OPTICAL PROPERTIES OF MAGIC-SIZED NANOCRYSTALS:

ABSENCE OF INHOMOGENEOUS LINE BROADENING

AND DIRECT EVIDENCE OF ENERGY TRANSFER

BETWEEN TWO MAGIC SIZES

by

Michelle Nagy

A thesis submitted in conformity with the requirements for the degree of Master of

Science, Graduate Department of Chemistry, University of Toronto

© Copyright Michelle Nagy (2009)

ii

Optical Properties of Magic-Sized Nanocrystals: Absence of Inhomogeneous Line Broadening and Direct Evidence of Energy Transfer Between Two Magic Sizes

Master of Science Thesis by Michelle Nagy (2009)

Department of Chemistry, University of Toronto

Abstract

Magic-sized nanocrystals (MSNs) are nanocrystals with a single size distribution.

They have narrow spectral features that do not exhibit inhomogeneous line broadening.

This enabled us to analyze homogeneous line broadening of CdSe and CdTe MSNs. In

solution, we observed two aggregated configurations of CdSe and CdTe MSNs. Sub-

peaks within MSN excitonic peaks were caused by these two aggregated configurations

and surface states. A two-dimensional photoluminescence spectrum of a mixture of

CdTe 427 nm and 500 nm MSNs gave direct evidence of Förster resonant energy transfer

(RET) between the two sizes of MSNs. Normalized experimental overlap between donor

emission and acceptor absorption spectra was on the order predicted by theory,

confirming that there is sufficient overlap for RET to take place in this system.

Additionally, within both aggregated configurations, the two sizes of MSNs were within

sufficient distance from one another for RET to occur.

iii

Acknowledgments

I’m finished! Finishing a Masters is not a one girl job. I would like to thank the

following people for all of their support.

After every meeting with Greg, I was pumped to start back at the drawing board.

When I got frustrated with my four peaks, he was always able to help me look at the

problem from another angle. I learned so much in my Masters through Greg’s guidance,

encouragement to learn independently, and making himself available to explain concepts

that were way over my head.

I would like to thank Kui and Ruibing for supplying me with an abundance of

samples and their continuous interest in the project.

I would like to thank everyone in the Scholes’ Group for teaching me new

concepts and instrumentation, helping me brainstorm the origin of my four peaks,

comforting me when my four peaks confused me, and celebrating with me when I found

solid evidence for their origin. Most of all, I would like to thank the Group members for

being great friends! Cathy, I owe you a blender! I will always be your goat. You were a

great teacher because you were so patient, explained concepts many different ways, had

the most useful papers on all subjects, and always made time for me. I will miss you and

our girl talks. Tihana, your eye for beauty made my PowerPoint slides and Illustrator

images much nicer; also it started great conversations in the lab. Tihana and Megan, I

will miss the wide variety of gossip that can be covered in one day. Working with

Marcus, I found out that I was very gullible. Thanks for all of your help on fluorescence.

Shun, I will miss our discussions about fine Scotch and rum. John, we had some great

times together! Your words for The Hat Game always made me laugh so hard. Vanessa

iv

gets the award for knowledge of theory; thanks. I have Carles to thank for my

understanding of energy transfer and programming skills. Haizheng, it was really nice to

get to know you, and great that we helped each other learn software to analyze our

fluorescence data. Elisabeta, we had some good laughs. I loved looking over the

sentences that made it onto our wall. Whenever I was confused about what parts to order

for the laser, Jeongho was there to rescue me (I swear he had all the catalogs memorized).

To my grad house neighbour Hoda, it was nice to get to know you. Yasser, thanks for all

the tasty treats you brought in. I still crave those pistachio ones. Anna, thank you for

teaching me about nanocrystal synthesis and how to avoid stripping off their ligands.

Yaser, I will miss the black board group meetings (I learned so much more that way).

Jun, thanks for taking over the construction of the laser set-up. Regardless of how little

time I spent with Tieneke, I still have scars to show for the fun times we had together.

To all the girls, Shun, and the rest of my baseball team: I will miss you. I had a

lot of fun playing in the mud! Year one and two could not have been more different, but

regardless of how well we played, we always had a blast. I will miss all of the good

times, laughing and trips to the bar!

My high school chemistry teacher, Mr. Bird, is the person responsible for my love

of science.* Your abilities as a teacher, your love of science, and your enthusiasm shaped

me into who I am today. Thanks!

My family and friends have given me the perfect balance between work and fun,

which kept me sane.† You have all been so loving, caring, and patient. I could not ask

for a better family! Grandpa Stacy and Grandpa Nagy, thank you for all of your love and

* I would also like to thank excitons. † Still up for debate.

v

support. I have always been grateful for your interest in my life. Grandpa Stacy, you

took it to the extreme when you tried to understand my undergraduate thesis. I

appreciated it. Jenn and Will, thanks for inviting me to Florida to take my mind off

research. Natalie, Allison, Emily, and Brooke, thanks for being the best girl cousins ever!

I loved hanging out with you at the cottage, talking, eating, walking, playing games – oh,

and did I mention eating? Adrian, Blake, Dave, and Andrew, you are my favourite boy

cousins. We always had a blast playing sports, watching movies, or eating. Aunt Louise,

thank you for driving me to the train every morning. We had a lot of fun trips! Aunt

Marie, Aunt Cathy, Uncle Jim, Uncle Tom, and Uncle Rich, thank you for your advice

and good times!

Mom and Dad, you are super loving parents and my very close friends. Mom, if it

was not for you, I would never have made it to the train on time. Your help getting

breakfast together and packing lunch allowed me to sleep in just a little bit longer, but I

swear that enabled me to get through undergrad. Our nighttime talks balanced my days

spent in the library by giving me some human contact. I have Dad to thank for all of the

gourmet meals; you are a great cook! You have taught me everything I know about

cooking, especially how to love it. Cooking was my savior in grad school because it

helped me relax after many long days of research. “Kisses!” I love you guys!

My friends are another major influence in my life. Mike, you were the best train

friend ever! I enjoyed your company so much. Leo, you made life fun but also kept me

on track. I will never forget our summer doing organic research together and all the fun

times afterward. ’Love you guys! Jenny, I have never had a friend so helpful and caring.

Ever since I bumped into you a hundred times on the second floor of the chemistry

building, you will always be “Number 2” to me. Scott, thank you for putting up with all

vi

of the sandwiches. I have had so much fun with all of you at our games nights. I have

Monique to thank for balancing my life with cheesecake and champagne. I miss having

every class with you! Brian, even though you were not in my research group, I

considered it close enough. I had a great time hanging out with you. Since grade school,

Dave and Kait have been great friends. Kait, you always brighten my day by being so

positive and friendly. Dave, regardless of what we did, I always had fun!

When it comes to support, best friends are there in the good times and bad. Jeff,

you were always there for me, whether it was lending an ear for a short coffee break or a

long rant, or helping to build great memories like cooking dinners, watching Star Trek,

going to a wine tasting, or hanging out at the bar. You introduced me to mushrooms and

Scotch; how can I not love you? If it was not for you I would not have finished my

thesis. Your amazing grammar skills and incredible patience are much appreciated.

You’re my favourite!

Thanks again, everyone! You have all been a great support to me throughout my

education, writing up, and general life. Keep in touch!

vii

Table of Contents

Title Page i

Abstract ii

Acknowledgments iii

Table of Contents vii

List of Figures ix

List of Tables xii

List of Acronyms xiii

1 Introduction

1.1 Semiconductor Nanocrystal Applications and Crystal Structure 1 1.2 Optical Spectra of Nanocrystals and Excitons 2 1.3 Fine Structure 4 1.4 Relaxation 6 1.5 Stokes Shift 9 1.6 Surface Traps 9 1.7 Inhomogeneous Line Broadening 10 1.8 Homogeneous Line Broadening 11 1.9 Phonons 12 1.10 Förster Resonance Energy Transfer 12 1.11 Magic-Sized Nanocrystals 15

2 Experimental Section

2.1 Synthesis of Nanocrystals 16 2.1.1 Synthesis of an Ensemble of Colloidal CdSe Nanocrystals 16 2.1.2 Synthesis of CdSe 463 nm Magic-Sized Nanocrystals 17 2.1.3 Synthesis of CdTe 427 nm and 500 nm Magic-Sized

Nanocrystals 17

2.2 Characterization Techniques

18

viii

3 Investigation of the Optical Properties of CdSe 463 nm Magic-Sized Nanocrystals in the Absence of Inhomogeneous Broadening

3.1 Two-Dimensional Photoluminescence Spectra 20

3.1.1 Comparison Between Spectra of CdSe 463 nm Magic-Sized Nanocrystals and an Ensemble of CdSe 492 nm Colloidal Nanocrystals

21

3.1.2 Homogeneous Line Broadening of CdSe 463 nm Magic-Sized Nanocrystals from 73 K to Room Temperature

26

3.2 Characterization of CdSe 463 nm Magic-Sized Nanocrystals

27

3.3 Identifying the Origin of Sub-peaks within the Excitonic Peaks in Two-

Dimensional Photoluminescence Spectra

31

3.3.1 High Resolution Two-Dimensional Photoluminescence Spectrum of the First Excitonic Peak of the CdSe 463 nm Magic-Sized Nanocrystals at 9 K

32

3.3.2 High Resolution Two-Dimensional Photoluminescence Spectrum of the First Excitonic Peak of the CdSe 463 nm Magic-Sized Nanocrystals at 92 K

34

3.3.3 Comparison of Room Temperature Absorption and Photoluminescence Excitation Spectra

36

3.3.4 Discussion and Determination of Sub-peaks within Excitonic Peaks

37

3.3.5 Calculation of the Electronic Coupling in Aggregated Magic-Sized Nanocrystals

41

3.4 Unsatisfactory Models for Sub-peaks within Excitonic Peaks

42

3.4.1 Acoustic and Longitudinal Optical Phonon-Assisted Transitions

42

3.4.2 Fine Structure 43 3.5 Comparison of CdSe 463 nm Magic-Sized Nanocrystals to Previously

Synthesized Nanoribbons and Platelets

44

3.6 Summary

45

4 Direct Evidence of Energy Transfer within CdTe 427 nm and 500 nm

Magic-Sized Nanocrystals

4.1 Two-Dimensional Photoluminescence Spectra of CdTe 427 nm and 500 nm Magic-Sized Nanocrystals

47

4.2 Characterization of CdTe 427 nm and 500 nm Magic-Sized Nanocrystals

50

4.3 Sub-peaks in excitonic peaks 53 4.4 Summary 55

References

56

ix

List of Figures

1.1 Energy level diagrams for related systems. Comparison of electronic energy levels in (A) molecules, (B) bulk semiconductors, and (C) semiconductor nanocrystals.

3

1.2 Fine structure states. Order of states in the first excitonic fine structure for spherical (A) CdSe and (B) CdTe NCs. The energy level spacing is not depicted. States are labeled with the amplitude of the projection of the excitons’ total angular momentum. Positive and negative total angular momenta correspond to spin ‘up’ and spin ‘down’, respectively. Dashed and solid lines represent dark optically forbidden states and bright optically allowed states, respectively.

5

1.3 Jablonksi diagram for organic molecules. Absorption occurs to a singlet excited states (|S1> or |S2>). Subsequently, an internal conversion step occurs, involving a fast non-radiative relaxation to the lowest excited state with the same spin multiplicity. This allows fluorescence emission from the lowest singlet excited state to the ground state. Alternatively, intersystem crossing can occur from the lowest singlet excited state to a triplet state, followed by internal conversion to the lowest triplet excited state. Emission from this lowest triplet excited state is known as phosphorescence.

