Polarization Studies of Coupled Quantum Dots

Home , Potential well, Quantum Dot

A thesis presented to

the faculty of the College of Arts and Sciences of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Swati Ramanathan

November 2007

2 This thesis titled

Polarization Studies of Coupled Quantum Dots

SWATI RAMANATHAN

has been approved for

the Department of Physics and Astronomy

and the College of Arts and Sciences by

Eric A. Stinaff

Assistant Professor of Physics and Astronomy

Benjamin M. Ogles

Dean, College of Arts and Sciences

Abstract

RAMANATHAN, SWATI , M.S., November 2007, Physics and Astronomy

Polarization Studies of Coupled Quantum Dots (91 pp.)

Director of Thesis: Eric A. Stinaff

This thesis examines photoluminescence spectra and polarized photoluminescence

spectra of coupled semiconductor quantum dots. Previous results on the polarization

memory of charge states in single quantum dots have demonstrated that different excitonic charge states have identifiable polarization signatures [1,2,3]. Our results indicate that coupled quantum dots have similar polarization signatures to single quantum dots. New studies on polarization memories of anticrossing regions in coupled quantum dots were undertaken, and polarization memories of anticrossing lines were tracked through the anticrossing region. Preliminary results indicate that the polarization memory of anticrossing lines shows a marked decrease with bias, reaches a minima at the centre of the anticrossing region, and then starts increasing again.

This work helps in the identification of spins, a necessary first step towards achieving spin control in quantum dots for the production of qubit states for quantum processing, and lays the groundwork for the production of entangled photon pairs.

Approved: ______

Eric A. Stinaff

Assistant Professor of Physics and Astronomy

Acknowledgements

I would like to thank my advisor, Dr. Eric Stinaff, without whose constant guidance and

mentoring, this thesis would not have been possible. His unwavering support and

willingness to clear my doubts and misconceptions is greatly appreciated. Thanks to his

excellent instruction, the unfamiliar field of condensed matter physics is not so unfamiliar to me anymore. His extremely high theoretical and experimental standards have inspired and helped me to raise my own standards. As a beginner in the field, that is probably the most important thing I could have ever learned.

I would like to thank my lab partners, Kushal Wijesundara, Mauricio Garrido, Anna

Opitz, and Ru Zhang for their willingness to help, to share lab resources, and for helping

keep a light hearted atmosphere even in the midst of serious data taking.

I would finally like to thank my family for their love and encouragement, which was

undiminished even by the long distance. I dedicate this thesis to one of my favorite

people in the world, my grandfather.

Table of Contents

Abstract...... 3

Acknowledgements...... 4

List of Tables ...... 8

List of Figures...... 9

List of Graphs ...... 11

Chapter 1: Introduction...... 12

1.1. Outline...... 13

1.2. Semiconductor Physics ...... 14

Chapter 2: Theory of Quantum Dots ...... 17

2.1. From Bulk to Lower Dimensions ...... 17

2.2. Quantum Wells ...... 18

2.3. Quantum Wires ...... 18

2.4. Quantum Dots ...... 19

2.5. Applications of Quantum Dots ...... 21

Chapter 3: Growth Techniques ...... 25

3.1. Self Assembled/Stranski-Krastanow Technique...... 26

3.2. MOCVD...... 28

3.3. MBE...... 29

3.4. Colloidally Grown QDs ...... 31

3.5. Comparison of Growth Techniques...... 32

Chapter 4: Optical Properties of Quantum Dots...... 34

4.1. Introduction...... 34

Chapter 5: Photoluminescence Spectroscopy ...... 37

5.1. Introduction...... 37

5.2. Experimental Setup...... 38

5.2.1. Sample...... 38

5.2.2. Lab Description ...... 38

5.3. Single Quantum Dots...... 41

5.3.1 Inference of Charge State of Single Quantum Dots...... 42

5.3.2 Binding Energy ...... 43

5.4. Coupled Quantum Dots...... 46

Chapter 6: Polarization Studies...... 50

6.1 Introduction...... 50

6.2. Working Principle of Liquid Crystal Retarder...... 54

6.3. Polarization Memory ...... 54

6.4 Exchange Interactions...... 56

6.4.1. Isotropic Exchange ...... 57

6.4.2. Anisotropic Exchange ...... 57

6.5. Anticrossing in Positive Trion ...... 59

6.6. Applications of Polarization Studies...... 60

Chapter 7: Data and Results...... 66

7.1. Anticrossing A ...... 68

7.2. Anticrossing B ...... 72

7.3. Anticrossing C ...... 74

Chapter 8: Conclusion and Future Directions...... 78

References...... 80

Appendix A...... 88

Appendix B ...... 89

Appendix C ...... 91

List of Tables

Table 1: Experimental Details Aperture A ……………………………….………..68

Table 2: Anticrossing A, Line 1……………………………………………...….…68

Table 3: Anticrossing A, Line 2………………………………………………...….70

Table 4: Experimental Details Aperture B…………………………………..……..72

Table 5: Anticrossing B, Line 2……………………………………………..……..72

Table 6: Experimental Details Aperture C……………………………………....…74

Table 7: Anticrossing C, Line 1……………………………………………..….….74

Table 8: Anticrossing C, Line 2………………………………………………....…76

List of Figures

Figure 1.1. Band Structure and Energy Gap of a Material ...... 16

Figure 2.1. Density of States of Bulk, Quantum Well, Quantum Wire, Quantum Dot .. 17

Figure 2.2. InAs band structure with electron and hole in C and V bands...... 19

Figure 2.3. Detection of antibodies using quantum dots ...... 22

Figure 3.1. Strain relaxation leading to S-K self-assembled growth ...... 27

Figure 3.2. MOCVD grown quantum dots ...... 28

Figure 3.3. MBE grown InAs/GaAs dots...... 30

Figure 3.4. Colloidal quantum dots (EviDots)...... 32

Figure 4.1. Single and Ensemble spectra...... 35

Figure 5.1. Excitonic states...... 37

Figure 5.2. Bias Map...... 40

Figure 5.3. Biasing of a single quantum dot (dot circled in red) ...... 42

Figure 5.4. Negative trion at voltage -0.65V ...... 43

Figure 5.5. Neutral exciton at voltage -1.18V ...... 44

Figure 5.6 . Positive trion at -0.76 V...... 44

Figure 5.7. Biasmap showing charge states...... 46

Figure 5.8. Coupled Quantum Dots ...... 47

Figure 5.9. Direct and indirect transitions ...... 47

Figure 5.10. Biasmap of Coupled Quantum Dot ...... 48

Figure 6.1. Electric field vector of RHC polarized light (following J.D. Jackson) ...... 52

Figure 6.2. Schematic of Setup...... 55

Figure 6.3. Excitonic Spin States...... 57

Figure 6.4. Possible configurations of the positive trion state...... 59

Figure 6.5. Biasmap showing positive trion configurations in anticrossing region...... 60

Figure 6.6. Polarization Bias Map ...... 61

Figure 6.7. High Resolution Polarization Bias Map: Example 1...... 62

Figure 6.8. High Resolution Polarization Bias Map: Example 2...... 63

Figure 6.9. Intensity of lines in anticrossing region with RHC polarization ...... 64

Figure 6.10. Intensity of lines in anticrossing region with LHC polarization ...... 65

Figure 7.1. Anticrossing lines ...... 67

List of Graphs

GRAPH 1: Anticrossing A, Line 1………………………………………….…….…69

GRAPH 2: Anticrossing A, Line 2………………………………………….……….71

GRAPH 3: Anticrossing B, Line 2…………………………………………………..73

GRAPH 4: Anticrossing C, Line 1…………………………………………………..75

GRAPH 5: Anticrossing C, Line 2…………………………………………………..77

Chapter 1 : Introduction

The earliest theoretical understanding of quantum dots came with the first seedlings of a

wildly successful theory, which then, still in its infancy, would eventually form the basis

for most of the technology of the 20th century. Quantum mechanics, the bedrock of

modern physics, was based on the simple and elegant assumption that energy was not

continuous as was previously believed, but instead came in discrete packets. It was

invoked by Bohr to successfully explain the stability of atoms in 1913, and has been

repeatedly invoked by almost every physicist since then; from Roy Glauber in the 1960’s, to explain the coherence of light [4], to Cornell, Wieman and Ketterle [5] in the 1990’s, who produced the first Bose-Einstein condensate. And in each instance, quantum mechanics has stood up to the rigor of experimental testing, and has emerged successful.

