic acid ligands is minimized in the reacting solution. Thus the reaction is
dominated by the Pb-cation-new carboxylate-ligand conjugate exchanging with the Pb
cation-oleate conjugate on the QD surface in which at least one important guiding rule for
carrying out ligand exchange – the conservation of QD surface charge [III.49] – is well
maintained.

Figure III.9. Schematic diagrams of the conventional approach to ligand exchange (a) and
of the cation-ligand unit exchange (b). In both cases, the reactive functional group of the
new ligand is generically denoted by a red X. In (a), the red dashed ellipse represents the
desired material removed (i.e. the oleate ligand only). However, for the case of oleate-
capped PbS QDs, a lead cation will leave the surface of the as-grown QD surface during
remove of the oleate ligands as indicated by the solid red ellipse in (b).

105

Figure III.10. Atomic structure of the ligands used to cap PbS QDs (a) as-grown oleate
ligands, (b) dodecanoate ligands (C12), and (c) octanoate ligands (C8). In the
schematics, black is carbon, white is hydrogen, and red is oxygen. Note that only the
oleate ligand has a single double bond. The extra electron in each structure is shared
between the atoms in COO
-
group.

III.4.1 Cation-ligand exchange experimental details
The experimental procedure for cation-ligand exchange is designed with the
objective of minimizing exposure to air, just as in the QD synthesis procedure. Basically,
the procedure for conjugated cation-ligand exchange consists of injecting as-grown PbS
QDs into a separately prepared solution of the conjugated Pb-ligand units for exchange in
octadecene. We carried out the cation-ligand exchange procedure on small and large

e
-

(c) C8, octanoate ion: CH
3
(CH
2
)
6
COO
-

(b) C12, dodecanoate ion: CH
3
(CH
2
)
10
COO
-

(a) C18, oleate ion: CH
3
(CH
2
)
7
HC=CH(CH
2
)
7
COO
-

carbon-carbon double bond
e
-

e
-

106
QDs for optical and structural characterization, respectively. For examining the
exchange process on small PbS QDs, the Pb-ligand conjugates were prepared as follows:
140 mg of lead oxide and the new ligand, either 180 mg of octanoic acid or 250 mg of
dodecanoic acid were dissolved in octadecene in an argon environment at a molar ratio of
slightly less than the stoichiometric ratio of 1:2 (typically ~1:1.9) at 100° C to form lead
octanoate or lead dodecanoate, respectively and then degassed. Ten milligrams of PbS
QDs in 0.5 ml octadecene were then injected without exposure to air, and the Pb-ligand
conjugate exchange reaction was allowed to proceed for 10 minutes at 100° C. PbS QDs
were removed and immediately centrifuged to produce a light brown precipitate that
contains mostly excess cation-ligand complexes and a clear, dark brown supernatant that
contains PbS QDs with new ligands. The supernatant was decanted, and PbS QDs with
new ligands were separated from the remaining solvent by precipitation with acetone and
dissolved in toluene.
Cation-ligand exchange on the large 6.2 nm QDs follows the same procedure but
with a reduced concentration of the new ligand to adjust for a lower ratio of the surface
area to volume as compared with the 2.6 nm PbS QDs. In a typical cation-ligand
exchange, 10 mg of lead oxide and 13 mg of octanoic acid or 19 mg of dodecanoic acid
were dissolved in octadecene under argon at 100° C to form lead octanoate or lead
dodecanote respectively. The solution was degassed for 10 minutes, and then 5 mg of 6.2
nm PbS QDs in 0.5 ml of octadence was injected at constant temperature and allowed to
react for 10 minutes. PbS QDs with new ligands were separated from the remaining
growth solution by precipitation with acetone and finally dissolved in toluene. The PbS
107
QDs, after exposure to lead octanoate or lead dodecanote, are hereafter referred to as C8-
capped and C12-capped, respectively.

III.4.2 Characterization of cation-ligand exchange
To ensure that the cation-ligand exchange procedure has resulted in
displacement of the as-grown oleate ligands, we checked that oleate ligands have been
removed from the as-grown samples. To this end, we used Fourier Transform Infrared
spectroscopy (FTIR) to investigate changes in the chemical bonds present in the samples
as shown in Figure III.11. More specifically, we used the presence and absence of the an
absorption peak due to C-H stretch at a carbon in a C=C double bond at 3005 cm
-1
that is
present in oleate ions [III.50]

but not in octanoate or dodecanoate ions. In Figure III.11,
the absence of a peak at 3005 cm
-1
for samples after exposure to with lead octanoate or
lead dodecanote (C8- and C12-capped) indicates that the oleate ligands have been
removed as a result of this conjugated cation-ligand exchange procedure.
2700 2750 2800 2850 2900 2950 3000 3050
C-H stretch at C-C
C-H stretch at CH
3
C-H stretch at C=C
Transmittance
Wavenumber (cm
-1
)
C8
C12
C18 as-grown

Figure III.11. Fourier
Transform Infrared (FTIR)
Spectroscopy (FTIR) of C8-,
C12-, C18-capped PbS QDs
showing the absence of C-H
stretch at the carbon-carbon
double bond after cation-
ligand exchange. The
absence of a stretch peak
confirms removal of oleate
groups from the surface of
the QDs as a result of cation-
ligand exchange.

108
Having now demonstrated that the as-grown oleate ligands have been removed,
next we investigate the effect of ligand exchange on QE. Comparisons of PL in solution
from the as-grown PbS QDs and PbS QDs after the cation-ligand unit exchange
demonstrate the success of our approach in preserving both size distribution and high QE.
Figure III.12 shows the typical PL behavior of the 2.6 nm diameter as-grown PbS QDs
(i.e. capped with C18) and the post-exchange PbS QDs with attached C8 and C12
ligands. The PL curves are normalized by the excitation power at 700 nm to illustrate the
preservation of the initial QE after ligand exchange. The QE of the as-grown PbS QDs
is 59+4% and the QE of the C8- and C12-capped QDs after cation-ligand exchange is
55+4%.
800 850 900 950 1000 1050 1100
0.000
0.005
0.010
0.015
0.020
PL (a.u.)
Wavelength (nm)
C8
C12
C18 - as-grown

Figure III.12. PL of C8, C12, C18 normalized by absorption strength illustrating the
preservation of high QE in the post ligand exchange QDs.

109
Concordance of the PL spectra of the C8-, C12-, and C18-capped PbS QDs in
solution illustrate that the size distribution has not changed as a result of the cation-ligand
exchange process. The strong sensitivity of the PL emission wavelength to the PbS
diameter contrasted against the lack of variation in PL curves before and after ligand
exchange, suggests negligible gain or loss of Pb cations. The benefit of using cation-
ligand complexes is apparent when comparing the PL of QDs before and after exposure
to octanoic acid without Pb cations after exposure to octanoic acid with ligands, QE
drops to 33% as shown in Figure III.13.

Figure III.13. PL of C18-as grown QDs before and after exposure to octanoic acid
without Pb cations showing a marked decrease in QE. The reaction conditions used in
this control experiment are the same as those in the ligand exchange description for C8,
except PbO is not included in the initial solution, and thus there are octanoic acid
molecules as ligands for exchange.

110
III.4.3 QD solids: Inter-QD separation control
Having established that the cation-ligand exchange process results in minimal QE
degradation, we examine structural characterization to determine inter-QD spacing of
these QDs when incorporated in densely packed films. The change in ligand length
should result in a change in the inter-QD spacing in aggregated QD assemblies that is
observable in transmission electron microscopy (TEM) of PbS QDs that have self-
assembled into close packed two-dimensional arrays. Characteristic TEM images for
some self-assembled C18-, C12-, and C8-capped PbS QDs are shown in Figure III.14.
These images reveal that the QD-QD separation is proportional to the length of the
ligands. The QD-QD edge-to-edge spacing averaged over about 80 pairs of each the as-
grown C18-capped PbS QD, C12-capped PbS QDs, and C8-capped PbS QDs is (2.1+0.5)
nm, (1.4+0.4) nm, and (1.0+0.2) nm, respectively. As the ligands determine the QD-QD
spacing when in arrays [III.51], such measurements suggest shown that and that the
separation is linear with the length of the ligands. For a carbon-carbon bond length of
1.15 Å, we see that the edge-to-edge spacing is, in each case, the approximately the
length of a single ligand molecule. This suggests that the ligands on adjacent QDs
overlap.
The beauty of our approach to ligand exchange is that we can create a series of
PbS QDs that each have the same size distribution and high QE; and only differ by the
length of the ligands that cap them. As we will see in the next chapter, this is an ideal
platform for studying inter-QD interactions that depend on inter-QD separation.

111

0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.5
1.0
1.5
2.0
2.5
d edge to edge (nm)
Length of Ligand Molecule (nm)
(d)

Figure III.14. Panels (a), (b) and (c) show TEM images of arrays of C8, C12, C18 used to
determine the ligand-length dependent spacing between QDs. Red lines illustrate the
variations in QD-QD edge to edge separation. Panel (d) show the linear relation between
edge-to-edge spacing with the length of the ligand molecule. The dashed red line is a
linear fit through three points. TEM images were obtained in bright field at 200 kV with
no objective aperture. The QDs are supported on a ~5 nm thick carbon film.

112
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Nanocrystallites into Three-Dimensional Quantum Dot Superlattices. Science,
1995. 270(5240) 1335-1338.

117
Chapter IV: Inter-QD NRET and competing processes

IV.1 QD solids: Background
In order to make QDs a viable component for optoelectronic applications, it is
necessary to bring together large numbers of quantum dots to form macroscopic QD
solids, and understand the flow of energy and charge in such solids. In addition to the
NRET-based device that is the subject of this dissertation, QD solids allow for realization
of a variety of other opto-electronic devices such as photodetectors [IV.1], Schottky-type
solar cells [IV.2], and solar cells based on the junction between n-type and p-type QD
solids [IV.3], but in these charge transport is the focus and thus inter-QD charge transport
has received a great deal of attention [IV.4- IV.7]. We are interested in exploiting NRET,
but quantifying the competing processes that occur in a QD solid such as geminate
recombination by radiative recombination or non-radiative processes and exciton
dissociation by inter-QD charge transfer is of equal importance. In general, all of these
processes can occur in a QD solid and therefore the study reported in this chapter is of
value far beyond the proposed application to an NRET based solar cell. The study
represents the most thorough investigation of inter-QD energy and charge transfer in
semiconductor QD solids. The electronic properties of such QD solids can be tailored by
choosing both the electronic structure of the quantum dots and their surface-
functionalization-dependent degree of electronic coupling, and while much effort in the
scientific community has been directed towards understanding densely packed and
electronically coupled QD solids, the PbS QD ensembles created by cation-ligand
118
exchange provide a platform that is uniquely suitable, as described below, for studies of
inter-QD energy and charge transfer.

IV.2 Inter-QD energy and charge transfer
Both energy transfer and charge transfer processes in QD solids are influenced by
the unavoidable variations in QD size and the attendant variations in electronic energy
levels. Although NRET is discussed in chapter I, the key ideas are reiterated here to
facilitate discussion of the experimental work.

IV.2.1 Inter-QD NRET
Energy transfer by NRET is a process by which a dipole associated with a
localized exciton such as in a QD (the donor) couples to a dipole in a neighboring QD
(the acceptor) to result in a process that simultaneously creates an exciton in the acceptor
while relaxing the donor exciton [IV.8]. The rate of the NRET between three-
dimensionally confined states such as in QDs, k
NRET
, is operationally well described by
the well-known Förster expression [IV.8] [IV.9],

(

)

∫

∞

(IV.1)

In eq. IV.1

is the radiative recombination rate of the donor in the absence of the
acceptor and can be obtained from k
rad
= QE/ 
PL
where QD is the donor quantum
efficiency, 
PL
is the PL intensity decay time,  is a factor that contains information on
119
the relative orientation of the two dipoles,

is the index of refraction of the medium,
and N
A
is Avogadro’s number,

is the normalized donor emission with the
quality ∫

∞

,

is the molar absorptivity of the acceptor, and is the
wavelength of light associated with the optical transition. Energy conservation (i.e.
spectral overlap between the donor emission and acceptor absorption) requires that the
donor QD is smaller and with larger band gap than the acceptor QD. Thus, NRET only
occurs from small QDs to larger adjacent neighboring QDs. Therefore from the inherent
variation in the as-synthesized QD sizes, the signature of NRET in a QD solid is a fast
photoluminescence (PL) decay of excitons in the small QDs (i.e. at the shorter
wavelengths in the time-integrated PL spectrum), and an accompanying initial rise and
then a slow decay in the photoluminescence intensity of the larger QDs (i.e. at the longer
wavelengths) [10]. The initial rise in PL intensity is a result exciton being excited in
large acceptors via NRET and the slow decay represents exciton decay by mechanism
other than NRET that are typically relative slow.
Energy transfer by non-radiative resonant energy transfer (NRET) between the
QDs has been demonstrated in CdSe QD solids [IV.10] [IV.11] and PbS QD solids
[IV.12], and the inter-QD NRET rate has been shown to decrease with decreasing
temperatures for CdTe QDs [IV.13] and increase with decreasing temperatures for PbS
QDs [IV.14].
IV.2.2 Exciton dissociation and Inter-QD charge transfer
The other mechanisms that contribute to exciton decay, as noted before, are
primarily radiative recombination, non-radiative recombination, and exciton dissociation
120
by charge transfer. QDs, by definition, require an energy barrier to confine the electrons
and holes and enable the quantum confinement effect. The energy barrier also largely
influences the transport of charges between quantum dots by acting as a barrier for charge
transfer between adjacent QDs. Charge transfer via tunneling between adjacent QDs
depends not only on QD-QD separation but also on the energy discontinuity between
their relevant energy state and that of the intervening surface ligand that defines the
energy barrier to charge tunneling. Energy conservation requires that the initial and final
states are in resonance, and therefore excitation by phonon absorption is necessary if the
initial state is at lower energy than the final state.
In dc charge transport processes, such as studied in the context of measurements
of charge mobility, the participating QD states are the single particle (electron or hole)
states. By contrast, in studies, such as here, focused upon examining charge transfer
pathways as competing processes to radiative decay or nonradiative transfer of the energy
of an exciton formed following photon absorption, the excitonic state is a two-particle
bound state. Thus, for either electron or hole to transfer from the QD, exciton unbinding
needs to occur. This requires (1) sufficient thermal energy or another driving force such
as an applied electric field to dissociate the exciton at a rate competitive with radiative
decay and (2) that electron for hole has access to suitable single particle energy states to
transfer to. In such a case, thermally-activated tunneling can provide a mechanism for
charge transfer. The generic form for the rate for thermally activated charge transfer via
tunneling, k
charge,
is given [IV.15] as,

121

[

] [ ] (IV.2)

where k
0
is the attempt frequency, E
a
is the activation energy for creating the charge to
transfer,  is the tunneling constant, and d is the thickness of the tunneling barrier.
Because the energies of the initial and final states involved in tunneling depend on QD
size, we expect that E
a
will be greatest for tunneling from the largest QDs within an
ensemble because the initial states in the largest QDs require the most energy to reach
resonance with a suitable final state in adjacent neighbor.
Inter-QD charge transfer is most often studied by transport measurements under
applied bias of carriers excited by light [IV.5], carriers introduced by electrochemical
charging [IV.6], and in field effect transistor structures [IV.16]. Beyond measurements
of transport under applied bias, photo-induced charge transfer resulting in exciton
dissociation has been studied by TRPL as a function of inter-QD separation [IV.17] and
PL as a function of temperature [IV.18]. Inter-QD energy and charge transfer both are
strongly influenced by the separation between the quantum dots, which in turn is largely
determined by the length of the ligands that cap them. Other studies of charge transfer
have focused on the effects of ligands and shown that charge carrier mobility in PbS QD
solids depends exponentially on ligand length [IV.15] and that the chemical nature of the
ligands strongly influences charge carrier mobility [IV.16] and photoconductivity
[IV.19]. Thermally activated charge trapping results in non-radiative recombination by
transfer of an electron or hole from an emissive state to localized surface state [IV.20].

