KTH Second Level Theses Micro-Photoluminescence Spectroscopy of Semiconductor Quantum Dots in the Telecom Regime

KAI WANG

KTH ROYAL INSTITUTE OF TECHNOLOGY E L E C T R I C A L E N G I N E E R I N G A N D C O M P U T E R S C I E N C E

DEGREE PROJECT IN NANOTECHNOLOGY SECOND LEVEL

STOCKHOLM, SWEDEN 2019

Micro-Photoluminescence Spectroscopy of Semiconductor Quantum Dots

in the Telecom Regime

Kai Wang

2019

Master’s Thesis

Examiner Prof. Val Zwiller

Academic adviser

Dr. Klaus Jöns Ms Katharina Zeuner

KTH Royal Institute of Technology

School of Electrical Engineering and Computer Science (EECS)

Department of Applied Physics

SE-100 44 Stockholm, Sweden

Abstract | i

Abstract

Quantum communication has huge potential to be the crucial component of the next generation of

communication. Based on the single photon sources, this technique can be realized. As for many candidates for acquiring single photon sources, semiconductor quantum dots (QDs) are one of the competitive alternates for this goal.

In this thesis, we aim for observing the advanced optical spectroscopy of semiconductor quantum dots grown with different structures and temperatures. QD sample growers grown five types of QD samples with different structures. Distributed Bragg reflector structure, position-controlled nanowire structure and parabolic structure are designed and grown, aiming to the enhancement on brightness of emission light from QDs. The highest efficiency of enhancement on the emission brightness of QDs is using nanowire structures. Besides, the relation between different temperatures for growing QDs and the fine structure splitting (FSS) of QDs was verified by micro-photoluminescence spectroscopy measurements. 545 °C is the most efficient temperature implied by the distribution of FSS of all measured QDs for growing semiconductor QDs, by which the FSS can be lowered.

We successfully assembled and aligned the delay line part, which is a significant component of HOM experiment. The delays range from 1593 ps to 2660 ps. Moreover, we built the network between QNP Lab located in the Albanova University Centre and Ericsson Lab set in Kista. We tested the stability of power and polarization of light transmitted in the fiber network. The results were to our expectation. We explored some methods for compensation for the fluctuations of power and polarizations.

In conclusion, this thesis work focus on the micro-photoluminescence spectroscopy of QDs and find good candidates for the further measurements. The stability measurements of power and polarization of light transmitted in the fiber network connecting QNP Lab with Ericsson Lab provides original test data as preparation work for the future research work.

Keywords

Quantum Communication, Single Photon Source, Semiconductor Qauntun Dots, Micro-photoluminescence Spectroscopy

Sammanfattning | iii

Sammanfattning

Kvantkommunikation har en enorm potential att vara den avgörande komponenten i nästa generations kommunikation. Baserat på singelfotonkällor kan denna teknik realiseras. Ett framgångsrikt sätt att producera singelfotonkällor är att tillverka kvantprickar av halvledarmaterial. I den här uppsatsen strävar vi efter att observera den avancerade optiska spektroskopin av kvantprickar i halvledarmaterial tillverkade med olika strukturer och under olika temperaturer. Kvantprickstillverkare tillverkade fem typer av kvantpricksprover med olika strukturer. Distribuerad Bragg-reflektorstruktur, positionskontrollerad nanotrådstruktur och parabolisk struktur är framtagna och tillverkade med förhoppningen om att förbättra ljusstyrkan från kvantprickarna. Den högsta effektiviteten för förbättring av kvantprickarnas ljusstyrka gavs av att använda nanotrådsstrukturer. Förhållandet mellan olika temperaturer vid tillverkning av kvantprickarna, samt dess fina strukturuppdelning (FSS) bekräftades genom mikrofotoluminescensspektroskopimätningar. Den mest effektiva temperaturen för att sänka FSS-värdet visade sig vara 545 ° C och härstammar från av fördelningen av FSS hos de specialtillverkade halvledarkvantprickarna. Vi har framgångsrikt monterat och justerat fördröjningslinjedelen, som är en viktig komponent i HOM-experimentet. Fördröjningarna sträcker sig från 1593 ps till 2660 ps. Dessutom byggde vi nätverket mellan QNP Lab i Universitetscentrum AlbaNova och Ericsson Lab i Kista. Vi testade stabiliteten i kraft och polarisering av ljus som överförts i fibernätet. Resultaten uppnådde våra förväntningar. Vi undersökte några metoder för kompensation av kraftfluktuationer och polarisationer. Sammanfattningsvis syftar denna uppsats med fokus på mikrofotoluminescensspektroskopi av kvantprickar på att hitta bra kandidater för de framtida mätningar. Stabilitetsmätningarna för effekt och polarisering av ljus som överförs i fibernätet mellan QNP Lab med Ericsson Lab tillhandahåller ursprungliga testdata som förberedelser för det framtida forskningsarbetet.

Nyckelord

Kvantkommunikation, singelfotonkällor, kvantprickar av halvledarmaterial, mikrofotoluminescensspektroskopi

Preface | v

Preface

Per aspera ad astra.

To the stars

vi | Acknowledgments

Acknowledgments

This thesis work could not be finished without my supervisors Dr. Klaus Jöns and Miss Katharina Zeuner. Without Katharina’s and Klaus’s patience and kind help, there is no way that I can develop myself the excellent experimental skills. Katharina and Klaus always encourage me which gives me confidence on research. I am motivated to pursue my PhD in the future.

I would like to thank my examiner Prof. Val Zwiller who open his research lab twice to me. He shows enough respect to my personal research interests. I really appreciate it.

Also, I would like to say thank you to Marijn Versteegh for his useful and kind suggestion for my PhD applications.

At last, I would like to thank all members of Quantum Nano Photonics group for accepting me as one of the members. I have been working with you for a whole year. Each day I was happy working with you. Thank you for helping me so much and suggestions for improving this thesis work and making sure of the quality of thesis work.

Thank you again!

Stockholm, 12/2019

Kai Wang

Table of contents | vii

Table of contents

Abstract ....................................................................................................................................................... i

Keywords ......................................................................................................................................................... i

Sammanfattning ........................................................................................................................................ iii

Nyckelord ...................................................................................................................................................... iii

Preface ....................................................................................................................................................... v

Acknowledgments ..................................................................................................................................... vi

Table of contents ...................................................................................................................................... vii

List of Figures ............................................................................................................................................ ix

List of Tables ............................................................................................................................................ xiii

List of Acronyms and Symbols ................................................................................................................... xv

1 Introduction ....................................................................................................................................... 1

2 Theoretical Background ...................................................................................................................... 5

2.1 Semiconductor quantum dots ........................................................................................................... 5

2.2 Excitation process of a QD ................................................................................................................. 8 2.2.1 Excitonic discrete energy levels in the s-shell of a QD .................................................................. 8 2.2.2 Excitonic fine structure splitting ................................................................................................. 11

2.3 Photon properties ............................................................................................................................ 12 2.3.1 Indistinguishability ...................................................................................................................... 13 2.3.2 Photon Entanglement ................................................................................................................. 14

3 Experimental methods ..................................................................................................................... 15

3.1 Micro-photoluminescence experimental setup ............................................................................... 15

3.2 Auto-correlation measurements ..................................................................................................... 16

3.3 Indistinguishability measurements ................................................................................................. 18

3.4 Stability measurements of quantum communication network ....................................................... 19

4 Semiconductor QDs emitting at telecom wavelengths ...................................................................... 27

4.1 The growth of semiconductor QDs with different structure ............................................................ 27 4.1.1 QDs samples without a distributed Bragg reflector (DBR) structure below the quantum dots . 28 4.1.2 QDs samples with a DBR structure below the quantum dots ..................................................... 29 4.1.3 QDs samples with a position-controlled nanowire structure ..................................................... 30

viii | Table of contents

4.1.4 QDs samples with a parabolic structure ..................................................................................... 31

4.2 Investigation of different growth conditions on the QD emission ................................................... 33 4.2.1 The influence of growth temperature on properties of QDs emission ....................................... 33 4.2.2 The influence of different structures of QD samples on the QD emission ................................. 37

5 Conclusions and Future work ............................................................................................................ 43

References ................................................................................................................................................ 45

List of Figures | ix

List of Figures

Figure 1-1. The schematic diagram of epitaxially semiconductor QDs and the energy level scheme. ............................................................................................... 2

Figure 1-2. The schematic diagram of cryogenic confocal micro-photoluminescence microscopy setup. ....................................................................................... 2