It is possibly one of the most well-established theories in the vast history of mankind’s quest to understand nature.

In their essence, quantum dots are mere physical manifestations of that inescapable

requisite of any introductory quantum physics course; the oft-encountered problem of a

particle in a three dimensional potential well. Indeed, a quantum dot is just such a

confining potential with spatial dimensions comparable to the confined electron or hole.

From these humble theoretical beginnings that have been around since the start of the last century, to current cutting-edge applications in the fields of lasers and medicine, there is

overwhelming consensus in the quantum dot research community that quantum dots have

come a long way.

1.1. Outline

This research draws heavily upon concepts from such diverse areas as condensed matter

physics, atomic physics, classical electrodynamics and electronics. Quantum mechanics,

of course, pervades this entire work, providing the basis for concepts such as energy level

quantization and Pauli’s exclusion principle. In this thesis, I shall attempt to give a

concise introduction to some of the physical concepts most relevant to this work.

Understanding the utility of these zero dimensional structures requires a firm grasp of the

band theory as applied to semiconductors, so a brief introduction to semiconductor physics is provided first.

Next, I shall discuss the role of quantization in bulk materials, and then the effect of decreasing the dimensionality of the material from 3-D to 0-D.

The methods used in manufacturing quantum dots are explained next, followed by a

discussion of the optical properties of first single quantum dots and then coupled

quantum dots. What follows is an explanation of how charge states of the quantum dot

can be deduced by optical probes.

The main focus of this thesis, however, is the study of the photoluminescence emission

from the quantum dot sample. Details of the experimental set up are provided, and data is

shown. Finally, polarization memory of photoluminescence of the sample is measured

and analyzed in detail. This forms the basis of the concluding discussion into the

possibility of inferring the spin states of the charges residing in the dot, and what this

might imply for spin state control.

1.2. Semiconductor Physics

The term semiconductor refers to a material at the border between conducting and

insulating. The most common types of semiconducting materials come from the class of

elements found in group IV of the periodic table, or compounds of group III - V or II - VI

elements, all of which have an average of four electrons in the valence band. A major

advantage of semiconducting materials is that their electrical characteristic can be dramatically changed in a relatively straightforward way.

The band theory of solids [6,7,8,9] is the foundation upon which most of semiconductor

physics rests. Electrons in a crystal with a periodic potential have Bloch wavefunctions,

which determine their band structure. When two atoms come together to form a

molecule, their wavefunctions combine to form bonding and antibonding orbitals. When

large numbers of atoms come together, these orbitals form bands. In the simplest terms,

these bands are wavefunctions which conform to the periodicity of the crystal. The ‘band gap’ in a semiconductor is the energy separation between the conduction and valence

band. Most semiconductors have band gaps smaller than 4 eV, and energies

corresponding to the visible or near infrared part of the spectrum. Under normal

temperature and doping conditions, electrons in a semiconductor are non-conducting, i.e.,

they lie in the valence band. Supplying the electron with energy equal to or greater than

its energy gap excites it from the valence to the conduction band, leaving behind an

electron deficit in the valence band. This deficit or ‘hole’ behaves like a positive charge.

In contrast, metals have an overlap in their conduction and valence bands, and insulators have very large band gaps, larger than 4 eV.

Electrons and holes, both having half-integer spins, are fermions. A consequence of

Pauli’s exclusion principle, which states that no two particles can occupy the same

quantum state, is that electrons are filled into the band’s energy levels as dictated by

Fermi statistics. The highest energy level is known as the Fermi level. And in

semiconductors, whose band gaps are of the order of kbT , the Fermi energy lies midway between the conduction and valence bands. Figure 1.1 shows us that the conduction band electrons have s-like wavefunctions and the valence band electrons have p-like wavefunctions.

bulk material 16 atom moleculemolecu l

conduction band s-like orbitals Band gap valence band p-like orbitals

Figure 1.1. Band Structure and Energy Gap of a Material

(After E. Hernandez and J. A. Venables, University of Sussex)

The density of states is defined as the number of available states per unit volume per unit energy. It allows us to determine how closely packed the energy states of a given system are. We use the usual notations where V=volume, m=effective mass of electrons or holes,

E=energy.

It is defined in 3-D as,

g(k)dk=(V/2π2)k2dk (1.1)

in k-space and,

g(E)dE=(1/2π2)(2m/ħ2)3/2E1/2dE (1.2)

in energy space.

Chapter 2 : Theory of Quantum Dots

2.1. From Bulk to Lower Dimensions

Much of our understanding of quantum dots comes from quantum mechanics, condensed matter physics, and semiconductor physics. This chapter discusses the transition from a bulk semiconductor to increasingly lower dimensional objects, and the change in material properties associated with that transition. To this end, we discuss heterostructures, or heterojunctions, which are composed of two materials with different bandgaps, thus bringing about the possibility of charge confinement. Confinement effects are well studied in the following heterostructures:

1) Quantum Wells

2) Quantum Wires or Nanowires

3) Quantum Dots

Figure 2.1. Density of States of Bulk, Quantum Well, Quantum Wire, Quantum Dot

(http://www.imperial.ac.uk/research/exss/research/semiconductor/qd/intro.htm)

2.2. Quantum Wells

The 1970’s saw extensive research into quantum well heterostructures, which are objects confined in one dimension. Confinement arises due to the difference in band gaps of the two materials of which the heterostructure is composed, say, InAs and GaAs. The band gap of InAs is ~ 0.36 eV, and that of GaAs is ~ 1.43 eV at room temperature. Their confinement is commonly described by the well-known square well potential or harmonic oscillator potential, which has the familiar result for an infinitely deep well;

2 2 2 2 En=ħ π n /2mL (2.1)

The density of states for a quantum well is given by the expression,

g(E)dE=(m/πħ2)dE (2.2)

where E is the energy. Quantum wells are currently used in optoelectronic devices such

as lasers, photodetectors, and the recent high density Blu-ray disc technology.

2.3. Quantum Wires

Quantum wires or nanowires are confined along two dimensions. They can be modeled as

two dimensional wells. They are non-Ohmic wires, because their widths are much

smaller than the mean free path of electrons in the bulk material [10]. They exhibit

interesting features like quantized conductivity. Carbon nanotubes are a widely studied

class of quantum wires formed from rolled up graphene sheets. Their structural

parameters determine whether they behave like metals or semiconductors [11]. Their

confining potential takes the form of a potential well in two dimensions, and they are free

to move in 1-D. The expression for their density of states is given by,

g(E)dE=(1/π)(2m/Eħ2)1/2dE (2.3)

Their density of states exhibit sharp Van Hove singularities. They are extremely high

density current carriers, and could find application as alternatives to cathode ray tubes for

flat panel television display [12].

2.4. Quantum Dots

A heterostructure confined in all three spatial dimensions having effectively a 0-D structure with zero degrees of freedom is called a quantum dot.