7

3.1 Optical spectra of colloidal CdSe NCs and MSNs measured at 9 K. (A) 2D PL spectrum of an ensemble of colloidal CdSe 492 nm NCs. Broad excitonic peaks at an emission energy of 2.50 eV suggest inhomogeneous line broadening. (B) 2D PL spectrum of CdSe 463 nm MSNs. Narrow, circular excitonic peaks are located at an emission energy of 2.73 eV; broad peaks are located between emission energies of 2.45 eV and 2.65 eV. (C) (I) (Black) 1D PLE spectrum of CdSe 492 nm NCs with an emission energy of 2.50 eV was obtained from cross-section I in (A). The excitation peak was omitted. (II) (Blue) NR PL spectrum of CdSe 492 nm NCs was obtained from cross-section II in (A). (III) (Red) Emission spectrum of CdSe 492 nm NCs with an excitation energy of 2.55 eV was obtained from cross-section III in (A). The excitation peak was omitted. (D) (Black) 1D PLE spectrum of CdSe 463 nm MSNs with an emission energy of 2.74 eV. (Blue) NR PL spectrum of CdSe 463 nm MSNs. (Red) Emission spectrum of CdSe 463 nm MSNs with an excitation energy of 2.81 eV. The excitation peak was omitted in the PLE and emission spectrum.

22

x

3.2 FWHM of first excitonic peaks exhibiting homogeneous line broadened.

(A) 2D PL spectrum of CdSe 463 nm MSNs measured at room temperature. (B) FWHM vs. temperature for the first excitonic peak of CdSe 463 nm MSNs, obtained by averaging the FWHM of the NR PL and emission spectra.

27

3.3 Schematic of embedded MSN cylinders and MSN aggregates. Diameters of individual MSNs are 2.05 nm. MSNs can assemble into two aggregated configurations. (A) Embedded MSN cylinders, comprising MSNs embedded in a fatty acid matrix, range in size with lengths of approximately 10 µm and widths of 0.1 µm to 1 µm. (B) MSN aggregates, comprising close-packed monolayers of MSNs, are approximately 80 nm × 30 nm × 2 nm.

28

3.4 STEM and confocal microscopy images of CdSe 463 nm MSNs. Embedded MSN cylinders are shown in STEM images (A), (B - bottom left corner), and a confocal microscopy image (C). MSN aggregates are shown in STEM images (D, E), and a confocal microscopy image (F). (A), (B - bottom left corner) STEM images and (C) a confocal microscopy image of embedded MSN cylinders. (D, E) STEM images and (F) a confocal microscopy image of MSN aggregates.

29

3.5 High resolution optical spectra of CdSe 463 nm MSNs’ first excitonic peak measured at 9 K. (A) 2D PL spectrum with sub-peak maxima labelled I – IV. (B-F) (Solid red line) Experimental data obtained from cross-sections of 2D PL spectrum, (solid grey lines) Gaussian fits, and (dashed blue lines) sums of the Gaussian fits. PLE spectra of (B) peaks I and III at an emission energy of 2.729 eV, and (C) peaks II and IV at an emission energy of 2.745 eV. Emission spectra of peaks (D) I, (E) II, and (F) III at excitation energies of 2.818 eV, 2.798 eV, and 2.777 eV, respectively.

33

3.6 High resolution optical spectra of CdSe 463 nm MSN’s first excitonic peak measured at 92 K. (A) 2D PL spectrum with sub-peak maxima labelled II and IV. At this temperature, peaks I and III are not resolved in the 2D PL spectrum. (B, C) (Solid red line) Experimental data obtained from cross-sections of 2D PL spectrum, (solid grey lines) Gaussian fits, and (dashed blue lines) sums of the Gaussian fits. (B) PLE spectrum of peaks II and IV at an emission energy of 2.748 eV. (C) Emission spectrum of peak II at an excitation energy of 2.794 eV.

35

xi

3.7 Absorption and PLE spectra of CdSe 463 nm MSNs measured at room

temperature. (Dashed red line) Absorption spectrum and (solid blue line) PLE spectrum are normalized at 463 nm. These two spectra do not correlate at all wavelengths.

37

3.8 An energy level model consistent with the position of sub-peaks within the first excitonic peak of CdSe 463 nm MSNs. (State 1) Bright state of embedded MSNs. (State 2) Bright state of MSN aggregates, 45 meV ± 5 meV lower than State 1 due to electronic coupling. (State 3) Dark state of embedded MSNs. (State 4) Dark state of MSN aggregates. State 3 and 4 have approximately the same energy. (State 5) A surface state is mixed with the excitonic states of embedded MSNs and MSN aggregates. The surface state is 19 meV ± 5 meV lower than the dark states. Absorption occurs to State 1 or 2 and emission occurs from States 3, 4, or 5.

39

4.1 Optical spectra of CdTe 427 nm and 500 nm MSNs measured at 9 K. (A) 2D PL spectrum of CdTe 427 nm and 500 nm MSNs. A cross-peak is present at the emission energy of the 500 nm MSNs and at the excitation energy of the 427 nm MSNs. (B) (Solid blue line) Emission spectrum of the cross-peak with an excitation energy of 3.03 eV, obtained from a cross-section of (A). (Dashed blue line) A Gaussian fit to the first excitonic peak at 2.97 eV for CdTe 427 nm MSNs. (Solid red line) PLE spectrum of the cross-peak with an emission energy of 2.54 eV, obtained from a cross-section of (A). (Dashed red line) A Gaussian fit to the second excitonic peak at 2.92 eV for CdTe 500 nm MSNs.

48

4.2 STEM and confocal microscopy images of CdTe 427 nm and 500 nm MSNs. STEM images of (A) embedded MSN cylinders and clusters of MSN aggregates, and (B) clusters of MSN aggregates. (C-I) Confocal microscopy images of (red) CdTe 427 nm and (green) 500 nm MSNs. (C) Low magnification image of fluorescence from both sizes of MSNs. (D-F) Fluorescence from the same cluster of MSN aggregates: (D) superposition of fluorescence from both sizes of MSNs; fluorescence from (E) 427 nm MSNs, and (F) 500 nm MSNs. (G-I) Fluorescence from the same embedded MSNs: (G) superposition of fluorescence from both sizes of MSNs; fluorescence from (H) 427 nm MSNs, and (I) 500 nm MSNs.

51

4.3 Contour plot of the 2D PL spectrum for CdTe 427 nm and 500 nm MSNs. Black circles mark sub-peaks within the excitonic peaks.

54

xii

List of Tables

3.1 Emission and excitation energies of the sub-peak maxima within the first excitonic peak of CdSe 463 nm MSNs measured at 9 K.

33

3.2 Emission and excitation energies of sub-peak maxima within the first excitonic peak of CdSe 463 nm MSNs measured at 92 K.

35

4.1 Emission and excitation energies of the first excitonic peak for CdTe 427 nm MSNs, CdTe 500 nm MSNs, and their cross-peak.

48

xiii

List of Acronyms

1D One Dimensional

2D PL Two-Dimensional Photoluminescence

3D Three Dimensional

AOTF Acousto-Optical Tunable Filter

EET Electronic Energy Transfer

FLN Fluorescence Line-Narrowing

FWHM Full Width at Half Maximum

HAADD High Angle Angular Dark Field Detector

LO Longitudinal Optical

MSN Magic-Sized Nanocrystal

NC Nanocrystal

NR PL Non-Resonant Photoluminescence

ODE Octadecene

PE Photon Echo

PL Photoluminescence

PLE Photoluminescence Excitation

QD Quantum Dot

RET Resonance Energy Transfer

STEM Scanning Transmission Electron Microscope

TA Transverse Acoustic

TOP Trioctylphosphine

TOPO Trioctylphosphine Oxide

1

1 Introduction

1.1 Semiconductor Nanocrystal Applications and Crystal

Structure

Semiconductor nanocrystals (NCs) are at the forefront of future light-emitting

technologies because of their uniquely size tunable optical properties. These properties

lead to applications including solar cells1, detectors2, diodes3, lasers4, 5, and quantum

computing6. Semiconductor NCs contain hundreds of unit cells, giving them a length

scale from nanometers to tens of nanometers in one or more dimensions. Great

improvements in synthetic techniques enabled NCs to be synthesized in a variety of sizes

and shapes.7 Additionally, NC ensembles with a size distribution smaller than a 5%

variation have be synthesised.8 The most common NCs are made of CdSe, CdS, CdTe,

InP, PbSe, and PbS.9

A crystal structure can be characterized by the positions of atoms within the unit

cell and its underlying Bravais lattice.10 During colloidal synthesis of the NCs, the

formation of a crystal structure is dependent on the temperature, pressure, and

concentration of monomer used.7 For example, CdSe can be either sphalerite (zinc-

blend) or hexagonal (wurtzite) structure depending on conditions and/or synthesis

procedure.11

NCs are synthesized with organic ligands attached to the NC’s outer layer,

passivating the NCs. Ligands allow NCs to be dispersed in different solvents, but can be

removed over time or by repeated washing. Typical organic ligands include

trioctylphosphine (TOP) or trioctylphosphine oxide (TOPO).8

2

1.2 Optical Spectra of Nanocrystals and Excitons

All of the phenomena and applications for NCs indicated in Section 1.1 are

similar because their function relies on the excitation of a NC. Photoexcitation of a NC

results in a confined electron and hole, which is formed when an electron is excited from

the valence band to the conduction band, leaving a hole in the valence band. The

interacting electron-hole pair is known as an exciton. This pair is bound relative to the

band gap by an attractive Coulombic interaction on the order of tens of meV for NCs.9

This attraction is favourable because the magnitude of the electron-electron repulsion

integral is smaller for the excited state than for the ground state.9

Excitons are quantum confined when at least one dimension of a NC is smaller

than the bulk exciton Bohr radius. The Bohr radius is defined by:

2

20

em

rµ

εh= ,

where m0 is the mass of the free electron, e is the dielectric constant and µ is the exciton

reduced mass.12 When a NC is smaller than the exciton’s Bohr radius, the size of the

exciton is determined by the shape of the NC and not the strength of the electron-hole

Coulombic interaction.13

The dimensions of quantum confinement play a large role on the optical

properties. NCs with three-dimensionally confined excitons are known as quantum dots

(QDs). They have discrete energy levels and narrow optical features due to this

excitation process. NCs with one-dimensionally confined excitons differ from QDs

because they typically have broad absorption features.14 Some examples of NCs having

one-dimensionally confined excitons are two-dimensional disks,14 quantum

3

Figure 1.1: Energy level diagrams for related systems. Comparison of electronic energy levels in (A) molecules, (B) bulk semiconductors, and (C) semiconductor nanocrystals.

wells,15 and nanobelts16. Excitons are also the primary photogenerated species in

photosynthetic light-harvesting complexes, conjugated polymers, and semiconducting

single-wall carbon nanotubes.9

Energy levels of NC excitons differ from electronic energy levels in molecules

(Figure 1.1A) and band structures in bulk semiconductors (Figure 1.1B). Molecules have

defined molecular orbitals and bulk semiconductors have extremely dense conduction

and valence bands. NCs have elements of both, with spread out energy levels and a band

gap similar to the gap between bulk semiconductor conduction and valence bands (Figure

1.1C). The energy levels within a ‘valence band’ region are closer together than those in

a ‘conduction band’ region.9 The drastic difference between molecules, bulk

semiconductors and NCs is their dielectric constant. Low dielectric constants are

important for the formation of excitons because high dielectric constants shield electron-

hole interactions.9

4

Energy levels of excitons determine the absorption and emission spectra of NCs.