Figure 2-1. The schematic diagram of band structure of conductors, semiconductors and insulators. For insulators, CB is separated far from VB leading to the almost impossible movement of electrons from VB to CB; the bandgap between CB and VB of semiconductors is not too large that there is a chance to excite the electrons in the valence band to conduction band with some external energy; as for conductors, their CB and VB overlap with each other that makes the materials conductive. .................................................................................................. 5

Figure 2-2. The density of states versus the energy E. For a bulk material (3D), the DOS is proportional to the square root of the energy E; for a quantum well (2D). the DOS is proportional to a constant which is shown in the figure as the energy steps; for a quantum wire (1D). the DOS is expotentially to the square root of the energy E; for a quantum dot (0D), the energy level is discrete. ................................................................ 7

Figure 2-3. The schematic diagram of the energy levels in the conduction and valence band of a QD. A two-dimensional harmonic oscillator model is applied to this approximation of the QD potential. Different states in the s-, p- and d-shell are shown in this diagram. ....................................................... 9

Figure 2-4. All possible states between s-shells in the CB and VB. The solid arrows are electrons in the s-shell of the conduction band and the dotted arrows are holes in the s-shell of the valence band. .............................................. 10

Figure 2-5. The simplified diagram of different types of excitation processes inside a QD. Resonant Excitation occurs between the s-shells inside the VB and CB. Between the higher shells like p- and d-shells inside the VB and CB, quasi-resonant excitation takes place. When the excitation energy is higher than the bandgap between CB and VB, there will be the non-resonant excitation. ..................................................................... 10

Figure 2-6. Biexciton-exciton cascade process in the ideal and real QDs. The left side can generate the entangled photons as the single photon source, where ideally there is no FSS that means that no information about the which-path of recombination can be known. The QDs with FSS can also produce entangled photons with oscillating states which can be resolved with good time resolution. ...................................................... 12

Figure 2-7. The schematic diagram of HOM interference experiment setup ...................... 13 Figure 2-8. The schematic diagram of the biexciton-exciton cascade process in a QD. ...... 14 Figure 3-1. The schematic diagram of micro-photoluminescence setup. A long-pass

(LP) filter blocks the lasers out of the light ............................................... 15 Figure 3-2. Hanbury Brown and Twiss experimental setup for measurement of g(2) (!)

function. This experimental set-up consists of micro-photoluminescence setup for the excitation of QDs and collection of photons emitted by QDs and an HBT-type interferometer with a 50/50 fiber beam splitter. Two SSPDs are used for detecting the photons. This experiment can be run under cw or pulsed excitation. Two SSPDs are connected to a correlator. This correlator in this schematic diagram shows the g(2) (!) function of cw excitation. ................ 17

x | List of Figures

Figure 3-3 [38]. Theoretical g(2) (!) function histogram under cw laser excitation (left) and pulsed laser excitation (right). In the left graph, the depth determines the value of g(2) and the width defines the radiation time; in the right histogram, the ratio between the area of middle peak (ideally equals to zero) and the average area of the edge peaks determines the value of g(2) under the pulsed laser excitation. .................. 17

Figure 3-4. The experimental setup of delay lines. .............................................................. 19 Figure 3-5. The delay time generated by PC-control moving stage along with z-axis. ......... 19 Figure 3-6. . The schematic diagram of experimental setup of stability measurement of

quantum communication network built between KTH Quantum Nano Optics Lab, KTH Kista Campus and Ericsson research labs. ..................... 20

Figure 3-7. The Poincare sphere with three stokes parameters as the three coordinates [41]. ........................................................................................................... 21

Figure 3-8. The measurement of changes of power and polarization of vertical polarization, linear (+45°) polarization and the reference laser. (a) shows the change of polarization of light from Kista campus with light from QNP Lab at vertical polarization;(b) shows the change of power of light from Kista campus with light from QNP Lab at vertical polarization; (c) shows the fluctuation of reference laser power in QNP Lab during vertical polarization measurement; (d) shows the change of polarization of light from Kista campus with light from QNP Lab at linear (+45°) polarization polarization;(f) shows the change of power of light from Kista campus with light from QNP Lab at linear (+45°) polarization polarization; (e) shows the fluctuation of reference laser power in QNP Lab during linear (+45°) polarization measurement. ........ 22

Figure 3-9. The power of the reference laser versus time recorded by powermeter (vertical polarization). ............................................................................... 23

Figure 3-10. Temperature, dew point and humidity changed versus time recorded by room sensor. ............................................................................................. 23

Figure 3-11. The power of the reference laser versus time recorded by power-meter (linear +45° polarization). ......................................................................... 25

Figure 3-12. Temperature, dew point and humidity changed versus time recorded by room sensor. ............................................................................................. 25

Figure 3-13. The 24-hour measurements of stability of power and polarization of light coming back from Kista Ericsson Lab with the incident light with vertical polarization, left-circular and linear (+$%°) polarization.(a), (b) and (c) shows the change of power of reference lasers measured in QNP Lab; (d), (e), (f) and (g), (h), (i) shows changes of power and polarization of light sent back from Kista Ericsson Lab, respectively. ...... 26

Figure 4-1. The schematic diagram of the structure of the QDs sample without a DBR structure. ................................................................................................... 28

Figure 4-2. The schematic diagram of the structure of the QDs sample No. 8344 and one piece of sample No. 8366 with a DBR structure that contains 20 pairs of GaAs/AlAs in total. ....................................................................... 29

Figure 4-3. The schematic diagram of the Top DBR structure of the sample No. 8366. ..... 30 Figure 4-4. The InP-based controlled-position nanowire structure of samples No.

CBE17-068, No. CBE17-069 and No. CBE17-072. ..................................... 31 Figure 4-5. The schematic diagram of the sample No. 8227 with a parabolic reflector

structure. ................................................................................................... 31 Figure 4-6. Micro-photoluminescence spectrum of a QD in the sample No. 8336. ............ 33

Figure 4-7. . All measured QDs from Sample No. 8334, No. 8335, No. 8336 and No. 8434 show different average value of fine structure splitting. ................... 34

Figure 4-8. The FSS of all measured QDs grown in sample No. 8358. ................................ 34 Figure 4-9. The distribution of emission wavelength of measured QDs in the samples

No. 8334, No. 8336, No.8343, No. 8335 and No. 8358 (λEW is the wavelength of emission from QDs). .......................................................... 35

Figure 4-10. . The distribution of emission wavelength of measured QDs in the samples No. 8334, No. 8336, No.8343 and No. 8335. .............................. 37

Figure 4-11. The FSS of all measured QDs in the sample No. 8344 and No. 8366 with DBR structures. ......................................................................................... 37

Figure 4-12. The distribution of emission wavelength of measured QDs in the sample No. 8344, one piece of sample No. 8366 without a top DBR structure and two pieces of No. 8366 with a top DBR structure. .............................. 38

Figure 4-13. The distribution of emission brightness of QDs in the sample No. 8344, one piece of No. 8366 without a top DBR structure and the other pieces of No. 8366 with a top DBR structure. ........................................... 39

Figure 4-14. FSS of all measured QDs in the samples No. CBE17-068/069/072. ............... 40 Figure 4-15. The distribution of emission wavelength of measured QDs in the sample

No. CBE17-068/069/072. ......................................................................... 41 Figure 4-16. The distribution of emission wavelength and brightness of measured QDs

at different areas in the sample 8227. (a) and (b) shows the distribution of emission wavelength and brightness of QDs at the area where the parabolic structure is grown; (c) and (d) shows the distribution of emission wavelength and brightness of QDs at the reference area where there is no parabolic structure. ............................... 43

List of Tables | xiii

List of Tables

Table 1. The initialization of growth setting for growing the QD samples without a DBR structure. ................................................................................................... 28

Table 2. InAs-based QDs samples without a DBR structure grown under different temperatures. ............................................................................................ 29

Table 3. The thickness of each GaAs/AlAs layer in the sample No. 8344 and No. 8366. .... 30 Table 4. The differences of growth conditions of three samples No. CBE17-

068/069/072. ........................................................................................... 31

List of Acronyms and Symbols | xv

List of Acronyms and Symbols

AFM atomic force microscopy BS

beam splitter

CB

conduction band

CCD charge-coupled device Cu copper cw continuous wave DBR

distributed Bragg reflector

DOS density of state e-h pair FS FSS FWHM Ga GaAs hh HOM HWP ICT InAs InGaAs lh

electron-hole pair fine structure fine structure splitting full width at half maximum gallium gallium arsenide heavy hole Hong, Ou and Mandel half-wave plate information and Communication Technology indium arsenide indium gallium arsenide light hole

MBE

molecular beam epitaxy

MCA multi-channel analyzer &PL micro-photoluminescence MOVPE metal-organic vapor-phase epitaxy

NPBS PBS PL QD SEM SSPD T TCSPC

non-polarizing beam splitter polarizing beam splitter photoluminescence quantum dot scanning electron microscopy super-conducting single-photon detector trion time-correlated single-photon counting

xvi | List of Acronyms and Symbols

VB X X* XX

valence band exciton charged exciton biexciton

1 Introduction

Nowadays, our society is experiencing the age of information where fast information dissemination and processing are based on optical communication in standard telecommunication fibers, belonging to classical communication which is inherently not secure. Thus, the security of the information is required along with the deepening of the information age. Quantum computation and communication technology based on a large network of optical fibers can be considered as a potential approach for secure and fast communication. Photonics and quantum information technology has been put forward and researchers have been working on improving the performance of quantum devices, aiming for quantum technology application on the commercial form. The core components of this technology [1] are single photon sources [2], single photon detectors [3] and photonic circuits [4,5]. For the future development of quantum technology, distant single photon sources which generate indistinguishable photons need to be explored.