Conduction Band GaAs GaAs InAs

1.43 eV 0.36 eV

Valence Band

Figure 2.2. InAs band structure with electron and hole in C and V bands.

Quantum dots are ‘nanocrystals’, a term reserved for crystals that have nanometer range

sizes in all three dimensions. They are typically made up of between 103 and 106 lattice atoms. Their confinement is often modeled as a simple harmonic oscillator potential with

Hamiltonian,

2 3 2 2 Ĥ = p /2m + Σ1 (1/2)mω0 r i (2.4) where the dimensionality of the oscillator is 3, m=effective mass of electron or hole, and r = size of the dot in the z direction. The eigenenergies are given by

En= (n+ 3/2)ħω0 (2.5)

To model the shape of the potential more accurately, other potentials have been used such

as the particle in a cone [13], particle in a pyramid [14] and particle in a lens [15].

One of the consequences of this potential is the resultant discrete excitonic energy states.

Dimensions comparable to the excitonic Bohr radius, defined as the separation between

the electron and hole, are required for the energy states to be treated as discrete. The

excitonic Bohr radius in semiconductors is ~200 nm, compared to ~1 nm in metals.

Semiconductor quantum dots are used and studied extensively because their larger size

makes for easier manufacture and control. Electronic Bloch wavefunctions in the

conduction band are s-like, while the confined electron state has levels that appear s-, p-

and d-like, which are an envelope of s-like Bloch wavefunctions. Hole wavefunctions, on

the other hand are intrinsically p-like, also with with s- ,p- and d-like envelopes.

As is the case with atoms, the density of states of a quantum dot takes on the form of a δ

function, leading to the popular description of quantum dots as ‘artificial atoms’. Higher

dimensional structures such as nanowires and quantum wells have a continuous density

of states in their unconfined dimensions, and therefore have a continuous absorption

spectrum. Quantum dot emission line widths are a few orders of magnitude larger than

natural atoms owing to their shorter lifetimes, which are on the order of a few

nanoseconds. This difference can be accounted for by sources of instabilities in the

quantum dot arising from mechanisms such as phonon interactions that do not exist in

natural atoms.

Of particular interest to this thesis are coupled quantum dots, or ‘artificial molecules’.

When two single dots interact with each other, they form a coupled system. Like natural

molecules, they exhibit features like bonding and antibonding orbitals. They reveal a host of other interesting properties that are studied using optical methods such as photoluminescence, photoluminescence excitation, and polarization.

2.5. Applications of Quantum Dots

Their high level of tunability, along with the tendency towards coupling lends quantum

dots to the following applications, some of which have yet to be realized.

22 Biosensors

Quantum dots are commonly used as fluorophores, or fluorescent tags that are attached to

specific biomolecules, for the detection of tumors [16]. The quantum dot emission

spectrum allows imaging and tracking of the biomolecule to which it is attached.

Quantum dots are much brighter than traditional organic dyes due to their high quantum

efficiency (also quantum yield, or percentage of absorbed photons that result in an

emitted photon). They also offer the added advantage of emission peak tunability over a

broad range of colors, without having to change the material system. This allows for a

specific color to be attached to a specific molecule (Fig 2.3).

Figure 2.3. Detection of antibodies using quantum dots

(M. P. Bruchez and C. Z. Hotz)

23 Quantum Dot LEDs

Quantum dot LEDs can emit at any visible or infrared wavelength due to their tunable bandgaps. Their structure makes them flexible, thus allowing them to be used in various forms such as coatings, paints and filters, giving them a huge advantage over conventional LEDs.

Broad spectrum LED lighting

The search for an ideal broad spectrum white light emitter with high efficiency drives a lot of lighting research today. LED white light emitters are blue-light emitting sources with a surface phosphor coating that emits yellow light. These LEDs appear white, but produce undesirable sharp blue peaks, and are therefore not true broad band emitters.

CdSe quantum dots coated on a blue light emitting LED source have already been found to produce true broadband white light with excellent color reproducibility. This effect achieved by reducing the size of the quantum dots, is believed to be a result of surface effects. Further research is aimed at improving their efficiency, which at present, is quite low [17].

Quantum Computers

Entangled charges or spins hold great promise in the implementation of qubits for quantum computers. Biexciton radiative decay in quantum dots occurs through two optically active exciton stages. Benson et al [18] have proposed that this mechanism could produce polarization entangled photon pairs. Akopian et al [19,20]] have demonstrated that this radiative cascade in single semiconductor quantum dots does

indeed produce entangled pairs of photons, as it satisfies the requirement that the two decay paths be identical (degenerate) other than having different polarizations [21].

Diode lasers

A quantum dot laser consists of a large number of quantum dots in a host material with a

pumping source that induces population inversion in the dots for lasing action. Quantum

dot lasers exhibit very small thermal fluctuations at room temperatures, and therefore

have highly stable power outputs, which are not possible with traditional semiconductor

lasers. Such a quantum dot laser has already been realized by Fujitsu Corporation and

Yasuhiko Arakawa [22] of the University of Tokyo. It achieves 10 Gbit/s over a

temperature range of 20 C to 70 C. Laser wavelength is 1.3 micrometers. This could lead

to the production of cheap, compact, high efficiency optical transmitters which might find

uses in diverse areas such as optical metro access systems and high-speed optical LANs

[23].

Chapter 3 : Growth Techniques

The two approaches to the manufacture of quantum dots are the top-down and the bottom-up or self-organized techniques. The top-down approach involves either

patterning through lithographic techniques or etching a sample down to the required

dimensions. Lithography was the main fabrication technique used in the late ‘80s [24] because it allowed the production of QDs with predefined dimensions, and was therefore

conducive to systematic studies of confinement effects as a function of structure [25,26].

This approach, however, was not free from defects and dislocations, which effectively

killed photoluminescence emission, leading to the development of new techniques such

as molecular beam epitaxy and metalorganic chemical vapor deposition, which were free

from surface defects.

The three possible growth mechanisms are the Frank-van der Merwe, Volmer-Weber,

and Stranski-Krastanow modes [27,28].

Frank-van der Merwe - Growth method where very smooth films are grown in by

depositing one monolayer over the other. The growing layer completely wets the surface

layer.

Volmer-Weber - The growing layer tends to roll up into a sphere in order to minimize its surface energy.

Stranski-Krastanow - The growing layer first wets the surface layer (wetting layer) and then there is the balance of forces changes during growth, causing the formation of islands.

3.1. Self Assembled/Stranski-Krastanow Technique

The self-organized growth technique is very popular technique in modern times because no defects are introduced during formation [3]. It can be achieved through the Stranski-

Krastanow growth mode. Necessary for this method are two lattice-mismatched materials, the material of the substrate (e.g. GaAs) and the material of the quantum dot

(InAs). It is important to note that this growth mode works when the depositing material has a larger lattice constant than the substrate material. When depositing the InAs (lattice constant = 6.06 Ǻngstroms) layer by layer on top of the GaAs (lattice constant = 5.65

Ǻngstroms), the epilayer is strained. The strain energy increases with epilayer thickness, and after a certain critical thickness, induces the formation of energetically favorable island structures. Because the formation of islands results in an increase in surface energy, there is an optimal island size where total energy is minimized. Dots form at 1.5 monolayers, or 4 Ǻngstroms. This method yields dots that are free of dislocations, and consequently have high quantum efficiencies for optical emission [29]. Dot sizes are roughly 6 nm in height and 20 nm in diameter, the exact size being determined by growth conditions. The 2-D layer of InAs formed prior to dot growth is known as the wetting layer. Nucleation occurs in disordered arrays. Dot densities vary significantly, but

typically lie between 109 and 1011 per square centimeter. Other III-V combinations can be

used, such as InAs on InP substrate. This technique also allows dots with II-VI materials

to be grown. The shape of self-assembled dots has been studied by XSTM, and for InAs

on GaAs, has been observed to have a truncated pyramid shape [30,31]. Vertical stacking

of dots can be easily achieved through this method because the new layer of materials

feels the strain field from the quantum dot underneath it, so there is a tendency for the strain field to induce self-assembly at that location. This is a very useful property in the study of coupled quantum dots.