122
IV.3 Dynamics of Competing NRET and Charge Transfer in PbS QD solids
Quantum dot – quantum dot interactions in PbS QD solids specially have
received much attention. Inter-QD non-radiative resonant energy transfer (NRET) in PbS
QDs with oleate ligands has been reported [IV.12], [IV.17], [IV.21] and an increase in
NRET efficiency at low temperatures is reported [IV.14]. Charge transport in PbS QDs
solids has received much attention in the context of improving the efficiency of PbS QD
based photovoltaics, and mostly these have been studies of inter- PbS QD charge transfer
by electrical measurements [IV.16],[ IV.22]. Additionally, studies of carrier mobility in
PbS QD solids extracted from electric current measurements has been reported to depend
exponentially on ligand length [IV.15]. Beyond dc electrical measurements, there are
some reports of optical investigations of charge transport in PbS QD solids. For example,
time resolved photoluminescence (TRPL) has been used to study photo-induced charge
transfer between thiol capped and strongly coupled PbS QDs as a function of QD-QD
separation [IV.17] though not in QD solids that also exhibit efficient PL and a
measurable signature of NRET.
As discussed in chapter III, high QE PbS QDs are typically lead rich and capped
with oleate ligands. The effect of ligands on inter-QD charge transfer in PbS QDs has
also been a subject of investigation and numerous studies reveal substantial differences
between cation rich PbS QDs (i.e. such as PbS QDs with oleate ligands) and anion rich
Pb QDs (such as those with thiol ligands [IV.23]). For instance, the PL peak wavelength
of oleate-capped PbS QDs solids exhibits blue shift with increasing temperature, whereas
the PL peak for ethanedithiol capped PbS QD solids show the opposite behavior, red shift
123
with increasing temperature [IV.18]. Additionally the luminescence intensity of PbS QD
solids treated with ethanedithiol is much less than for PbS QD solids featuring oleate
ligands [IV.18]. The PL behavior of the ethanedithiol capped PbS QD solids is
explained by the authors as a band-like charge transport behavior that determined by
exciton break up and therefore the PL behavior, but the same model was not applied to
the oleate-capped PbS QD solids because of the opposite trends in PL peak position with
temperature. These observations suggest that comparisons between PbS QDs with
different ligands must be cautious in considering effects of ligands and surface chemistry.
IV.3.1 The unique platform QD solid platform enabled by cation ligand exchange
Although both energy and charge transfer have been identified and studied in PbS
QD solids, so far these studies have only addressed them individually. Hence the
motivation for the present systematic investigation of the competition between the two
processes. The cation-ligand exchange described in chapter III was developed to create
a unique series of QD solids reported in chapter III that are especially suited to study this
competition. The PbS QD solids used in the investigations here all feature PbS QDs of
the same surface chemistry, high quantum efficiency, and size distribution and differ only
in one major attribute: the inter-QD average separation as controlled by the length of the
ligand on the QD surface.
The study reported here thus enlarges and complements previous studies that
typically varied only one parameter such as temperature or QD-QD separation. Because
both energy and charge transfer are dependent on the energies of the initial and final
states involved that in turn depend on the QD size and the size distribution of nearest
124
neighbors, it is crucial for fair comparisons to probe the same size QDs within the same
size distribution in each QD solid. We exploit wavelength selective TRPL to investigate
behavior of specific QDs sizes (with corresponding specific emission wavelength) within
the ensemble distribution in the same QD solid. Furthermore, we vary both temperature
and inter-QD separation to extend and complement the current understanding of the
competing processes of energy transfer, charge transfer, and radiative recombination in
PbS QD solids (indicated schematically in Fig. IV.1) derived largely from studies that
varied only one parameter - either temperature or ligand. In the process we confirm
several previous findings while also revealing new aspects whose consistent
understanding together with the existing picture allows a more holistic view and
understanding.
We are particularly interested in small, oleate capped 2.6 nm average diameter
PbS QDs with size range from ~2.3 nm to ~3.1 nm diameter. QDs of this size range
have absorption peaks in the range of 1.7 to 1.3 eV, and as described in chapter III, the
photoluminescence peaks are seen to be red-shifted by between 150 meV to 300 meV
with respect to the absorption peaks, an observed phenomena attributed to the
involvement of states other than the expected quantum confined states (i.e 1S
h
, 1S
e
, etc.),
dubbed as midgap states [IV.24] [2 IV.5]. It is then likely that such gap states also play
an active role as the initial or final states in the energy transfer and charge transfer
processes as our findings discussed below will indicate.
Furthermore, for the PbS QDs with sizes of interest here, the difference in energy
between the 1S
h
level of the largest quantum dots studied here (diameter ~3.1 nm) and
125
the highest occupied energy level of the average size QD here (diameter ~2.6 nm) is
around 30 meV, about the same as thermal energy at room temperature. By contrast the
difference in the 1Se level between the largest and averaged sized QDs is about 100 meV
[IV.26][IV.27]. Therefore, in these QD solids, inter-QD single particle charge transfer
involving the quantum confined states is likely to be more facile for holes, particularly at
low temperatures. A schematic of competing processes for the case of PbS QDS of the
size range of interest here is shown in Fig. IV.1. This band diagram reflects the fact that
the 1Sh levels vary less with QD size than the 1S
e
levels.

Figure IV.1. Illustrative QD size-dependent energy diagrams for PbS QD ensembles
examined. Red lines (solid and dashed) denote intrinsic quantum confined states and blue
lines midgap (MG) states arising from defects, most likely surface states. Green, brown,
and red (solid bold) arrows represent, respectively, absorption, fast non-radiative
relaxations, and emission. The blue arrow represents hole transfer. E
MG
is the energy of
the mid-gap state that can participate in light emission (middle well) or even NRET (left
well).

r
Smaller QD
Larger QD
NRET
Activated
Tunneling
Photon
emission
d

Excited
States
Medium QD
E 1S
h

~ 30 meV
e
-

h
+

E
MG

E
MG

E
MG

E
Stokes

1S
h

1S
e

126
IV3.2 Preparation of QD dilute solutions and solids
The PL and TRPL measurements of QDs in dilute solution and in QD solid were
carried out down to liquid nitrogen temperatures to provide reference behavior of non-
interacting QDs needed for analysis and interpretation of the QD solid studies. To this
end, solutions were prepared by dissolving the PbS QDs in heptamethylnonane, a waxy
solvent without a definite melting point, at concentrations of 0.2 mg/ml. Within the
temperature range from 297K to 80K the appearance of the QD – heptamethylnonane
solution is optically clear. This concentration corresponds to an average QD – QD
separation of 50 nm which is sufficiently large to effectively stop any QD-QD
interactions.
QD solids are created by depositing QDs from solution by drop casting from
toluene solutions of 2 mg/mL onto glass substrates. For ready reference, recall that the
transmission electron microscopy (TEM) studies of QD-QD spacing as shown in
Fig.III.14 reveal that the inter-QD edge-to-edge spacing, d, for C8-, C12-, and C18-
capped PbS QDs is 1.0+0.2 nm, 1.4+0.4 nm, and 2.1+0.5 nm, respectively. As the
ligands determine the inter-QD spacing when in densely packed QD solids [IV.28], we
expect that the separations between QDs on carbon film and glass should be the same.

IV.4 Optical properties of PbS QD solids
Three classes of TRPL data are presented and analyzed: (1) isolated QDs in
solutions that enable gathering information on the temperature dependence of the
combined radiative and non-radiative decay rates without communication between the
127
QDs, (2) the smallest QDs in the solid ensemble that emit at 880 nm and have a high
probability of having larger QDs as nearest neighbors so that NRET can be the dominant
decay mechanism; and (3) the largest QDs in the ensemble that emit at 1080 nm and have
negligible decay by NRET (owing to lack of energy matching neighbors) and thus
provide insight into charge (electron or hole) transfer when compared with their decay
rates as isolated QDs in dilute solution (which represent the sum of radiative and non-
radiative decay rate). The dependence of energy/charge transfer dynamics on the varied
inter-QD separation and temperature provides a key to reveal some of the factors
affecting the transfer dynamics, such as the significant role of the local dielectric
environment.

IV.4.1 Photoluminescence and the ensemble behavior of PbS QDs in solution and in
QD solids.
Figure IV.2(a) shows time integrated PL intensity for C8- and C18-capped PbS
QDs in dilute solutions of a heptamethylnonane at 297 K and at 80 K. All four PL curves
in Fig. IV.2(a) are normalized by peak height to illustrate the invariance of the peak
position and line width with temperature and ligand length consistent with previous
reports on similar sized PbS QDs [IV.29] [IV.30]. The invariance of PL linewidth with
temperature suggests that the homogenous broadening of the emission from single QD,
typically attributed to electron-phonon coupling [IV.31] [IV.32] is small compared to the
heterogenous linewidth due to the size distribution of QDs within the sample.
128
Figure IV.2(b) shows the time-integrated PL behavior of the C8- and C18-capped
QDs in QD solids at 297K and 80K. The PL curves for each ligand length in Fig. IV.2(b)
are scaled proportionally so that their peak height at 80K is one. At room temperature
there is a pronounced red-shift with respect to the PL spectrum in solution (Fig. IV.2a)
and is indicative of NRET of the excitons in the small quantum dots to the larger ones.
We note that, due to variations in the thickness of drop-cast films between the C8-capped
and C18-capped QD solids, a comparison of the total PL intensity of QD solids with
different ligands is not possible. However, upon lowering the temperature change in the
total PL intensity for C8-capped QDs is greater than for C18-capped QDs suggesting a
ligand-length dependent quenching mechanism at high temperatures. There is also a
reduction in the emission intensity at the blue edge of the spectrum, enhanced emission at
the peak wavelength and red edge of the spectrum, and overall increase in the total PL
intensity. Similar temperature dependence of oleate capped, similar sized PbS QDs in
QD solids has been reported [IV.18]. The PL linewidths of the QD solid spectra,
compared to the QDs in solution, become narrower with reducing temperature as seen in
Fig. IV.2(b), a behavior observed by several groups [IV.18]. The summary of PL
linewidths is shown in Fig. IV.2(c) showing the temperature independence for QDs when
in solution and strong reduction in line width when the QDs are in QD solids. Figure
IV.2(c) also illustrates that the line width does not change appreciably as a result of the
cation-ligand exchange processes.
129

Figure IV.2. (a) Normalized photoluminescence curves for the C8 - and C18 -capped QDs
in solution at 80 K and 297 K. There is the absence of line narrowing and peak shift
which is characteristic of small PbS QDs. Arrows in panel (a) identify the wavelengths
monitored in TRPL m easurements: 880 nm for small QDs and 1080 nm for large QDS.
(b) Photoluminescence curves for C8 - and C18 -capped PbS QDs in dense packed QD
solids at 80 K and 297 K. Note the reduction of emission at 880nm and enhancement of
emission at peak and longer wa velengths. Note also the red -shift and line narrowing
from panel (a) to (b). Panel (c) shows the full width half max energies for the QD is
solution and in QD solids at 80 K and 297 K. These results for C18 -capped QDs are
consistent with tre nds reported in the literature [IV.18] [IV.29].

Greater insight into and understanding of the temperature dependent PL shown in
Fig. IV.2(b) is obtained from the exciton decay dynamics extracted from the measured
TRPL decay behavior discussed next. Numerous studies have shown that the TRPL
800 850 900 950 1000 1050 1100 1150 1200
0.0
0.2
0.4
0.6
0.8
1.0
1.2

Normalized Photoluminescence
Wavelength (nm)
C18, 297K
C18, 80K
C8, 297K
C8, 80K
(a)
800 850 900 950 1000 1050 1100 1150 1200
0.0
0.2
0.4
0.6
0.8
1.0
1.2

Photoluminescence
Wavelength (nm)
C18 297K
C18 80K
C8 297K
C8 80K
(b)
C8 C12 C18
60
80
100
120
140
160
180
200
220
240

QD Sample
QD-Solid - 297K
QD-Solid - 80K
QDs in Solution - 297K
QDs in Solution - 80K
FWHM (meV)
(c)
130
decay rate for QD solids decreases with increasing detection wavelength [IV.12],[ IV.21].
Rather than investigate the PL decay for a large number of detection wavelengths, we
find that the extreme red and blue edges are most interesting and primarily focus at these
wavelengths. The black arrows in Fig. IV.2(a) and IV.2(b) mark the wavelengths used to
denote small QDs (880 nm) and large QDs (1080 nm).

IV.4.2 Photoluminescence decay dynamics in PbS QD solids
IV.4.2.1 Control experiments: decay dynamics in dilute solution
In sufficiently dilute solution of QDs in heptamethylnonane that eliminates QD-
QD interaction contributions, the room temperature radiative decay behavior of the
smallest (880 nm) and largest (1080nm) PbS QDs is shown in Figure IV.3(a) for C8 and
C18 QDs. We observe essentially no dependence of the PL decay behavior either on the
QD size within the size distribution or on the capping ligand length at room temperature.
Figure IV.3(b) shows the characteristic decrease in the decay rate with decreasing
temperature for the case of the C8-capped QD emitting at 1080 nm.
The solution decay rates k
solution
, can be determined by fitting the measured TRPL
intensity to a single exponential function,

[ (

)] (IV.3)

where 
solution
-1
= k
solution

and C and A are constants that depend on experimental factors
such as dark counts and integration time. Fitting Equation IV.3 to the data of Figure IV.3,
131
at room temperature we find the well-known long radiative lifetimes of over two
microseconds [IV.12] for lead sulfide QDs of less than about 4 nm [IV.33]. The
variation with temperature of the in-solution decay rate is the greatest for the 1080 nm
emitting (i.e. the largest) QDs as shown in Figure IV.4 (a).

Figure IV.3. (a) Time resolved photoluminescence intensity from C8 and C18 - capped
QDs in dilute solution at roo m temperature for 1080 nm emitting (large) QDs and 880 nm
emitting (small) QDs. The four curves essentially overlap showing that neither the ligand
exchange process nor the ligand length affects the in -solution PL decay dynamics. (b) PL
decay behavior of 1080nm emitting C8 -capped QDs in solution as a function of
temperature showing the decreased decay rate with decreasing temperature.

At room temperature the decay rate does not depend on ligand length or QD size
(detection wavelength). However, as the temperature is reduced the decay rate decreases
dramatically for the 1080 nm emitting QD and is largely temperature independent for the
smaller 880 nm emitting QDs.
As we will see, the most important findings are the ligand length independence
and the temperature dependence for the largest QDs. Fitted values of k
solution,1080nm
range
0.0 2.5 5.0 7.5 10.0 12.5 15.0
0.01
0.1
1

I
PL,solution
(t)
Time ( s)
C8, 880 nm
C8, 1080 nm
C18, 880 nm
C18, 1080 nm
0 5 10 15 20 25
0.01
0.1
1

Time ( s)
I
PL,solution
(t)
80K
150K
220K
297K
(a) (b)
297 K C8-Capped, 1080 nm
132
from about (1/2400) (ns
-1
) at room temperature to (1/5800) (ns
-1
) at 80K and, at any
temperature within the range examined here, are independent of ligand length.

Figure IV.4. (a) Influence of QD size on temperature dependence of in-solution decay
rate. Summary of in-solution decay rates as a function of temperature. In panel (b)
closed triangles are measurements on C18-capped QDs, open symbols are measurements
on C8-capped QDs. In-solution decay for C12-capped QDs (closed stars) was measured
only at 297K and consistent with the C8- and C18-capped QD behavior at that
temperature.

IV.4.2.2 Small QDs and inter-QD NRET
In a dense QD solid the exciton decay dynamics change in many regards with
respect to their in-dilute-solution behavior. Figure IV.5 summarizes the PL intensity
dynamics behavior of the small (880nm emitting). Figure IV.5(a) shows the room
temperature PL decay for emission at 880 nm for all ligand cappings (C8, C12, and C18).
As expected, owing to the transfer to nearby larger QDs, the decay rate at 880 nm
increases with decreasing ligand length and thereby decreasing average QD center-to-
center separation, r. The PL decay dynamics as a function of temperature down to 80K is
0 5000 10000 15000 20000 25000
0.01
0.1
1

I
PL
(t)
Time (ns)
C18 880nm 80K
C18 1080nm 80K
C18 880nm 297K
C18 1080nm 297K
850 900 950 1000 1050 1100 1150
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500

80K
150K
220K
Decay Time (ns)
Wavelength (nm)
297K
(a)
(b)
133
illustrated by the behavior of the C18 capped QDs shown in Figure IV.5(b). As the
temperature is reduced, an increase in the decay rate of the small, 880 nm emitting, QDs
is observed for all ligand lengths.

Figure IV.5. (a) PL intensity decay behavior for 880 nm emitting QDs with C8, C12, and
C18 ligands. The light green lines are the fits to equation (IV.4). Note the clear increase
in decay rate with reduction of ligand length. Panels (b) and (c) show the decay behavior
of the C8-capped and C-18 capped PbS QDs respectively. They clearly show an increase
in decay rate as temperature is reduced.

0 50 100 150 200 250 300 350 400
0.01
0.1
1

I
PL,880nm
(t)
Time (ns)
0 200 400 600 800 1000
0.01
0.1
1

C8
C12
I
PL,880nm
(t)
Time (ns)
C18
297K
C8
80K
297K
0 100 200 300 400 500 600
0.01
0.1
1

80K
150K
220K
I
PL,880nm
(t)
Time (ns)
297K
C18
(a)
(b) (c)
Small QDs, 880 nm detection
134
The TRPL responses for emission at 880 nm for all three ligand lengths and all
temperatures cannot be fit well to single exponential decay functions. They are, however,
well fit to a stretched exponential as given by Equation (IV.4):

[ (

)

] (IV. 4)

where 
1
and b determine the overall rate,

, through the expression,
[IV.21]

(

)

(

) Γ(

) (IV.5)

Stretched exponentials represent the characteristic behavior of a decaying population that
has a distribution of decay rates [IV.21]. This suggests that the local environment around
each 880 nm emitting QD varies in terms of the size distribution of nearest neighbor
NRET acceptors as well as possible defects and traps present in a given QD’s local
environment.

IV.4.2.3 Large QDs and inter-QD charge transfer
In the same QD solids, the nearly largest QDs that emit at 1080 nm at room
temperature display TRPL behavior as shown in Figure IV.6(a) for the three ligand
lengths. An initial increase in intensity is indicative of excitons being fed via NRET from
the adjacent smaller QDs. A clear rise is observed for all ligand lengths at all
135
temperatures investigated here. Following the initial rise, there is a decay that, unlike the
880nm decay, is fitted well with a single exponential. The rise and decay times, 
rise,1080nm

and 
1080nm
, of the large QDs are obtained by fitting the measured PL intensities,
I
PL,1080nm
(t), to,

[- (-

τ

) (-

τ

)] (IV.6)

We denote the decay rate of the largest QDs in the QD solid as

These decay rates in the solid are considerably faster than the decay rates in
solution and increase with decreasing ligand length. Figure IV.6 (b) and (c) shows the
characteristic trend in 1080nm PL decay with temperature for the case of C8-capped and
C18-capped QDs. As the temperature is reduced, both the rise rate and the decay rate
decrease. At all temperatures and for all ligand lengths the decay rate is nevertheless
always faster than the solution decay rate.