In a photon generation process, single emitters send a photon at a time, which can be attached with digital information 0 and 1 [6]. As for an ideal single photon source, several physical properties are significant to give a description of an ideal single photon source. The first is single-photon purity which means that a light field contains no more than one photon. It guarantees the security of quantum communication [7]. The second is the indistinguishability. The photons must be indistinguishable because the key idea of many quantum technologies is a two-photon quantum gate that one photon entangles with the other photon. It requires effective photon-to-photon interactions. Last but not least, the brightness of single photon sources is also important because there is optical loss in the optical fiber for the communication.

In recent years, researchers have studied the physical properties of semiconductor quantum dots (QDs) and identified the huge potential of semiconductor QDs for quantum applications. QDs are nanometer-size confined structure where electrons and holes are trapped in three dimensions. Epitaxially-grown semiconductor quantum dots [8] which is shown in figure 1-1 plays an important role that the growth of the interface of semiconductors can be controlled for developing devices on chips and can tune the emission wavelengths of QDs for different applications. In our experiments, for the great need for quantum communication via optical fiber, we have developed efficient single-photon sources at the telecom C-band (1530 – 1570 nm) to minimize the loss in the fiber.

Figure 1-1. The schematic diagram of epitaxially semiconductor QDs and the energy level scheme.

A micro-photoluminescence spectroscopy experimental setup was used as is shown in figure 1-2. It was used for the measurement of excitonic fine structure splitting of the epitaxial semiconductor QDs emitting entangled photon pairs at the telecommunication C-band. Photons emitted from QDs were characterized by continuous and pulsed lasers and superconducting single photon detectors.

Figure 1-2. The schematic diagram of cryogenic confocal micro-photoluminescence microscopy setup.

Chapter 2 includes the theoretical background for understanding this thesis work. Beginning

with basic ideas about semiconductor properties, then it moves to the part where confined structures with low dimensions, for example, quantum wells, wires and dots are discussed. The optical excitation and recombination processes of a QD are present afterwards. Besides, the measurements to characterize entanglement and indistinguishability of generated photons are given.

Chapter 3 described several experimental methods used for this thesis work. At the beginning,

this chapter introduces the experimental setup for micro-photoluminescence spectroscopy of QDs. Besides, the principle of an auto-correlation measurement is illustrated. Then, the delay line was built for measurements of distinguishability and the characterization of fibers was performed.

Chapter 4 shows the results of measured properties of semiconductor QDs at cryogenic

temperature around 8K. Then, more semiconductor samples with different structures for the enhancement for brightness and minimization of excitonic fine structure splitting of QDs is given. Besides, the influence of the temperature on semiconductor QDs growth is studied in this chapter.

Chapter 5 gives a detailed conclusion of the finished work during this thesis and an outlook

for development of semiconductor QDs and their application in the future.

2 Theoretical Background

The following chapter concludes the theoretical background required for the deep understanding of the QDs for this thesis. Basic concepts on QDs are given [9-11]. It also gives a brief overview of the excitonic fine structure splitting of QDs [9]. Lastly, the properties of the photons generated from semiconductor QDs covering the entanglement of single photon pairs and indistinguishability are given [10].

2.1 Semiconductor quantum dots

Based on the bandgap energy between conduction band (CB) and the valence band (VB), the materials can be distinguished between insulators, semiconductors and conductors. Figure 2-1 shows the schematic diagram of the band structure of insulators, semiconductors and conductors. Usually CB and VB of conductors overlap with each other leading to the easier movement of free electrons in CB. For insulators, the band gap Eg between CB and VB is too large (more than 4 eV) which means the electrons are difficult to be excited from VB to CB. The band gap Eg of semiconductors is between 0.1 eV to 4 eV [12].

Figure 2-1. The schematic diagram of band structure of conductors, semiconductors and insulators. For insulators, CB is separated far from VB leading to the almost impossible movement of electrons from VB to CB; the bandgap between CB and

VB of semiconductors is not too large that there is a chance to excite the electrons in the valence band to conduction band with

some external energy; as for conductors, their CB and VB overlap with each other that makes the materials conductive.

According to De Broglie’s statement each particle can be described by a wave with a certain wavelength

" = ℎ% (2.1)

Where h≈ 6.62607×10-34 Js is Planck constant and p the momentum of the particle. Thus, a free electron in a vacuum can be described as:

+(,, .) = /!(#∙%&'() (2.2) Where t being time, position r, wave vector k and 0 the angular frequency. The modulus of k is given by:

1 = |3| = 2πλ (2.3)

The gradient of the wave function +(,, .) can be derived with equation (2.1):

∇+(,, .) = 8+(,, .)89 /* +

8+(,, .)8; /+ +

8+(,, .)8< /, (2.4)

= >1*+(,, .)/* + >1++(,, .)/+ + >1,+(,, .)/, (2.5)

= >ℏ A%*/* + %+/+ + %,/,B+(,, .) (2.6)

= >ℏ %̂+(,, .) (2.7)

Where kx, ky and kz being the modulus of the three components of the wave vector k in the

x-,y-and z- direction；ex, ey and ez are the unit vectors along with the x-, y- and z-direction.

The %̂ is called the momentum operator which is defined as:

%̂ = −>ℏ∇ (2.8) Thus, substituting equation (2.2) and (2.8) into equation (2. 7) and then we can acquire that:

−>ℏ∇/!(#∙%&'() = %̂/!(#∙%&'() (2.9) ℏ3/!(#∙%&'() = %̂/!(#∙%&'() (2.10)

%̂ = ℏ3 (2.11)As is known in physics, in classical physics, the kinetic energy E is defined as:

J = 12KL

- = (KL)-2K = M-

2K (2.12)

Considering quantum mechanics, E is the eigenvalue of +(,, .), which is known as the time-independent Schrödinger equation that is given below:

− ℏ-2K∇-+(,, .) = J+(,, .) (2.13)

ℋ+(,, .) = J+(,, .) (2.14)

ℋ = − ℏ-2K∇- (2.15)

Where ℋ is the Hamiltonian. Expanding equation (2.13) then we can get that

− ℏ-2K A>-1*- + >-1+- + >-1,-B/!(#∙%&'() = J/!(#∙%&'() (2.16)

Thus, it is easily to obtain that

J = ℏ-1-2K (2.17)

The equation (2.17) describes the relationship between E and k when a free particle moves in a vacuum. However, in semiconductors, the size of three dimensions x, y and z-direction and lattice influence the movement of free electrons which requires considering the effective mass m* for better approximation. Typically, the effective mass of electrons and holes are

written as K.∗ and K0

∗ . When the size of the potential wells is comparable to the de Broglie wavelength of electrons, quantum confinement effect works [13]. According to the number of dimensions that are confined, it can be divided into quantum wells (2D confinement), quantum wires (1D confinement) and quantum dots (0D confinement) [14]. In these confinement structures, the de Broglie wavelength is given as follows:

"12 =ℎ

O3K.,0∗ 12P

(2.18)

Where K.,0∗ is the effective mass of the electron and the hole; kB the Boltzmann constant; T

the temperature. In a QD, the particle is trapped in all three dimensions and this is the reason why the only one discrete energy level is allowed in a QD [13]. This can be described more detailed in solid-state physics where the density of states (DOS) is used generally to calculate the number of states which can be occupied at different energy level with different confinement structures like bulk materials (3D), quantum wells, wires and dots [13]. Figure 2-2 shows the difference of DOS versus energy for 3D, 2D, 1D and 0D confinement structures.

Figure 2-2. The density of states versus the energy E. For a bulk material (3D), the DOS is proportional to the square root of

the energy E; for a quantum well (2D). the DOS is proportional to a constant which is shown in the figure as the energy steps; for a quantum wire (1D). the DOS is expotentially to the square root of the energy E; for a quantum dot (0D), the energy level

is discrete.