MBE and MOCVD extensively employ the Stranski-Krastanow growth mode. Epitaxial

methods such as these involve ordered growth on monocrystalline layers of the substrate

and are advantageous because growth can be highly controlled.

Figure 3.1. Strain relaxation leading to S-K self-assembled growth

(Image from http://www.fkf.mpg.de)

3.2. MOCVD

Metalorganic Chemical Vapor Deposition alternatively known as Metalorganic Vapor

Phase Epitaxy (MOVPE) is an epitaxial method used to fabricate compound semiconductors from surface reactions of organometals or metal hydrides. Pyrolysis of the chemicals occurs at the substrate surface at pressures on the order of a few kPa, eventually leading to crystal growth. Self organized growth of quantum dots is possible with this technique, despite the limited initial success in growing binary InAs dots due to the occurrence of large three-dimensional dislocated In-rich clusters which co-existed with the quantum dots. This problem was circumvented by switching off the arsine flux

during growth interruption. Heinrichsdorff et al [32] investigated the effect of different In

concentrations in InGaAs grown on GaAs. Dot densities were found to increase with

increasing layer thickness, whereas dot heights decrease. The size of the nanocrystals depends strongly on growth temperature [28]. Growth at 800 C leads to a base width of

200 nm, whereas growth at 720 C leads to a base width of 70 nm [33].

Figure 3.2. MOCVD grown quantum dots

Defect free layer of InAs quantum dots grown over GaAs (After Bimberg, Grundmann, Ledentsov)

3.3. MBE

Molecular Beam Epitaxy is a technique of depositing single crystals, developed by Bell

Laboratories in the late ‘60s by J. R. Arthur and A. Y. Cho.

MBE growth on a substrate is achieved through the slow deposition of submonolayer material on a substrate, at either high or ultra high vacuum (108 kPa). Deposition rates are typically between 0.001 and 0.3 micrometers per minute. Pre-defined ratios of ultra pure elements like Ga and As are heated separately in quasi-Knudsen (cells with heating filaments and a water cooling system used to control the temperature of the evaporating content) effusion cells. They evaporate, forming long mean-free path ‘beams’ to the substrate wafer, where they are ultimately deposited. Deposition occurs when the evaporated elements then condense on the substrate where they finally react with each other.

RHEED (Reflection High Energy Electron Diffraction) is used to monitor the growth of crystal layers. A smooth/flat surface produces a RHEED pattern of lines, whereas a rough surface produces a RHEED pattern of dots. RHEED can be used to determine exactly when a layer has been fully deposited, and its feedback is sent to computer controlled shutters in front of the effusion cells, allowing control over the amount of the evaporated material. This single atom layer precision is of great importance in the fabrication of precision structures such as quantum dots, quantum wells and LEDs.

Submonolayer deposition of InAs on GaAs substrate leads to the self-organizational

formation of wire-like monolayer high islands. Depending on the InAs coverage, the

resultant structures may be regarded as either broken quantum wires or quantum dot

arrays. Growth interruptions of 10 to 40 s are required to allow the dots to reach their

equilibrium sizes [28].

The MBE grown InAs dot is capped with a partial layer of GaAs. Flash heat is then

applied, and the InAs dot is fully capped with GaAs. This kind of truncation, as discussed

before, produces stronger quantization just as decreasing well width of a quantum well

would produce larger energy level spacings.

200nm

Figure 3.3. MBE grown InAs/GaAs dots

(Z. R. Wasilewski, et. al., J. Cryst. Growth 201/202, 1131 (1999))

3.4. Colloidally Grown QDs

Inorganic quantum dots can be prepared from techniques developed in organic chemistry.

Colloidal quantum dots are a suspension of inorganic dots in an organic or aqueous

solution.

This method is best used for II-VI semiconductors (such as CdSe, CdTe etc.), which

easily crystallize. Semiconductors that have a III-V configuration are covalent, and would

need to overcome large energy barriers to crystallize [29].

Colloidal quantum dots are grown by the rapid addition of reagents to a hot co-ordinating

solvent. The temperature of the solvent is high enough to decompose the reagents,

resulting in supersaturation of the species. This leads to the nucleation of nanocrystals.

The material and size of these nanocrystals is controlled by reaction conditions such as

time, concentration, temperature and chemical composition of reagents. Higher

temperatures and longer reaction times can lead to larger sizes of nanocrystals. Size

variations are typically on the order of 10% [34].

When the required size of the nanocrystal is achieved, further reaction is stopped by

cooling. The nanocrystals are then removed from their growth solutions and a suitable nonsolvent is added, in which they form a colloidal suspension. Next, size selective precipitation methods are applied to further narrow down the size variations to 5%. And,

32 as with all quantum dots, a decrease in diameter leads to a blueshift in emission

wavelength.

Figure 3.4. Colloidal quantum dots (EviDots)

(Evident Technologies www.evidenttech.com)

3.5. Comparison of Growth Techniques

MOCVD and MBE are comparable methods, both free from dislocations and defects.

MOCVD growth involves the highly combustible silane gas, and therefore requires very

strict adherence to safety regulations [35]. MBE is therefore the more commonly used

method. Both these techniques lead to dots with very few defects, uniform size, and high

quantum yield. They are, however, expensive and slow techniques.

Colloidally grown quantum dots are cheap and easy to produce in large quantities. Water

soluble dots are especially useful in biological applications such as tagging molecules

[36]. Colloidal growth is also one of the least toxic growth techniques. Dot density in this

method can be easily controlled in this method simply by dilution.

However, colloidally grown quantum dots are less stable than epitaxially grown quantum

dots because they easily photobleach and degrade in the presence of light due to the

formation of unstable chalcogen oxides [29]. The quantum yield of colloidal dots is lower

than MBE and MOCVD grown dots due to large surface effects. They show a tendency

to ‘blink’, i.e., randomly stop emitting photoluminescence, due to charge localization effects at defect sites on the surface. They also wander, i.e., their peak emission exhibits shifts on the order of 0.02 eV on timescales of ~100 s. This is thought to be a result of the excited state coupling to the photoinduced changes on the nanocrystal surface [37].

Eliminating surface effects can increase the photoluminescence yield of colloidally grown quantum dots. This is often achieved by a process called passivation, where the surface is passivated by a monolayer of the solvent ligands. Efficiency can be raised up to

50% [29] by minimizing surface effects. This is achieved by coating the core with a

larger bandgap material thus confining the carrier to the core.

Chapter 4 : Optical Properties of Quantum Dots

4.1. Introduction

The spectral emission mechanism of quantum dots can be simply described as follows. A photon excites the electron in the semiconductor from the valence band to the conduction band, thus leaving behind a hole. The electron and hole are Coulomb-correlated, and therefore form a bound state of lower energy known as the exciton. The subsequent recombination of the electron-hole pair gives rise to the observed emission spectrum.

Exciton relaxation through Coulomb scattering [38] in the QD is so rapid (it occurs on a timescale of a few picoseconds) that most excitons are found in the ground state prior to radiative recombination [24].