The absorption and emission spectra are tunable when the size of a NC is altered because

this changes the energy levels. Additionally, the properties of NCs are affected by shape,

material, crystal structure and symmetry. The absorption and photoluminescence (PL)

maxima of smaller NCs are more blue shifted compared to larger NCs. Large NCs have

closely packed energy levels in comparison to smaller NCs. This property can be

understood by modeling a NC as a quantum particle in a box.

An electronic band gap in a NC is affected by the size of the NC and defined as

the energy difference between the valence and conduction ‘bands’. Electrons, holes or

excitons cannot propagate within the band gap region.11 In quantum confined systems,

the energy difference between the electronic band gap and the exciton transition energy

(optical gap) is known as the exciton binding energy.17 The binding energy of a NC is

affected by its diameter. For QDs, the exciton binding energy is inversely proportional to

the size of the QD. A QD with a diameter from 2-4 nm has an exciton binding energy

ranging from 200-50 meV.9

1.3 Fine Structure

NC’s resemblance to both molecules and bulk semiconductors gives rise to many

unique properties. In organic molecules, the exchange splitting between the single and

triplet states is hundreds of meV. The exchange splitting in bulk semiconductors is much

smaller, on the order of µeV to meV, because the exciton wave function is delocalized

over the bulk semiconductor. Semiconductor NCs have a size-dependent exchange

splitting, which is on the order of meV, which is a magnitude between that for organic

5

Figure 1.2: Fine structure states. Order of states in the first excitonic fine structure for spherical (A) CdSe and (B) CdTe NCs. The energy level spacing is not depicted. States are labeled with the amplitude of the projection of the excitons’ total angular momentum. Positive and negative total angular momenta correspond to spin ‘up’ and spin ‘down’, respectively. Dashed and solid lines represent dark optically forbidden states and bright optically allowed states, respectively.

molecules and bulk semiconductors.9 With regards to the exchange splitting and many

other properties, NCs have values between those of molecules and bulk semiconductors.

Due to the magnitude of the exchange interaction of an electron-hole pair in NCs,

the energy levels of the electron and hole must be considered simultaneously. Electron-

hole exchange interactions, intrinsic crystal field, and shape asymmetry from a perfect

sphere split the lowest energy exc itonic state into eight- fold degenerate states.18, 19 This

is known as the fine structure. Shape anisotropy and long-range exchange interactions

might also cause splitting.20-22 These levels are tens of meV apart, with order and spacing

that depends on the band gap, size, and shape of the NCs.18

In Figure 1.2A and 1.2B, the order of states in the first excitonic fine structure is

shown for both spherical CdSe and CdTe NCs, respectively. However, the energy level

spacing is not depicted. Energy level spacing is affected by NC diameter.18, 23 Mixing of

electron and hole angular momenta caused by an electron-hole exchange interaction can

6

give rise to fine structure of states, which are the eigenfunctions of the total angular

momentum. Therefore, the fine structure states in Figure 1.2 are identified by the

amplitude of the projection of the excitons total angular momentum. The exciton’s

angular momenta are obtained from addition of the angular momenta of the electron and

hole, which can be ±1/2 for the electron and ±1/2 or ±3/2 for the hole. To a first

approximation, the electron spin ‘up’ states are distinguished as having positive total

angular momentum while spin ‘down’ are negative. In Figure 1.2, the solid lines

represent the bright or allowed states, which are energy levels that the excitons can be

created in. The dotted lines represent dark or forbidden states, which are states that the

exciton cannot be excited to from the ground state; however, excitons can relax to these

dark states from other excited states.24

1.4 Relaxation

Little is known about the mechanism of relaxation in nanoscale systems.25 After

photoexcitation of a NC, relaxation within the excitonic fine structure occurs when there

is an energy transfer between an electron and hole. Relaxation within the fine structure

follows preferred non-radiative decay pathways. Kinetics of specific relaxation pathways

within the fine structure of NCs have previously been estimated.25 Originally it was

believed that relaxation within the fine structure solely occurred down a “step- ladder” to

lower energy states.25

7

Figure 1.3: Jablonksi diagram for organic molecules. Absorption occurs to a singlet excited states (|S1> or |S2>). Subsequently, an internal conversion step occurs, involving a fast non-radiative relaxation to the lowest excited state with the same spin multiplicity. This allows fluorescence emission from the lowest singlet excited state to the ground state. Alternatively, intersystem crossing can occur from the lowest singlet exc ited state to a triplet state, followed by internal conversion to the lowest triplet excited state. Emission from this lowest triplet excited state is known as phosphorescence.

Understanding non-radiative transitions following photoexcitation of NCs is key

to NCs dynamics. Relaxation processes in nanocrystals are more complex, but analogous

to that in organic molecules. Photoexcitation and relaxation processes within organic

molecules can be explained using a Jablonski diagram.11 As shown in Figure 1.3,

excitation occurs to the singlet vibrational level of |S> excited states, e.g. |S1> or |S2>.

Subsequently, there is a fast non-radiative relaxation between energies of the same spin

multiplicity to the lowest singlet vibrational level. This relaxation is called internal

conversion, and results in energy dispersion through high frequency modes; e.g. the

carbon-hydrogen (C—H) stretch is around 3000 cm-1.25

8

From the lowest singlet vibrational level, two subsequent relaxations are possible,

as shown in Figure 1.3. One involves the emission of a photon through fluorescence

from the single state. Another is known as intersystem crossing, which is a non-radiative

relaxation to a triplet state having a different spin multiplicity. Internal conversion occurs

to the lowest triplet state. The rate of emission from the triplet state is slow because

emission to the ground state is forbidden. Emission from this triplet state is called

phosphorescence.

Absorption and relaxa tion in NCs differs from that in organic molecules in that

NCs exhibit strong spin-orbit coupling26. This results in a mixed character of the

electronic states in NCs. The excitonic and fine structure states of NCs are not

eigenfunctions of spin, as in organic molecules, but are eigenfunctions of the angular

momentum.25

Fine structure states of spherical CdSe and CdTe are shown in Figure 1.2A and

1.2B, respectively. The relaxation in NCs is more complex but still analogous to

molecules in that they exhibit internal conversion and intersystem crossing.11 In NCs,

excitation occurs to an optically allowed bright state (states represented by solid lines in

Figure 1.2). Subsequently, relaxation occurs within the fine structure states, which

prefers specific non-radiative decay pathways.25, 27 Relaxation may occur to an optically

dark, spin-forbidden state analogous to triplet states in molecules. Emission occurs when

an electron and hole recombine and radiation is emitted.11

9

1.5 Stokes Shift

A Stokes shift is an energy difference between the fluorescence and absorption

maxima. The fluorescence maximum is always at a lower energy than the absorption

maximum, resulting in a so-called red shift. The Stokes shift is equal to the energy

difference between the fine structure optically bright and optically dark states. It is

influenced by the spacing of fine structure energy levels, relaxation processes within

QDs, and the size distribution of QD ensembles.11 The resonant Stokes shift is typically

caused by a spin triplet dark exciton ground state. The electron-hole exchange interaction

can create this dark ground state.18, 23 Experimentally it has been observed that with

decreasing QD diameter the Stokes shift increases.18 This observation is consistent with

theory because the electron-hole exchange interaction increases with increased QD

diameter.18

1.6 Surface Traps

The treatment of NC surfaces with organic ligands affects solubility and plays a

large role in the light emitting properties of NCs. Properties affected by the surface of

NCs become more important when the NCs diameter decreases because the surface-to-

volume ratio increases.28 A NC with a 1 nm radius has a surface-to-volume ratio of 3:2.*

Atoms on the surface of the NC will have positions slightly shifted compared to the

interior crystal structure. This creates states within the energetically forbidden band gap

of the bulk solid, which are called surface traps or surface states.29 Surface states emit

* For spheres, Surface Area : Volume

32

34

:4 rr ππ= .

10

from a lower energy than the absorption because energy levels are created within the

band gap.30 Electrons and holes can be trapped within a surface state. This affects the

excited state dynamics of NCs. Trapped charges reduce the radiative rate of

recombination, which could decrease the quantum yield of a NC sample.30 Passivation of

a NC means that the surface is bonded to a species with a much larger band gap, which

eliminates energy levels within the band gap.29 Therefore, imperfect passivation of a NC,

for example dangling bonds, could cause surface traps. This has been confirmed in PL

studies29 and studies where NCs have been capped with inorganic groups, for example

ZnS31. Defects in the crystal structure are another cause of surface states.29 Surface traps

are not fully understood because they are relatively optically inactive and have a

heterogeneous distribution of energy levels.32, 33 Population lifetime of surface states

range from nanoseconds to milliseconds.33

Surface states close in energy to the band gap can mix with NC energy levels,

which might change the spacing of energy levels.30 If a dark surface state mixes with an

optically active state, the resulting mixed state could have sufficient oscillator strength to

be optically active.30

1.7 Inhomogeneous Line Broadening

In previous NC studies, results are limited by inhomogeneous line broadening34, 35

due to a broad size distribution of NCs. Probing size-dependent properties in an

ensemble results in many indistinguishable signals, each corresponding to NCs of

different sizes. Inhomogeneous broadening is temperature independent.9

11

Many methods have been developed to decrease inhomogeneous line broadening.

Synthesis of colloidal NCs can be optimized to have less than 5% variance in the average

NC diameter.8 Using these NCs, inhomogeneous line broadening can be further reduced

by investigating a small fraction of similarly sized NCs within an ensemble. Methods of

probing this fraction include fluorescence line-narrowing (FLN),30, 36, 37 nanosecond

pump-probe spectroscopy,38 hole burning,39, 40 near-field scanning probe microscopy,41

and photon echo (PE) spectroscopy40 (including two-pulse, three-pulse stimulated, and

accumulated PE spectroscopy). These methods reduce inhomogeneous broadening, but

results might still be complicated by a size distribution of NCs probed. Investigations of

single NCs are possible; however, they have many limitations. Peak shape is obscured by

spectral diffusion,42, 43 and the properties of individual NCs are not representative of

ensembles properties.

1.8 Homogeneous Line Broadening

Signals are often obscured by homogeneous line broadening. Homogeneous line

broadening is caused by the emission of thermal acoustic phonons (discussed below),44, 45

and increases with increasing temperature.9 Homogeneous line broadening is negligible

at low temperatures because phonons do not scatter the ground state (phonon emission is

forbidden due to energy conservation).45 NCs have narrow homogenous broadening

compared to organic materials, which could be due to their more ridged structure.9

12

1.9 Phonons

Phonons are quanta of energy associated with crystal vibrations. If the

modulation of adjacent atoms is out of phase, the vibrations result in optical phonons. An

in phase modulation results in acoustic phonons. The movement of adjacent atoms in

relation to the vibrating wave determines whether the two types of phonons are further

classified as longitudinal (move in same direction) or transverse (move in perpendicular

directions).11

The most common phonons in CdSe are longitudinal optical (LO) and transverse

acoustic (TA).11 In CdSe the LO-phonon mode has a frequency of 207 cm-1.9 Acoustic

phonons are quantized torsional and spheroidal modes, which depend on the NC size, and

range from 5-40 cm-1.9 A NC’s line shape is affected by homogeneous line broadening,

which is mainly caused by TA-phonons.9

1.10 Förster Resonance Energy Transfer

Resonance energy transfer (RET) involves the transfer of energy between an

electronically excited ‘donor’ system (atom, molecule, or NC) and an ‘acceptor’ in close

proximity. This proceeds through a complex mechanism and does not occur by

uncorrelated emission and absorption of the donor to acceptor.46 RET results in overlap

of the donor’s fluorescence spectrum and the acceptor’s absorption spectrum. If overlap

of these spectra is not observed, then RET is not present. Energy conservation is

dependent on the efficiency of this overlap.46 RET is possible because of weak

Coulombic coupling between the donor and acceptor.46 In the weak coupling limit, there

are a few assumptions made in Förster theory for RET. Firstly, after electronic excitation

13

of the donor, the surroundings will equilibrate on a timescale shorter than that of RET.