Thus, the discrete energy levels inside a QD makes it possible to generate the single photon for the quantum communication.

2.2 Excitation process of a QD

For the reason that in the typical InGaAs QDs the confinement in z-direction is much stronger that in x- and y-direction, we usually apply an infinite potential well model to calculate the eigenvalue of energy and the band structure of a QD. The energy eigenvalues of the energy band structure depend on the confinement in the z-direction [15].

2.2.1 Excitonic discrete energy levels in the s-shell of a QD

Since the better approximation of QDs is two-dimensional potential well [16, 17], then the Hamiltonian of a 2D harmonic oscillator is given by:

ℋ = 12K.,0

∗ Q + 12K.,0∗ 04-(9- + ;-) (2.19)

Then the discrete energy levels can be written as

J5,6 =ℎ042R (2S + |T7,!| + 1) (2.20)

Where n= 0, 1, 2, … and lazi= 0, ±1, ±2, … represents the principle quantum number and

azimuthal quantum number, respectively. 00 is the angular frequency of the harmonic oscillator. In the shell structure of the QD, the shell index s can be written as:

U = 2S + |T7,!| = 0, 1, 2, … (2.21)

In QDs, the name of the energy level follows the rules in the atomic orbitals [18, 19]. Thus, the different shells in QDs are labeled as s, p, d, … according to the value of the shell index. In each shell, the shell number and the azimuthal quantum number determines the states.

For example, in the p-shell, the states are |1, −1⟩ and |1, 1⟩ where the first number is the shell number and the second is azimuthal quantum number which is shown in fig 2-3.

Figure 2-3. The schematic diagram of the energy levels in the conduction and valence band of a QD. A two-dimensional harmonic oscillator model is applied to this approximation of the QD potential. Different states in the s-, p- and d-shell are

shown in this diagram.

As for the degeneracy d of each shell, according to the Pauli exclusion principle, each state can allow two electrons with different spin configuration which are spin-up and spin-down, thus d can be expressed as:

X = 2(U + 1) = 2, 4, 6, … (2.22) An electron is carried from the valence band to the conduction band with any type of excitation. These quasi-particles are named as excitons (X). Excitons can be treated as the spherical particles whose Bohr radius is larger than the lattice constant, giving the stronger confinement than bulk materials [20, 21]. The radiative recombination of the exciton is called photoluminescence (PL) where there is the emission of a photon. Besides excitons, there are biexcitons (XX)(two holes and two electrons) and trions X± (an exciton pulsing an excess electron or hole) existing during the radiative recombination process. The spin quantum number Se = ±1/2, and the projection of heavy hole spin is Shh = ±3/2. For the X, there are two different states existing that are bright states and dark states according to the transition selection rules. In dark excitons, the electron and the heavy hole have the same spin direction which means that the secondary angular momentum quantum number Mj = ±2. For the bright excitons, Mj = ±1. Fig 2-4 shows all possible states between s-shells in the CB and VB.

Figure 2-4. All possible states between s-shells in the CB and VB. The solid arrows are electrons in the s-shell of the conduction

band and the dotted arrows are holes in the s-shell of the valence band.

Different excitation processes determine the difference of the crucial properties of single photons emitted by semiconductor QDs. These properties include lifetime, polarization, indistinguishability and internal quantum efficiency. We distinguish the excitation process into three types which are resonant excitation to the s-shell, quasi-resonant excitation to higher shells like p- and d-shells and non-resonant excitation into barriers, respectively [22], as is shown in Fig 2-5.

Figure 2-5. The simplified diagram of different types of excitation processes inside a QD. Resonant Excitation occurs between the s-shells inside the VB and CB. Between the higher shells like p- and d-shells inside the VB and CB, quasi-resonant excitation

takes place. When the excitation energy is higher than the bandgap between CB and VB, there will be the non-resonant

excitation.

Non-resonant optical excitation During this excitation process, the excitation energy must be higher than the bandgap between the CB and VB to generate the electron-hole pairs. The electrons in the CB and the holes in the VB interact via phonons in the bulk materials to form the excitons where the electrons and the holes of excitons recombine with each other to emit single photons. Quasi-resonant optical excitation For the quasi-resonant excitation process the external energy excites the electrons to form the excitons with holes in the p-shell or other higher shells. Then these excitons relax from p-shell to the lower shell and recombine to generate the single photons Resonant optical excitation There is a direct excitation into the s-shell in a QD. The excitons recombine to emit single photons without extra relaxation time unlike the quasi-resonant excitation.

2.2.2 Excitonic fine structure splitting

An ideal quantum dot possesses a perfect symmetry around its grown axis which the states should be energetically degenerated. However, in practice, these grown QDs are typically asymmetric which leads to the energy splitting in the X which is called excitonic fine structure splitting [23]. The fine structure splitting can be calculated as follows by using the

spin operators for the electrons and holes which are YZ e,i and YZ h,i, respectively and

Hamiltonian [\exch [24, 25]:

[\.*80 = − ] ^_!YZ0,! ∙ YZ.,! + a!YZ0,!9 ∙ YZ.,!b

!:*,+,,

, (2.22)

where x, y and z are the spatial axes and ai, bi are the coupling constants of the spin operators for the electrons and holes, respectively. According to equation (2.22), for the X± states it can be understood that there is no FSS because these states can be considered as spin singlet states [24] that vanishes the products in the equation (2.22). For the biexciton states, electrons and holes are both in singlet states leading to the vanishing products. More detailed information can be found in M. Bayer [25]. For this thesis, only the bright state plays the role, thus, the formula for the bright state is given by:

∆J;<< =38 Aa* − a+B + Ad* − d+B (2.23)

Where dx and dy are the coupling constants of the interaction perpendicular to the grown axis. For the ideal QDs, the symmetry in the x-y plane leads to the same value of these

coupling constants, resulting in no FSS. The fine structure splitting plays an important role in the bright exciton states because the XX and the X follow a cascade process where the XX recombines first and then it’s the turn for the recombination of the X. As is shown in Fig 2-6, if the X is degenerate, the spin of the X can’t be distinguished [26], leading to the superposition polarization of the emitted photons. As a result, this cascade process can be used to generate entangled photon pairs for quantum communication [27].

Figure 2-6. Biexciton-exciton cascade process in the ideal and real QDs. The left side can generate the entangled photons as

the single photon source, where ideally there is no FSS that means that no information about the which-path of recombination

can be known. The QDs with FSS can also produce entangled photons with oscillating states which can be resolved with good time resolution.

Nowadays, a significant number of research groups are working on minimizing the energy splitting with applying an electric or magnetic field on QDs and improving the growth methods [28-31]. Combination of vertical electrical field and external stress is also a potential method to reduce the FSS [32].

2.3 Photon properties

To ensure the quality of quantum communication, there are several significant requirements for the single photons generated by QDs. One is that the photons emitted by QDs should be indistinguishable for most quantum application. The other is that these single photons must be entangled meaning the state of one photon is dependent on the state of the other photon which can satisfy the requirements of two-photon quantum gates, quantum key distribution (QKD) and entanglement swapping. Besides, the brightness and the single photon purity of the QDs are also required to some degree.

2.3.1 Indistinguishability

Many quantum technologies require indistinguishable single photons for an effective interaction between photons [7]. The whole excitation and recombination processes should be indistinguishable which requires that the wavepackets of two single photons should be overlapped with each other. In practice, the experimental QDs don’t show perfect indistinguishability of the single photons due to time jitter, spectral diffusion [33]. The distinguishability is characterized by the mean overlap of the photon wavepacket written as M. The mean overlap of two-photon wavepackets can be measured by two-photon interference method where the Hong-Ou-Mandel experiment is set up for measuring the interference [34]. As is shown in Fig 2-7, the two indistinguishable single photons with the same pure quantum state are sent into the beam splitter to coalesce into a pair detected at either one of the two outputs. In principle, only one detector will detect this pair of photons if they have the same pure state. The HOM visibility which is used to describe the quantum interference is applied to describe the degree to the coalescence. The visibility VHOM is given as follows [7]:

*!"# = ,$ − ,∥,$

(2.24)

where ,$ is the coincidence count and ,∥ is the second-order coincidence count that is measured

between the two outputs. The indistinguishability can be written as:

3 = *!"# 45& + 6&265 7 (2.25)

where R and T are reflection and transmission, respectively.

Figure 2-7. The schematic diagram of HOM interference experiment setup

For an ideal QD, M=1 means that it is the perfect indistinguishability. Considering the impurity for the real QDs, the indistinguishability is characterized by M* which is given by [7]:

!∗ = !+ $"(0) (2.26) where $"(0) is the second-order correlation that used for characterizing the purity

of the single photon, which is zero when the QDs are the ideal.