IV.5 Discussion
IV.5.1 General trends in the luminescence decay rate with temperature
The extracted decay rates for the small and large size QDs in the three different
solids for are shown as a function of temperature from 297K to 5.2K in Figure IV.7.
Note that the 880 nm decay rates for all ligand lengths at both room temperature and 80
K are much faster than the corresponding in-solution decay rates. At all temperatures the
880 nm PL decay rate shows strong ligand length dependence. The overall change with
136
temperature is less pronounced for 880 nm emission than for 980 nm and 1080 nm
emission wavelengths discussed below. Because the 880 nm decay rates for QD solids
are much faster than the measured decay rates of all other sizes, we deduce that the
measured 880nm rates largely reflect NRET, i.e.

.

Figure IV.6. Summary of 1080 nm decay in a QD-solid: (a) shows the increasing decay
rate with decreasing ligand length. The thin green lines are fits to eq (IV.6) and clearly
show a rise in PL intensity at short times. Panels (b) and (c) shows the decrease in decay
rate with reduction of temperature for C8-capped and C18-capped QDs respectively. For
all 1080 nm decay curves with C8, C12, and C18 ligands for the temperature range
covered here, there is a detectable rise in the initial PL intensity which is characteristic of
excitons being fed by NRET from smaller, adjacent QDs.

0 5000 10000 15000 20000 25000
0.01
0.1
1

I
PL,1080 nm
(t)
Time (ns)
0 500 1000 1500 2000 2500 3000
0.01
0.1
1

C8 C12
I
PL,1080 nm
(t)
Time (ns)
C18
297K
220K 150K
80K
297K
0 5000 10000 15000 20000
0.01
0.1
1

297K
220K
150K
80K
I
PL,1080nm
(t)
Time (ns)
C8
C18
Large QDs, 1080 nm detection
(a)
(b) (c)
137
For 1080 nm emission, Figure IV.7 reveals a markedly different decay rate
behavior with change in temperature. Although at room temperature, like the 880nm
decay, there is significant dependence on the ligand length, at 115 K and below, unlike
the 880 nm emission, the 1080nm decay rates are approximately equal for all three ligand
lengths. Moreover, this 1080nm decay rate is only slightly faster than in solution. In our
samples, the QDs emitting at 1080 nm are sufficiently large that there is negligible
probability of having a still larger nearest neighbor NRET acceptor. These observations
point to the presence of temperature-dependent competing decay pathways potentially
involving breakup of the exciton of the larger QDs into electron and hole. Indeed, as we
noted earlier (viz. Figure IV.1), the difference in energy between the 1S
h
level of a 1080
nm QD and that of an average size nearest neighbor is much less than the difference in
the energy of their 1Se levels. Moreover, the variation in the 1Sh energy values is
expected to be within the thermal fluctuations at room temperature [IV.26] [IV.27].
Thus hole transfer from larger quantum dots to adjacent smaller QDs is expected
to be considerably faster than electron transfer from larger QDs to adjacent smaller QDs.
The observed behavior of the PL intensity decay rates summarized in Figure IV.7
reinforce the earlier deduction that NRET dominates the decay in the small QDs (880 nm
emission) and charge transfer dominates decay in largest QDS (1080 nm emission). We
thus analyze the data of Figure IV.7 in terms of a physical model of the QD environment
to assess this emerging picture.

138

Figure IV.7. Trends in photoluminescence decay rates for both small and large QDs for
C8-, C12-, and C18-cappings with temperature. The small and large QDs show the
opposite general behavior, but in both cases the decay rate is largely temperature
invariant below 150K. For all cases, the both the large and small QDs, the decay rates
increase with decreasing ligand lengths at all temperatures.

Although our cation-ligand exchange process has allowed us to create the series
of QD solids featuring QDs that vary primarily by the length of the capping ligands, an
attendant change is the increase in the PbS volume fraction of the QDs solids with
decrease in the ligand length. As described below, we find that it is necessary to account
for the effect of the changes in PbS volume fraction on the dielectric properties of the
QDs solids to understand the observed exciton decay dynamics reported in the preceding
discussion.
0.01 0.1
1E-4
1E-3
0.01
0.1

5.2K
1E-1
1E-2
297K
150K
C8
C12
C18
Decay Rate (ns
-1
)
1/T (K
-1
)
Large QDs (Solid Symbols)
Large QDs
In-Solution:
Crosses
Small QDs (Open Symbols)
139
IV.5.2 The effect of ligand length on the effective medium dielectric constant of the
PbS QD solid
In order to consistently understand both 880nm and 1080nm decay behaviors it is
necessary to account for the QD solid effective dielectric constant (i.e. the dielectric
function of the composite medium of the ligands and PbS QD cores) on the charge and
energy transfer processes. For QD solids with PbS average diameter of 2.6 nm and
average edge to edge d of spacing 1 nm (C8), 1.4 nm (C12), and 2.1 nm (C18) as
determined by the TEM studies we estimate that the PbS volume fraction is 0.28, 0.20,
and 0.13 for the C8-, C12-, and C18-capped QDs respectively. The variations in PbS
volume fraction for the cases of close packed C8- and C18-capped QDs is shown in
Figure IV.8.
To estimate the dielectric constant of such a composite medium, we use the
Bruggeman effective medium approximation [IV.34] given in the expression below for a
system with components.

∑

(IV.7)

where

is the effective medium dielectric constant of the composite material,

is
dielectric constant of the host material (as explained below), and

and

are the
dielectric constants and volume fraction of the i
th
component. In the Bruggeman
effective medium approximation, the effective medium dielectric constant is assumed to
be equal to the host material dielectric thus no distinction regarding which component is
140
assumed to be the host or matrix is necessary. Therefore this approximation is well
suited for composites with multiple components with substantial volume fraction such as
the case here. Our observation that the QD-QD edge to edge spacing is approximately the
same as the length of one ligand molecule suggests that the ligands extend radially from
the QD surface and that ligands on adjacent QDs overlap. In this picture, the ligands will
also extent to fill the interstitial space between QDs, and thus we model the QD solid as a
two component material consisting of PbS and alkane ligands [IV.35].

Figure IV.8. Schematic illustrating the effect of ligand length on volume fraction of the
lead sulfide crystalline cores (blue circles) in the QD solid for the case of overlapping
ligands (rendered in grey) on adjacent QDs. The ligands are approximately equal to or
greater than the QD diameter, so the volume fraction of PbS changes considerably with
ligand length. The schematic is drawn with realistic proportions assuming 2.6 nm
diameter and d values from TEM images.

R
QD
+
l
ligand

R
QD

r, C18
d, C18

r, C8
R
QD

d, C8
R
QD
+
l
ligand

C8-Capped QDs
C18-Capped QDs
PbS
PbS
Ligands
Ligands
141
The static and optical frequency dielectric constants of alkane ligands are both
approximately two [IV.36] [IV.37]. The bulk values of PbS dielectric constants (static

and optical (

) values of 169 and 17.2, respectively) are used. We estimate
that QD solids with C8, C12, and C18 ligands have effective medium static dielectric
constant

= 8.2, 4.6, 3.2 and effective optical frequency dielectric constant

=
4.0, 3.3, 2.7 respectively. It is worth noting that many reports have suggested that the
dielectric constant of QDs decreases with respect to bulk values [IV.38] [IV.39] [IV.40].
The optical dielectric constant of PbS QDs has been previously estimated [IV.38] to be in
the range of 14.5+1.8: at most ~25% less than its bulk value of 17.2. Incorporating such a
reduction in PbS dielectric constant, however, translates into at most 10% reduction in
the effective dielectric constant of the QD solid given the small volume fraction of the
QD involved and thus does not significantly impact the discussion below.

IV.5.3 Inter-QD Energy transfer and the influence of effective medium dielectric
constant
Turning to the small QDs, in Figure IV.9 we plot the decay rates for the 880 nm
against the inverse sixth power of average QD-QD center to center separation, r. The
linear dependence and near-zero intercept at room temperature suggests that the PL decay
mechanism is dominantly NRET as suggested by eq. (IV.1). The temperature
dependence reveals previously unidentified interesting trends including an increase in the
NRET rate at low temperatures that saturates below 150K and a clear and large non-zero
intercept that increases with decreasing temperature.
142

Figure IV.9. (a) Summary of NRET rates for C8 -, C12 -, and C18 -capped QDs as a
function of 1/r
6
. Although at room temperature there is a near -zero intercept that is
expected from the Förster expression, there is clearl y a deviation at lower temperatures .

There are two aspects of the small QD decay behavior that must be investigated:
the non-zero intercept that at face value suggests a deviation from the Förster expression
at low temperature and the increase in NRET rate with decreasing temperature. To
address the former, we first account for the changes in effective medium dielectric
constant with ligand length. From Eq. (IV.1) we see that the NRET rate is proportional
to the inverse fourth power of medium index of refraction which suggests that the Förster
Radius will be greatest for the C18-capped QDs and the smallest C8-capped QDs.
Thus in order to compare NRET rates in different QD solids we must normalize
the Förster Radius by the factor (n
CX
/n
C18
)
4
, where CX indicates the ligand C8, C12, or
C18. These normalized NRET rates, plotted in Figure IV.10 as a function of the inverse
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.00
0.02
0.04
0.06
0.08

3.6 3.4 3.8 4.0 4.4
1/r
6
(1/nm
6
) (x1E3)
5.0
r (nm)
k
NRET
(ns
-1
)
220K
150K
80K
297K
880 nm
143
sixth power of QD-QD center-to-center separation r for each temperature, are seen to fall
on lines that, within the measurement errors, converge to the origin. This affirms that
NRET is indeed the dominant decay mechanism for the smallest QDs at all temperatures
studied here. This also shows that the increase in NRET rate achieved by reducing r
through ligand exchange with shorter ligands is partially counteracted by the increase in
the effective index of refraction owing to the attendant increase in the PbS volume
fraction.

Figure IV.10. NRET rates normalized by the fourth power of the effective medium index
of refraction with fitted lines that pass near the origin as expected from equation (IV.1)
and thus suggesting that NRET is the dominant decay mechanism.

The measured NRET rates (Figure IV.9) increase with decreasing temperature,
consistent with a previous study [IV.14]. The expression for NRET is valid at any
temperature so long as the absorption and emission spectra are taken at that temperature
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
1/r
6
(1/nm
6
) (x1E3)
Normalized k
NRET
(ns
-1
)

220K
150K
80K
297K
880 nm
144
[IV.41]. Indeed for the temperature range of 297K to 80K the ensemble PL and
absorption [IV.42] spectra of the PbS QDs used for this study are essentially temperature
invariant, suggesting a temperature invariance of the overlap integral and Förster radius.
This observation however is intriguing as the opposite would be concluded if one
merely applied the equations for NRET rate and Förster radius (Equation IV.1) derived
for an ensemble of donor-acceptor pairs in which all donors and acceptors have similar
emission and absorption characteristics and recognized that the radiative decay rate
decreases slightly with decreasing temperature. A potential explanation to the opposite
observed behavior here and previously is that Equation IV.1 may not be directly
applicable to ensemble averaged PbS QD absorption and emission spectra since the
NRET rate is controlled by the very different emission/absorption characteristic and
temperature dependence of the local QD pairs compared to the ensemble average. Indeed,
the PL from individual PbS QDs is known to have a strong temperature dependence with
unusually large PL line width on the order of 100 meV at room temperature [IV.43]
[IV.44] and thus considerably less than the ensemble line widths.
Moreover, the decreased charge transfer rate within the QD solid at decreasing
temperature may be another contributing factor to the apparent increase of NRET rate. As
a result of the lower charge transfer rate, a QD is expected to have lower probability of
having charged QDs (with electron/hole occupying 1S
e
/1S
h
) as neighbors. Since 1S
e
/1S
h

occupied QDs have reduced light absorption involving 1S
e
/1S
h
transition due to Pauli
blocking as observed in intentionally doped PbS QD [IV.45], an increase in the NRET
145
rate is expected at lower temperature due to the decreased probability that a potential
acceptor will be charged.

IV.5.4 Inter-QD Charge transfer and the ligand length dependent activation energy
for change transfer
To investigate the charge transfer behavior, we focus on the enhancement in the
decay rate of the 1080 nm emitting QDs in the QD solid over their decay rate in solution
that represents the contribution to decay that is enabled by the presence of adjacent QDs.
For the 1080 nm decay, the quantity [k
QD Solid,1080nm
– k
solution,1080nm
] versus the QD-QD
edge-to-edge spacing, d, for all three ligand lengths at four temperatures is plotted in
Figure IV.11.

Figure IV.11. (a) Illustrative TRPL curves showing the enhancement in 1080nm decay
rate for QDs in QD solid (bold lines) over the same sized QDs in solution (thin lines).
Panel (b) shows the quantitative values of enhancement in decay rate of the 1080nm
emitting QDs in the QD-solid over the same sized QDs in dilute solution as a function of
QD edge-to-edge separation, d, determined from TEM measurements. The lines are
guides to the eye and show a clear change in slope with temperature.

0 1000 2000 3000
0.01
0.1
1
C8, C18 In Solution

PL
= 2400 ns
C8 - QD Solid

PL
= 365 ns

I
PL
(t)
Time (ns)
C18 - QD Solid

PL
= 1300 ns
1.0 1.2 1.4 1.6 1.8 2.0 2.2
1E-5
1E-4
1E-3

d (nm)
[k
QD-Solid,1080nm
- k
Solution,1080nm
] (ns
-1
)
220 K
150 K
297 K
(b)
80K
(a)
146
Note the exponential dependence of [k
QD Solid,1080nm
– k
solution,1080nm
] on d at all
temperatures but with varying slope down to ~150 K. It saturates below ~125 K to the
behavior shown at 80 K. An exponential dependence of charge transfer rate on QD-QD
spacing (~exp(- d)) at room temperature has been reported for thiol-capped PbS QDs
solids [IV.17] in time resolved photoluminescence measurements and in electrical
measurements investigating charge carrier mobility [IV.15] This exponential dependence
suggests charge motion via tunneling [IV.15][ IV.17].
.
Our temperature dependent
measurements summarized in Figure IV.11 reveal however a dramatic decrease in the
rate of decay with separation. Fitting the data at 297K and 220K suggests  values of
1.85 nm
-1
and 0.96 nm
-1
respectively, though as shown below this fitting methodology
cannot capture the full charge transfer behavior.
A richness to the charge transfer process is revealed since the data indicate the
need for either a temperature dependent tunneling parameter  or a ligand-length
dependent activated density of charge carriers available for tunneling (see E
a
in Equation
(IV.2)). For perspective, considering the most basic relationship between and the
energy barrier √

[7] where

is the electron or hole effective mass in
the barrier and

is the tunneling barrier, and is the reduced Planck’s constant. A
change in  from 1.85 nm
-1
and 0.96 nm
-1
would require an approximate four fold
decrease either the effective mass or energy barrier, which is not likely to be the case in
our system due to the temperature insensitivity of both of these parameters.
The drastic change in slope with decreasing temperature in Fig. IV.10 thus points
towards the presence of a ligand length-dependent activation energy for creation of
147
unbound carriers to tunnel. Fitting the data in Figure IV.10 for each ligand length (i.e.
each QD-QD separation) with an Arrhenius form in the range from room temperature
down to 150° K shown in Figure IV.12 gives estimate of this thermal activation energy,
E
a
(see Equation (IV.2))
,
for C8-, C12-, and C18-capped QDs as 81+7meV, 67+5meV,
and 37+10meV, respectively. We recall that although the lengths of the three ligands are
significantly different, their chemical binding groups to the Pb in the PbS QDs are the
same. Thus we reasonably expect the energy barriers to be nearly the same (within the
experimental uncertainties) and expect a single value of the tunneling parameter  to be
operative for all three ligand length cases. This expectation is supported by evidence of
tunneling through alkane chains of various lengths grafted onto gold that showed found
that the tunneling parameter through is independent of alkane chain length [46].

Figure IV.12. Arrhenius plot showing the ligand length dependent activation energy for
charge transfer.

In Figure IV.13 we thus plot the QD-QD distance dependence of the quantity
0.003 0.004 0.005 0.006 0.007
1E-4
1E-3

C18
C8
[k
QD-Solid,1080nm
- k
solution,1080nm
] (ns
-1
)
1/T (K
-1
)
C12
148
[k
QD Solid,1080nm
– k
solution,1080nm
]/exp(-E
a
/kT) using the above noted extracted values of E
a

for each ligand length. The data in the range ~300 K to ~150 K are seen to collapse onto
a universal line, suggesting that tunneling is indeed the mechanism controlling the
exciton decay behavior of the larger QDs in this temperature range.
From Figure IV.13 we estimate the tunneling parameter  to be 3.3 nm
-1
. This is
significantly greater than what would be estimated from the 297 K data only (1.85 nm
-1
)
without consideration of the ligand-length dependent activation energy. This finding
illustrates the complexities of the charge transfer process and the sensitivity on local
dielectric environment.

Figure IV.13. After accounting for the ligand-length dependent activation energy we find
that the distance dependence due to the tunneling parameter is nominally the same for
temperatures in the range from 150K to 297K. The line is a best fit and we find that the
temperature independent value of the tunneling parameter is 3.3 nm
-1
.