Secondly, the electronic coupling between the donor and acceptor is smaller than

coupling to the surroundings, which is evident from the absorption line shape.46

The electronic coupling between the donor and acceptor, V, is the sum of the

Coulombic coupling, VCoul, and the short-range coupling, Vshort . VCoul is present when two

systems are within any distance for spin-allowed RET. Vshort depends on the wave

function overlap between of the donor and acceptor. In Förster theory, it is assumed that

V ˜ VCoul. The coupling can further be approximated as a dipole-dipole interaction,

Vdip-dip, between the transition dipole moments of the donor, µD, and acceptor, µA.46

341

RVV AD

dipdip

µκµπε

=≈ − ,

where ? is an orientation factor that depends on the angle between µD and µA, R is the size

of the center-to-center separation between the donor and acceptor, and e is the dielectric

constant of the medium.46 For RET in NCs, transition dipole moments obey selection

rules for circularly polarized light.18

Recent theoretical calculations have shown that the dipole-dipole approximation

for RET can accurately predict the electronic coupling for NCs. 47 It was also deduced

that the dipole-dipole approximation can be used when the center-to-center separation of

NCs is on the order of the NC dimensions. Experimentally, the average distance of

electronic energy transfer (EET) in NCs is 1-8 nm,47 which is on the order of the diameter

of a NC. The dipole-dipole approximation breaks down for RET between organic

molecules with a center-to-center separation on the order of the molecules’ dimensions.47

Research in the area of EET between weakly coupled molecular systems has been

extensively studied and is well understood. However, EET between NCs or between NCs

14

and molecules is not well understood. EET has been observed between two sizes of

QDs,48-52 NCs and organic polymers,53-55 and NCs and molecular probes (fluorophore

tagging in biological systems)56-59. NCs have been used as probes in long-range RET for

distances up to 13 nm.60

Long-range RET from smaller to larger CdSe QDs in a close packed solid has

been reported.48 This was deduced from the reduction in luminescence and lifetime of

the smaller QDs and a corresponding increase in luminescence and lifetime of the larger

QDs. Dipole-dipole interactions allowed RET in these close-packed CdSe QD solids.61

Recently, Förster energy transfer has been observed in densely packed large PbS QDs.52

Förster RET by electrostatic coupling has been observed between layers of

different sized core-shell CdSe/ZnS QDs capped with TOPO.49 The RET rate was

determined to be 1.33 ns-1 ((750 ps)-1) from the smaller to larger QDs using time-resolved

PL and instantaneous PL spectroscopy. In another study, RET was shown in layered

assemblies of mixed-sized water soluble CdTe QDs, which were passivated with

oppositely charged stabilizing molecules.50 This reduced interlayer distance enabled a

faster rate of energy transfer of 20 ns-1 ((50 ps)-1).

RET between two sizes of QDs is typically observed in solid structures of QDs, as

in the examples above; however, few publications have identified RET between QDs in

solution. Förster RET has been reported between two sizes of water soluble CdTe QDs

capped with thioglycolic acid in a single water droplet.51 The droplet changed colour

when water evaporated, which brought QDs close enough for long-range dipole-dipole

RET to occur.

15

1.11 Magic-Sized Nanocrystals

Structures that have a large stability and a narrow size distribution can be

considered to have a ‘magic number’ of atoms.62 Some examples of compounds

containing a magic number of atoms include fullerenes,63 and metal clusters64, 65.

Extremely small QDs with diameters from 1 nm to 2 nm are often called nanoclusters.

Nanoclusters have a high probability of being magic-sized nanocrystals (MSNs), which

exhibit extremely narrow absorption features characteristic of a single size distribution.66

Many different sizes of magic-sized CdSe clusters were synthesised and

photoluminescence excitation (PLE) was observed for clusters with 32 atoms.67, 68 Many

sizes of CdSe MSNs have been synthesised.69-72

16

2 Experimental Section

2.1 Synthesis of Nanocrystals

CdSe 463 nm MSNs and a mixture of CdTe 427 nm and 500 nm MSNs

investigated in this thesis were obtained from Dr. Kui Yu’s laboratory at the National

Research Council.72 CdSe samples were previously characterized as MSNs.72, 73 This

assignment is further supported by our investigation of the samples’ optical properties,

discussed below. The name assigned to a NC sample refers to the wavelength

corresponding to the first absorption maximum; this wavelength is not to be confused

with the MSN size. CdSe and CdTe MSNs were synthesized using a procedure slightly

altered from that described in Reference 72. Detailed procedures are given in the

following subsections.

2.1.1 Synthesis of an Ensemble of Colloidal CdSe Nanocrystals

First, an ensemble of colloidal CdSe NCs capped with TOPO was synthesized

using methods described in Reference 74. This ensemble had a size distribution of

2.23 nm ± 4%, found from the ensemble’s room temperature first PLE peak using a

previously published calibration curve.75

17

2.1.2 Synthesis of CdSe 463 nm Magic-Sized Nanocrystals

In a 50 mL three-necked round-bottom flask under vacuum, 160.1 mg (0.6 mmol)

of Cd(Ac)2·2H2O and 91.4 mg (0.4 mmol) of myristic acid (CH3(CH2)12COOH) were

mixed in 3.58 g of octadecene (ODE). This solution was heated to 120ºC for 120 min.

After 120 min. under vacuum, the solution was exposed to nitrogen gas and cooled to a

temperature of 100ºC. In another vial, 7.92 mg (0.1 mmol) of Se was dissolved in

99.52 mg of TOP. Under sonication, the vial was heated at 60ºC for one hour, which

produced TOPSe. The TOPSe was added to the above-mentioned round-bottom flask at

100ºC. To ensure all TOPSe was collected, the vial was rinsed with 0.5 g of ODE, and

the washings were collected in the round-bottom flask. The mixture was degassed for a

total of 15 min. by alternating between vacuum (4 min.) and nitrogen (1 min.). The

temperature increased to 120ºC, and after one hour at 120ºC, the temperature was

increased to 220ºC at a rate of 20ºC/min. When the temperature reached 220ºC, the CdSe

463 nm MSN sample was removed from the reaction flask.

2.1.3 Synthesis of CdTe 427 nm and 500 nm Magic-Sized

Nanocrystals

In a 50 mL three-necked round-bottom flask under vacuum, 213.9 mg (0.8 mmol)

of Cd(Ac)2·2H2O and 62.1 mg (0.266 mmol) myristic acid (CH3(CH2)12COOH) were

mixed in 4 g of ODE. This solution was heated at 120ºC for two hours before being

cooled to 100ºC under nitrogen gas. In another vial, 12.76 mg (0.1 mmol) of Te was

dissolved in 70.5 mg of TOP. Under sonication, the vial was heated at 60ºC for three

hours, which produced TOPTe (a yellowish solution). The TOPTe was added to the

18

above-mentioned round-bottom flask at 100ºC. To ensure all TOPTe was collected, the

vial was rinsed with 1 g of ODE, and the washings were collected in the round-bottom

flask. The mixture was degassed for a total of 13 min. and 30 s by alternating between

nitrogen (30 s) and vacuum (4 min.). The temperature was increased to 120ºC, and after

two hours at 120ºC, the temperature was increased to 200ºC at a rate of 20ºC/min. When

the temperature reached 200ºC, a sample containing a mixture of CdTe 427 nm and

500 nm MSNs was removed from the reaction flask. The two sizes of CdTe MSNs could

not be separated.

2.2 Characterization Techniques

The ensemble of colloidal CdSe NCs was dispersed in a small amount of toluene;

all MSN samples were dispersed in a small amount of octadecene. For characterization, a

small amount of a sample in its original solvent was dispersed into a 6:1 mixture of

isopentane/methylcyclohexane. The optical absorbance of each sample was measured in

a 1 cm cuvette. The absorbance values for 492 nm CdSe NC ensemble, the CdSe 463 nm

MSN sample, and the mixture of CdTe 427 nm and 500 nm MSNs were 1.06, 2.5, and

0.96 and 0.43, respectively.

Room temperature absorption and PLE spectra were preformed on a CARY100

BIO UV/Vis spectrophotometer and CARY Varian florescence spectrophotometer,

respectively. Scanning transmission electron microscope (STEM) images were taken

with a Hitachi HD-2000 with an acceleration voltage of 200kV and a high angle angular

dark field detector (HAADD). The laser confocal microscope used was a Leica TCS SP2

with a Coherent Innova 90C laser with an output power of 130mW at an excitation

19

wavelength of 364 nm. The lens used was a HCS PL APO CS 63 x 1.4 with a drop of oil

between the sample and lens.

Steady-state two-dimensional photoluminescence (2D PL) spectra were measured

with a J-YHoriba Fluorolog-3-22 spectrofluorimeter, with a 450 W xenon arc light source

and a Peltier-cooled Hamamatsu R928 PMT photo-detector. For 2D PL measurements,

samples were placed between sapphire plates with a 1 mm path length under high

vacuum in a closed cycle Helix Technology Corporation CTI-Cryogenics Model-22

helium cryostat. The emission/excitation slit widths were altered to optimize the

resolution and signal-to-noise ratio. Passbands of 0.5 nm, 1 nm, 0.75 nm, and 0.5 nm

were used for the 492 nm NCs, the 427 nm and 500 nm CdTe MSNs, the CdSe 463 nm

MSNs, and the CdSe 463 nm MSN high resolution scans, respectively. 2D PL spectra

were obtained by combining a series of individual emission spectra taken over a range of

excitation energies using a monochromator.

20

3 Investigation of the Optical Properties of

CdSe 463 nm Magic-Sized Nanocrystals in the

Absence of Inhomogeneous Line Broadening

MSNs are characterized as an ensemble of single sized NCs with narrow optical

features. In Section 3.1, CdSe 463 nm MSNs were studied by 2D PL spectroscopy.

Optical features were narrow and did not exhibit inhomogeneous line broadening,

allowing homogeneous line broadening to be studied as a function of temperature. In

Section 3.2, we determine that CdSe 463 nm MSNs form into two aggregated

configurations: embedded MSN cylinders and MSN aggregates. In Section 3.3, we

examine sub-peaks found within the first excitonic peak of the CdSe 463 nm MSNs, and

determine that they arise from energy levels of the two configurations, and mixing

between surface states and MSN excitonic states. In Section 3.5, we compare these

MSNs to previously published nanoribbons and platelets, and suggest that close-packed

MSN aggregates play a role in forming nanoribbons and platelets during synthesis.

3.1 Two-Dimensional Photoluminescence Spectra

A colloidal ensemble of CdSe 492 nm NCs, having diameters of 2.23 nm ± 4%,

exhibited inhomogeneous line broadening due to its broad size distribution. In this

Section, we analyze the inhomogeneous line broadening of this ensemble. In contrast, no

21

inhomogeneous line broadening was observed for the CdSe 463 nm MSNs. At high

temperatures, CdSe 463 nm MSNs were affected by homogeneous line broadening. In

the absence of inhomogeneous line broadening, it was possible to determine that

homogeneous line broadening increased linearly with temperature for CdSe 463 nm

MSNs.