Quantum dot energy states are tunable to a very high degree owing to the fact that their energy spacing depends on the height of the quantum dot. Quantization is determined by the height of the dot; decreasing the height of the dot narrows down the walls of the potential well, increasing the strength of quantization and giving the expected quantum mechanical result of larger energy spacing between levels. Hence, by changing the height of the quantum dot, its emission peak can be controlled. The heights of the dots normally lie in the range of 1-10 nm, and their emission peaks lie in the infrared region of the spectrum.

A quantum dot ensemble results in a spectrum broadened due to small inhomogeneities in dot size. Other sources of broadening include alloying, charge state and local

environment. This type of inhomogeneous broadening leads to line widths of about 50 to

100 meV, completely obscuring charging and multiexciton effects (seen at a few meV),

the main physical phenomena of interest to this thesis. Single dots, at ideally low temperatures, have line widths of just a few μeV. Consequently, our studies focus primarily on the properties of single or coupled dot systems. To this end, we employ in situ submicron sized apertures that allow us to probe only a few dots at a time. We use in

situ techniques because they possess greater stability, since the relative spacing between

the dot and the aperture is fixed, offering higher spatial resolution.

Single QD

QD Ensemble Intensity (arb. units) WL x 2500

150 100 50 0 -50 Δ E Relative to S shell (m eV)

Figure 4.1. Single and Ensemble spectra

Broadening of the ensemble completely obscures the phenomena under study. This figure also shows the wetting layer which lies higher in energy than the quantum dot because its height is smaller than the height of the quantum dot, and therefore has stronger confinement, i.e., more widely spaced energy levels. The wetting layer is an example of a quantum well, with confinement only along the direction of its height.

(After E.A. Stinaff)

It should be noted that the same result of limiting the number of dots under study can be achieved through other methods such as,

i) near-field scanning optical microscopy (nsom)

ii) confocal microscopy and

iii) preparation of low density samples either by dilution in colloidal samples, or

preparation of solid state samples under special growth conditions using self-

organization techniques.

Chapter 5 : Photoluminescence Spectroscopy

5.1. Introduction

Quantum dots may be optically probed by various techniques such as

electroluminescence, photoluminescence, cathodoluminescence; which employ different

excitation mechanisms.

Photoluminescence (PL) is one of the most commonly used spectroscopic techniques to

study quantum dots. Photoluminescence emission occurs when the quantum dot is excited

by an incoming photon which is off resonance with the excitonic energy. Typically, the

incoming photon excites the electron from the valence band to the wetting layer, leaving behind a hole. The electron relaxes back to the conduction band through phonon interactions, and finally, recombination occurs with the emission of a photon. The diagram below shows the main excitonic states.

neutral exciton positive trion negative trion

e e e e

h h h h

Figure 5.1. Excitonic states

5.2. Experimental Setup

5.2.1. Sample

The samples we study are obtained through collaboration with the Naval Research

Laboratory, where they are grown using an MBE system suitable for III-V materials.

They are InAs islands grown on GaAs substrate. They have a width of about 20 nm, and are truncated as described earlier in the chapter on growth techniques, to heights of 2.5 nm. They can be modeled as lens shaped objects, with small anisotropies. They are enclosed in a Schottky structure (discussed in Chapter 8) to allow biasing and selective charging. They are vertically stacked with a 4 nm separation between dots.

5.2.2. Lab Description

The lab was set up in late 2006 and has been fully operational for a couple of months. Its primary, although not exclusive, aim is to study quantum dots through spectroscopic techniques. The main lab equipment is listed as follows:

1) Trivista 3-stage spectrometer.

2) Tsunami laser

3) Closed cycle cryostat

A more detailed description of the lab equipment may be found in Appendix B. The software used in this experiment is discussed in Appendix C.

39 5.2.3. Experimental Variables

There are several variables that can be controlled in the experiment. The temperature was

fixed at ~10 K for most of the experiments to minimize thermal effects. The laser power

hitting the sample was adjusted from ~1 mW to ~50 mW depending on the strength of the

lines seen. The excitation was nonresonant, mostly carried out with the laser (more

detailed equipment description in Appendix) set to 880 nm. The spectrometer gratings

most commonly used were the 750 and 1100 groove gratings. All experiments involved

bias dependent studies, where the bias voltage was varied from around -2.0 V to ~0.5 V

in step sizes ranging from 0.02 V to 0.001 V. The integration time at a given bias was

varied from 5 s to 120 s, and consequently, a bias scan could take anywhere from 20

minutes to 20 hours.

Biasmaps provide a convenient method for the study of bias dependence of dot emission.

The bias map below shows the voltage dependent emission of the quantum dot. Each

slice of the map represents the entire spectrum at a given voltage. This representation

makes it very easy to identify direct and indirect transitions, given that they have different bias dependences.

Data taking is a long process, so in the interest of time, we run relatively short scans (20

min) on most apertures. If the aperture looks interesting, we carry out a longer integration

time, high bias resolution scan on it to bring out its interesting features, and also so we

can do detailed data analysis on it. Since the sample stays fixed, we note the co-ordinates

of all the samples we study, in the event that we might want to get back to them.

Figure 5.2. Bias Map

The biasmap of the dot shown below is a stack of spectra taken from -2.0 V to -0.5 V. The red line shows the spectrum at a bias of -0.99 V and the black line shows the spectrum at -1.27 V. The spectrum shows both direct and indirect transitions in a coupled quantum dot towards the right.

5.3. Single Quantum Dots

In the following biasmap of a single quantum dot, we see the neutral exciton, negative trion, and hole. What is also seen is a slight quadratic Stark shift that can by derived using second order perturbation theory, with the applied electric field treated as a perturbative effect. The Stark shift is an electric field dependent effect, and is seen in natural atoms as either a shift or splitting of spectral lines. In quantum dot semiconductor structures, it is known as the quantum confined Stark shift. In single dots, it occurs because the electron and hole of the exciton are pulled in different directions by the applied field.

An estimate of the quadratic Stark shift [39] is given by the equation,

3 2 ΔV=-(9/4)ε2aex E (5.1)

Where ε2 = relative permittivity of the semiconductor, aex = excitonic Bohr radius and E = magnitude of electric field.

The diagram below shows the effect of biasing on a single quantum dot. The arrows below show either electrons tunneling into the dot or tunneling outside the dot.

Reverse bias Forward bias electrons tunnel out electrons tunnel in

Figure 5.3. Biasing of a single quantum dot (dot circled in red)

5.3.1 Inference of Charge State of Single Quantum Dots

The dot is embedded in an n type Schottky structure to allow application of a bias voltage. (Appendix A) When the dot energy level coincides with the energy of the Fermi level, electrons can easily tunnel into the dot. A lower electric field favors negatively charged trions, as there is a high probability of electrons tunneling into the dot. Coulomb repulsion prevents more electrons from tunneling in, an effect known as Coulomb blockade. Due to this effect, we are able to deduce the presence of single charges in the quantum dot. Increasing the reverse bias of the dot increases the probability of the electrons tunneling out, leaving behind holes [40]. Charging events turn on or off at certain voltages. Thus, bias dependent studies of single quantum dot photoluminescence

[41], arising from intradot exciton recombination, can reveal a wealth of information about the charging behavior of the dot.

5.3.2 Binding Energy

The different charge states have unique binding energy signatures. Relative strengths of

the Coulombic interactions can be determined as a result of these signatures. The positive

trion (X+) is usually seen to lie above the neutral exciton (X0) in energy. The negative

trion (X-) has the lowest binding energy of the excitonic states. From this we infer that in

the positive trion, which has two holes and an electron, the electrostatic repulsion

between the holes is greater than the total attraction between each of the holes with the

electron. The neutral exciton, with one electron and one hole, has only an attractive term.