2.3.2 Photon Entanglement

Quantum entanglement started with a famous Gedanken experiment called EPR paradox published by Einstein, Podolsky and Rosen in 1935 [35]. It is a physical phenomenon where two and more particles entangle with each other which means that measuring one of these entangled particles instantaneously changes other particles’ state independent on the distances between these particles. Along with the development of quantum information technology, the need of the quantum entanglement has risen. Benson et al. suggested that the biexciton-exciton cascade process of a QD would generate the pairs of entangled photons which are polarization-entangled [27]. This biexciton-exciton cascade process consists of the radiative decay of biexciton state to either of the two bright exciton states, and then the bright exciton relaxes to the ground state with radiation [36]. Fig 2-8 shows the biexciton-exciton cascade process in a QD schematically.

Figure 2-8. The schematic diagram of the biexciton-exciton cascade process in a QD.

3 Experimental methods

This chapter introduces the experimental methods applied in this work in detail. For characterizing the optical properties of QDs, several different measurement techniques have been used and are given in the following sub-sections.

3.1 Micro-photoluminescence experimental setup

Figure 3-1. The schematic diagram of micro-photoluminescence setup. A long-pass (LP) filter blocks the lasers out of the light

emitted from the QDs. In the cryostat, a stack of x,y, and z piezo positioners is set up for moving samples .

For observing the optical properties of QDs, we used a micro-photoluminescence setup as is shown in Figure 3-1. There are main three components which are a pumping laser system for exciting the samples to generate charge carriers, a confocal microscope to focus laser on the sample and collect the PL signals from the QDs and a detector consisting of a charge-coupled device (CCD) camera and a spectrometer. Since the recombination of charge carriers in the samples can generate either photons, phonons or AUGER-electrons, in case of PL spectroscopy, the photons are the only ones need to be detected. During the excitons’ lifetime, thermal activation will have influence on QD confinement. To guarantee high recombination rate of excitons, the interaction between phonons should be decreased as much as possible. The samples are put into a cryostat for cooling down to temperatures of T= 8 K. The sample is fixed on a stack of x,y,z three piezo positioners. For exciting the quantum dots to emit the photons, we use a continuous wave (CW) He-Ne and a tunable pulsed-laser during the whole experiments. The He-Ne and Toptica laser are usually used for characterization of the QD samples and fiber coupling.

To observe single QDs and measure the PL spectroscopy of these QDs we should ensure as few QDs as possible will be excited at the same time. This requires that the excitation area on the sample should be quite small. Otherwise the spectra of these excited QDs will overlap with each other which makes it hard to distinguish from these QDs. In addition, the cryostat is equipped with a white light source and a CCD camera to image the sample surface and observing the sample movement. To ensure that the pattern of the excitation laser is adjusted as small as possible, the z-piezo positioner along the vertical direction was controlled by PC to move to make sure that the sample is at the position of focal point of the laser where the excitation area of the sample is the smallest. Long-pass filters are set to suppress the reflected lasers in the detection part. We also installed a supplementary polarization analyzing setup in front of the spectrometer. It comprises a motorized HWP and a PBS. The HWP rotates the polarization of the incident light, while the PBS only transmits p-polarized light to the spectrometer. Light with s-polarization is reflected. This allows to measure the polarization of the PL signal, by continuously rotating the HWP and taking a spectrum in every step.

3.2 Auto-correlation measurements

To distinguish whether a light source is a thermal, coherent or non-classical light source, second-order correlation measurements need to be applied. According to the definition of non-classical light, a single QD, as a quantum emitter, should emit a single photon at a time. To give the demonstration of the single-photon property of the QDs, we perform second-order correlation measurements under pulsed laser excitation in a setup [37], shown in Fig 3-2. A transmission spectrometer or a fiber filter is used for acquiring the pre-filtered PL emission from a single QD. This spectrally filtered emission is divided into two equal beams after a 50/50 fiber beam splitter which are afterward detected by two arms in an HBT-type interferometer. In this experimental setup we use SSPDs with low dark count rates 30/s, quantum efficiency 15% and 25%, and a temporal resolution of 20 ps. One of the two SSPDs acts as the starting trigger of a precise electronic time clock. The other one gives the stopping trigger to the correlator (HydraHarp 400). As for the stopping signal, before it is fed to the correlator, there is a delay fixed electronically. The correlation measurements in this work are time-tagged. Once the correlator receives every arriving photon, each photon gets a time stamp and the sync of the laser gets a time stamp. Afterwards, a time-tag analysis software is used for building the histograms.

Figure 3-2. Hanbury Brown and Twiss experimental setup for measurement of g(2) (=) function. This experimental set-up

consists of micro-photoluminescence setup for the excitation of QDs and collection of photons emitted by QDs and an HBT-type interferometer with a 50/50 fiber beam splitter. Two SSPDs are used for detecting the photons. This experiment can be

run under cw or pulsed excitation. Two SSPDs are connected to a correlator. This correlator in this schematic diagram shows

the g(2) (=) function of cw excitation.

The correlator builds up a histogram in each channel corresponds to a certain time delay between the starting and stopping signal. With an external delay fixed electronically, we can manually shift the one of the SSPDs signals to the zero-delay position. Typically, the time delay is set on the zero position in the middle of the histogram. Ideally, at a zero-delay position, g(2) (0) should be zero because there is no coincidence for a single photon source. Typically, a delay time is much longer than the correlation time. For coherent light, there is

no correlation and g(2) (e) is a constant, which is named Poisson level. For a Fock state |S⟩ [38]:

f(-)(0) = 1 − 1S (3.1)

For an ideal single photon source with n=1, g(2) (0)=0.

Figure 3-3 [38]. Theoretical g(2) (=) function histogram under cw laser excitation (left) and pulsed laser excitation (right). In the

left graph, the depth determines the value of g(2) and the width defines the radiation time; in the right histogram, the ratio

between the area of middle peak (ideally equals to zero) and the average area of the edge peaks determines the value of g(2)

under the pulsed laser excitation.

For the pulsed laser excitation, in the right histogram of Fig 3-3, the difference of two edge peaks is laser pulse repetition. If it is a perfect single photon source, there should be no

coincidence at delay e=0 because a photon should not be detected by the two SSPDs at the same time. Under the pulsed laser excitation, the second order correlation function can be expressed as [39]:

f>?6@.1(-) (0) = gAB

g<B(3.2)

Where AMP is the area of middle peak and ASP is the average area of the edge peaks.

3.3 Indistinguishability measurements

We built the delay lines part for the indistinguishability measurement which is shown in figure 3-4. It is used for telecom regime. The beam splitter is 50/50. A PC-controlled moving stage generates the delay by changing the optical path length that used in the experiments. This moving stage continuously moves along with z-direction from + 80 mm to – 80 mm. The step for each movement is 20 mm. As is shown in the figure, the fiber coupling efficiency of shorter path and longer path is 77.2 % and 66.7 %, respectively. A laser at 1550 nm is connected into the input of the delay line. The output of the delay line needs to be connected to the superconducting single photon detectors. Since SSPDs are highly sensible, there were attenuators mounted before the laser was sent into the SSPDs. Once the laser is detected by SSPDs, a time tagged file for different positions of the stage will be recorded. Then these time tagged files will be analyzed by ETA software to get the peaks generated by lasers. According to positions of the stage, photons will be found at a different time delay. The difference between the peaks is the delay time we generate, as is shown in Fig. 3-5. The delay time ranges from 1593 ps to 2660 ps when the stage moves from + 80 mm to - 80 mm.

Figure 3-4. The experimental setup of delay lines.

Figure 3-5. The delay time generated by PC-control moving stage along with z-axis.

3.4 Stability measurements of quantum communication network

We built the experimental setup for measuring the stability of polarization and power of single photons emitted from KTH Quantum Nano Optics Lab to KTH Kista Campus via optical fibers, as shown in Fig 3-5. It aims to observe the environmental influence like temperature, humidity, etc. on the stability of quantum communication network. Before the photons emitted by the QD is guided into fiber network between Ericsson research labs in Kista and KTH QNP Lab in downtown Stockholm, a polarimeter (Thorlab PAN5710IR3) is

set to check the polarizations of the photons controled by "/2 and "/4 waveplates. Linear polarizations including horizontal, vertical, + 45° and - 45° and circular polarizations (left- and right-hand circularly) are chosen to be measured. To describe these measurements, stokes parameters are defined for quantitation. After confirming the expected polarization, we send the laser into a 10/90 beam splitter. 90% of the laser is sent to Ericsson research

labs in and the rest 10% of the laser is set as the reference laser measured in the KTH QNP Lab. The reference laser passed through the polarization beam splitter and then was measured by two powermeters (Thorlab PM 100D) which were connected to a laptop for recording the data for 13 times measurements.