3.1.1 Comparison Between Spectra of CdSe 463 nm Magic-Sized

Nanocrystals and an Ensemble of CdSe 492 nm Colloidal

Nanocrystals

The study of 2D PL is valuable because more information can be collected from

these spectra than one dimensional (1D) emission and PLE spectra. 2D PL spectrum can

be used to determine the size distribution of an ensemble; recently we used this technique

to investigate ensembles of colloidal CdTe QDs.76 The excitation and emission energies

of a NC are size dependent; therefore, ensembles with a broad size distribution will

exhibit a range of excitation and emission energies. This range of energies creates

elliptical peaks in the 2D PL, which is characteristic of inhomogeneously broadened

ensembles. For samples with no inhomogeneous line broadening, the entire sample will

have the same excitation and emission energy; therefore, the peaks in the 2D PL will be

circular.

Figure 3.1A shows a 2D PL spectrum of an ensemble of CdSe colloidal NCs

measured at 9 K. This sample exhibited a room temperature first absorption peak at

492 nm. In a 2D PL spectrum, the white diagonal line is the excitation peak.

22

Figure 3.1: Optical spectra of colloidal CdSe NCs and MSNs measured at 9 K. (A) 2D PL spectrum of an ensemble of colloidal CdSe 492 nm NCs. Broad excitonic peaks at an emission energy of 2.50 eV suggest inhomogeneous line broadening. (B) 2D PL spectrum of CdSe 463 nm MSNs. Narrow, circular excitonic peaks are located at an emission energy of 2.73 eV; broad peaks are located between emission energies of 2.45 eV and 2.65 eV. (C) (I) (Black) 1D PLE spectrum of CdSe 492 nm NCs with an emission energy of 2.50 eV was obtained from cross-section I in (A). The excitation peak was omitted. (II) (Blue) NR PL spectrum of CdSe 492 nm NCs was obtained from cross-section II in (A). (III) (Red) Emission spectrum of CdSe 492 nm NCs with an excitation energy of 2.55 eV was obtained from cross-section III in (A). The excitation peak was omitted. (D) (Black) 1D PLE spectrum of CdSe 463 nm MSNs with an emission energy of 2.74 eV. (Blue) NR PL spectrum of CdSe 463 nm MSNs. (Red) Emission spectrum of CdSe 463 nm MSNs with an excitation energy of 2.81 eV. The excitation peak was omitted in the PLE and emission spectrum.

23

Inhomogeneous line broadening is observed for this ensemble, as identified by the

elliptical peaks in the 2D PL. The NC’s mean diameter and size distribution were found

from the ensemble’s room temperature first PLE peak using a previously published

calibration curve.75 The ensemble contains NCs with diame ters of

2.23 nm ± 4%, which is evidence of inhomogeneous broadening. Compared to

measurements taken at 9 K, peaks at room temperature (not shown) are red-shifted in

emission and excitation by approximately 70 meV, which is most likely due to a change

in external strain or an intrinsic shift of band gap to higher energy with lower

temperatures.77 The intensity is also reduced at higher temperatures, likely due to

activated quenching by surface traps.33 Similar changes were observed for single CdTe

studies.78

In comparison, Figure 3.1B shows a 2D PL spectrum measured at 9 K for CdSe

MSNs where inhomogeneous line broadening is not observed. This is deduced from

circular peaks at an emission energy of 2.73 eV. This sample has a room temperature

first absorption peak at 463 nm. In Figure 3.1B, the broad peaks between the emission

energies of 2.45 eV and 2.65 eV are most likely due to low energy (deep) trapped surface

states.

Further quantitative information about the inhomogeneous line broadening of an

ensemble of colloidal NCs can be extracted from a 2D PL spectrum. The axes of a 2D

PL spectrum are excitation energy versus emission energy. A vertical cross-section of a

2D PL spectrum is a 1D PLE spectrum. Each peak in a 2D PL spectrum represents a

shoulder in a 1D PLE spectrum. A non-resonant (NR) PL spectrum can be obtained by

taking a diagonal cross-section through a peak. This spectrum will provide information

on the excitation and emission energies of all sizes of NCs in the ensemble. A horizontal

24

cross-section yields an emission (resonant PL) spectrum, which provides information

about the emission energies a small size distribution of NCs within the ensemble.

From the 2D PL spectrum shown in Figure 3.1A, we can infer more information

about the ensemble of colloidal CdSe 492 nm NCs. A 1D PLE spectrum, shown as I in

Figure 3.1C (black), was obtained from cross-section I in Figure 3.1A. It has an emission

energy of 2.50 eV. The excitation peak was omitted from Figure 3.1C. A NR PL

spectrum was obtained from cross-section II in Figure 3.1A, and is depicted as II in

Figure 3.1C (blue). Its peak is broad due to the excitation of an ensemble of NCs with a

broad size distribution, which results in elliptically shaped 2D PL peaks (as in Figure

3.1A). This NR PL peak has a full width at half maximum (FWHM) of approximately

220 meV ± 20 meV. An emission spectrum was obtained from cross-section III in Figure

3.1A and is shown as III in Figure 3.1C (red). The excitation peak in the emission

spectrum was omitted. Its peak, with a consistent excitation energy of 2.55 eV, has a

FWHM of 103 meV ± 5 meV, which is 53% thinner than the FWHM of the NR PL

spectrum. This difference in FWHM indicates that only a small fraction of NCs within

the ensemble are excited. Therefore, the colloidal CdSe 492 nm NC sample in this study

is comprised of an ensemble of NCs with a size distribution that causes inhomogeneous

line broadening.

It is shown that, within the limits of our instrument, no inhomogeneous line

broadening is observed for the CdSe 463 nm MSNs (shown in Figure 3.1D). For the

CdSe 463 nm MSN sample, the FWHM of the NR PL (blue) and emission (at excitation

energy of 2.81 eV) (red) spectra are 29 meV ± 5 meV and 26 meV ± 5 meV, respectively.

These widths are most likely limited by the resolution of our instrument, which is

approximately 5 meV. Since these two spectra have the same FWHM (within error), it

25

implies that the whole ensemble is composed of MSNs with the same optical properties

as those observed in the emission spectrum (a fraction of the ensemble). This suggests

that the CdSe 463 nm MSNs are monodisperse; therefore, they do not exhibit

inhomogeneous line broadening, within the resolution of our instrument. The 1D PLE

spectrum (black) of the CdSe 463 nm MSNs is also shown in Figure 3.1D. It has an

emission energy of 2.74 eV. The excitation peak was omitted in the PLE and emission

spectrum in Figure 3.1D.

Even more information can be extracted from the 2D PL. In the colloidal CdSe

492 nm NCs, the excitation energy difference between the first two excitonic peaks is

0.27 eV ± 0.015 eV, which is comparable to the previously reported value of 0.25 eV for

similarly sized QDs (observed at 10 K).38 For the CdSe 463 nm MSNs, the difference in

excitation energy between the first two excitonic peaks in the 2D PL spectrum is

0.16 eV ± 0.015 eV, which is smaller than in previous reports,38 indicating that the optical

properties of the MSNs might be different than those of QDs.

For ensembles of colloidal CdSe 492 nm NCs with a distribution of diameters, the

Stokes shift in the first excitonic peak was found. The Stokes shift changes

approximately linearly with respect to the emission and excitation energies. NCs in the

ensemble with emission energy of 2.522 eV ± 0.005 eV and 2.617 eV ± 0.005 eV have

Stokes shifts of 46 meV ± 5 meV and 58 meV ± 5 meV, respectively. It should be noted

that the change in Stokes shift with NC size is not consistent for each peak in the 2D PL

spectrum.

26

3.1.2 Homogeneous Line Broadening of CdSe 463 nm Magic-Sized

Nanocrystals from 73 K to Room Temperature

Emission of thermal acoustic phonons44, 45 causes homogeneous line broadening,

which increases with increasing temperature. Homogeneous line broadening is negligible

at low temperatures.45 Size dependent properties are obscured by inhomogeneous line

broadening in previous studies of NC ensembles.9 Since inhomogeneous line broadening

is absent for CdSe 463 nm MSNs, homogeneous line broadening can be clearly observed

and characterized.

A room temperature 2D PL spectrum of CdSe 463 nm MSNs is shown in Figure

3.2A. Compared to the 9 K spectrum (Figure 3.1B), room temperature emission peaks in

the 2D PL spectrum are red shifted by approximately 70 meV and the intensity is

reduced.78 At 9 K, the FWHM of the first excitonic peak, obtained by averaging the

FWHM of the NR PL and emission spectra, was 28 meV ± 5 meV. At room temperature,

the FWHM of the first excitonic peak was 77 meV ± 5 meV, which is approximately

180% broader than at 9 K. This room temperature value is comparable to previously

observed single QD emission bandwidths, which can be as narrow as 50 meV.79 The

change in FWHM is solely caused by homogeneous broadening.

Figure 3.2B shows the average FWHM of the NR PL and emission spectra for the

first excitonic peak measured from 73 K to 300 K. Homogenous line broadening caused

a change in FWHM. Homogenous line broadening above 73 K increases linearly with

increasing temperature. Observation of this linear relationship is rare, since

inhomogeneous line broadening is usually present in other studies.

27

Figure 3.2: FWHM of first excitonic peaks exhibiting homogeneous line broadened. (A) 2D PL spectrum of CdSe 463 nm MSNs measured at room temperature. (B) FWHM vs. temperature for the first excitonic peak of CdSe 463 nm MSNs, obtained by averaging the FWHM of the NR PL and emission spectra.

It should be noted that deep trapped surface states are not observed in the room

temperature 2D PL spectrum (Figure 3.2A). At 9 K (Figure 3.1C), broad peaks located at

emission energies 0.1 eV to 0.3 eV lower than the MSN excitonic peaks are evidence of

deep trapped surface states. Therefore, there may be a thermally activated transition

between the deep trapped surface states and excitonic energy levels of the MSN.

3.2 Characterization of CdSe 463 nm Magic-Sized

Nanocrystals

In this Section, characterization of CdSe 463 nm MSNs is discussed. It is

apparent from STEM and confocal microscopy images that CdSe 463 nm MSNs arrange

28

Figure 3.3: Schematic of embedded MSN cylinders and MSN aggregates. Diameters of individual MSNs are 2.05 nm. MSNs can assemble into two aggregated configurations. (A) Embedded MSN cylinders, comprising MSNs embedded in a fatty acid matrix, range in size with lengths of approximately 10 µm and widths of 0.1 µm to 1 µm. (B) MSN aggregates, comprising close-packed monolayers of MSNs, are approximately 80 nm × 30 nm × 2 nm.

in two aggregated configurations, illustrated in Figure 3.3 and described below. CdSe

MSNs readily crashed out of solution, suggesting that these configurations most likely

form prior to STEM preparation.

STEM and confocal microscopy images aid in the characterization of MSN

aggregated configurations. One configuration is shown in Figures 3.4A-3.4C. Figures

3.4A and 3.4B were taken by STEM; Figure 3.4C is a confocal microscopy image. At

low magnification (Figure 3.4A), this configuration appears as long cylinders, which at

higher magnification (Figure 3.4B, lower left) are clearly made up of MSNs embedded in

a fatty acid matrix and suspended from one another. We refer to this configuration as

‘embedded MSN cylinders’. These cylinders range in size with a width of 0.1 µm to

29

Figure 3.4: STEM and confocal microscopy images of CdSe 463 nm MSNs. Embedded MSN cylinders are shown in STEM images (A), (B - bottom left corner), and a confocal microscopy image (C). MSN aggregates are shown in STEM images (D, E), and a confocal microscopy image (F). (A), (B - bottom left corner) STEM images and (C) a confocal microscopy image of embedded MSN cylinders. (D, E) STEM images and (F) a confocal microscopy image of MSN aggregates.