In the negative trion, with two electrons and one hole; we infer that the attraction between each of the electrons with the hole is greater than the repulsion between the electrons.

X-

Figure 5.4. Negative trion at voltage -0.65V

X-

Figure 5.5. Neutral exciton at voltage -1.18V

X+ X0

X-

Figure 5.6. Positive trion at -0.76 V

45 Positive trion interactions:

2(e-h) – h-h

Neutral exciton interactions

e-h

Negative trion interactions

2(e-h) – e-e

We note from the spectra that 2(e-h) – h-h > e-h > 2(e-h) – e-e , (5.2)

from which we conclude that the e-e interaction is the strongest, followed by e-h, and

finally h-h. The negative trion is found roughly at 5 meV lower than the neutral exciton.

The positive trion and neutral exciton are separated by around ±2 meV [46].

The three spectra pictured above show how the relative intensities of the three lines

change as the voltage is changed, signaling bias dependent charging behavior. It also illustrates the usefulness of biasmaps in tracking such changes in wavelength. The biasmap shown below contains all the information contained in the above spectra, and a lot more. Without the biasmap, it would have been hard to track the switching on and off of charge states.

46 X+

X- Energy

Negative electric field

Figure 5.7. Biasmap showing charge states

5.4. Coupled Quantum Dots

Coupled QDs are analogous to natural molecules. Linear combination of atomic orbitals

(LCAO model) gives rise to two possible combinations of single quantum dot (atomic) wavefunctions [42,43]. These are the symmetric and antisymmetric states, also called bonding and antibonding orbitals. Bonding orbitals are lower in energy, and therefore the most stable. Thus, the formation of bonding and antibonding orbitals is indicative of coupling.

47 InAs

4 nm

InAs

Figure 5.8. Coupled Quantum Dots

Figure shows InAs islands grown on GaAs. The two dots usually have slightly different sizes, and are separated by 4 nm.

The spectra of coupled quantum dots reveal a high bias dependence [44], because changing bias changes the energy levels of one dot relative to the other (Figure 5.9). In the previous section, we discussed single dots where intradot exciton recombination (blue line) was the source of photoluminescence. In coupled dots, we also observe interdot recombination (red line), where electrons and holes from different dots recombine. The

Stark shift in this case is linear, and at least an order of magnitude stronger than in single dots.

Forward bias Reverse bias

Figure 5.9. Direct and indirect transitions

The Stark shift is given by,

ΔV=E.(d+(hB+hT)/2) (5.3)

where E = electric field, d = dot separation, hB & hT are the heights of the bottom and top dot respectively.

Figure 5.10. Biasmap of Coupled Quantum Dot

Biasmap of coupled quantum dot showing an anticrossing (circled) and an indirect transition.

Anticrossings are signatures of bonding and antibonding orbitals, and therefore signatures of quantum mechanical coupling. They occur when the charge carrier in one dot tunnels into the other dot. Anticrossings are avoided energy level crossings that come about as a result of Pauli’s exclusion principle, which forbids two particles from occupying the same quantum state. In atomic physics, the analogous principle is the well known

Wigner-Von Neumann no-crossing theorem.

Chapter 6 : Polarization Studies

6.1 Introduction

Polarization studies are a useful tool in gleaning information about the spin states of charge carriers in the quantum dot. A thorough understanding of the various mechanisms that can affect the spin state of the dot is required in order to use spin states as qubits for quantum information processing.

Using the standard classical electrodynamical treatment (following Classical

Electrodynamics, J. D. Jackson) of polarization, we have the plane wave electric field and the magnetic fields (each satisfying Maxwell’s equations), given by,

Е(x,t) = Єe(ikn.x-iωt) (6.1)

B(x,t) = βe(ikn.x-iωt) (6.2)

respectively, where Є, β and n are constants. The direction of propagation of the electromagnetic wave is perpendicular to both the electric and the magnetic field.

The most general description of a plane wave propagating in the direction k is expressed as,

(ikn.x-iωt) Е(x,t) = (ε1E1 + ε2E2) e (6.3)

51 where ε1 and ε2 are the polarization vectors of waves E1 and E2 . E1 and E2 are complex,

containing phase information. If both their phases are equal, then equation (6.3)

represents linearly polarized light. The resultant polarization vector makes an angle θ

with ε1, and has magnitude E.

-1 θ = tan (E2/ E1) (6.4)

2 2 E=√(E 1+E 2) (6.5)

When E1 and E2 have a relative phase difference, equation (6.3) represents elliptical

polarization, which is the most general case of polarization.

However, we are mostly concerned with circular polarization, the case where E1 and E2 are equal and have a phase difference of 90˚.

We can then modify (6.3) to read

(ikn.x-iωt) Е(x,t)=E0(ε1±iε2)e (6.6)

where the – sign refers to right hand circularly polarized (RHC) light, where the rotation

of the polarization vector is clockwise, and the + sign refers to left hand circularly

polarized light (LHC), where the above rotation is counterclockwise. The frequency at

which the rotation occurs is ω.

y 52

Figure 6.1. Electric field vector of RHC polarized light (following J.D. Jackson)

A photon with RHC or LHC polarization has angular momentum +1 or -1, respectively.

The conservation of angular momentum requires that exciting a dot with +1 polarization should produce an exciton with the same total spin, i.e., +1. The conservation of angular momentum provides, in theory, a method of measuring spins in charged exciton states of the quantum dot. The strain field in the quantum dot removes the degeneracy between the light and heavy holes [55]. The heavy holes (spin 3/2) are of primary interest to us, and we do not consider the light holes (spin 1/2) because they have very high energy levels when confined. This necessarily implies that the hole has a spin up (+3/2) state and the electron has a spin down state (-1/2). Similarly, if the sample is hit with LHC polarized light, the exciton produced has an electron with spin +1/2 and a hole with spin -3/2.

The negative trion, with two electrons in the valence band and a hole in the conduction

band, has electrons aligned with opposite spin, following Pauli’s principle. The spin that

plays a role in polarization studies, therefore, is the unpaired spin of the hole[1,46].

Similarly, polarization studies on the positive trion reveal information about the spin state of the unpaired charge carrier, which in this case is the electron [47].

For polarization experiments, we additionally used liquid retarders and linear polarizers

in order to:

(i) control the polarization of light entering the sample, and

(ii) detect a specific type of polarization, i.e., RHC, LHC, linear or horizontal.

The laser produces light that is linearly polarized, and the light is sent through another

linear polarizer in order to ensure the elimination of all other polarization components.

Linearly polarized light is then sent into a liquid crystal retarder (described below), which

is set to produce right hand circularly polarized light. This light is then made to hit the

sample so it may be absorbed by the quantum dot. The second liquid crystal retarder

checks for both RHC and LHC polarization.

6.2. Working Principle of Liquid Crystal Retarder

LCRs are capable of slowing down one component of light relative to the other. The

amount of retardance can be controlled by changing the voltage. The retardance

determines the phase difference between the two components, E1 and E2, and therefore

determines whether the light that comes out has vertical, horizontal, RHC or LHC

polarization. A retardance corresponding to λ/4 gives RHC polarized light, and 3λ/4 gives

LHC polarized light.

6.3. Polarization Memory

If the absorption and recombination processes produce no change in polarization of the

system, the emitted light should retain its RHC polarization. If there is a change in

polarization, due to some internal process, then the emitted light should be LHC polarized. If the emitted light shows no marked preference to be RHC or LHC, then it is clear that the internal process destroys the polarization memory of the incoming light

[48,49].