Figure 3-6. . The schematic diagram of experimental setup of stability measurement of quantum communication network built

between KTH Quantum Nano Optics Lab, KTH Kista Campus and Ericsson research labs.

These stokes parameters are related to the polarization ellipse and intensity of the photons. They can be expressed as follows [40]:

Y4 = h

YC = h% cos 2l cos 2m

Y- = h% sin 2l cos 2m

Y9 = h% sin 2m (3.3)

Where I the intensity of the light, and p is the degree of polarization ranging from 0 to 1. l

and m are the spherical coordinates of the vector (S1,S2,S3), as is shown in Fig 3-6.

Figure 3-7. The Poincare sphere with three stokes parameters as the three coordinates [41].

The stokes vector is defined as +⃗ = -#'#(#)D3

. . According to the definition, here are some

common states of polarization of photons:

pCC44

q [rs><rS._TtrT_s><_.>rS p C&C44

q u/s.>v_TtrT_s><_.>rS

pC4C4

q w>S/_s(+45°)trT_s><_.>rS p C4&C4

q w>S/_s(−45°)trT_s><_.>rS

pC44C

q y>fℎ.ℎ_SXv>svzT_strT_s><_.>rS p C44&C

q w/{.ℎ_SXv>svzT_strT_s><_.>rS

Three states of polarization including vertical, linear ( +45° ) and left-hand circular

polarizations were measured with different time. As for the vertical and linear (+45°) polarizations, first time measurement was taken around 3.6 hours. The measurement of changes of polarizations and power are shown in Fig 3-7. The power of light coming back from Kista Ericsson Lab, showing in Fig 3-7 (d) and (e), are relatively stable compared with

the incident light sent from QNP Lab at vertical and linear (+45°) polarizations which are shown in Fig 3-7 (c) and (f) respectively. There were little fluctuations in two polarization states beyond expectation. The light from Toptica Laser at 1550 nm was guided in the polarization-maintaining fiber to the fiber collimator. Then more stability measurements on

vertical, linear (+45°) and left-circular polarizations were recorded by the polarimeter and powermeters set in QNP Lab. In these subsequent measurements, there was a 12-hour stability measurement with vertical and linear (+45°) polarizations of incident light sent from QNP Lab being recorded to compare with the change of room temperature, humidity and dew point recorded by QNP Lab room sensor at the same time.

Figure 3-8. The measurement of changes of power and polarization of vertical polarization, linear (+45°) polarization and the

reference laser. (a) shows the change of polarization of light from Kista campus with light from QNP Lab at vertical polarization;(b) shows the change of power of light from Kista campus with light from QNP Lab at vertical polarization; (c)

shows the fluctuation of reference laser power in QNP Lab during vertical polarization measurement; (d) shows the change of

polarization of light from Kista campus with light from QNP Lab at linear (+45°) polarization polarization;(f) shows the change

of power of light from Kista campus with light from QNP Lab at linear (+45°) polarization polarization; (e) shows the

fluctuation of reference laser power in QNP Lab during linear (+45°) polarization measurement.

As is in the purple circle shown in Fig 3-8 and 3-9, the maximum power difference of this measurement with vertical polarization of the incident laser is 2.3*10-5 W. Compared to the changes in the yellow and orange circles, the changes in humidity correspond to the changes of power during these periods. As for temperature and dew point, there is no obvious relation with the power change.

0 1 2 3-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 1 2 334

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Figure 3-9. The power of the reference laser versus time recorded by powermeter (vertical polarization).

Figure 3-10. Temperature, dew point and humidity changed versus time recorded by room sensor.

The maximum power difference is 5.4*10-5 W, shown in the red circle area in Fig. 3.10. The changes in four green circle areas shown in Fig 3-10 correspond to the changes of humidity marked with yellow circles in Fig 3-11. However, between 22:00 p.m. and 00:00 a.m., the change of humidity didn’t bring large fluctuation in the power, according to Fig 3-10 and 3-11.

0.00006

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from 12:00-2:30 AM

0 11.288.465.64

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er (W

)

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Powermaximum difference 2.3e-5 W

Figure 3-11. The power of the reference laser versus time recorded by power-meter (linear +45° polarization).

Figure 3-12. Temperature, dew point and humidity changed versus time recorded by room sensor.

As is shown in Fig 3-12, there were obvious fluctuations existing for stability measurements with three different polarization states of Toptica lasers, which are vertical, left-circle and

linear +45° polarization respectively. However, as is shown in the (a), (b) and (c) in Fig 3-12, compared to vertical and left-circle polarization, power of reference laser during the linear

0 2 4 6 8 10 12

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+45° polarization measurement was smaller because the beam splitter was used before the incident laser was sent into the first fiber collimeter shown in Fig 3-5.

Figure 3-13. The 24-hour measurements of stability of power and polarization of light coming back from Kista Ericsson Lab

with the incident light with vertical polarization, left-circular and linear (+GH°) polarization.(a), (b) and (c) shows the change

of power of reference lasers measured in QNP Lab; (d), (e), (f) and (g), (h), (i) shows changes of power and polarization of

light sent back from Kista Ericsson Lab, respectively.

Besides, with the incident laser with left-circle polarization, the stability of light from Kista Ericsson Lab is better than another two polarizations, showing in (g), (h), and (i) in Fig 3-12. In the red circle area in Fig 3-12 (i), there is a sharp peak appearing in the time region ranging from 15 to 20 hours. As is shown in Fig 3-13, a zoom-in-y-axis graph, there is a rapid change during 15-20 hours. As is mentioned above, the beam splitter is not the type of polarization-maintaining which means that polarizations of lasers transmitted through this beam splitter are changeable. Also, this beam splitter is sensible that it will easily change the output power of lasers once people touch this beam splitter. Since there was a sudden change during 15-20 hours, there should someone touching the beam splitter or fibers, leading to those sharp peaks showing in the (i) in Fig 3-12. To avoid the worse situations appearing, the non-polarization-maintaining beam splitter should not be used for the whole setup.

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d

4 Semiconductor QDs emitting at telecom wavelengths

To be an ideal single photon source for quantum communication at telecom wavelengths, it needs to fulfill several requirements according to the different types of applications. To be a single photon source, it means that the source should emit only one photon at a time. Ideally, the second order correlation function g(2) (0) should be zero with no more than one photon at a time. And the laser field gives the g(2) (0)=1 [7]. As for the application in real life, the value of g(2) (0) needs to be as low as possible. For the application in the quantum information processing, a single photon source with high purity is required because it can guarantee the generation of minimum errors which is beneficial to the security of quantum communication and quantum computing. Indistinguishability is one another significant characteristic of single photon for many applications. As mentioned before, the photons must be indistinguishable because it needs the effective interactions between two entangled photons which means that the state of one photon determines the state of the other photon for long-distance quantum communication. Furthermore, the brightness of a single photon source should also be guaranteed.

In this thesis work, we pay attention to epitaxial semiconductor QDs as the single photon source for quantum communication at telecom C-band (1530 nm – 1565 nm). Based on this aim, we tried to optimize the QD growth for lower fine structure splitting (FSS) with generation of entangled photon pairs.

4.1 The growth of semiconductor QDs with different structure

In this work, we prepared InAs-based QDs in GaAs grown by metal-organic vapour-phase epitaxy (MOVPE) method in Kista Campus. There are four different structures of QDs samples, which are samples without a distributed Bragg reflector (DBR) structure, with a DBR structure, with a nanowire structure and with a parabolic structure, respectively. For these samples without a DBR structure, Calos Nunez Lobato made a growth series with different growth temperatures of QDs, which were set at 515 °C, 530 °C, 545 °C and 560 °C, respectively. We found the lowest FSS in the sample No. 8335 whose QDs were grown at 545 °C, suggesting that the most suitable temperature for QDs is 545 °C. The samples with a DBR structure and top DBR structure were also grown by Carlos. Sofiane Haffouz grown the samples with a position-controlled nanowire structure. Carlos Nunez Lobato and Thomas Lettner grown the samples with a parabolic structure.

4.1.1 QDs samples without a distributed Bragg reflector (DBR) structure below the quantum dots

Sample No. 8334, No.8335, No.8336 and No.8343 are the samples without a DBR structure. As is shown in Fig 4-1, it contains five layers in the QD samples. Sample No. 8358 is grown with the same parameters of these samples without a DBR structure until growing the capping layer. The difference is that the capping layer is grown in 2 steps: the first 10 – 20 nm of this layer is grown at the QDs growth temperature followed by the growth of the rest of the capping layer at 700 °C.

Figure 4-1. The schematic diagram of the structure of the QDs sample without a DBR structure.