1.0 1.2 1.4 1.6 1.8 2.0 2.2
1E-3
0.01
0.1

[k
solid,1080
- k
solution,1080
]/exp(-E
a
/kT)
d (nm)
297 K
220 K
150 K
Ea,C18 = 37 meV
Ea,C18 = 67 meV
Ea,C8 = 81 meV
= 3.3 nm
-1

149
The origin of the ligand length dependent activation energy for charge transfer is
likely dominated by the sum of two terms: (1) the difference in energy between the 1Sh
level of the largest (1080 nm emitting, ~3.1 nm diameter) QDs and the 1Sh level of the
average size QD (~2.6 nm diameter),

, which is around 30 meV

as noted before
and, (2) the cost of electrostatic energy for dissociating an exciton within a QD into an
electron-hole pair in neighboring QDs,

, which can be reasonably estimated as

where

is the exciton dissociation energy for electron-
hole separation to infinite distance and

is the attractive
Coulomb energy between an electron and a hole residing in two neighboring QDs [IV.4].
We assume that the intra-QD exciton screening is only dependent on the optical dielectric
constant of the PbS QD. Thus

is considered independent of the choice of ligands and
estimated using [IV.47]

. Using PbS QD dielectric constant

=
17.2 and QD radius of the largest QDs, R
QD
=1.55 nm, gives

~ 97 meV. On the other
hand,

depends significantly on the ligand lengths which influence the PbS
volume fraction and thus the effective medium dielectric constant. As noted earlier,

of the C8-, C12-, C18-QD solids is estimated to be 8.2, 4.6, 3.2. Such decrease in
effective dielectric constant from C8- to C18- QD solids overcompensates for the small
increase in QD center-to-center distance resulting in a net increase in the attractive
Coulomb energy between electron and hole in neighboring QDs with longer ligands. For
C8-, C12-, and C18-capped QD solids,

is estimated to be 45, 74, 91 meV.
Thus the activation energy (E
a
), the sum of

and

, is
150
estimated to be 82, 53, 36 meV for C8-, C12- and C18- QD solid. The span in the
estimated activation energy of 46 meV between C8- and C18-capped QDs reasonably
explains the span of the thermal activation energy for charge transfer of 44+13 meV
between C8- and C18-capped QDs extracted from the measurements.

IV.6 Summary of findings on inter-QD energy and charge transfer
The work in this chapter represents the findings of a first-of-a-kind systematic
study of the exciton decay dynamics in PbS QD solids as a function of QD size, inter-QD
separation, and temperature that has revealed a fuller view and enabled a clearer
understanding of competing processes controlling exciton decay dynamics as a function
of QD size. We find that energy transfer to larger adjacent QDs via NRET can be made to
dominate exciton decay in quantum dots at all temperatures and inter-QD separations.
For the largest QDs that do not have much probability of having a yet larger QD as an
adjacent energy acceptor, the exciton decay rate above about 125 K depends strongly on
the ligand and is substantially faster than the decay rate in solution. The temperature
dependence of the exciton decay rate of these larger QDs reveals that the enhanced (over
solution) decay rate in the QD solid is dominantly a thermally activated charge (here
most likely hole) tunneling process involving single particle states of adjacent QDs. With
decreasing inter-QD distance, the activation energy for creating unbound carriers that can
tunnel increases which can be attributed to the increase of energy cost required to
dissociate exciton into neighboring QDs resulting from the increase in the QD solid
effective dielectric constant. Finally, at temperatures below about 100K, the decay rate of
151
these larger QDs in the solid saturates at a value independent of ligand length and
indistinguishable from the value in dilute solution, clearly indicating that the PL decay
controlling processes are internal to the QD (i.e. independent of the environment). This
“isolation” as a function of decreasing temperature suggests that the exciton decay likely
involves transition in which either the initial or final state is potentially a state in the
intrinsic 1S
e
-1S
h
gap of the QD, possibly localized at the surface of the QD. Although
our measurements cannot identify the originating or terminating single particle states
involved in the PL decay and thus discriminate between 1Se, 1Sh, or midgap state,
photoinduced absorption [IV.25] and TRPL [IV.33] studies carried out on PbS QDs of
these larger sizes (~3 nm) have reported the presence of subgap states.
.
Our findings are
consistent with the presence of electron subgap states as the PL decay in our PbS QDs
may also be from an electron that has relaxed from the initial quantized 1S
e
state to a trap
state before combining with the hole in the 1S
h
state. Indeed, our finding from TRPL
studies that the charge motion is dominated by the holes in these PbS QD solids is
consistent with the photoconductivity study based findings [IV.48].
The implications, for NRET-based photovoltaic energy conversion, of the
competing energy and charge transfer dynamics in QD solids as a function of ligand
length and temperature revealed by the present study are somewhat subtle and can be
summarized as follows. The efficiency of the NRET process from the small, here 880
nm emitting, QDs is given by the ratio of NRET rate to the total decay rate, i.e. sum of
radiative, defect-related non-radiative, NRET, and charge transfer (to another QD) rates.
Given the NRET rate dependence on the inverse sixth power of the inter-QD separation,
152
minimizing the separation at face value appears to be the straight forward approach to
enhancing NRET rate but the presence of the inverse fourth power of the refractive index
of the medium in the expression for the Förster radius R
0
, quantum dots of materials
having high dielectric constant, such as PbS in the current study, lead to a compensating
reduction in R
0
owing to the attendant higher volume fraction of PbS and thus higher
refractive index of the effective medium. This counteracts the full gain from separation
reduction. There is thus a need for optimization between the QD material dielectric
function and the packing fraction of the QDs.
In the present case, at room temperature, ligand exchange from C18 to C8
increases the NRET rate of the small QDs from approximately (1/100) (ns
-1
) for C18 QD
solid to (1/25) (ns
-1
) for C8 QDs solid, a gain of a factor of four. The corresponding
behavior of the large QDs shows their PL decay rate to increase from approximately
(1/1300) (ns
-1
) to (1/360) (ns
-1
).

153
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158
Chapter V: PbS QDs on Silicon: The Interface, NRET, and Charge
Transfer

V.1 The QD – Substrate Separation
The studies of inter-QD energy and charge transfer discussed in the preceding
chapter underpin estimating and optimizing a photo-created exciton reaching a QD at the
QD – semiconductor interface and thus having a chance to transfer its energy to the
semiconductor. In this chapter we thus discuss the findings of our high-resolution
transmission electron microscope (HRTEM) studies of the structure and
photoluminescence (PL) studies of the optical behavior of this interfacial region
undertaken to shed light on the factors that control NRET from the QD adsorbed on the
semiconductor to the semiconductor substrate. While the motivation for the study of
atomic-scale structure stems from the specific proposed NRET-based photovoltaic
device, the HRTEM studies described this chapter are directly applicable to examination
of QD-substrate interfaces present in essentially all QD-based optoelectronic devices as,
in general, the use of QDs in optoelectronic devices invariably involves at least one
interface between the QDs and a solid substrate. Such heterojunctions allow for a rich
range of optoelectronic (light emission [V.1], detection [V.2]), photonic (waveguides
[V.3], cavities[V.4], etc.) and electronic (diodes , transistors [V.5], etc.) technologies
aimed at applications ranging from optical communications, information processing,
sensing biomolecular and biological agents [V.6][V.7], solar photon harvesting and
conversion to power [V.8] or fuel [V.9], and many others. Most QD-based devices
159
utilize electron or hole transfer at a QD – semiconductor heterojunction [V.10]. However,
NRET between three-dimensionally confined states (such as in molecules and quantum
dots) and semiconductor substrates has been analyzed within a point dipole
approximation by Stavola, Dexter, and Knox [V.11]. Recently, experiments
demonstrating NRET from QDs to a substrate [V.12] [V.13] or vice-versa [V.14] have
been demonstrated. The physics of energy and charge transfer across the functionalized
QD – substrate interface can be discussed utilizing the schematic energy diagram of a QD
(here PbS) on a substrate (here silicon) as shown in Figure V.1. It illustrates the
importance of the thicknesses of the ligands and the surface chemical layer as they
together the distance of transfer and their chemical compositions determine the energy
barriers to be overcome in the transfer process.
The separation between the QD and the semiconductor substrate is thus a most
important parameter that must be determined, understood, and controlled in classes of
devices that employ appropriately functionalized QDs as the initial sensor of radiation,
molecules, or biomolecules and the substrate as a transducer and /or an amplifier of the
inevitably weak signal from the QDs. The response of the charges (electrons and holes)
in nanocrystal – semiconductor hybrid structures to external disturbance, most commonly
owing to impinging photons or an applied electrical field or both, is widely recognized to
be impacted by the specific ‘local’ structural and chemical nature of the interfacial region
of the hybrid system, which for QDs must be influenced by the characteristics of the
organic ligands present on their surface that largely determine how the QDs interact with
their environment, and the surface chemical layer that is inevitably present on the
160
semiconductor surface. Knowledge of the structural and chemical nature of the QD-
substrate heterostructure thus enables a more reliable parameterization of physical model
on which the energy/charge transfer processes depends, such as the crystal orientation of
the QDs, the physical separation between the QDs and substrate, and the presences of
interface/surface disorder/impurity with associated electronic states.

Figure V.1. Band diagram for PbS QDs on Si for the case of 2.6 nm average diameter
(with absorption peak at 810 nm). In addition to the alignment of energy levels in the
PbS QD and silicon with respect to each other, the separation between the QD and silicon
surface is of key importance. In general, the separation is determined by the ligands on
the QD and the surface chemical layer (native oxide, for example) that are present on the
silicon surface with surface density of states schematically shown by the green line.
Electron affinities and ionization potential of the QD are from Refs [V.15] [V.16].
IP
PbS 810
=
5.0 eV

PbS QD
t
ligand

E
vac
= 0


Si
=
4.05 eV
IP
Si
=
5.15 eV
d
QD- S u rf a ce


PbS, 810
=
3.55 eV
h
e
E
f

1.1 eV
p-Si
Oleate
Ligand
Surface
Layer
1S
e

E
MG

1S
h

E
CB

E
VB

NRET
161
Given the significance of the QD – substrate separation, a first-of-kind cross-
sectional, high resolution transmission electron microscopy study to determine it was
undertaken and is discussed next. In this novel approach, nanocrystal quantum dots are
dispersed on electron transparent nanopillars to enable simultaneous imaging of the entire
composite: the QD, the substrate, and the interfacial region. Our specific system is of
course the combination PbS QDs on silicon nanopillars. The structural study is
complemented by measurements of photoluminescence from the QDs directly adjacent to
silicon. The findings show that light emission from PbS QDs on silicon (i.e. without any
intervening layer) is effectively quenched, which we attribute to dominance of charge
tunneling from PbS QDs to Si in such a situation.
We note that charge and energy transfer processes are sensitive to changes in the
separation between initial and final states on the order of an angstrom [V.10], and
consequently, investigations of the QD-semiconductor surface structure should provide
spatial information on the same scale. Plan-view transmission electron microscopy
imaging of nanocrystals residing on ultrathin semiconductor substrates, which enables
orientations of adsorbed QDs, to be discerned has been demonstrated by our group
[V.17]. However, in this geometric arrangement information about the interface or the
behavior of the ligands cannot be determined. Additionally, from the AFM height-
signature of QDs on a solid substrate [V.18], one may infer that the QD-subtrate spacing
if the QD diameter is independently known sufficiently accurately however, the detailed
behavior of the ligands at the interface and how they affect separation between the two
remains inaccessible. Moreover, AFM-based approaches have the limitations that the tip-
162
QD interactions depend strongly on the imaging conditions [V.19] that introduce great
difficulty in measuring precisely the total height of the QD, let alone providing an
estimate of the QD-substrate separation with precision better than a nanometer.
Thus the detailed behavior of the QD ligands at the interface and how they affect
the separation with the substrate had remained unexamined until the studies undertaken
as part of this dissertation. It is well known that the ligands effects on inter-QD spacing
as we also showed in Chapter III. Our, as well as the work of others [V.20][V.21],
suggests that there exists overlap among ligands on neighboring quantum dots in a QD
solid and that the inter-QD spacing can be approximately equal to the length of one
ligand molecule. However, for the case of QDs adsorbed on a rigid substrate the
separation between the two has simply not been examined until these studies.

V.2 An approach to imaging the QD-semiconductor interface
Our approach to imaging the structure of nanocrystals adsorbed on semiconductor
surfaces and the interfacial region employs a new and innovative approach to preparing
TEM specimens. Rather than the standard ion-milling of the substrate to electron
transparency, we use here nanoscale electron beam lithographic patterning and dry
etching techniques to create nanopillars of electron-transparent thickness and with top
surfaces that are without significant departures from the atomically flat surface of the
starting semiconductor substrate (here silicon) wafers, as indicated schematically in
Figure V.2. Indeed, this approach has, for the first time, enabled simultaneous atomic-
resolution imaging of the composite hybrid system, including the heterojunction. Our
163
approach provides two primary benefits for imaging. First, it enables tilting the
nanopillar array bearing TEM specimen to access a crystallographic zone axis that is
known to be parallel to the nanopillar top surface thus allowing unambiguous
determination of the nanocrystal lattice orientation with respect to the substrate (silicon)
surface. Other approaches to thinning specimens by using ion beams or mechanical
polishing are not able to create atomically smooth surfaces with well-defined
crystallographic orientations that are necessary for this investigation. Second, the QDs
are deposited onto the nanopillars as a final step, thus ensuring that they are not
contaminated or damaged in the TEM specimen preparation process.

Figure V.2. Schematic of the arrangement of QDs on a substrate surface oriented to
allow imaging of the cross-sectional interface. For QDs sitting on the top surface, it is
possible to image the QD-semiconductor interface in cross section. The patterns on the
nanopillar side surface are drawn to indicate the characteristic shape of sidewalls created
by Bosch etching as described in section V.2.1 below.

An additional benefit of our approach to TEM specimen preparation is that the
QDs can be imaged without the convolution of any other material in the path of the
164
impinging electron beam, such as encountered in the common-place approach of plan
view imaging of nanocrystals on an amorphous carbon support layer over copper mesh or
silicon nitride window. Furthermore, these simpler traditional approaches cannot allow
for direct and unimpeded cross sectional imaging of the QD – substrate interface due to
obstruction of the beam at high tilt angles that are necessary to have the electrons
impinge parallel to the amorphous carbon or silicon nitride surface.

V.2.1 Our new TEM specimens
A key part of this investigation is the development of a new approach to TEM
specimen preparation. The TEM Specimen preparation method reported here stems
from an unique investigation in the silicon microelectronic fabrication arena; there are no
silicon structures created by dry etching for use as precisely fabricated platforms for
HRTEM studies.
The Si nanopillar array bearing TEM specimens were prepared by electron beam
lithography (EBL) and anisotropic dry etching using the Bosch process [V.22]. First,
silicon (001)+0.1º wafers were sequentially degreased by sonication in trichloroethylene,
acetone, methanol, and deionized water and then dipped in concentrated HF to remove
the native oxide. EBL with HSQ resist was performed as described in Chapter II.4. The
EBL patterns are arrays consisting of 100 nm wide stripes that are 5 m long oriented
along the Si [-110] direction and spaced 5 m apart in the [-110] direction, 100 m apart
in the [110] direction, and cover an area of 1 mm
2
. HSQ remaining after developing has
properties similar to amorphous SiO
x
and is thus an appropriate etch mask for DRIE.
165
We optimize etch parameters to yield relatively small sidewall undulations that
are a well-known result of the cyclic Bosch process [V.22] using an Oxford Plasmalab
100. We used the following two sets of parameters for Si etching and polymer deposition
respectively to protect the etched sidewalls: (1) Etch step time of 4 seconds, 30 sccm of
SF
6
, 500 W ICP power, 40 W RF power, and 10 mTorr of SF
6
and (2) Deposition step of
5 seconds, 80 sccm of C
4
F
8
, 500 W ICP power, 10W RF power, and 18 mTorr of C
4
F
8
.
After repeating five cycles of the etch – deposition process, the etch depth (i.e. the height
of the nanopillars) is approximately 600 nm.
Following dry etching, the substrate with nanopillars was cleaved along the [-110]
direction through the array of NPs and then the cleaved surface was glued to a gold-
coated, TEM slotted disc with Gatan G2 epoxy such that the array of NPs was centered in
the slot. It is necessary to use gold coated grids in order to allow for the specimens to be
etched in HF as a final step because other metals commonly used for TEM grids such as
copper or nickel are aggressively attacked by HF. The nanopillars were encapsulated in
wax to prevent them from breaking during mechanical polishing. Great care was
required to prevent the nanopillars from breaking during mechanical polishing. The
substrate with nanopillars should be at ~220 C and the wax must be fully melted before it
is allowed to come in contact with the nanopillars. Once encapsulated with wax, the
sample was thinned by mechanical polishing in the direction perpendicular to the
substrate normal to a thickness of 80-100 m to allow for use in standard TEM specimen
holders. After polishing the TEM specimen was rinsed thoroughly with acetone and
methanol and subsequently etched three times in 49% HF for 30 seconds with 1 minute
166
deionized water rinse after each HF etch to remove the remaining HSQ resist. After the
final rinse, the TEM specimens were immediately transferred to methanol and dried by
blowing the methanol from the specimen.
An illustrative scanning electron microscope (SEM) image of a nanopillar after
etching and SEM images of the TEM specimen are shown in FigureV.3. All SEM
images were taken with the Hitachi 4800 SEM with cold field emission gun at 1 kV
accelerating voltage.

Figure V.3. Scanning electron microscope images of a TEM specimen as prepared using
procedures described in the text. Panel (a) shows an as-etched pillar. Panels (b), (c), and (d)
show the same TEM specimen at different magnifications. The circled region in (b) and (c) is
enlarged in (c) and (d) respectively. In (b), the circular 3 mm diameter gold coated slotted grid is
shown. In (c) the thickness of the wafer in the direction of the beam of approximately 100 m.
Panel (d) shows a high magnification view of a part of one nanopillar. The red arrows in (a) and
(d) indicate the direction ([110]) of impinging electrons in the TEM.