1 µm and a length on the order of 10 µm. In Figure 3.4B, embedded MSNs (bottom left

corner) overlap with a cluster of MSN aggregates (top right corner), described in more

detail below. From this image, it is difficult to estimate the thickness of the embedded

MSN structure. From STEM, the diameters of individual MSNs were found to be

2.1 nm ± 0.3 nm, which corresponds to the average diameter predicted by the first

absorption peak.75

30

The second configuration is a close-packed monolayer of MSNs, which we refer

to as ‘MSN aggregates’. MSN aggregates are shown in Figures 3.4D-3.4F. Figures 3.4D

and 3.4E are STEM images; Figure 3.4F is a confocal microscopy image. An individual

MSN aggregate can be seen in Figure 3.4E. It has a length of 80 nm ± 3 nm and width of

30 nm ± 3 nm. A straight white line indicates a fold in an MSN aggregate. From a fold,

the thickness of a MSN aggregate can be measured to be 2.0 ± 0.3 nm. The width of an

MSN aggregate is equal to the diameter of a MSN; therefore, MSN aggregates are

monolayers of close-packed MSNs. Similar aggregates have been observed for GaSe.80

Clusters of MSN aggregates were often observed at junctions between two

embedded MSN cylinders, as shown in Figure 3.4D (magnified from Figure 3.4A).

Clusters of MSN aggregates range in size from hundreds of nm to tens of µm, as shown

in Figures 3.4D-3.4F.

Narrow PLE peaks provide further evidence that MSN aggregates are close-

packed monolayers of MSNs. In Figure 3.1D (black), this sample exhibits narrow PLE

features consistent with three-dimensionally confined excitons (see also narrow

absorption features shown in Figure 3.7, below). A continuous crystal lattice over an

entire MSN aggregate would give rise to a one-dimensionally confined exciton. One-

dimensionally confined excitons characteristically have broad absorption features.14

Therefore, due to the narrow optical features, MSN aggregates do not have a continuous

crystal lattice over the entire MSN aggregate. That is, MSN aggregates are composed of

close-packed MSN that each have three-dimensionally confined excitons. The excitons

are not delocalized over the aggregates.

We did not observe crystal structure within MSN aggregates. Upon the

aggregation of MSNs, individual MSN crystal lattices are not be aligned. However,

31

another study on similar MSNs claims to have observed crystal structure within both

individual MSNs and MSN aggregates.73

The confocal microscopy images in Figures 3.4C and 3.4F emitted at a

wavelength of 466 nm ± 5 nm (shown in yellow). Therefore, the embedded MSNs

(Figure 3.4C) and MSN aggregates (Figure 3.4F) emit at the same wavelength, within

error. This provides further evidence that the two aggregated configurations are

composed of the same MSNs. The embedded MSN cylinders are clearly visible in Figure

3.4C, where the laser power was increased using an acousto-optical tunable filter

(AOTF); they are not visible at lower laser power, as in Figure 3.4F. Additional

arguments supporting the characterization of the MSN aggregates structure are discussed

in Sections 3.3.3 and 3.3.4.

Multiple attempts were made to isolate the different configurations of MSNs;

however, they were unsuccessful. All configurations readily crashed out of solution,

even without centrifugation or washing with methanol. Filtration was not attempted

because of the entwined nature of the two configurations of MSNs, and because larger

quantities of sample were not available.

3.3 Identifying the Origin of Sub-peaks within the Excitonic

Peaks in Two-Dimensional Photoluminescence Spectra

In the 2D PL spectrum of CdSe 463 nm MSNs measured at 9 K, excitonic peaks

are not obscured by homogeneous or inhomogeneous line broadening. The absence of

32

this convolution of signals enables analysis of sub-peaks within the excitonic peaks. In

this Section, the origin of these sub-peaks is determined.

3.3.1 High Resolution Two-Dimensional Photoluminescence

Spectrum of the First Excitonic Peak of the CdSe 463 nm Magic-

Sized Nanocrystals at 9 K

Figure 3.5A is a high resolution 2D PL spectrum of the first excitonic peak of the

CdSe 463 nm MSNs measured at 9 K. Four sub-peaks are observed within the first

excitonic peak. The four sub-peaks are labelled I – IV in Figure 3.5A and the positions of

their maxima are given in Table 1. Their positions were resolved by fitting PLE and

emission spectra to Gaussians. In Figures 3.5B-3.5F, the solid red lines are experimental

data from cross-sections of 2D PL spectrum, solid grey lines are Gaussian fits, and

dashed blue lines are sums of the Gaussian fits. Peaks I and III were obtained by taking

PLE spectra at an emission energy of 2.729 eV (Figure 3.5B) and peaks II and IV at an

emission energy of 2.745 eV (Figure 3.5C). Emission spectra of peak I (Figure 3.5D), II

(Figure 3.5E), and III (Figure 3.5F) have excitation energies of 2.818 eV, 2.798 eV, and

2.777 eV, respectively. The location of peak IV was deduced from the PLE spectrum

shown in Figure 3.5C.

33

Figure 3.5: High resolution optical spectra of CdSe 463 nm MSNs’ first excitonic peak measured at 9 K. (A) 2D PL spectrum with sub-peak maxima labelled I – IV. (B-F) (Solid red line) Experimental data obtained from cross-sections of 2D PL spectrum, (solid grey lines) Gaussian fits, and (dashed blue lines) sums of the Gaussian fits. PLE spectra of (B) peaks I and III at an emission energy of 2.729 eV, and (C) peaks II and IV at an emission energy of 2.745 eV. Emission spectra of peaks (D) I, (E) II, and (F) III at excitation energies of 2.818 eV, 2.798 eV, and 2.777 eV, respectively.

Table 3.1: Emission and excitation energies of the sub-peak maxima within the first excitonic peak of CdSe 463 nm MSNs measured at 9 K.

Emission Energy (eV) ± 0.005 eV

Excitation Energy (eV) ± 0.005 eV

I 2.728 2.821 II 2.747 2.799 III 2.726 2.771 IV 2.745 2.754

34

3.3.2 High Resolution Two-Dimensional Photoluminescence

Spectrum of the First Excitonic Peak of the CdSe 463 nm Magic-

Sized Nanocrystals at 92 K

At temperatures above 92 K, the two peaks with lower emission energy (I and III)

are no longer distinguishable from noise. Figure 3.6A is a high resolution 2D PL

spectrum of the first excitonic peak of the CdSe 463 nm MSNs at 92 K. In Figure 3.6B

and 3.6C, the solid red lines are experimental data obtained from cross-sections of 2D PL

spectrum, solid grey lines are Gaussian fits to peaks, and dashed blue lines are the sums

of the Gaussian fits. Figure 3.6B is the PLE spectrum of peaks II and IV at an emission

energy of 2.748 eV. Figure 3.6C is the emission spectrum of peak II at an excitation

energy of 2.794 eV.

An additional change in the 2D PL spectrum with increased temperature is the

change in the relative energy difference between peaks. At 9 K, the excitation energy

difference between peak II and IV is 45 meV ± 5 meV, and at 92 K it decreases to

37 meV ± 5 meV. The reason for this difference in excitation energy is discussed below.

35

Figure 3.6: High resolution optical spectra of CdSe 463 nm MSN’s first excitonic peak measured at 92 K. (A) 2D PL spectrum with sub-peak maxima labelled II and IV. At this temperature, peaks I and III are not resolved in the 2D PL spectrum. (B, C) (Solid red line) Experimental data obtained from cross-sections of 2D PL spectrum, (solid grey lines) Gaussian fits, and (dashed blue lines) sums of the Gaussian fits. (B) PLE spectrum of peaks II and IV at an emission energy of 2.748 eV. (C) Emission spectrum of peak II at an excitation energy of 2.794 eV.

Table 3.2: Emission and excitation energies of sub-peak maxima within the first excitonic peak of CdSe 463 nm MSNs measured at 92 K.

Emission Energy (eV) ± 0.005 eV

Excitation Energy (eV) ± 0.005 eV

II 2.748 2.794 IV 2.748 2.757

36

3.3.3 Comparison of Room Temperature Absorption and

Photoluminescence Excitation Spectra

At room temperature, the absorption and PLE spectra of the CdSe 463 nm MSNs

are not superimposable and, moreover, the intensity of peaks in the absorption spectrum

change with reaction time during sample synthesis.73 Yu et al. monitored the synthesis of

a CdSe 463 nm MSN with absorption spectroscopy.73 They found that initially the first

excitonic peak maximum was at 454 nm with a corresponding PLE peak of 456 nm,

which is close to our observed 458 nm PLE peak. With longer reaction time, a peak at

463 nm grew in and the 454 nm decreased and is no longer visible after 60 min.73 The

room temperature absorption spectrum (dashed red line) and PLE spectrum (solid blue

line) for the CdSe 463 nm MSNs are normalized at 463 nm and are shown in Figure 3.7.

The absorption and PLE spectra do not correlate at lower wavelengths because light

scatters off aggregate configurations of MSNs, which increases the intensity of the

absorption spectrum with decreasing wavelength. The first excitonic peak in the

absorption spectrum was fit to a Gaussian and has a sole maximum at 463 nm ± 1 nm.

The first excitonic peak in the PLE spectrum has two maxima (sub-peaks) at

458 nm ± 1 nm and 464 nm ± 1 nm, which correspond to sub-peaks II and IV in Figure

3.6A, respectively. This is consistent with samples reacted for 60 min. or more.

Therefore, from the work done by Yu et al.,73 sub-peak II appears initially during

synthesis, and sub-peak IV grows in with increased reaction time. After 60 min., sub-

peak II is no longer visible in the absorption spectrum; however, it’s corresponding PLE

sub-peak is still present. With longer reaction times, the absorption intensity of sub-peak

II is lower than sub-peak IV, but they have comparable emissions. Thus, the aggregated

37

Figure 3.7: Absorption and PLE spectra of CdSe 463 nm MSNs measured at room temperature. (Dashed red line) Absorption spectrum and (solid blue line) PLE spectrum are normalized at 463 nm. These two spectra do not correlate at all wavelengths.

configuration corresponding to sub-peak II has a higher quantum yield than the

configuration corresponding to sub-peak IV.

3.3.4 Discussion and Determination of Sub-peaks within Excitonic

Peaks

The origin of the four sub-peaks within the first excitonic peak of the CdSe

463 nm MSNs is deduced by considering the two aggregated configurations of the MSNs,

information from the 2D PL at 9 K and room temperature, and the intensity changes in

the absorption and PLE spectra with reaction time. It is predicted that sub-peaks II and

IV correspond to embedded MSNs and MSN aggregates, respectively. Sub-peaks I and

38

III are believed to be due to emission from a surface state after relaxation from the bright

state of embedded MSNs and MSN aggregates, respectively.

It is well known that in molecular aggregates, the molecular singlet (bright) state

is split into two energy levels due to electronic coupling. Therefore, the sole molecule

and molecular aggregate will have slightly different excitation energies. In aggregated

NCs, the magnitude of electronic coupling between states depends on the intensity of the

transition to that state.80 Singlet states have strong electronic coupling because the

transition from the ground state to a singlet state is allowed. This will cause the singlet

state to split into two states, with the intensity of the electronic coupling equal to half of

the energy difference between the new states. The aggregated NC will excite to the lower

split energy state. Figure 3.8 is a model for the energy levels corresponding to the four

sub-peaks within the first excitonic peak. The (individual) embedded MSNs will excite

to an unshifted bright state giving rise to sub-peak II, which corresponds to State 1 in

Figure 3.8. The MSN aggregates will excite to a lower energy split bright state,

45 meV ± 5 meV below the original bright state (i.e. the difference in excitation energy

of sub-peak II and IV in Table 1), giving rise to sub-peak IV, which corresponds to State

2 in Figure 3.8.