Here are the tables of detailed grown conditions of the QD sample without a DBR structure.

Table 1. The initialization of growth setting for growing the QD samples without a DBR structure. Initialization of growth setting: V/III =200, ptot=100 mbar, Annealing at 700°C, Rotation 80 rpm

Layer Growth Temperature

(°C)

Thickness of the layer

(nm)

Growth time (s) Properties of the

layer

GaAs 700 100 240

AlAs (sacrificial) 700 200 92.5 Fast oxidation under SEM Darker Line

Metamorphic Buffer Layer

(MMBL)

InxGa(1-x)As

700 1150 ~ 3100 to 3400 Relaxation 85%,

x= 0.38.

Undulation from 20

to 30 nm.

InAs QDs Varible - 4 PL 1400-1600 nm.

Large FSS.

Low counts ~ 600.

V/III ~400

Capping InGaAs

x=0.30

530 205 ~ 270 to 770 Indistinguishable

interface under SEM

There are five layers growing in these samples. At the bottom of the sample, showing in the Fig 4-1, the thickness of GaAs layer is 100 nm which is grown at 700 °C. Then, a layer of AlAs is grown above the GaAs layer whose thickness is 200 nm. After growning an AlAs layer, the metamorphic buffer layer (MMBL) InxGa(1-x)As is grown with thickness of 1100 nm ~1520 nm under 700 °C, where x=0.38 at the end. Following this step, the InAs-based QDs are grown on top of MMBL. In the end, the capping layer InGaAs is grown on the top of the sample. The thickness of this layer is aimed to grown at 200 ~ 300 nm. It is hard to distinguish the interfaces under SEM. A DBR structure has no influence on FSS. Besides, the brightness of these four samples is low, counted around 600 photons per second.

Table 2. InAs-based QDs samples without a DBR structure grown under different temperatures.

Sample Number 8334 8335 8336 8343

Growth Temperature of QDs (°C)

515 545 530 560

Mean Emission Wavelengths (nm)

1537 1530 1530 1524

The QDs layers pf the sample No. 8334, No.8335, No.8336 and No.8343 were grown under 515 °C, 545 °C, 530 °C and 560 °C, respectively, which is shown in Table 2.

4.1.2 QDs samples with a DBR structure below the quantum dots

A distributed Bragg reflector (DBR) is a light-enhanced structure containing alternate layers made of semiconductor materials with a high refractive index which makes it work as a reflecting mirror to enhance the light emitted from QDs. The samples No. 8344 and No. 8366 are grown with a DBR structure below their metamorphic buffer layers. In this case, there are no sacrificial AlAs layer grown above the GaAs layers. The DBR structure contains 20 pairs in total. One pair is formed by one layer of GaAs with aimed thickness of 115 nm and the other one layer of AlAs with aimed thickness of 134.4 nm. The schematic diagram of the whole structure of sample No. 8358 is shown in Fig 4-2.

Figure 4-2. The schematic diagram of the structure of the QDs sample No. 8344 and one piece of sample No. 8366 with a DBR structure that contains 20 pairs of GaAs/AlAs in total.

According to SEM measurements, thickness of sample No. 8344 and 8366 is shown in the Table 3.

Table 3. The thickness of each GaAs/AlAs layer in the sample No. 8344 and No. 8366. Sample Number Thickness of GaAs layer

(nm) Thickness of AlAs layer

(nm) Stopband (nm)

8344 120 108 1450

8366 115 127 1540

There is difference between sample No. 8344 and another two pieces of sample No. 8366. Compared to No. 8344, there is an additional top DBR structure in these two pieces of sample No. 8366. This additional top DBR structure contains of 4 pairs in total where one layer of SiO2 is grown by chemical vapour deposition (CVD) followed by one layer of Si3N4. Ideally, the thickness of one SiO2 layer and one Si3N4 is 269.1 nm and 203.9 nm, respectively, showing in Fig 4-3.

Figure 4-3. The schematic diagram of the Top DBR structure of the sample No. 8366.

4.1.3 QDs samples with a position-controlled nanowire structure

Our collaborators at NRC in Canada in the group of Dan Dalacu grown these samples No. CBE17-068, No. CBE17-069 and No. CBE17-072, which were grown with InAsP/InP nanowire structures, using chemical beam epitaxy on Fe-doped InP (1 1 1) B substrates with trimethylindium and pre-cracked phosphine (PH3) and arsine (AsH3) as precursors of indium, phosphorus and arsenic, respectively [42]. The nanowires are grown with Au catalyst particles in a combined selective area during the VLS process (420 – 435 °C and 2 sccm) [43, 44]. This kind of structure enhanced the light emission from QDs by two orders of magnitude [42]. The structure of these three samples are shown in Fig 4-4.

Figure 4-4. The InP-based controlled-position nanowire structure of samples No. CBE17-068, No. CBE17-069 and No. CBE17-

072.

The differences of these samples No. CBE17-068, No. CBE17-069 and No. CBE17-072 are shown in the Table 4.

Table 4. The differences of growth conditions of three samples No. CBE17-068/069/072. Sample Flow meter Arsine flow (sccm) Dot growth time

(s) Dot growth

temperature (°C) No. CBE17-068 60% As2 3 3 435 No. CBE17-069 99% As2 5 3 435 No. CBE17-072 37.5% As1 7.5 3 435

4.1.4 QDs samples with a parabolic structure

Since the light emission from QDs has multi-directions, leading to the low brightness observing during the measurements. To collect the photons emitted along different directions, this parabolic structure was designed to be used as a mirror to focus most of the emitted photons to enhance the ligh of QDs.

Sample No. 8227 is grown with a parabolic structure which is shown in Fig 4-5. The core idea is that the InAs-based QDs are grown at the focal point of a concave mirror.

Figure 4-5. The schematic diagram of the sample No. 8227 with a parabolic reflector structure.

Fabrication of this parabolic reflectors structure requires several processing steps, which made by Calos Nunez Lobato and Thomas Lettner. At the beginning, samples were patterned and coated with photoresist on the surface. Then, to acquire the expected parabolic shape, the resist needs to be reflowed. The InGaAs capping layer was etched and then a layer of gold evaporated on the top of the etched capping layer as the reflecting mirror. By growing the QDs with a parabolic reflector structure, the efficiency of collecting photons emitting from QDs was enhanced as expectation.

4.2 Investigation of different growth conditions on the QD emission

4.2.1 The influence of growth temperature on properties of QDs emission

In this chapter, micro-photoluminescence spectra were recorded. Here is an example shown in the Fig. 4-6. These following plots for each measured sample shows the distribution of emission wavelength and brightness, implying the relations between grown conditions and properties of QDs emission.

Figure 4-6. Micro-photoluminescence spectrum of a QD in the sample No. 8336.

4.2.1.1 The influence of growth temperature on FSS of QDs emission

To find the relation between the growth temperature of QDs and the FSS of QDs, we observed and measured 27 QDs, 26 QDs, 35 QDs for No. 8334, No. 8336, and No. 8343, respectively. As for sample No. 8335, we measured 26 QDs at the edge of the sample and 39 QDs at the centre of the sample. The FSS of all measured QDs are shown in Fig 4-6.

1535 1540 1545 1550 1555 1560 1565

0

200

400

600

800

Cou

nts

(arb

. uni

ts)

Wavelength (nm)

X XX

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

20eVFSS µ88.19= (27 QDs)

# of

QD

s

FSS (µeV)

8334

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

20

eVFSS µ15.24= (26 QDs)

# of

QD

s

FSS (µeV)

8336

Figure 4-7. . All measured QDs from Sample No. 8334, No. 8335, No. 8336 and No. 8434 show different average value of fine

structure splitting.

The average value of FSS of the QDs in the sample No. 8335 is smaller than the average value of FSS of QDs in the sample No. 8334, 8336 and 8343, showing in Fig 4.-6. It implies that the most efficient growth temperature of QDs is at 545 °C, bringing the lowest FSS 9.05 µeV) of QDs. As is shown in Fig 4-7, the average of FSS of QDs grown in the sample No. 8358 is 8.80 µeV.

Figure 4-8. The FSS of all measured QDs grown in sample No. 8358.

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

20eVFSS µ79.16= (35 QDs)

# of

QD

s

FSS (µeV)

8343

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

20(39 QDs)eVFSS µ66.11=

# of

QD

s

FSS (µeV)

8335 Center

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

20eVFSS µ05.9= (26 QDs)

# of

QD

s

FSS (µeV)

# of QDs

4.2.1.2 The influence of growth temperature on the wavelengths of QDs emission

According to micro-photoluminescence spectra, we recorded the emission wavelengths of each measured dot in the samples No. 8334, No. 8336, No.8343, No. 8335 and No. 8358, showing in Fig 4-9. These plots show the distribution of emission wavelength of QDs in each sample.