SCHEMATIC OF EXPERIMENTAL SETUP

Spectrometer

Figure 6.2. Schematic of Setup

Polarization memory is given by the following equation, where the superscript of I in eq

(6.1) indicates detected intensity of RHC (+) or LHC (-) polarization states, and the

subscript refers to polarization of excitation. We will restrict ourselves to cases where

the excitation light RHC polarized, since from symmetry considerations, we should expect to obtain the same results for LHC polarized light.

−+ − II ++ P = −+ (6.7) + II ++

We already know of two processes that can change spin. They are the exchange

interactions.

6.4 Exchange Interactions

Exchange interactions remove the high degeneracy of electron and hole spin states,

giving rise to fine structure in the quantum dot spectrum. The total angular momentum is

given by Fz .

Fz=sz+jz (6.8)

Where sz and jz are the spin projections of the electron (±1/2) and the heavy hole (±3/2)

respectively [50].

We deal with the isotropic and anisotropic exchange, where the former is 10 times greater

in magnitude than the latter. The exchange Hamiltonian is given by,

e h e h e h Ħex = (Δ0 /2) σz σz + (Δ1 /4)(σx σx + σy σy ) (6.9)

where σi refers to the standard Pauli spin matrices.

6.4.1. Isotropic Exchange

The isotropic exchange interaction occurs when the degeneracy between the spin down-

down and up-up states (Fz = ±2) and spin up-down (Fz = ±1) states is removed. Fz = ±1 is optically allowed, and Fz = ±2 is a nonradiative state. The energy shift between them is

given by Δ0 [51].

6.4.2. Anisotropic Exchange

The anisotropic exchange, also known as the long range exchange interaction occurs due

to in-plane anisotropy of the dot. It splits the up-down and down-up spin configurations.

It is characterized by an energy shift of Δ1. We can use this knowledge to predict what the polarization memories of the exciton states should be.

X0 X+ X-

Figure 6.3. Excitonic Spin States

In the neutral exciton, the electron and hole are both provided by the incoming photon, and are both unpaired, and so they experience strong anisotropic exchange. This

exchange causes mixing, and wipes out spin memory.

The positive trion is formed when a pre-existing hole charge state is excited by a photon,

creating an additional electron-hole pair. The hole provided by the photon flips spin if required, in order to obey Pauli’s exclusion principle, and the electron provided by the photon, being unpaired, can exist in either spin state. The positive trion, therefore, has two holes interacting with one electron. The exchange interaction between electron and the spin up hole is equal to the exchange between the electron and the spin down hole, but with the opposite sign. So there is no net exchange anisotropic term. Hence, spin states are preserved, and the positive trion is expected to show a positive polarization memory.

The negative trion is formed when a pre-existing electron is excited by a photon, which

provides it with an additional electron and hole. Exchange interactions and mixing during

the relaxation and recombination process determine whether or not the polarization

signature of the light is retained. Negative trions show either positive or negative

polarization memories, depending on whether or not they undergo a spin flip [45, 52].

Relaxation through a single particle spin flip are suppressed in QDs [53, 54].

59 6.5. Anticrossing in Positive Trion

As discussed before, the anticrossing regions allow us to visually track quantum

mechanical phenomena such as Pauli’s exclusion principle. What we generally observe are hole-hole anticrossings, which are much weaker than e-e anticrossings. A biasmap showing an anticrossing region is displayed below.

10 10 + X+ X 20 11

Figure 6.4. Possible configurations of the positive trion state

10 X+ 20

10 X+ 1 1 Energy

Negative Electric Field

Figure 6.5. Biasmap showing positive trion configurations in anticrossing region

The underlined charges are involved in recombination

6.6. Applications of Polarization Studies

• A detailed knowledge of polarization states is essential to the production of

entangled pairs of photons.

• Polarization studies provide an alternative method for deducing the charge state of

an exciton since each state has a unique polarization memory signature.

• Experimental data have been used to work out the values of exchange anisotropy

and tunneling [51].

Figure 6.6. Polarization Bias Map

A preliminary scan with interesting features (circled ) such as the one below, may lead to a long integration time, long resolution scan.

Figure 6.7. High Resolution Polarization Bias Map: Example 1

This scan is taken in higher voltage and spectrometer resolution than the one shown before. The integration time of this scan is much longer, so as to improve the signal to noise ratio. The anticrossing region is seen.

Figure 6.8. High Resolution Polarization Bias Map: Example 2

Figure 6.9. Intensity of lines in anticrossing region with RHC polarization

Figure 6.10. Intensity of lines in anticrossing region with LHC polarization

Chapter 7 : Data and Results

Polarization memory was calculated using the following equation that we came across earlier, + − + − II + P = + −

+ + II +

In order to avoid large errors, the following data points were discarded:

(i) points with a large background,

(ii) data points with very low counts that could not be properly discerned, and

(iii)for the purpose of this thesis, data points which crossed other lines.

Polarization memories of anticrossings in three dots were calculated. For our preliminary analysis, we simply measured peak intensities. We are currently working on writing software to fit these lines to Lorentzian shapes.

Referring to the figure below (Fig 7.1), the cursor is positioned on the same point in both pictures, and there is a clear intensity difference between the LHC and RHC polarized lines. The two anticrossing lines studied are marked with ovals and stars. They are always

seen in anticrossings, but with varying intensities. In graphs and tables, the first one is referred to as anticrossing line 1, and the second one is referred to as anticrossing line 2.

Intensity of RHC Intensity of LHC

Figure 7.1. Anticrossing lines

Three different anticrossings were observed, and polarization memories of lines 1 and 2 were measured. The anticrossings will be referred to as anticrossing A, anticrossing B and anticrossing C in the graphs that follow. Errors are calculated using the following formula,

Error = (1/√(I(LHC)+I(RHC)))*100

68 7.1. Anticrossing A

Table 1: Experimental Details: Aperture A

Date and time 200707181846 Sample name R050103G-B5 Aperture Co-ordinates H3.89-V7.40 Laser Wavelength 900 nm Laser power 40.6 mW Sample Temperature 14.95K Integration time 60s Grating 1100 centered at 970 nm

Table 2: Anticrossing A, Line 1

Bias (V) I(RHC) I(LHC) P(%) Error

-1.124 11319 5420 35.24105 0.55552 -1.176 7717 3562 36.83837 0.677833 -1.2 3266 1540 35.91344 1.037433 -1.208 2186 1016 36.53966 1.271788 -1.216 1521 640 40.76816 1.555253 -1.22 1018 499 34.21226 1.843508 -1.224 971 464 35.33101 1.897478 -1.228 716 343 35.22191 2.208557 -1.232 310 208 19.69112 3.122168 -1.236 249 146 26.07595 3.589017 -1.244 358 194 29.71014 3.044207 -1.268 710 375 30.87558 2.173406

69 Graph 1 : Anticrossing A, Line 1

Polarization Memory vs. Bias

25 Polarization Memory %

-1.28 -1.26 -1.24 -1.22 -1.20 -1.18 -1.16 -1.14 -1.12 Bias Voltage (V)

Table 3: Anticrossing A, Line 2

Bias (V) I(RHC) I(LHC) P(%) Error -1.308 2584 1632 22.58065 1.096118 -1.296 1510 1006 20.0318 1.416908 -1.292 1415 846 25.16586 1.499193 -1.288 851 728 7.78974 1.780837 -1.284 668 545 10.14015 2.032895 -1.28 1311 802 24.08897 1.549731 -1.276 1299 689 30.6841 1.605382 -1.264 498 333 19.8556 2.465228 -1.26 642 315 34.16928 2.320942 -1.256 689 376 29.38967 2.191083 -1.252 603 357 25.625 2.301469 -1.248 1072 466 39.40182 1.840656 -1.244 969 386 43.02583 1.969448