The above assignment of sub-peaks II and IV as embedded MSNs and MSN

aggregates, respectively, is further confirmed by their quantum yields. As indicated in

Section 3.3.3, the configuration corresponding to sub-peak II has a higher quantum yield

than the configuration corresponding to sub-peak IV. NCs that are passivated more

effectively with organic ligands will have less of a tendency to aggregate and will have a

higher quantum yield. MSN aggregates form because MSNs are not sufficiently

39

Figure 3.8: An energy level model consistent with the position of sub-peaks within the first excitonic peak of CdSe 463 nm MSNs. (State 1) Bright state of embedded MSNs. (State 2) Bright state of MSN aggregates, 45 meV ± 5 meV lower than State 1 due to electronic coupling. (State 3) Dark state of embedded MSNs. (State 4) Dark state of MSN aggregates. State 3 and 4 have approximately the same energy. (State 5) A surface state is mixed with the excitonic states of embedded MSNs and MSN aggregates. The surface state is 19 meV ± 5 meV lower than the dark states. Absorption occurs to State 1 or 2 and emission occurs from States 3, 4, or 5.

passivated and embedded MSNs are passivated more effectively. Therefore, embedded

MSNs will have a higher quantum yield than MSN aggregates.

Additional evidence that embedded MSNs and MSN aggregates correspond to

sub-peaks II and IV, respectively, is obtained from an intensity change in absorption

spectra with reaction time. Since MSNs within an embedded MSN are separated by fatty

acids, it is predicted that they will have optical properties indistinguishable from

individually passivated MSNs. Since sub-peak II appears first during synthesis, it is

predicted that individually passivated MSNs (embedded MSNs) would also form first

during synthesis. Sub-peak IV appears with increased reaction time, and it is predicted

40

that over time individual MSNs would aggregate to form MSN aggregates.

Experimentally, sub-peak IV has a high intensity absorption peak because there is a large

quantity of densely MSN aggregates, as is evident from Figure 3.4. Meanwhile, sub-peak

II has a low intensity absorption peak because despite comprising large cylinders,

embedded MSNs are less densely packed than MSN aggregates.

We observed that sub-peaks II and IV have the same emission energy, within

error. Sub-peak II emits from State 3 in Figure 3.8, which is a dark state for embedded

MSNs (individual MSNs). Peak IV emits from State 4 in Figure 3.8, which is a dark state

for the MSN aggregates. State 3 and 4 have the same emission energy because dark

states have low oscillator strength, meaning the electronic coupling and splitting is

negligible. State 3 is 52 meV ± 5 meV below State 1 (corresponding to the Stokes shift

of the embedded MSNs) and State 4 is 9 meV ± 5 meV below State 2 (corresponding to

the Stokes shift of the MSN aggregates).

It is predicted that peaks I and III are due to emission from a surfaces state (State

5 in Figure 3.8), which is mixed with excitonic states of the embedded MSNs and MSN

aggregates, respectively. This allows the transfer of energy from MSN excited states to a

surface state. It is predicted that after excitation to bright states of embedded MSNs or

MSN aggregates, relaxation can occur to either the sur face state or a dark state. At

temperatures above 92 K, sub-peaks I and III are no longer observed (discussed in

Section 3.3.2). At 92 K, there is insufficient thermal energy to excite a MSN from the

mixed surface state to a dark state. This decrease in signal could be related to a similar

decrease in peak intensity with increased temperature corresponding to deep trapped

states (Figure 3.1C and 3.2A). Above 92 K, sub-peaks I and III may not be observed

either because recombination from the mixed surface state is less favourable, or the

41

signal’s intensity could decrease to noise level with increased temperature.78 The energy

difference between State 5 and State 3 (or 4) is 19 meV ± 5 meV, which corresponds to

the difference between emission energies for sub-peaks I and II, and sub-peaks III and

IV, in Figure 3.5A.

Therefore, it is predicted that sub-peaks II and IV correspond to embedded MSNs

and MSN aggregates, respectively. We suspect that sub-peaks I and III are due to the

emission from a surface state, which is mixed with embedded MSNs and MSN

aggregates excitonic states, respectively. These conclusions were determined by

considering the two aggregated configurations of the MSNs, analyzing the 2D PL at 9 K

and room temperature, and intensity changes in the absorption and PLE spectra with

reaction time.

3.3.5 Calculation of the Electronic Coupling in Aggregated Magic-

Sized Nanocrystals

Theoretical calculations of the electronic coupling for MSN aggregates is of the

same order of magnitude as the experimental electronic coupling responsible for splitting

the bright state in MSN aggregates. Assuming that MSN aggregates are composed of a

close-packed monolayer of MSNs, each MSN has six nearest neighbours. The electronic

coupling constant between two NCs is inversely proportional to the NC radius cubed.47

For two 2 nm CdSe QDs oriented head-to-tail with center-to-center separation of 2 nm,

the coupling constant is approximately 50 cm-1. Assuming electronic coupling only

occurs between adjacent MSNs, the total energy lowering of the bright state compared to

a lone QD’s bright state is approximately 130 cm-1. Theoretically, the magnitude of

42

electronic coupling is equal to half the energy difference between the split bright states.

Experimentally, the energy difference between State 1 and 2 in Figure 3.8 is 45 meV

(which is half the energy difference between the split bright states), which yields an

electronic coupling of 363 cm-1. The theoretical coupling is smaller, but within the same

order of magnitude, as the experimentally derived coupling.

3.4 Unsatisfactory Models for Sub-peaks within Excitonic

Peaks

Many spectroscopic techniques were unable to determine the origin of four sub-

peaks in the first excitonic peak. One major difficulty was that aggregated configurations

of MSNs readily crash out of solution and scatter light, which obscure spectroscopy

signals. Fluorescence time decay spectroscopy was measured, but the signal was

scattered. Pump probe spectroscopy was not attempted because scattering would affect

the signal and, due to sample aggregation and consequent decrease in dispersed MSN

concentration, a high enough optical density could not be obtained.

3.4.1 Acoustic and Longitudinal Optical Phonon-Assisted

Transitions

Acoustic and LO phonon-assisted transitions play a role in excitation and

recombination properties of NCs.81 The multiple sub-peaks in the first excitonic peak are

not due to LO phonons because the emission and excitation energy difference between

sub-peaks is not equal to the known LO phonon energy of 25 meV (see Tables 1 and 2

43

for maxima of peaks at 9 K and room temperature, respectively). Additionally, the

relative positions of peaks change with temperature, which is not characteristic of

phonon-assisted transitions.

3.4.2 Fine Structure

The fine structure of the first excitonic state of CdSe NCs is split into 8 levels due

to electron-hole exchange interactions, anisotropies caused by the crystal field, and the

asymmetry of NCs.19 These levels are tens of meV apart, with order and spacing that

depends on the band gap, shape, size, and structure of the NC.18 Attempts were made to

find a fine structure model based on the theoretical energy levels for a spherical CdSe NC

with a diameter of 2 nm18 that could account for the four sub-peaks. A sufficient fine

structure model was not found because several discrepancies were not accounted for.

First, the model would require two specific decay pathways and transitions from one

pathway to the other would not be allowed. Transitions between fine structure states

have been observed;25 therefore, the restriction to relax along one decay pathway could

not be justified. Alternatively, if fine structure states could relax through both pathways,

then additional sub-peaks should have been present in the first excitonic peak. Second,

the sub-peak predicted to excite to and emit from the ±1L state (sub-peak IV) was more

intense than the sub-peak predicted to excite to the ±0U state and emit from the ±1L state

(sub-peak II), which has a higher oscillator strength (see Section 1.3). Third, a sub-peak

was assigned to the excitation of a dark state plus a phonon assisted transition (sub-peak

III), which should be a weak transition. This assignment is unlikely because the sub-peak

intensity was similar to the intensity of the sub-peak predicted to excite to the ±0U state,

44

which has high oscillator strength. From the above complications it is evident that the

four sub-peaks in the first excitonic peak are most probably not due to fine structure

states.

3.5 Comparison of CdSe 463 nm Magic-Sized Nanocrystals

to Previously Synthesized Nanoribbons and Platelets

We have shown that the CdSe 463 nm MSNs orient themselves in two aggregated

configurations, embedded MSNs and MSN aggregates, which have similar optical

properties. We concluded that MSN aggregates were comprised of close-packed

monolayers of MSNs (discussed in Section 3.2) because their absorption features are

characteristic of three-dimensionally confined excitons, not one-dimensionally confined

excitons.

It is speculated that previously published structures identified as nanoribbons and

platelets are composed of monolayers of close-packed MSNs. Similar narrow absorption

features have been observed in CdSe nanoribbons82 and platelets83. The synthesis of

platelets83 and MSNs72 are similar. It is well known that optical properties depend on the

structure of the NCs.18, 38 MSNs, nanoribbons, and platelets have similar optical

properties. For example, the room temperature first absorption peaks of MSNs,

nanoribbons, and platelets are 463 nm, 449 nm, and 462 nm ± 2 nm, respectively.

Furthermore, the difference between the first two absorption features of the MSNs,

nanoribbons, and platelets are 26 nm, 26 nm, and 27 nm, respectively. Additionally, the

MSN aggregates, nanoribbons, and platelets have similar thickness (smallest dimension)

of 2.05 ± 0.3 nm, 1.4 nm,82 and approximately 1.9 nm,83 respectively. Since CdSe MSN

45

aggregates, nanoribbons, and platelets have similar thickness, it is not surprising that they

have similar, narrow optical properties. For all of these structures, narrow optical

properties characteristic of three-dimensionally confined excitons are observed.

Therefore, it is predicted that close-packed MSN aggregates play a role in forming

nanoribbons and platelets during synthesis.

3.6 Summary

A colloidal ensemble of CdSe 492 nm NCs exhibited inhomogeneous line

broadening due to its broad size distribution. In Section 3.1, the inhomogeneous line

broadening was analyzed. In contrast, CdSe 463 nm MSNs did not exhibit

inhomogeneous line broadening. The absence of this convolution of signal enabled the

analysis of homogeneous line broadening. Homogeneous line broadening was found to

increase linearly with temperature for CdSe 463 nm MSNs.

In Section 3.2, we determined that CdSe 463 nm MSNs formed two aggregated

configurations: embedded MSN cylinders and MSN aggregates. A dispersion of CdSe

463 nm MSNs readily precipitated from solution, implying that these aggregated

configurations formed prior to STEM preparation.

We examined four sub-peaks found within the first excitonic peak of CdSe

463 nm MSNs, in Section 3.3. Two higher emission energy sub-peaks were caused by

the absorption and emission of embedded MSNs and MSN aggregates. Two lower

emission energy sub-peaks arose from mixing between surface states and excitonic states

of the two aggregated configurations.

46

In Section 3.5, previously published nanoribbons and platelets were compared to

MSNs. These three structures had similar thicknesses (smallest dimension) and exhibit

comparable narrow absorption features. Optical properties depended on the structure of

NCs;18, 38 therefore, similar optical features suggested that nanoribbons and platelets are

in fact composed of close-packed MSNs.