500 m
50 m
400 nm

(c)
(c
)
(d)
1 m
[110]
[001]
(a)
Top Surface of Si
wafer before

[-110]
(b)
[-110]
[001]
~100 m
167

V.2.2 Deposition of PbS QDs onto nanopillars
When depositing QDs onto the nanopillars, it is important to minimize deposition
of non-volatile impurities, which are present in the QD solution. The solution is thus not
allowed to evaporate, as it would result in residues on the sample surface. Large PbS
QDs were deposited onto the nanopillars by placing the TEM specimen on teflon and
then submersing it in approximately 10 L of a dilute solution of 0.1 mg PbS QD per mL
toluene. After 10 seconds, the solution is blown off. This process typically results in five
to ten QDs on top of each nanopillar. Although QDs are deposited onto all surfaces of the
nanopillars, in this study we are only interested in those that are on the nanopillar top
surface.

V.3 High resolution TEM images of PbS QDs on Si
High resolution TEM images of PbS QDs adsorbed onto the top of silicon
nanopillars are shown in Figures V.4 and V.5. TEM imaging was accomplished using
the FEI Titan with an objective lens aberration corrector. The objective-lens spherical
aberration coefficient was tuned to approximately -5 m. The instrument is operated at
300kV utilizing phase contrast imaging with no objective aperture.
These images were all obtained with the TEM specimen oriented parallel to the
silicon [110] zone axis, as indicated by the inset diffraction pattern in Figure V.4. This
orientation is tuned such that incident electrons impinge parallel to the nanopillar top
(001) surface within an accuracy of +0.1º. For these microscope settings, all low index
168
planes that are parallel or nearly parallel (as discussed below) will create visible lattice
fringes in the HRTEM images.

Figure V.4. (a) High resolution image of a PbS QD on a silicon nanopillar with (001) top
surface. The beam is oriented along the Si [110] zone axis as determined from the inset
diffraction pattern of the silicon nanopillar in a region away from any QDs. The visible
planes and their spacings are identified, and the spacing between the PbS QD crystalline
surface as indicated by the lowest point visible on the {111} plane indicated by the white
arrow and the silicon crystalline lattice as indicated by the red lines is ~0.6 nm. This
image is from sample number 092512-14b.

Si {111}
planes
Top Surface
of Si NP
PbS {111}
0.34 nm
PbS {220}
0.21 nm
(00-2)
(002)
(1-11) (-111)
(2-20)
(-220)
(-11-1) (1-1-1)
169
In Figure V.4, lattice planes in both the PbS QD and silicon nanopillar are clearly
visible. For all of these TEM images the electron beam is oriented parallel to the silicon
nanopillar top surface, thus enabling the QD - semiconductor surface to be imaged.
Because the nanopillars extend only 600 nm from the substrate surface and the TEM
specimen is approximately 100,000 nm thick after mechanical polishing (see Fig. V.2),
tilting to orientations other than along the Si [110] zone axis results in the top or bottom
of the specimen impeding the view of the QDs. We have achieved the desired goal of
being able to observe the structure of the interface, but for specimens as shown in Figure
V.2 the range of viewing angles is limited.

V.3.1 Crystallographic orientation of QDs with respect to the substrate and
preferential adsorption orientation
The different lattice planes visible in the different QDs are due to uncontrolled
variation in adsorbed QD orientation with respect to the incident beam, and the different
orientations allow for phase contrast from different sets of planes within the QDs.
We note that interpretation of lattice fringes in very small nanocrystals should be
done with caution [V.23] due to the fact that in sufficiently small nanocrystals significant
diffraction can occur at orientations far from the Bragg condition because of the large
reciprocal lattice spots. The radius of the reciprocal lattice spot for a spherical quantum
dot, which is also the length of the upper limit for excitation error from the Bragg
condition that can allow for phase contrast, is 1/D
QD
where D
QD
is the quantum dot
diameter which is in this case the specimen thickness, L, as discussed in section II.3.2).
170
For phase contrast from a set of planes with spacing d
hkl
, the upper limit for tilt angle,

max
, away from the Bragg condition that can still allow for diffractions and thus phase
contrast imaging is 
max
=Sin
-1
[d
hkl
/D
QD
] [V.24]

. For PbS QDs with an average diameter
of 6 nm, the PbS (111) planes, which have the greatest spacing of any observed here of
d
111
= 0.34 nm, have a value of 
max
= 3.3°. This means that the fringes observed in some
images presented herein may not be projections of lattice planes that extend directly into
the page of the two dimensional images, but that they may be tilted by up to 3.3°. This
level of uncertainty does not significantly change the analysis or discussion below.
In Figure V.4 the PbS (111) planes, spaced 0.34 nm apart, are observed to be
oriented ~ 19+2° from the silicon surface (001) plane. This is close to the angle of 19.5°
between (111) and (112) planes of PbS and suggests a preferential adsorption of the PbS
QDs with (112) plane parallel to the silicon surface. Additionally, the {220} planes
visible in Fig. V.4 are observed to be oriented ~ 71+2° from the silicon surface which is
close to the angle between (-202) and (112) of 73.2° further suggesting that a (112) plane
is parallel to the silicon. Other illustrative TEM images shown in Figure V.5 reveal
variations in the PbS QD orientation with respect to the substrate and variations in QD
shape. In Figure V.5(a) and (b), the angle between the (111) planes of a PbS QD and the
silicon surface is 19+2° as in Figure V.4. However, the PbS QD imaged in Figure V.5(c)
has a different orientation with respect to the silicon surface, and reveals its (002) planes
with spacing of 0.30 nm oriented 3+1° to the silicon nanopillar surface (001) plane. This
suggests that the PbS (001) plane is parallel to the silicon surface. Such variations in

171

Figure V.5. Variations in PbS QD shape and orientation with respect to the silicon
substrate. All three images were taken under the same conditions and with the incident
electrons in the same orientation with respect to the silicon nanopillar. In (a) and (b) the
angle between the PbS {111} planes and the (001) silicon top surface is 19+2°, same
angle observed for the QD in Fig. V.4, suggesting a preferential adsorption by the {112}
plane adjacent to the silicon. Panel (c) shows that the PbS {002} planes are 3+1° from the
(001) silicon top surface, suggesting that other orientations are possible. These images
are from sample number 092512-14b.

(b) (a)
(c)
PbS {111} PbS {111}
PbS {002}
2 nm 2 nm
2 nm
172
orientation suggest local fluctuations in the competition between attractive forces
between the QD and the substrate during adsorption. We note that both the (112) and
(001) planes are charge neutral for the rock salt structure, suggesting preferential
orientation of these planes parallel to the silicon, though additional investigation will be
necessary to confirm this preferential adsorption orientation.

V.3.2 Spacing between QDs and substrate surface
Next we investigate the issue of the separation between the QD and crystalline
silicon. In the images in Figures V.4 and V.5(a), we observe a disordered layer up to 2
nm thick is present at the Si surface and is probably native oxide before PbS QD
deposition. Although we expected the native oxide to be about one nm thick [25], the
observed 2 nm thickness suggest that the native oxide layer is not uniform and that we are
observing the maximum projection. This native oxide layer is also visible in TEM
specimens before PbS QD deposition as shown in Figure V.6. This observation confirms
that the disordered layer did not result from incidental deposition of non-volatile species
in the PbS QD – toluene solution. HRTEM images of the TEM specimen before the
removal of the remaining HSQ by HF etching. Also note the near atomically flat surface
of the TEM specimen before removal of the HSQ resist as shown in Figure V.6 (b).
The image in Figure V.4 suggests that the QD crystalline planes extend closer to
the silicon nanopillar than can be observed with clarity through the native oxide which
includes the region of the ligands. The closest spacing between a visible lattice plane of
PbS QD and crystalline Si surface in Figure V.4 we estimate as marked and is ~0.6 nm.
173

Figure V.6. TEM images of silicon nanopillars Pillars without PbS (a) before removal of
HSQ by HF etching and (b) after removal of the HSQ. In (a), the near atomic level
smoothness on the Si top surface is observed. The HSQ is amorphous. Clearly there are
only two phases: crystalline silicon and HSQ. In (b), the amorphous native oxide is
observed after HF etching but before the PbS QDs were deposited. These phase contrast
images were taken with the electron beam along the [110] zone axis with no objective
aperture in the JEOL 2100F at USC.

Averaged over ten QDs on Si nanopillars imaged, the spacing is found to be 0.95+0.4
nm. This separation is likely due to the combination of the intervening QD ligands and
the native silicon oxide at the location of the QD – silicon interface. To further
investigate the separation we analyze the images in Figure V.4 and Figure V.5(a) using
Fourier processing to identify QD lattice extending closer towards to the crystalline
silicon through the amorphous region than is clearly visible in the TEM images.
Fourier filtered images with only spatial frequencies corresponding to the PbS
{111} and {222} and Si {002} planar spacing are shown in Figure V.7. Fourier filtered
images in Figure V.7(b) show that for the case of image in figure V.7(a), PbS {111}
(a)
(b)
174
planes extend closer to the silicon than can be distinguished in the TEM images and
appear to be directly adjacent to the crystalline silicon. However, for the QD imaged in
Figure V.7(d), the spacings observed in the TEM image and corresponding Fourier
filtered image in Figure V.7(e) are approximately the same. Because the PbS planes are
likely hidden in the amorphous layer the average separation observed in the TEM images
of 0.95 nm should be taken as the upper limit of separation between the QDs and the
crystalline silicon, d
QD-surface
. Additionally, it is certain that the separation contributed by
the QD ligand steric effect is less than 0.95 nm on average observed in the TEM images
on account of the non-uniform native oxide present on the silicon.
Clearly, separations due to ligand steric effect are significantly smaller than the
~2 nm length of the oleate ligands (C
18
H
33
O
2
) that are present on the as-grown QD
surface. This suggests that ligands on the PbS QD facet facing the silicon are either bent,
compressed, or do not extend radially from the PbS QD surface.
Regardless of the reason why the spacing is observed to be much less than the
length of the oleate ligands, the measured separation between the QDs and the underlying
substrate is of central importance, of course, in affecting both charge and energy transfer
rates between the two. Besides the separation, charge transfer between these two
components depends also on the energy barriers arising from the discontinuity in the
relevant energy states operative in the QD, the ligand, any intervening layer (often a
native oxide) to the underlying semiconductor, and in the semiconductor. Thus
information on the chemical nature of the interfacial region is also important.

175

Figure V.7. Fourier filtered images. (a) and (b) show the TEM image and Fourier filtered
images respectively of the of the QD in Figure V.4. The filtered image was created using
the points in the Fourier transform circled in (c) that include the PbS (111) and (222)
(blue circles) and the Si (002) (red circles) to highlight the edge of the crystalline silicon
and the crystalline PbS QDs. Red arrows in (a) and (b) point to the same lattice plane,
and two {111} planes are visible in (b) (as indicated with blue arrows). These {111}
planes are not visible in (a) suggesting that the separation due to the native oxide and
ligands can be much less than observed in the TEM images. However, for the QD shown
in images (d) and (e) that correspond to the QD in Figure V.5(a), the separation appears
to be approximately equal.

V.4. Optical response of PbS QDs on silicon and silicon with thick SiO
2

Next, we discuss the impact of the interfacial region on the photoluminescence
(PL) behavior of the sub-monolayer PbS QDs dispersed upon Si (001) substrates. For
(a) (b)
(c)
(f)
(e)
(d)
2 nm
2 nm
176
these experiments, optical responses from a monolayer of PbS QDs on varying substrates
are measured, and thus substrates that can potentially influence the majority of the PbS
QDs that are monitored. Note that this experiment is distinctly different from the studies
of PbS QD solids in chapter IV wherein a small fraction of the PbS QDs were adjacent to
glass substrates and thus a small and negligible fraction of the PbS QDs interact directly
with the substrate.

V.4.1 QD monolayer sample preparation by dip coating
Samples for photoluminescence measurements consist of sub-monolayer coverage
of small PbS QDs deposited onto silicon (001) or SiO
2
-on-silicon (001) substrates
prepared by dip coating. Prior to QD deposition, the substrates were cleaned by
degreasing in trichloroethylene, acetone, methanol, and deionized water. The silicon
substrates were dipped in HF and rinsed briefly in deionized water. It is expected that the
silicon samples will have a minimal thickness of native oxide of up to ~ 2 nm as a result
of the water rinse and air exposure after HF etching. Dip coating is performed
following the method of Dimitrov [V.26] to create well-ordered monolayers. Substrates
were immersed in PbS QD - toluene solutions of 0.5 mg/ml and extracted at a rate of 10
m/s. Dip coating is performed in glove box, and substrates with QDs are mounted into
a cryostat in the glove box and transferred to the photoluminescence setup without
exposure to air and measured under vacuum.
QD monolayer films are characterized by atomic force microscopy (AFM) in
tapping mode to determine the coverage of QDs. AFM measurements detect height
177
differences on the scale of one quantum dot diameter, thus easily discriminate between
layer thicknesses of zero, one, or multiple QDs. Characteristic AFM images of the sub-
monolayer films on Si and Si with 20 nm SiO
2
are shown in Figure V.8. These AFM
images show that the coverage on both substrates is essentially the same at about 0.75
ML with less than 5% coverage of QDs thicker than a single monolayer. The laser spot
size is approximately 100 m in diameter and thus sufficiently large to sample an average
coverage of 0.75 ML. Therefore comparisons of PL intensity between the two samples
are meaningful.

Figure V.8. AFM images of sub ML coverage of PbS QDs on Si (a) and Si with 20 nm
of SiO
2
(b) that show approximately the same coverage of QDs. The color scale bar
inset in each image is 10 nm.

V.4.2 Photoluminescence of PbS QDs on Si and Si with thick SiO
2
Figure V.9 shows the room temperature PL from sub-monolayer of QDs
dispersed, using the same procedures, on Si (001) and on a 20 nm thick SiO
2
layer on Si
PbS QDs on Si PbS QDs on SiO
2

1 m
1 m
178
(001). The total luminescence intensity from the PbS QDs on Si is seen to be at least fifty
times lower than when on 20 nm of SiO
2
on silicon.

Figure V.9. Photoluminescence from sub-monolayer coverage of PbS QDs on 20nm SiO
2

on Si and on Si with ~2 nm native oxide showing significant quenching of emission from
the QDs in the latter case. The background PL signal from substrates without PbS QDs is
subtracted from each curve. Error bars represent the standard deviation of three PL
measurements at different locations on the same substrate.

The surface chemistry of both of these samples, and that of the 20 nm thick SiO
2
,
is similar in terms of chemical species directly interacting with the adjacent PbS QDs and
their oleate ligands. Thus, we expect that the structure of the ligands and the resulting
separation will be similar in all three cases. We note that the possibility of lead salt QDs
losing their ligands when deposited onto a silicon substrate as reported by some authors
[V.27] is not likely to have occured for the PbS QDs deposited here since the PbS QDs
deposited on thick SiO
2
surfaces are optically active indicating well-passivated surfaces.
We attribute the difference in PL intensity between the PbS QD on Si and on 20 nm thick
800 850 900 950 1000 1050 1100
0
1
2
3
Photoluminescence (a.u.)
Wavelength (nm)
PbS QDS on
20 nm SiO
2

on Si
PbS QDS
on Si
179
SiO
2
to be a result of the primary competing intrinsic mechanisms for quenching
involving the silicon substrate as an acceptor: energy transfer or charge transfer. Energy
transfer is expected because the PL emission spectra of the PbS QDs overlaps with the Si
absorption spectra, enabling PbS QDs and silicon to act as a donor-acceptor pair for non-
radiative resonant energy transfer. Charge transfer is possible for electrons since the
electron affinity of PbS QDs of the size used in PL measurements here is in the range of
3.5 to 3.7 eV below the vacuum level

which is well above conduction band edge in
silicon which is 4.05 eV below vacuum level. Hence an excited electron in the PbS QDs
will be in resonance with energy states within the silicon conduction band and have finite
probability of transfer to silicon without necessarily requiring phonon participation.
Indeed, our previously reported study [V.13] of transient photocurrents induced in Si
nanowires due to energy and charge transfer from excitons generated in PbS QDs has
established the efficient occurrence of these transfer processes. The former has been
further confirmed by studies of PbS QD to Si NRET with thin (<5 nm) SiO
2
spacers
[V.28].

V.5. Summary of PbS QDs on crystalline Si studies
In summary, we have obtained the first atomic-resolution TEM-based images of
nanocrystal quantum dots, the semiconductor substrate on which these resides, and the
interfacial region between these phases [V.29]. These composite structures are the
subject of efforts focused upon exploring the potential use of colloidal nanostructures for
applications in wide ranging, cost-effective technologies including light emission,
180
radiation detection, biochemical and biological sensing, and even quantum information
processing but have surprisingly not seen too many efforts to holistically and
integratively examine the interfacial atomic level structure and its direct connections to,
and ramifications for, the electronic (electrical and optical) response. To realize such
TEM imaging, we developed and introduce here an innovative approach to TEM
specimen preparation for cross-sectional examination of QD – substrate systems. For the
case of oleate-capped PbS QDs on silicon, our TEM images show immense richness in
local orientations as well as variations in the adsorbed nanocrystal shape. This has
significant consequences for the variations in the electronic response of individual
nanocrystal quantum dots. Likewise, the measured local separation between the QDs and
the substrate to which efficient information transfer is critical exhibits variations with
potentially significant consequences for information transfer rate inhomogeneity, even as
the average separation is substantially less than the length of the ligands that cap the QDs.
Together, these two generic effects thus must be better understood and controlled to
implement reliable design of QD based devices and system architectures. The electron
microscope studies presented are complemented with a brief inclusion here of
photoluminescence measurements. These measurements show that the emission from
PbS QDs can be controlled and that energy and charge can be transferred efficiently to
adjacent acceptor channels possessing high charge mobility for both electrons and holes,
such as Si.