71 Graph 2 : Anticrossing A, Line 2

Polarization Memory vs. Bias

15 Polarization memory %

-1.31 -1.30 -1.29 -1.28 -1.27 -1.26 -1.25 -1.24 Bias (V)

7.2. Anticrossing B

Table 4 : Experimental Details: Aperture B Date and time 200707062234

Sample name R050103G-B5

Aperture Co-ordinates H3.89-V7.42

Laser Wavelength 880 nm

Laser power 10.15 mW

Sample Temperature 13.98 K

Integration time 50s

Grating 1100 centered at 965 nm

Table 5: Anticrossing B, Line 2

Bias (V) I(RHC) I(LHC) P(%) Error

-1.337 141 97 18.48739 4.603373

-1.329 123 111 5.128205 4.624023

-1.322 96 104 -4 5.001001

-1.325 135 98 15.87983 4.647176

-1.317 75 49 20.96774 6.385592

-1.312 91 65 16.66667 5.681286

73 Graph 3: Anticrossing B, Line 2

Polarization Memory vs. Bias

0 Polarization Memory %

-5

-10

-1.340 -1.335 -1.330 -1.325 -1.320 -1.315 -1.310 Bias Voltage (V)

7.3. Anticrossing C

Table 6 : Experimental Details: Aperture C Date and time 200707072218 Sample name R050103G-B5 Aperture Co-ordinates H3.89-V7.36 Laser Wavelength 880 nm Laser power 37.5 mW Sample Temperature 14.18 K Integration time 60 s Grating 1100 centered at 965 nm

Table 7 : Anticrossing C, Line 1

Bias (V) I(RHC) I(LHC) P(%) Error

-1.203 3303 1732 31.20159 1.009193 -1.217 1888 990 31.20222 1.334839 -1.227 1388 752 29.71963 1.546109 -1.238 690 390 27.77778 2.173144 -1.243 474 254 30.21978 2.651893 -1.249 344 196 27.40741 3.072457 -1.283 287 147 32.25806 3.440513 -1.29 218 105 34.98452 3.998117

Graph 4: Anticrossing C, Line 1

Polarization Memory vs. Bias

30 Polarization Memory (%) Polarization

-1.30 -1.28 -1.26 -1.24 -1.22 -1.20 Bias Voltage (V)

Table 8 : Anticrossing C, Line 2

Bias (V) I(RHC) I(LHC) P(%) Error

-1.325 343 185 29.92424 3.113157

-1.315 317 151 35.47009 3.323065

-1.309 264 123 36.43411 3.65783

-1.304 228 130 27.3743 3.773382

-1.284 293 168 27.11497 3.324609

-1.276 265 150 27.71084 3.505541

-1.268 360 183 32.59669 3.076789

-1.264 358 183 32.3475 3.081794

-1.261 383 189 33.91608 3.00137

77 Graph 5: Anticrossing C, Line 2

Polarization Memory vs. Bias

30 Polarization Memory % 28

-1.33 -1.32 -1.31 -1.30 -1.29 -1.28 -1.27 -1.26 Bias Voltage (V)

Chapter 8 : Conclusion and Future Directions

Preliminary data indicate that there may be a trend in polarization memory of

anticrossing lines. As lines anticross, the polarization memory decreases, approaches a

minima near the centre of the anticrossing region, and then starts to increase again. We can theoretically model this using the concept of exchange interactions. As one charge

carrier (hole, in this case) tunnels out of the first dot and into the second dot, the

exchange anisotropy increases because we can effectively ignore the hole that now

resides in the second dot, since intradot exchange interactions are much stronger than

interdot exchange interactions. Large exchange anisotropy brings about mixing of states

and a partial erasing of polarization memory. We do not expect this erasing of

polarization memory to be complete, because we will need to take into account the interaction of the hole spin in the other dot.

What we observe at present is probably only a part of the whole picture, but it fits with

our theory. Following this thesis, continued analysis will take place with higher

integration time to increase intensity counts. Higher bias resolution will ensure more data

points, for a more detailed study. It will also include the deconvolution of the polarization

memory of two crossed lines into polarization memory of two single lines.

More research in this area has been planned, where detailed studies of dots with different separation widths shall be performed. This will allow us to study anticrossing strength as a function of separation and the effects that the change in coupling strength has on polarization. These experiments are critical for understanding the subsequent spin interactions present in these quantum dot molecules. A clear understanding of the polarization signatures of coupled quantum dots is a crucial step toward control of the spin states in these systems.

Plans are also underway to perform additional studies on colloidal quantum dots obtained from the Dept. of Chemistry at Ohio University. In addition, quantum ring samples recently obtained from the University of Arkansas will allow us to carry out other original experiments.

References

[1] Ware, M. E. et al. Polarized Fine Structure in the Photoluminescence Excitation

Spectrum of a Negatively Charged Quantum Dot. 95, 177403 (2005).

[2] Doty, M. F. et al. Spin Interactions in InAs Quantum Dots and Molecules. PSS 243,

3859 (2006).

[3] Ponomarev, I. V. et al. Theory of Spin States in Coupled Quantum Dots. PSS 243,

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Appendix A

Schottky Structure

Band bending occurs when two materials with different Fermi energies are placed

together. They may be composed of the same basic material but may have different levels of doping. In this structure of n-doped GaAs alongside undoped GaAs, there is an excess of electrons near the n-doped region. This escapes into the n-GaAs/GaAs boundary region which raises the Fermi level of the undoped GaAs region. This effect is strongest at the region closest to the interface, where the influence of the electrons from the n- doped region is the strongest. It decreases linearly as you move away from the interface, with the band eventually relaxing into a more natural state.

Band Bending GaAs (10nm)

AlGaAs InAs (2.5 nm) barrier (40 nm) Schottky contact Fermi level

GaAs (200 nm) AlGaAs n-doped barrier GaAs (80 nm) GaAs

interface region InAs

Appendix B

Lab Equipment

Trivista 3 Stage Spectrometer: The Acton Trivista spectrometer made by Princeton

Instruments has three stages, giving it great flexibility since it can be used in additive or subtractive mode. The three diffraction stages also make it a very versatile, high resolution instrument. Each stage can be set to one of the three diffraction gratings, (300,

750 and 1100 groove/mm) depending on the resolution or the quantum efficiency required at a certain wavelength. It can also be used as a single stage or double stage spectrometer by using stages as mirrors. The liquid nitrogen-cooled silicon CCD detector is located after the final stage. It can be used in both imaging and spectroscopy mode.

Trivista 3 Stage Spectrometer

Tsunami Laser: The Tsunami laser, made by Spectra Physics, uses a Ti-sapphire crystal

and has a birefringent filter. The laser is tunable between 700 and 1000 nm. It can be

operated in either continuous wave (CW) or pulsed mode capable of delivering

femtosecond pulses. Its maximum power output is 2 W. Its wavelength range is ideally

suited to our spectroscopy experiments, specifically photoluminescence excitation studies, since resonant wavelengths of the quantum dots lie in the near IR range. We can also carry out non resonant photoluminescence experiments where the electron is excited to the wetting layer.

Tsunami laser

Helium Cryostat: The closed cycle Helium cryostat is capable of maintaining the sample at ~10 K. The sample is mechanically isolated from the cryostat to prevent movement resulting from vibrations.

Closed cycle He cryostat

Appendix C

Labview, by National Instruments, was used to control most of the lab equipment

including the spectrometer, laser wavelength, liquid crystal retarders, temperature control and power meter. Data was plotted using Origin and Microsoft Excel.

Most of the major programs were written by Eric Stinaff, and some of the smaller ones

were a group effort by all the lab members.