47

4 Direct Evidence of Energy Transfer

within CdTe 427 nm and 500 nm Magic-

Sized Nanocrystals

Direct evidence of Förster energy transfer between 427 nm and 500 nm CdTe

MSNs is presented in this chapter. Donor emission and acceptor absorption spectral

overlap is observed, and this overlap is analyzed in Section 4.1. To further characterize

energy transfer, the composition of CdTe 427 nm and 500 nm MSNs is investigated in

Section 4.2. The mixture of MSNs is composed of two aggregated configurations:

embedded MSN cylinders and MSN aggregates. In Section 4.3, it is determined that

Förster energy transfer occurs between these two sizes of MSNs in both aggregated

configurations.

4.1 Two-Dimensional Photoluminescence Spectrum of

CdTe 427 nm and 500 nm Magic-Sized Nanocrystals

A 2D PL spectrum can give direct evidence for Förster energy transfer between

MSNs. In this Section, we will analyze a cross-peak in the 2D PL spectrum of CdTe

427 nm and 500 nm MSNs to determine the Förster energy transfer in these samples. We

will find that the spectral overlap of the donor (emission) and acceptor (absorption)

spectra are comparable to theoretical calculations.

48

Figure 4.1: Optical spectra of CdTe 427 nm and 500 nm MSNs measured at 9 K. (A) 2D PL spectrum of CdTe 427 nm and 500 nm MSNs. A cross-peak is present at the emission energy of the 500 nm MSNs and at the excitation energy of the 427 nm MSNs. (B) (Solid blue line) Emission spectrum of the cross-peak with an excitation energy of 3.03 eV, obtained from a cross-section of (A). (Dashed blue line) A Gaussian fit to the first excitonic peak at 2.97 eV for CdTe 427 nm MSNs. (Solid red line) PLE spectrum of the cross-peak with an emission energy of 2.54 eV, obtained from a cross-section of (A). (Dashed red line) A Gaussian fit to the second excitonic peak at 2.92 eV for CdTe 500 nm MSNs.

Table 4.1: Emission and excitation energies of the first excitonic peak for CdTe 427 nm MSNs, CdTe 500 nm MSNs, and their cross-peak. Emission Energy (eV) Excitation Energy (eV) First excitonic peak: 427 nm MSNs 2.97 eV 3.00 eV First excitonic peak: 500 nm MSNs 2.56 eV 2.59 eV First excitonic peak: cross-peak 2.54 eV 3.03 eV

49

Figure 4.1A shows a 2D PL spectrum of 427 nm and 500 nm CdTe MSNs

measured at 9 K. A cross-peak is observed in the 2D PL spectrum at the emission energy

of the 500 nm MSNs and at the excitation energy of the 427 nm MSNs. The position of

the first excitonic peaks of 427 nm and 500 nm MSNs, and the cross-peak between the

first excitonic peaks, are given in Table 1. Figure 4.1B shows two 1D spectra obtained

from cross-sections of the 2D PL spectrum (Figure 4.1A). The first is an emission

spectrum of the cross-peak with an excitation energy of 3.03 eV (solid blue line). The

427 nm MSN’s first excitonic peak at 2.97 eV was fit to a Gaussian (dashed blue line).

The second is a PLE spectrum of the cross-peak with an emission energy of 2.54 eV

(solid red line). The 500 nm MSN’s second excitonic peak at 2.92 eV was fit to a

Gaussian (dashed red line).

Förster energy transfer occurs between the donors (427 nm MSNs) and the

acceptors (500 nm MSNs). In Figure 4.1A, the cross-peak arises from energy being

transferred from the emitting state of 427 nm MSNs to the exc ited state of 500 nm MSNs.

In Förster energy transfer theory, the overlap of the donor’s emission spectrum (dashed

blue line, Figure 4.1B) and the acceptor’s absorption spectrum (dashed red line, Figure

4.1B) is required. The normalized overlap between the donor emission and acceptor

absorption spectra is 5.58×10-4 cm, which is on the order predicted by theory.84

Therefore, there is sufficient spectral overlap for Förster energy transfer. Thus, the 2D

PL spectrum of the 427 nm and 500 nm MSNs gives direct evidence for Förster energy

transfer.

50

4.2 Characterization of CdTe 427 nm and 500 nm Magic-

Sized Nanocrystals

In this Section, it is determined that CdTe 427 nm and 500 nm MSNs are

composed of two aggregated configurations: embedded MSN cylinders and MSN

aggregates. Their structures and optical properties are discussed. The two aggregated

configurations of CdTe MSNs are similar to configurations of CdSe 463 nm MSNs

discussed in Chapter 3.

The aggregated configurations of the mixture of CdTe 427 nm and 500 nm MSNs

are visible in STEM images in Figures 4.2A-4.2B, and confocal microscopy images in

Figures 4.2C-4.2I. In the confocal microscopy images, green and red regions represent

fluorescence from the 427 nm and 500 nm MSNs, respectively.

MSN aggregates and clusters of MSN aggregates are visible in Figures 4.2A-4.2F.

In Figure 4.2A there is evidence of sheet- like structures, which are assumed to be

monolayers of close-packed MSNs similar to previously discussed of CdSe MSN

aggregates (Chapter 3). However, the CdTe MSN aggregates vary in size and shape,

which is not consistent with CdSe MSNs. The resolution of the STEM images in Figures

4.2A-4.2B are low because the sample contained a large excess of organic material (e.g.

synthesis by-products; excess ligand molecules). Therefore, it is difficult to identify the

exact structure of the MSN aggregates. Clusters of MSN aggregates on the order of

hundreds of nanometers to tens of micrometers are observed.

Embedded MSNs consist of MSNs held at a distances from one another by fatty

acids. They form cylinders, as shown in Figures 4.2A, 4.2C, 4.2G-4.2I. Embedded MSN

cylinders vary in width from 10-50 nm and in length from 10-20 µm. The distance

51

Figure 4.2: STEM and confocal microscopy images of CdTe 427 nm and 500 nm MSNs. STEM images of (A) embedded MSN cylinders and clusters of MSN aggregates, and (B) clusters of MSN aggregates. (C-I) Confocal microscopy images of (red) CdTe 427 nm and (green) 500 nm MSNs. (C) Low magnification image of fluorescence from both sizes of MSNs. (D-F) Fluorescence from the same cluster of MSN aggregates: (D) superposition of fluorescence from both sizes of MSNs; fluorescence from (E) 427 nm MSNs, and (F) 500 nm MSNs. (G-I) Fluorescence from the same embedded MSNs: (G) superposition of fluorescence from both sizes of MSNs; fluorescence from (H) 427 nm MSNs, and (I) 500 nm MSNs.

52

between the MSNs in the fatty acid matrix cannot be determined from the STEM images

because embedded MSN cylinders are three-dimensional, and multiple overlapping layers

are imaged. The two sizes of MSNs (in the mixture of 427 nm and 500 nm MSNs) could

not be distinguished in the STEM images. On average, individual MSNs in this mixture

are approximately 2.2 nm ± 0.3 nm in diameter, as determined by STEM.

The location and configuration of the two sizes of CdTe MSNs can be determined

from the confocal microscopy images in Figures 4.2C-4.2I. The green and red regions

represent fluorescence from the 427 nm and 500 nm MSNs, respectively. Figure 4.2C

shows typical fluorescence from this sample at low magnification. It shows both sizes of

CdTe MSNs and the two aggregated configurations.

A cluster of MSN aggregates, comprised of both 427 nm and 500 nm MSNs, is

shown in Figures 4.2D-4.2F. Figure 4.2D is the superposition of the fluorescence from

both sizes. The emission from 427 nm and 500 nm MSNs are shown individually in

Figures 4.2E and 4.2F, respectively. The two sizes of MSNs are not evenly distributed

throughout the MSN aggregates; however, they overlap in many regions. This implies

that MSNs show a preference for aggregation with other MSNs of the same size.

An embedded MSN cylinder is shown in Figures 4.2G-4.2I. Figure 4.2G is a

superposition of the fluorescence from both sizes; the emission from the 427 nm and

500 nm MSNs are shown individually in Figures 4.2H and 4.2I, respectively. These three

images demonstrate that the two sizes of MSNs are evenly distributed throughout the

embedded MSN cylinders. That is, there is no preference for MSNs of the same size to

embed in a fatty acid matrix.

53

4.3 Sub-Peaks in Excitonic Peaks

In this Section, sub-peaks within excitonic peaks are analyzed and Förster energy

transfer between MSNs is analyzed in more depth. We find that energy transfer occurs

between CdTe 427 nm and 500 nm MSNs in both aggregated configurations.

Excitonic peaks in the 2D PL spectrum (Figure 4.1A) were fit to Gaussians and

multiple sub-peaks were resolved from within excitonic peaks. Figure 4.3 is a contour

plot of the 2D PL spectrum in Figure 4.1A and the black circles show the locations of

maxima indicating multiple sub-peaks. Only the sub-peaks within the first excitonic

peaks of each size of MSNs, and their cross-peak, are displayed. Multiple sub-peaks in

other excitonic peaks were not studied. The observation of multiple sub-peaks in CdTe

MSNs is consistent with the multiple sub-peaks observed in the first excitonic peak of

CdSe 463 nm MSNs (discussed in Section 3.3).

We infer that the multiple sub-peaks in the CdTe and CdSe samples have the

same origin (discussed thoroughly in Chapter 3). That is, within an excitonic peak, the

sub-peak at highest emission and lowest excitation energy is due to MSN aggregates; the

sub-peak at highest emission energy and highest excitation energy is due to embedded

MSNs; the sub-peaks at lower emission energy correspond to emission from a surface

state, which is mixed with the excitonic states of the MSN aggregates (lowest emission,

lowest excitation sub-peak) or embedded MSNs (lowest emission, highest excitation sub-

peak). The four sub-peaks are not well resolved for 427 nm MSNs.

The cross-peak in Figure 4.3 has four sub-peaks because emission is possible

from dark states of either embedded MSNs or MSN aggregates (peaks at higher emission

energy) or the surface state, which is mixed with the aggregated orientations’ excitonic

54

Figure 4.3: Contour plot of the 2D PL spectrum for CdTe 427 nm and 500 nm MSNs. Black circles mark sub-peaks within the excitonic peaks.

states (peaks at lower emission energy). It was deduced from the cross-peak that energy

transfer occurs between the two sizes of MSNs in both aggregated configurations. The

multiple sub-peaks in the cross-peak with higher excitation energy suggest that there is

energy transfer from a 427 nm embedded MSN (donor) to a 500 nm embedded MSN

(acceptor). The multiple sub-peaks in the cross-peak with lower excitation energy

suggest there is energy transfer from a 427 nm aggregated MSN (donor) to a 500 nm

aggregated MSN (acceptor). These statements are supported by the confocal microscopy

images in Figures 4.2D-4.2I, which show that both sizes of MSNs are close together in

both configurations. In both aggregated configurations, the distance between MSN was

estimated to be on the order of a few nanometers. Energy transfer could occur in both

structures when the donor and acceptor are a few nanometers apart.47, 60 Energy transfer

is observed between the two sizes of MSNs in both embedded MSN cylinders and MSN

aggregates.

55

4.4 Summary

Direct evidence of Förster energy transfer between CdTe 427 nm and 500 nm

MSNs is obtained from a cross-peak in the 2D PL spectrum. Normalized experimental

overlap between donor emission and acceptor absorption spectra (5.58×10-4 cm) is on the

order predicted by theory.84 This indicates there is sufficient spectral overlap for RET to

occur. Additionally, within both aggregated configurations, the two sizes of MSNs are

within sufficient distance from one another for RET to occur.

56

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