181
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184
Chapter VI: Quantum dot - nanostructured silicon hybrid photovoltaic
devices

VI.1 The NRET-based solar cell
The NRET-based solar cells discussed in Chapter I consist of light absorbing QDs
dispersed around an array of high charge-mobility channels for transport and collection of
photogenerated carriers. Their overall efficiencies is the product of the individual
efficiencies of the sequential steps involved in energy conversion: absorption, inter-QD
NRET, QD-to-channel NRET, and charge transport within the channels. We chose to
explore the implementation of an NRET solar cell for the combination of PbS QD
dispersed in Si channel arrays. While the primary focus of this chapter is the design and
fabrication of the silicon transport-channel arrays, the geometry of these arrays influence
all steps in the energy conversion process. One of the basic objectives in fabricating a
hybrid PbS QD – silicon NRET based solar cell is minimizing the average number of
inter-QD NRET events that are necessary to have energy migrate from the QDs in which
it is absorbed to QDs adjacent to the transport channels. Recall that the value m in
equation I.13

[ ∑

]

is related constraints the inter-channel spacing as m it is the number of QD nearest
neighbors required to span half the distance between channels (see Figure VI.1). By
minimizing the spacing between adjacent transport channels, w, the number of QDs for a
185
given inter-QD spacing needed to span the distance, m = w/2r, is minimized, where r is
the QD center-to-center separation. Thus minimizing the number of inter-QD NRET
events necessary to transfer energy to QDs adjacent to transport channels. Additionally,
the depth (d) of the transport channels oriented parallel with the impinging light
determines the thickness of the QD layers that absorbs light.

Figure VI.1. Cross section schematic of silicon-nanowall solar cell architecture. This
geometry allows the entirety of the structure to be connected electrically to the metallic
top contact while still allowing the QDs to be deposited into the open trenches as a final
step. To emphasize the silicon architecture, only one QD is shown here Note that the
nanowalls have aspect ratio of 10-20. The nanowalls and QD are not to scale.

186
Therefore, the channels must be of sufficient depth to absorb most of the impinging light.
Moreover, in the proposed NRET based solar cells, there are dominantly two different
contributions to photocurrent: (1) photocurrent due to carriers excited by NRET from the
QDs to the transport channels and (2) photocurrent due to carriers excited by direct
absorption of light in the transport channels. We are focused on understanding the
former, but must be able to characterize both contributions in order to isolate the effects
related to NRET. With these issues in mind, the subject of this chapter is our approach
and work towards fabricating nanostructured silicon solar cell architectures that are a
suitable platform for undertaking an initial study of NRET based photovoltaic energy
conversion.

VI.2 Nanostructured silicon – QD solar cell fabrication: advantages of a nanowall-
based structure
The successful functioning of any semiconductor electronic device relies in part
on two characteristics: (1) the control of dopant and atomic composition profiles thereby
controlling the topography of chemical potential in space within the device and (2)
control of defects that may impede charge transport. All devices have interfaces of some
type, and in most cases these interfaces introduce defects. For devices that require
nanostructured features and heterogeneous interfaces (such as those between silicon and
an organic or QD monolayer), interface characteristics can become the central issue
determining device performance. Controlling these two characteristics in nanoscale
devices is difficult because the high surface to volume ratio at the nanoscale inevitably
187
creates a source of localized surface defects that can trap charges and act as
recombination centers. These influence chemical potential in space and thereby couple
the two characteristics.
To design and fabricate effective QD-nanostructured solar cell devices, important
requirements must be met. First, the architecture of the transport-channel array must be
optimized to enable the highest possible transfer of absorbed (by the QDs) energy Thus
besides the estimation of the average number of inter-QD NRET events needed to
transport the energy from where the light in absorbed to the QD adjacent to the transport
channels as discussed before, the areal density of QDs that are adjacent to the transport
channels needs to be maximized This demands choosing between an array of nanowalls
or nanopillars being mindful of the other device requirements such as ability to make
effective contacts. Second, the devices must be designed such that the contribution due to
direct photon absorption in the transport channels can be examined without the QDs.
This in turn allows quantification of the component of photocurrent due to NRET when
the QDs are added. In effect, devices must be fully processed with electrical contacts
before the QDs are deposited. Third, in a related requirement, the QDs must not be
damaged during the solar cell fabrication process. For this reason, it is also beneficial to
deposit the QDs as a final step thus eliminating exposure the of QDs to other chemicals
used in the fabrication process as discussed below.
In order to allow for QDs to be deposited as a final step, the top ohmic contact
must not prevent the ability to disperse QDs around the transport channels. Additionally,
the top contact must be in electrical contact with the entirety of the upper half of the
188
device in order to make a direct path for current from the p-side to the external circuit. In
order to achieve this, transport channels consisting of long thin nanowalls are appropriate
as shown in Figure VI.1. Although nanowire arrays would maximize the interfacial area
between the QDs and the transport channel as originally proposed [VI.1] contacting and
overall fabrication considerations guide the choice of an array of closely spaced
nanowalls with an axial p-n junction as shown in Figure VI.1.
In order to maximize the contribution to photocurrent due to NRET, it is
necessary to arrange the PbS QDs by size as shown in Figure I.4 to direct the transfer of
energy towards the transport channels. Control of PbS QD deposition to create size-
graded structures has not yet been achieved and is left for future work.

VI.3 Nanowall device fabrication
A fabrication process for creating test devices featuring nanowalls as shown in
Figure VI.1 was established utilizing electron beam lithography (EBL) for patterning and
deep reactive ion etching into a Si wafer with an established p-n junction. This approach
has two primary benefits: first, EBL allows for great flexibility in terms of feature size
and layout due to the ease of changing exposure patterns. Second, by choosing an
appropriate starting silicon wafer (i.e. one with an existing p-n junction), the doping
profile can be established before the nanowalls are created. The following provides
details related to the starting Si wafer and the nanowall array fabrication process.
In typical high efficiency planar silicon solar cells, the minority-carrier diffusion
length base is on the scale of 100 m [VI.2], i.e., light absorbed at 100 m from the
189
depletion region of the p-n junction can effectively contributes to photocurrent. Our
objective is to investigate conversion of the energy of photons absorbed by the
sufficiently thick (~2 m) of QDs by NRET to silicon, thus overcoming the only
limitation of Si as solar cell material. Therefore we deliberately designed a solar cell
having a short minority-carrier diffusing length in the silicon substrate in order to
minimize the contribution to photocurrent from direct absorption deep in the silicon
wafer. This can be achieved by utilizing wafers with high dopant concentrations because
minority carrier diffusion length is proportional to dopant concentration [VI.3]. The
substrate is n-type silicon with arsenic doping at 1E19/cm
3
with two microns of p-type
silicon at nominally 2E18/cm3 boron doping. These custom silicon substrate p-n
junctions contain an epi-layer grown by chemical vapor deposition and were procured
from Lawrence Semiconductor Research Laboratories in Tempe Arizona (LSRL).
Dopant concentrations were determined by spreading probe resistance measurements
performed at LSRL.

VI.3.1 Nanowall solar cell fabrication
The fabrication process can be divided into two main parts:
(1) Etching to create nanowalls. This process is accomplished using electron beam
lithography to define the nanowalls, reactive ion etching to transfer the pattern
established by the EBL into the silicon dioxide layer used as an etch mask for deep
reactive ion etching, and deep reactive ion etching using the Bosch Process.
190
(2) Construction of metallic contacts using electron beam lithography to define the top
contacts around arrays of nanowalls, deposition of metals, and lift-off.
Some of the key features of the photovoltaic device are shown in Figure VI.2. In
addition to the contact grids and trenches which form the nanowalls, there are two
additional key features: (1) An isolation trench, and (2) A large contact pad for wire
bonding an external lead. The first is important for defining the solar cell area.
Knowledge of the precise device area is essential in order to determine the impinging
radiative power, which in turn is necessary, along with the current-voltage measurements,
to estimate the power conversion efficiency. To define the area of the solar cell, we etch
a deep trench around the array of nanowalls and the top contact. This trench separates
majority carriers from the contacts and thereby prevents photocurrent from carriers
generated by absorption in silicon outside the isolation trench. The contact pad is
necessary to use a wire bonder to connect a thin gold wire to the external circuit. Gold of
thickness greater than 100 nm is necessary to form a robust bond. The wire is separated
from the nanowalls to ensure that the wire will not shadow the device during optical
characterization.
The device areas (se Figure VI.2) are each 1 mm
2
and divided into (100 m)
2

subregions. Within each subregion, there are 240 trenches, each approximately 200 nm
wide lying on 400 nm pitch. Each trench is 96 m long, leaving a 1 m margin between
the trenches and the 2 m wide contact bar.

191

Figure VI.2. A schematic showing the geometry and key features of the solar cell device.
(a) shows the full 1 mm
2
device. The region in the dotted box in (a) is enlarged and
shown in panel (b). The black squares in (a) represents the area of nanowall arrays and in
(b) the black bars represent trenches. The trenches are actually 200 nm wide and not
drawn to scale in panel (b). In both panels, the yellow represents the contact bars that
wrap around the regions with the nanowall arrays, the blue represents the isolation trench
and the pink is the top surface of the silicon wafer. The purpose of the isolation trench is
to define the total area of the solar cell as described in the text.

The first set of process steps are designed to create an array of nanowalls. A schematic of
the key steps with parameters for part (1) is shown in Figure VI.3.

192

Figure VI.3. Process steps involved in fabrication of nanowalls using deep reactive ion
etching.

We note that the substrates, as received from LSRL, were covered with approximately
300 nm of silicon dioxide, which was removed by HF etching. Also, 120 nm of dry
thermal silicon dioxide is grown before step 1 in Figure VI.3 by dry oxidation at 1100 C
for 110 minutes the processing starts.
193
Electron beam lithography is an ideal tool for defining the geometry of test
structures because the ease of changing exposure patterns and of changing the width and
pitch of the nanowalls. In electron beam lithography, the minimum feature size is
proportional to resist thickness. As explained below, the PMMA EBL resist acts as a dry
etch mask allowing for pattern transfer onto a silicon dioxide layer, which is the DRIE
etch mask. Therefore, PMMA resists with sufficient thickness to withstand etching must
be used during pattern transfer. After EBL exposure and developing, the EBL pattern is
transferred into the 150 nm of dry oxide by using the PMMA as an etch mask for reactive
ion etching in a CHF
3
/Ar gas mixture with a four-to-one ratio at 200W, 35 mTorr, and 5
minutes. This work was performed at the UCLA Center for Nanoscience clean room.
The nanotrenches are formed by etching with the Bosch Process (a review can be
found in reference [VI.4]). Five parameters can be varied for each the etching and
deposition processes: ICP power, RF power, gas flow, gas pressure, and etch time. For
these experiments, we use the same parameters to etch nanowalls and create the
nanopillars as used in TEM studies described in Chapter V: (1) Etch step time of 4
seconds, 30 sccm of SF
6
, 500 W ICP power, 40 W RF power, and 10 mTorr of SF
6
and
(2) Deposition step of 5 seconds, 80 sccm of C
4
F
8
, 500 W ICP power, 10W RF power,
and 18 mTorr of C
4
F
8
. These nanotrenches as well as the nanopillars described in
Chapter V, require etching with small undulations. In order to increase nanowall height,
we use 25 etch-deposition cycles to penetrate 2 microns as opposed to the five cycle
protocol used to create 600 nm tall nanopillars in Chapter V.
194
The contacts require three metal deposition steps: one to create the contact bars
around the nanowalls, one to create a thick gold pad for wire bonding, and one to contact
the back side of the wafer. Due to the heavy doping in both the p- and n-type layers, this
process of forming ohmic contacts is straightforward [VI.5] and is depicted in Figure
VI.4.

Figure VI.4. Process steps to create the top and bottom metallic contacts. Step numbers
continue from those in Figure VI.3.
195
Two conflicting requirements demand that we use two metallization steps when creating
the top contacts. First, for lift-off, the total thickness of the deposited metal should be
considerably less than the resist thickness, otherwise it will not be possible to dissolve
metal remaining under the resist in unwanted areas. The PMMA thickness used is 300
nm, thus we deposit only 50 nm of metal. Second, 150 nm of Au is required to form a
robust wire bond. The top contact bars are created using an electron beam lithography
and lift-off process. We use a two layer EBL resist to fabricate the contact pads. A three
layer top contact is constructed, nominally with 30 nm Pt, 10 nm Cr, and 10 nm Au.
After deposition of these three metal layers, the remaining PMMA is dissolved in acetone
to lift off the deposited metal in regions other than the desired contact. The structure is
annealed to form a platinum silicide contact. The Cr acts as a barrier layer between the Pt
and the Au, and the Au protects the Cr from oxidation during annealing. We perform a
second lift-off process using a photolithography-defined mask to create a thick layer for
wire bonding. Three micron thick AZ5214 resist is used to define the pattern (a single
[100 m]
2
square) and 150 nm of Au is deposited before soaking in acetone overnight to
lift-off unwanted metal.
Photovoltaic devices without nanowalls were fabricated wafer to act as
experimental control. In these cases the EBL pattern only contained the isolation trench.

VI.3.2 I-V curves for nanowall solar cells
Figure VI.5 shows SEM images of the fabricated solar cell and its key features:
(a) a cross section of high aspect ratio, high pitch nanowalls, (b) a cross section of the
196
region of the deep isolation trench, and (c) the top contact grid between regions of
nanowalls.

Figure VI.5. SEM images of trenches created by Bosch etching, the isolation trench and
the contacts in the complete device. Panel (a) shows cross section of typical deep etched
trenches and resulting nanowalls. The pitch is 400 nm and the nanowall aspect ratio is
17. Panel (b) shows a cross section of the deep etched nanotrenches and the much larger
and deeper isolation trench. Note that this image was taken in a sample that did not
have the top contact, which would be present on the surface between the isolation trench
and the nanowalls. Panel (c) shows a top view of a device after deep reactive ion etching
and top-contact fabrication with PtSi – Cr – Au.

2 m
Isolation
trench
2 m
400 nm
(a)
(b)
(c)
Top Contact
197
I-V curves for the device is shown in Figure VI.6. These curves were collected using an
Agilent 4156B semiconductor parameter analyzer. This instrument is sensitive to
currents on the scale of a few pA and no special shielding is necessary for measurements
of these I-V curves. Measurements of the I-V curves here do not require any special
shielding. The light excitation source was a TiS laser tuned to 850 nm with the power of
100 mW/cm
2
. Panel (a) shows the I-V curve for a control device without nanowalls and
panel (b) shows the I-V curve for a device with 200 nm trenches. These have efficiencies
of 3.3% and 0.34%, respectively. The device without trenches has short circuit current
(I
SC
) and open circuit voltage (V
OC
) of 6.9 mA/cm
2
and 610 mV respectively. The
device in Fig. VI.6 (b) with trenches has I
SC
of 2.6 mA/cm
2
and V
OC
of 280 mV.

0.0 0.2 0.4 0.6 0.8
-10
-8
-6
-4
-2
0
2
Current Density (mA/cm
2
)
Volts (V)
(a)
0.0 0.1 0.2 0.3
-3
-2
-1
0
1
Current Density (mA/cm
2
)
Volts (V)
(b)

Figure VI.6. Laser illumination I-V curves for solar cells without (a) and with (b)
trenches. For both, curves were created with laser excitation at 850 nm and 100 mW/cm
2

(the equivalent power to sun light at AM1.5). Note the voltage and current scales; the
device without trenches is substantially more efficient. The device without trenches (a)
was from lot #031010 and device in (b) is part of lot #042210.

198
nanowalls is approximately 2.5 times less than in the control devices. This drastic
reduction in short circuit current is most like likely a result of reduction in minority
carrier diffusion length, which is limited by surface recombination. These results
highlight the need to passivate the surfaces of the nanowalls.

VI.4 Nanowall surfaces and sidewall recovery
All of the devices we developed had foreign chemical species present on the
surface; those we intentionally deposited or those unintentionally introduced such as
native oxides as discussed in Chapter V. Characteristics of the chemical species present
at the surface play an important role in influencing the properties of the surface states
such as their energy within the semiconductor band gap. These characteristics determine
if the surface state will act as an acceptor, donor, or be amphoteric. Therefore the nature
of electrical properties of a real semiconductor surface will depend on both the doping of
the semiconductor and on the nature of the surface states present. In general, the surface
states can act as traps that result a net migration of free majority carriers to the surface to
create surface space charge layers and an electric field at the surface. Surface states
provide recombination pathways that allow for non-radiative recombination and for
excited electrons and holes [VI.6].
Surface states are localized states that generally have energies that are within the
bulk band gap. The density of these states, either having energy deep within the bandgap
or their donor- or acceptor-nature, largely determine how they influence carrier lifetime
in a nanowall solar cell. There are two general approaches to understanding the
199
localized surface states that correspond to intrinsic and extrinsic properties, both of which
are always present in varying degrees, in semiconductor devices. Intrinsic surface states
due to disorder lead to a U-shaped density of states in the bulk semiconductor bandgap
[VI.5]. Extrinsic surface states result from foreign impurities and localized defects
present at the surface.
There will be surface band bending in most cases unless the surface states act
entirely as acceptors (donors) on p-type (n-type) semiconductors, which is usually not the
case. It is clear that (1) the majority carriers will determine the direction of band
bending (for the case where the surface adsorbates or overlayer itself doesn’t introduce a
net charge) and (2) the band bending will attract minority carriers and trap them in the
spatial region where the defect density (surface states) is highest.
Silicon surfaces generally have a high density of surface states because of
homopolar bonding [VI.7]. Typically, the range of surface states varies from a maximum
of about 1E14/cm
2,
which is approximately one defect state per surface atom to a
minimum of ~1E10/cm
2
for the Si – SiO
2
with dry thermal oxide [VI.8]. Atomically
rough silicon surfaces with wet chemical passivation have surface state densities of about
1E12/cm
2
[VI.9]. Chemical treatments of planar Si (111) surfaces with covalently
bonded alkane chains have been prepared with surface density as low as 3E9/cm
2
[VI.10].
Dangling bonds from silicon and oxygen act as donors and acceptors, respectively
[VI.11]. Therefore, in most cases we assume that the surface will have both acceptors
and donors, and that there will always be migration of charge to the surface.
200
Because, as argued above, the electric field within the surface depletion region
acts to attract minority carriers, it is desirable for the purpose of reducing surface
recombination to use highly doped materials and reduce the surface state density as much
as possible, and thereby minimize the fraction of carriers generated within nanowire that
will be pulled to the surface by the field.
Current state of the art silicon solar cells use Al
2
O
3
passivation on the p-type base
layer and SiN
x
to passivate the n-type layer [VI.12]. Al
2
O
3
introduces fixed negative
charges of high density 1E12 – 1E13/cm
2
[VI.12]. These charges repel the minority
electrons and create a surface on p-type silicon with low surface recombination velocity.
It is clear that Al
2
O
3
passivation on n-type silicon would have the opposite effect and
attract minority holes and thus have detrimental effects. SiO
2
and SiN
x
generally
introduce fixed positive charges, and are therefore used to passivate n-type silicon
[VI.12]. These examples point out one of the major problems with an axial p-n junction
nanowire solar cell; the most effective surface passivation materials are not the same for
n-type and p-type materials. However, for the case of the nanowall structure, it is not
currently possible, to passivate n-type and p-type sections of the nanowalls separately.
As a result of the fabrication process described Section VI.3, we expect three
generic types of surface defects: (1) chemical defects due to impurity atoms and
molecules, (2) structural defects created from the energetic ions used to etch the silicon,
and (3) intrinsic surface state defects due to dangling bonds. Thus, we took steps to
remove possible structural damage and reduce the density of dangling bonds on nanowall
surfaces using chemical passivation routes.
201
VI.4.1 Sidewall smoothing by thermal oxidation
For surfaces with small scale undulations, oxidation rates are faster in regions that
are locally convex than those which are locally concave [VI.13]. Therefore, cycles of
oxidation and oxide removal can reduce the amplitude of undulations on sidewalls. To
remove these undulations, we used cycles of dry thermal oxidation at 900º C for 25
minutes in flowing oxygen followed by etching in 1:1 HF-methanol mixtures for one
minute. Note that submersing nanowall samples in HF-water mixtures does not etch all
thermal oxides from the trenches. This is likely due to the high surface tension of HF in
water, which prevents wetting inside the nanotrenchs. After oxidation and etching, the
samples were cleaved parallel to the trenches and mounted to allow for cross section
imaging and imaged in contact mode AFM. Results are shown in Figure VI.7.

202

Figure VI.7. Reduction in sidewall scallop amplitude by thermal oxidation and etching as
determined by AFM. Panel (a) is sidewall roughness of as-etched sidewalls. Panels (b)
and (c) show the sidewall after one and two oxidation-etch cycles, respectively. (d)
Shows profiles of the scalloping in (a-black), (b-red) and (c-blue). The dashed line
represents the wafer surface and the curves are offset vertically for clarity and the scale is
relative. Note that the color scale bar on the left applies to all three images, and the
image size is 2.5 m
2
for each.

VI.4.2 Chemical approaches to surface passivation
For consistency within our overall scope of research, we control surface
passivation approaches such that these do not introduce thick layers on the Si nanowall
0 500 1000 1500 2000 2500
0
10
20
30
40
50
60
70
80
Sidewall Profile (nm)
Etch Depth (nm)
(b) 1X Dry Oxide
(c) 2X Dry Oxide
(a) As-DRIE
30 nm
0 nm
(d) AFM profiles
203
surface. Thick layers would ultimately limit energy transfer from the QDs to the
nanowalls. This limitation precludes use of thick dry-oxide passivation methods, which
are known to have low surface state density with silicon [VI.14].
A common approach to surface passivation of silicon is to chemically graft stable
alkane chains to the dangling orbitals on the silicon surface. This approach is attractive
where the goal is improving power conversion efficiency in nanowall solar cells because
the methyl groups introduce very little steric hindrance between QDs and silicon.
Chemical passivation is achieved using the method developed by Lewis et. al. [VI.10][
VI.15]. A three step process aimed at forming covalent bonds between silicon atoms at
the surface and carbon atoms in the methyl groups is as follows:

1. The sample is cleaned in oxygen plasma at 200 mTorr and 100 W for two
minutes. Then the sample (either a completed solar cell with contacts or a blank
substrate, is etched in HF-methanol 1:7 for 3 minutes. Note that in the case of
completed solar cells, the gold metal contacts will not be etched. Then the
samples are rinsed briefly in water, dried under nitrogen flow, and immediately
transferred to the glove box.
2. Methylization is achieved by first grafting chlorine atoms to the silicon surface.
The freshly HF etched samples are heated in mixtures of chlorobenzene,
phosphorus pentachloride (PCl5), and benzoly peroxide for 45 minutes at 95C.
3. The sample is then rinsed in chlorobenzene and transferred to a solution of
tetrahydofuran and CH
3
MgCl and heated at 120C for 12 hours. During this
204
period, the CH
3
groups displace Cl atoms at the surface. Finally the samples are
then rinsed with tetrahdrofuran and acetone.

The samples are not exposed to air during steps two and three. Note that a reaction flask
capable of withstanding high pressures is necessary for step three because the reaction is
carried out at temperatures above the boiling point of tetrahydrofuran.

VI.4.3 Characterization
The methylation process results in a decrease in surface energy as indicated by
contact angle measurements. The contact angle with a water droplet is 73 degrees after
five days in air, which is substantially higher than the 40 degree angle observed in the
control samples (i.e., a samples prepared using Step 1 only). These relations are shown
on Figure VI.8. However, this value is less than the expected value of 85-95 degrees for
methylation of Si [VI.15], suggesting the process could be further improved.
The objective of the surface treatments is to reduce surface state density and the surface
recombination velocity. These reductions help increase minority carrier lifetime and
minority carrier diffusion length. Results of the passivation approaches can be seen in
the I-V curves of solar cells before and after surface treatments as shown in Figure V1.8
(b). These solar cells were excited with AM1.5 illumination with a Newport class A
solar simulator and I-V curves are collected with the Agilent 4156B. We observe an
increase in I
sc
from1.9 mA/cm
2
to 3.3 mA/cm
2
after CH
3
passivation, suggesting that the
minority carrier diffusion length of electrons has increased as a result of this chemical
treatment.
205

Figure VI.8. (a) Contact angle measurements of samples with fully functionalized
methylization and control substrates (i.e., before and after passivation with CH
3
groups).
(b) I-V Curves for solar cells with as-DRIE sidewalls, after CH
3
passivation, and after
sidewall smoothing and CH
3
passivation. The I-V curves in (b) are from cells from lot
#092611.

However, the shape of the I-V curve changes as a result of the CH
3
passivation
and the open circuit voltage decreases indicating a probable change in the difference in
quasi-Fermi levels across the p-n junction as a result of the CH
3
passivation.
Additionally, the I-V curves for the samples with and without sidewall smoothing are
similar suggesting that sidewall smoothing is not a good approach to increasing minority
carrier lifetime. These results suggest that CH
3
passivation can reduce surface
recombination rates and enhance short circuit current. In addition, they suggest that
surface damage resulting from physical etching is not the primary cause of low
efficiency. With illumination of 1 sun at AM1.5 in a Newport solar simulator, power
conversion efficiencies of the as-DRIE etched, CH
3
passivated and sidewall smoothed
and CH
3
passivated cells are 0.18%, 0.27%, and 0.23% respectively.

206
VI.5 Conclusions
Design and fabrication of PbS QD - nanostructured silicon solar cells was
completed with the objective of creating a platform to study energy transfer from QDs to
silicon. Our experiments hinged on two important necessities: first, we require solar cells
that can be characterized with and without QDs. This allows us to quantify the
contribution to photocurrent due to direct absorption in the silicon and due to
enhancement in photocurrent and photovoltage resulting from the presence of the QDs
and energy transfer from the QDs to the silicon. Second, the QDs cannot be allowed to
be damaged by processing steps subsequent to their deposition. Because the QDs are
sensitive to air, it’s ideal to deposit the QDs as a final step, thus avoiding oxidation
problems. The approach we took to satisfy these two requirements is to use long thin
silicon nanowalls. These stand between deeply etched nanotrenches and have metallic
contacts connected to the margins of the regions with the nanotrenches and nanowalls as
shown in Figure VI.1. As these nanotrenches are openly exposed, QDs can be deposited
after contacts have been formed and the nanowall surface treatments have been applied.
This approach allowed us to successful create photovoltaic devices, albeit with
low power conversion efficiency limited by surface recombination. Surface passivation
with –CH
3
groups increases the short circuit current by 60% over the as-etched devices,
but the overall power conversion efficiency of the passivated device is still low.

207
VI.6 Chapter VI References
VI.1. S. Lu and A. Madhukar, Nonradiative Resonant Excitation Transfer from
Nanocrystal Quantum Dots to Adjacent Quantum Channels. Nano Lett., 7 (2007)
3443.
VI.2. A. Goetzberger, J. Knoblach and B. Voss, Crystalline Silicon Solar Cells1998:
Wiley.

VI.3. M.E. Law, E. Solley, M. Liang and D.E. Burk, Self-Consistent Model of Minority-
Carrier Lifetime, Diffusion Length, and Mobility. IEEE Electron Device Letters,
12 (1991) 401-403.

VI.4. H.V. Jansen and et al., Black silicon method X: a review on high speed and
selective plasma etching of silicon with profile control: an in-depth comparison
between Bosch and cryostat DRIE processes as a roadmap to next generation
equipment. Journal of Micromechanics and Microengineering, 19 (2009) 033001.

VI.5. W. Monch, Semiconductor Surfaces and Interfaces, 2nd Ed. 1995.

VI.6. P. Bhattacharya, Semiconductor Optoelectronic Devices. 2nd ed1997, Singapore:
Pearson Education.

VI.7. S. Kurtin, T.C. McGill and C.A. Mead, FUNDAMENTAL TRANSITION IN THE
ELECTRONIC NATURE OF SOLIDS. Physical Review Letters, 22 (1969) 1433.

VI.8. G.D. Wilk, R.M. Wallace and J.M. Anthony, High-k gate dielectrics: Current
status and materials properties considerations. Journal of Applied Physics, 89
(2001) 5243.

VI.9. Y. Yamashita, A. Asano, Y. Nishioka and H. Kobayashi, Dependence of interface
states in the Si band gap on oxide atomic density and interfacial roughness. Phys.
Rev. B, 59 (1999) 15872-15881.

VI.10. W.J. Royea, A. Juang and N.S. Lewis, Preparation of air-stable, low
recombination velocity Si(111) surfaces through alkyl termination. Vol. 77. 2000:
AIP. 1988-1990.

VI.11. K. Ziegler, Distinction between donor and acceptor character of surface states in
the Si;SiO
2
interface. Appl. Phys. Lett, 32 (1978) 249-251.

VI.12. G. Agostinelli, A. Delabie, P. Vitanov, Z. Alexieva, H.F.W. Dekkers, S. De Wolf
and G. Beaucarne, Very low surface recombination velocities on p-type silicon
wafers passivated with a dielectric with fixed negative charge. Sol. Energy Mater.
Sol. Cells, 90 (2006) 3438-3443.
208

VI.13. H.I. Liu, D.K. Biegelsen, F.A. Ponce, N.M. Johnson and R.F.W. Pease, Self-
Limiting oxidation for fabricating sub-5 nm silicon nanowires. Applied Physics
Letters, 64 (1994) 1383.

VI.14. G.A. Armin, Surface passivation of crystalline silicon solar cells: a review.
Progress in Photovoltaics: Research and Applications, 8 (2000) 473-487.

VI.15. A. Bansal, X. Li, S.I. Yi, W.H. Weinberg and N.S. Lewis, Spectroscopic Studies
of the Modification of Crystalline Si(111) Surfaces with Covalently-Attached
Alkyl Chains Using a Chlorination/Alkylation Method. The Journal of Physical
Chemistry B, 105 (2001) 10266-10277.

209
Chapter VII: Conclusions

VII.1 Conclusions
The studies that comprise this dissertation are aimed at understanding a new type
of hybrid solar cell that is based on non-radiative resonant energy transfer (NRET) from
absorbers such as nanocrystal quantum dots to high mobility charge carrier transport
channels. The NRET-based solar cell offers the potential to bypass the limitations of the
so-called hybrid excitonic solar cells arising from the large exciton binding energy and
poor charge (electron and hole) transport following exciton break at the heterojunction of
the light absorbers and the substrate to which these are attached.
The preceding four chapters have presented research in four critical areas that
together contribute to understanding and assessing the potential of the NRET-based
photovoltaics solar energy conversion to electricity: work and related studies directed at
creating materials platforms – chemically functionalized PbS QDs and silicon
nanostructures – and investigating inter-QD energy transfer and the QD – substrate
interface and energy and charge transfer from QDs to silicon. There investigations have
led to three key accomplishments and contributions to the general field of colloidal
quantum dots contained in this dissertation. These accomplishments are of potential
value for all studies of QD-based optoelectronic devices.
First is our new approach to ligand exchange using conjugated cation-ligand
complexes as exchange units [VII.1]. By developing an understanding of PbS QD
surface chemistry and recognizing that (1) lead-terminated surfaces on PbS QDs are
necessary for high quantum efficiency and (2) oleate groups on as-grown PbS QDs leave
210
the QD surface bound to a Pb cation we developed an approach to ligand exchange that
ensured that the PbS QDs remained Pb terminated after ligand exchange. This was
achieved by using pre-conjugated lead-ligand complexes.
This approach enabled creating QDs with desired surface chemical ligands
replacing the ones from the parent as-grown batch of QDs each with nominally the same
quantum efficiency and size distribution. This accomplishment allowed creating a unique
set of three PbS QD solids that differ primarily in the nearest neighbor inter-QD average
separation as determined by direct measurements from TEM images and the absence of
any significant reduction in the as-synthesized high PL efficiency. This unique set of QD
solids in turn allowed for the second accomplishment: a systematic study of the
temperature and inter-QD separation dependence of the QD-size dependent exciton decay
dynamics in PbS QD solids that provided a deeper understanding of the competition
between energy and charge transfer in the same QD solid. We found that the energy
transfer rate from the smaller to a larger QD dominates charge transfer and increases with
decreasing temperature. The charge transfer rate from the largest QDs in the solid
decreases with decreasing temperature and fits the characteristics of a thermally activated
process in which the activation energy for charge transfer increases with decreasing inter-
QD separation. Furthermore, we showed that to understand both processes it is necessary
to account for the ligand-length dependence of the effective medium dielectric constant
of the QD solid owing to the change in the volume fraction of PbS QDs. We showed that
the increase in effective medium dielectric constant with decrease in ligand length acts to
(1) partially hinder inter-QD NRET for QDs with short ligands and (2) increases the
211
energy barrier for charge transfer by screening the coulomb attraction between an
electron and hole on adjacent QDs [VII.2].
Next we performed a study of the QD – semiconductor substrate interface. In this
work, we developed a new approach to imaging QDs absorbed on solid substrates that for
the first time allowed direct imaging of the QD-substrate interface in a cross sectional
view [VII.3]. Using microelectronic fabrication techniques of electron beam lithography
and reactive ion etching rather than traditional techniques such as ion milling commonly
used to create TEM specimens, we fabricated electron transparent nanopillars with
known crystallographic orientation and atomically flat top surfaces which, when covered
with absorbed QDs, provide a suitable platform for imaging the QD-semiconductor
interface. We found that the separation between the adsorbed PbS QDs and the
crystalline silicon substrate is significantly less than the length of the organic ligands that
cap the QDs.
Although these accomplishments each stand as significant contributions to the
general field of colloidal quantum dots, the NRET based solar cell theme ultimately
motivated all aspects of this work. Thus substantial progress was made in developing
protocols for etching high aspect ratio Si nanowalls and fabricating silicon solar cell
structures with nanoscale charge transport channels.
As described in Chapter I, the overall efficiency of the NRET solar cell depends
on the product of the individual efficiencies of the sequential processes involved in
energy conversion [VII.4] as listed and discussed below:
212
1. The probability that a solar photon impinging on solar cell will be absorbed by a QD,
f
ab
.
2. The probability that an exciton generated in any QD i, (i=1,m) away from the QD
adjacent to the transport channel (labeled QD
0
) reaches QD
0
by sequential QD-to-
QD NRET events,

.
3. The probability of NRET from an adjacent QD to the inorganic charge transport
channel,

.
4. The probability of transport of excited electron and hole create by NRET in the
transport channels to the external contacts, 
trans.

Thus the overall power conversion efficiency is thus,

(VII.1)

where

is the maximum efficiency for a single junction solar cell.
For the case of the C8-capped QDs 3.6 nm QD-QD center to center separation,
the inter-QD NRET rate is (1/25) ns
-1
and the sum of the competing processes including
inter-QD charge transfer is (1/360) ns
-1
thus giving

= 93%. For inter-QD NRET
processes directed towards the nanowall in a size graded structure the probability that
energy from an absorbed photon reaches the QDs adjacent to the transport channels is

[ ∑

] (VI.2)
213
For structures with spacing between nanowalls, w, of 200 nm and inter-QD center-to-
center separation, r, of 3.6 nm as is the case for C8-capped QDs, and m = 28. For this
case, the inter-QD,

is estimated to be 47%. If the separation between
adjacent nanowalls is reduced to 100 nm,

increases to 70%.
We see in PL studies in Chapter V that energy and charge transfer from the QDs
to silicon is efficient as indicated by the 50 fold decrease in total PL intensity for QDs on
Si as compared the total PL intensity of the QDs on silicon with thick (20-140 nm) SiO
2
.
Under the assumption that the decrease in PL intensity observed in QDs on Si with
respect to the QDs on the thick SiO
2
is due to energy and charge transfer from QDs to
silicon, the sum of the energy and charge transfer rate is much faster than the radiative
decay rate. Further work as described below in section VII.2.3 is necessary to determine
the rate of NRET from the QDs to silicon and

, but the efficient quenching of PL
is a promising sign that NRET from PbS QDs to Si is an efficient process.
Our work suggests that the QD to QD energy transfer and QD to transport
channels energy transfer steps can be made to be efficient. Preliminary results on our
nanowall solar cell devices, point to the need for considerable work directed toward
surface passivation to create solar cell architectures with efficient charge transport, 
trans,

in order to create a reasonably efficient photovoltaic device.

VII.2 Future Work
The four most important areas for continued research are
214
(1) to develop the ability to deposit QDs layer-by-layer and ordered by size within the
trenches between the nanowalls,
(2) to investigation the temperature dependence of the rise times observed in the large
QDs in the QD solids
(3) further investigations the competition between energy and charge transfer from the
PbS QDs to silicon, and
(4) to develop characterization techniques to study the minority carrier diffusion lengths
in the nanowall photovoltaic structures.
These research topics are discussed below.

VII.2.1 Future Work related to the synthesis and surface ligand manipulation of
PbS QDs and layer-by-layer deposition of PbS QDs
Continued work in the area of PbS QDs is related ligand exchange and shell
growth. In the heart of this dissertation in chapters III and IV, we only use three ligand
lengths and none shorter than eight carbons. This is primarily a results of the necessity
have the QDs in solution after ligand exchange and the tendency for QDs with short
ligands to agglomerate.
A popular method of ligand exchange to reduce inter-QD separation is to perform
the ligand exchange after the QDs are deposited onto a solid substrate. As described in
Chapter III, for the case of PbS QDs, this method typically employs ethanedithiol as new
ligands and has been shown to increase inter-QD charge transport [VII.5]. A major
drawback of this approach is that the effect of ligand exchange on QE of the post-ligand
215
exchange QDs cannot be easily determined because the QDs are necessarily
agglomerated on a solid substrate. A possible improvement on the solid-phase approach
with dithiols is to use solid phase ligand exchange with lead-ligand complexes that are
short in length such as lead-acetate (Pb(CH
3
COO)
2
). Such short lead-ligand complexes
would not likely be sufficient keep the QDs disperse in non-polar solvents and thus
demand that the exchange be done on QDs already absorbed onto solid substrate. The
advantage of using lead-acetate is that we have already shown that lead-cation based
ligand exchange in solution is successful in preserving the QE of the QDs.
Beyond the studies of cation ligand exchange, there are possible investigations
related to QD surface chemistry that are enabled by the new approach to imaging QDs on
silicon nanopillars. Although the purpose of the work in Chapter V was to investigate the
interface between the QDs and a solid crystalline substrate, the imaging arrangement
used in those experiments also provides the capability to view the QDs without
obstruction from any amorphous carbon or other support film. Although in the particular
TEM instrument and imaging conditions used for these studies we are unable to directly
observe the carboxylate ligands on the facets not facing away from the silicon due to their
low-Z and the poor chemical contrast in phase contrast imaging at 300 kV used here, we
think that the our approach to QD imaging would be the ideal way to directly investigate
QD surface chemistry on facets facing away from the silicon. Most common QDs
ligands are composed of carbon-containing organic molecules. Therefore the presence of
carbon support film in the electron beam path would convolute direct imaging of the
ligands or investigations by chemical sensitive techniques the chemistry and bonding of
216
the ligands to the QD in chemical sensitive techniques. Figure VII.1 shows very high
resolution images of the edges of two QDs. Ligands are not distinguished in these
imaging conditions, but it may be possible to observe them using low voltage scanning
TEM [VII.6].

Figure VII.1. HRTEM of QD edges without the obstruction of amorphous carbon film or
other support. The oleate ligands (~2 nm long) are not distinguished in these imaging
conditions, but the edges of the QDs are clearly distinguished against the vacuum.

VII.2.2 Further Studies Related to Inter-QD energy transfer and the temperature
dependence of large QD rise times
The systematic TRPL studies reported in Chapter IV have left a few issues
unresolved. One observation that could lead to further investigation is related to the rise
times in the long wavelength (large QD, NRET acceptor) TRPL. It is known that the
rise in PL intensity at short times in the red edge of the PL spectrum of QD solids is an
indication of excitons being fed into the relatively large QDs by NRET from smaller
1 nm
1 nm
217
adjacent QDs [VII.7], and we also observe a rise in the PL intensity at short times for the
large, 1080 nm, QDs. However the interesting observation is that as the temperature is
reduced from room temperature to 80K, the short wavelength decay rate that is
dominated by NRET increases and the long wavelength rise rate decreases. This effect
is shown in Figure VII.2. If the rise in the long wavelength PL intensity was only due to
NRET from smaller QDs, we would expect that temperature dependence in long
wavelength rise time would match the trends in short wavelength decay if NRET was
primarily responsible for both. The fact that at low temperature we observe a rise in long
wavelength PL that has a duration that is much greater than many decay times of the
small QD suggests that the rise in long wavelength PL decay is not only a result of
excitons being fed by NRET from smaller nearest neighbors.

Figure VII.2. TRPL curves illustrating the opposite trends with change in temperature
for the short wavelength decay rate and long wavelength rise rate for the case of C8-
capped QD solid. In panel (a) at 297K the 880nm decay and 1080nm rise occur on
similar time scales, but in panel (b) the same QD solid at 80K shows 880 nm decay that is
occurs much faster than the 1080nm rise.

218
VII.2.3 Further studies of PbS QD to Si NRET and charge transfer
In chapter V we showed that PL intensity of PbS QDs on Si is at least 50 times
less than the PL intensity of PbS QDs on Si with 20 nm of SiO
2
. As argued in Chapter V,
both energy and charge transfer are contributing to the quenching of the PL of the PbS
QDs. The next step for research in this area is to design a set of experiments that can
distinguish between the energy and charge transfer from PbS QDs to silicon. The set of
experiments would follow the work discussed in Chapter IV for QD-solids on glass
substrates on inter-QD energy and charge transfer by investigating the size, temperature,
and separation dependence of PL of intensity of PbS QDs on silicon substrates. The QD
– silicon separation can be controlled by growing thin layers of SiO
2
on the silicon with
thicknesses between 1 and 10 nm. To study charge transfer from PbS QDs to silicon we
can use QDs that are sufficiently large that the exciton energy is less than the Si bandgap
and therefore unable to act as an NRET donor to silicon. Figure VII.3 shows
preliminary results for the QD size dependence of PL intensity for PbS QDs on Si and
SiO
2.
The ensemble of QDs labels as ‘Size 2” are approximately 4 nm in average
diameter and are sufficiently large that they cannot act as NRET donors for Si, whereas
the “Size 1” with average size of 2.5 nm can act as NRET donors For these QDs we
observe a strong quenching of emission when on Si. The total PL intensity is 20 times
less for the QDs on silicon than for the QDs on thick SiO
2
. Figure III.1 shows that the
1S
e
level for PbS QDs is at higher energy than the silicon conduction band edge for PbS
QDs with absorption peak up to ~1200 nm which includes the “Size 2” regime here.
Therefore NRET from Size 2 QDs to the silicon is not possible, but charge transfer of an
219
excited electron in the Size 2 QD to silicon is possible due to the matching excited state
within the Si conduction band. Thus this size 2 is an appropriate platform to study charge
transfer from PbS QDs to Si.

Figure VII.3. PL behavior for two sizes of PbS QDs on silicon and silicon with thick,
140 nm SiO
2
. PL emission from Size 1 (average diameter 2.5 nm) overlaps with the
silicon absorption spectra shown in pink thus making the Size 1 – Si pair a potential
donor-acceptor pair for NRET. The emission from the larger Size 2 (average diameter of
4 nm) does not overlap with the Si absorption spectra meaning NRET from Size 2 to
silicon does not occur. However, we still observe significant quenching in the Size 2
QDs on Si. This suggests that the quenching of PL from Size 2 QDs on Si can be
attributed to be primarily a consequence of charge transfer.

Quenching of PL for Size 2 QDs on Si suggest that charge transfer is significant and
further experiments investigating the temperature dependence of PL decay dynamics for
both average sizes of QDs would further elucidate this behavior.

800 900 1000 1100 1200 1300 1400 1500
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0

Absorption Coef. (cm
-1
)
Photoluminescence (a.u.)
Wavelength (nm)
0
100
200
300
400
500
600
700
800
Size 1
Size 2
Si
Absorption On
SiO
2

On
SiO
2

On Si
On Si
220
VII.2.4 Future work on silicon nanowall photovoltaic structures and minority
carrier lifetime investigations
Given the complexity of understanding charge transport in semiconductor
nanowires with axial p-n junctions it is essential to have experimental tests to
characterize the effects of surface passivation on minority carrier transport.
In general, there are two approaches to characterizing minority carrier transport in
semiconductor nanostructures: spatial measurements to estimate diffusion length or
temporal measurements to estimate carrier lifetimes [VII.8]. In the former, usually a
probe that is significantly small compared to the nanowire length is used to locally excite
minority carriers away from the junction. Then the current of excited minority carriers is
measured as a function of excitation distance from the junction. Diffusion lengths are
then extracted from the distance dependent current, either induced by an electron beam
induced currents [VII.9][VII.10] or a near-field optical microscope tip [VII.11]. For
temporal type measurements, an energy source, usually either optical or electrical, is used
to create a steady, out of equilibrium state. The energy source is rapidly changed or
turned off and one measures the time it takes for the system to relax to equilibrium.
Carrier lifetimes have been investigated in nanowire p-n junction studies by reverse
recovery transient measurements [VII.12], and time resolved photoluminescence at low
temperature [VII.13]. One of these two approaches is necessary to characterize further
work on chemical passivation of the nanowall devices.

221
VII.3 Chapter VII References
VII.1. Z. Lingley, S. Lu and A. Madhukar, A High Quantum Efficiency Preserving
Approach to Ligand Exchange on Lead Sulfide Quantum Dots and Interdot
Resonant Energy Transfer. Nano Letters, 11 (2011) 2887-2891.

VII.2. Z. Lingley, S. Lu and A. Madhukar, The Dynamics of Energy and Charge
Transfer in Lead Sulfide Quantum Dot Solids. Journal of Applied Physics, 115
(2014) 084302.

VII.3. Z. Lingley, K. Mahalingham, S. Lu, G.J. Brown and A. Madhukar, Nanocrystal-
semiconductor interface: Atomic-resolution cross-section transmission electron
microscope study of lead sulfide nanocrystal quantum dots on crystalline silicon.
Nano Research, 7 (2013) 219-227.

VII.4. S. Lu and A. Madhukar, Nonradiative Resonant Excitation Transfer from
Nanocrystal Quantum Dots to Adjacent Quantum Channels. Nano Lett., 7 (2007)
3443.

VII.5. Y. Liu, M. Gibbs, J. Puthussery, S. Gaik, R. Ihly, H.W. Hillhouse and M. Law,
Dependence of Carrier Mobility on Nanocrystal Size and Ligand Length in PbSe
Nanocrystal Solids. Nano Letters, 10 (2010) 1960-1969.

VII.6. O.L. Krivanek, M.F. Chisholm, V. Nicolosi, T.J. Pennycook, G.J. Corbin, N.
Dellby, M.F. Murfitt, C.S. Own, Z.S. Szilagyi, M.P. Oxley, S.T. Pantelides and
S.J. Pennycook, Atom-by-atom structural and chemical analysis by annular dark-
field electron microscopy. Nature, 464 (2010) 571-574.

VII.7. C.R. Kagan, C.B. Murray and M.G. Bawendi, Long-range resonance transfer of
electronic excitations in close-packed CdSe quantum-dot solids. Physical Review
B, 54 (1996) 8633.

VII.8 D.K. Schroder, Semiconductor Material and Device Characterization2006,
Hoboken, New Jersey: John Wiley & Sons Inc.

VII.9. J.E. Allen, E.R. Hemesath, D.E. Perea, J.L. Lensch-Falk, LiZ.Y, F. Yin, M.H.
Gass, P. Wang, A.L. Bleloch, R.E. Palmer and L.J. Lauhon, High-resolution
detection of Au catalyst atoms in Si nanowires. Nat Nano, 3 (2008) 168-173.

VII.10. C. Gutsche, R. Niepelt, M. Gnauck, A. Lysov, W. Prost, C. Ronning and F.-J.
Tegude, Direct Determination of Minority Carrier Diffusion Lengths at Axial
GaAs Nanowire p–n Junctions. Nano Letters, 12 (2012) 1453-1458.

222
VII.11. A. Soudi, P. Dhakal and Y. Gu, Diameter dependence of the minority carrier
diffusion length in individual ZnO nanowires. Appl. Phys. Lett, 96 (2010)
253115-3.

VII.12. Y. Jung, A. Vacic, D.E. Perea, S.T. Picraux and M.A. Reed, Minority Carrier
Lifetimes and Surface Effects in VLS-Grown Axial p–n Junction Silicon
Nanowires. Advanced Materials, 23 (2011) 4306-4311.

VII.13. O. Demichel, V. Calvo, A. Besson, P. No , B. Salem, N. Pauc, F. Oehler, P.
Gentile and N. Magnea, Surface Recombination Velocity Measurements of
Efficiently Passivated Gold-Catalyzed Silicon Nanowires by a New Optical
Method. Nano Letters, 10 (2010) 2323-2329

Abstract (if available)

Abstract This dissertation comprises a study aimed at understanding the competing dynamics of energy and charge transfer in quantum dot (QD) solids and from QDs to crystalline semiconductor substrates to assess a new type of hybrid solar cell that is based on non‐radiative resonant energy transfer (NRET) from light absorbers such as nanocrystal QDs to high mobility charge carrier transport channels such as silicon nanopillars. The NRET‐based solar cell offers the potential to bypass the limitations of the so‐called hybrid excitonic solar cells arising from the large exciton binding energy and poor charge (electron and hole) transport following exciton break at the heterojunction of the light absorbers (such as organic dyes and QDs) and the substrate to which these are attached (such as polymers and inorganic nanowires). Use of NRET places both the electron and hole generated following exciton break‐up in the same medium for transport unlike the excitonic solar cells studied so far which result in only one type of charge transferring to another medium. ❧ As a platform to investigate a NRET solar cell we employed lead sulfide nanocrystal QDs as light absorbers and silicon as the acceptor transport channel for the NRET generated electrons and holes. Given NRET as the basic physical process at the core of the new type of solar cell the dissertation focused on examining: (1) synthesis of and surface ligand exchange for high quantum efficiency lead sulfide quantum dots, (2) studies of inter‐QD NRET and competing inter‐QD charge transfer as a function of inter‐QD average separation and temperature, (3) structural and optical characteristics of lead sulfide quantum dots adsorbed on crystalline silicon surfaces, and (4) fabrication and examination of prototype colloidal PbS QD - silicon nanopillar array solar cell. ❧ The work in these four areas has each provided insights into and new results for the field of quantum dots, QD‐based solids, and QD based opto‐electronic devices that are of generic value. The need for maintaining the high quantum efficiency (QE) of the as‐synthesized PbS QDs while exchanging the surface ligands with new ones better suited for the device lead us to introduce a new approach to ligand exchange that employs pre‐conjugated lead cation – ligand complexes as units that replace the lead cations bound to their as‐grown ligand, thus maintaining the Pb‐rich stoichiometry that suppresses defect formation while gaining the ability to control the length of the ligands. ❧ The ability to control the length of the ligands allowed control over the QD‐QD separation in densely packed films referred to as QD‐solids. These QD solids of controlled and experimentally determined average inter‐QD separation enabled the first systematic study of exciton decay dynamics involving competition between separation‐dependent QD to QD NRET and QD to QD charge transfer as a function of temperature and quantum dot size. Our principal findings are: (1) the NRET rate from smaller to larger QDs increases with decreasing QD‐QD average separation as the inverse sixth power, as expected

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Asset Metadata

Creator Lingley, Zachary R. (author)

Core Title Non-radiative energy transfer for photovoltaic solar energy conversion: lead sulfide quantum dots on silicon nanopillars

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Publication Date 09/02/2014

Defense Date 04/30/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag energy transfer,lead sulfide,ligand exchange,OAI-PMH Harvest,photovoltaics,quantum dots,transmission electron microscopy

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Madhukar, Anupam (committee chair), Cronin, Stephen B. (committee member), Malmstadt, Noah (committee member)

Creator Email zachlingley@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-469151

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