Figure 4-9. The distribution of emission wavelength of measured QDs in the samples No. 8334, No. 8336, No.8343, No. 8335

and No. 8358 (λEW is the wavelength of emission from QDs).

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20

nmEW 13.1547=l(27 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8334

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20

nmEW 11.1542=l(26 QDs)

# of

QD

sEmitting Wavelength (nm)

8336

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20

nmEW 07.1541=l(35 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8343

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20nmEW 91.1523=l

(39 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8335 Center

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20

nmEW 23.1554=l(26 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8335 Edge

1510 1520 1530 1540 1550 1560 1570 15800

2

4

6

8

10

12

14

16

18

20

nmEW 42.1551=l(37 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8358

As for samples No. 8334, No. 8336 and No. 8343, the average emission wavelength of QDs are 1547.13 nm, 1542.11 nm and 1541.07 nm, respectively. Sample No. 8335 shows difference on emission wavelength of QDs between the centre and the edge of the sample. The average of emission wavelength of the central part of No. 8335 is 1523.91 nm, which is smaller than 1554.23 nm the one that is the average emission wavelength of the edge of No. 8335. Compared with No. 8334, No. 8336 and No. 8343, the higher grown temperature of QDs brings the shorter emission wavelength of QDs.

4.2.1.3 The influence of growth temperature on emission brightness of QDs emission

200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

18

20countsBrightness 679=

(27 QDs)

# of

QD

s

Brightness (counts)

8334

200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

18

20

(26 QDs)

# of

QD

s

Brightness (counts)

8336countsBrightness 950=

200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

18

20countsBrightness 538=

(35 QDs)

# of

QD

s

Brightness (counts)

8343

200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

18

20countsBrightness 644=

(39 QDs)

# of

QD

s

Brightness (counts)

8335 center

Figure 4-10. . The distribution of emission wavelength of measured QDs in the samples No. 8334, No. 8336, No.8343 and No.

8335.

According to micro-photoluminescence spectra of measured samples No. 8334, No. 8336, No.8343 and No. 8335, plots for each sample describes the distribution of emission brightness of QDs, showing in Fig 4-9. In these samples, the QDs in the sample No. 8336 were the brightest compared to the others. It implies that lower grown temperature may be beneficial to the emission brightness of QDs.

4.2.2 The influence of different structures of QD samples on the QD emission

4.2.2.1 A DBR reflector structure grown on the QD samples

Figure 4-11. The FSS of all measured QDs in the sample No. 8344 and No. 8366 with DBR structures.

From the Fig 4-10, FSS of measured QDs in the sample No. 8344 and No. 8366 didn’t decrease so obviously which implies that DBR structure cannot lower FSS. The distribution of emission wavelength and brightness of measured QDs in the sample No. 8344, one piece of sample No. 8366 without a top DBR structure and two pieces of No. 8366 with a top DBR structure is shown in Fig 4-11 and 4-12.

200 400 600 800 1000 1200 1400 16000

1

2

3

4

5

6

7

8

9countsBrightness 607=

(26 QDs)

# of

QD

sBrightness (counts)

8335 Edge

0 5 10 15 20 25 30 350

2

4

6

8

10

12

14

16

18

20

# of

QD

s

FSS (µeV)

8344(32 QDs)eVFSS µ18.6=

0 5 10 15 20 25 30 350

2

4

6

8

10

12

14

16

18

20eVFSS µ81.7= (27 QDs)

# of

QD

s

FSS (µeV)

8366

Figure 4-12. The distribution of emission wavelength of measured QDs in the sample No. 8344, one piece of sample No. 8366

without a top DBR structure and two pieces of No. 8366 with a top DBR structure.

The piece of No. 8366 without a top DBR structure shows longer average emission wavelength of QDs than the other two pieces of No. 8366 with a top DBR structure. As is shown below, it can be found that the emission brightness of QDs in the pieces of sample No. 8366 with a top DBR structure is more than twice and five times of one piece of No. 8366 without a top DBR structure and No. 8344, respectively. Besides, compared to the distribution shown in Fig 4-10, the brightness of samples with DBR structures is much larger than those samples without DBR structures. It implies that the DBR structure can be grown for the enhancement of collection of emitted photons from QDs. Also, the additional top DBR structure grown on two pieces of No. 8366 brings much stronger enhancement on the emission brightness of QDs.

1500 1510 1520 1530 1540 1550 1560 15700

2

4

6

8

10

nmEW 12.1533=l(32 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8344

1500 1510 1520 1530 1540 1550 1560 15700

2

4

6

8

10

nmEW 27.1555=l(18 QDs)

# of

QD

s

Emitting Wavelength of QDs (nm)

8366 without top DBR

1500 1510 1520 1530 1540 1550 1560 15700

2

4

6

8

10

nmEW 13.1551=l

# of

QD

s

Emitting Wavelength of QDs (nm)

8366 with top DBR(22 QDs)

Figure 4-13. The distribution of emission brightness of QDs in the sample No. 8344, one piece of No. 8366 without a top DBR

structure and the other pieces of No. 8366 with a top DBR structure.

4.2.2.2 A nanowire structure grown on samples

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 550002468

1012141618202224262830

(32 QDs)

countsBrightness 531=

# of

QD

s

Brightness (counts)

8344

0 500 1000 1500 2000 2500 3000 3500 4000 4500 500002468

1012141618202224262830

countsBrightness 1322=

(18 QDs)

# of

QD

s

Brightness (counts)

8366 without top DBR

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 550002468

1012141618202224262830

countsBrightness 2863=

# of

QD

s

Brightness (counts)

8366 with top DBR

(22 QDs)

0 10 20 30 40 50 6002468

1012141618202224262830

eVFSS µ845.4= (8 QDs)

# of

QD

s

FSS (µeV)

CBE17-068

0 10 20 30 40 50 6002468

1012141618202224262830

eVFSS µ399.5= (29QDs)

# of

QD

s

FSS (µeV)

CBE17-069

Figure 4-14. FSS of all measured QDs in the samples No. CBE17-068/069/072.

Compared to the value shown in the Fig 4-6 and Fig 4-10, the samples grown with the InP-based nanowires structure also have lower fine structure splitting than the samples with a DBR structure and the samples without a DBR structure. The growth position of nanowires were predefined with Ebeam lithography. This nanowire structure improves the efficiency of collection of emitted photons from QD samples which is verified by the distribution of emission brightness of QDs in the samples No. CBE17-068/069/072, as is shown follows.

Figure 4. 15. The distribution of emission wavelength of QDs in the sample No. CBE17-068/069/072.

0 10 20 30 40 50 6002468

1012141618202224262830

eVFSS µ646.6= (49 QDs)

# of

QD

sFSS (µeV)

CBE17-072

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

2

4

6

8

10

12

14

16

18

20countsBrightness 3571=

# of

QD

s

Brightness (counts)

CBE17-068

(7 QDs)

1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

2

4

6

8

10

12

14

16

18

20countsBrightness 1291=

# of

QD

s

Brightness (counts)

CBE17-069

(24 QDs)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

2

4

6

8

10

12

14

16

18

20countsBrightness 1265=

# of

QD

s

Brightness (counts)

CBE17-072

(24 QDs)

However, as is shown in Fig 4-14, there is an obvious shortcoming of these samples that the emission wavelength of QDs grown in these samples is far away from 1550 nm what wavelength we desire for quantum communication.

Figure 4-15. The distribution of emission wavelength of measured QDs in the sample No. CBE17-068/069/072.

1000 1050 1100 1150 1200 1250 1300 1350 14000

2

4

6

8

10

12

14

16

18

20nmEW 5.1182=l

# of

QD

s

Emitting Wavelength of QDs (nm)

CBE17-068

(7 QDs)

1000 1050 1100 1150 1200 1250 1300 1350 14000

2

4

6

8

10

12

14

16

18

20

nmEW 33.1233=l

# of

QD

s

Emitting Wavelength of QDs (nm)

CBE17-069

(24 QDs)

1000 1050 1100 1150 1200 1250 1300 1350 14000

2

4

6

8

10

12

14

16

18

20nmEW 50.1187=l

# of

QD

s

Emitting Wavelength of QDs (nm)

# of QDs(24 QDs )

4.2.2.3 A parabolic structure grown on the sample

Figure 4-16. The distribution of emission wavelength and brightness of measured QDs at different areas in the sample 8227.

(a) and (b) shows the distribution of emission wavelength and brightness of QDs at the area where the parabolic structure is

grown; (c) and (d) shows the distribution of emission wavelength and brightness of QDs at the reference area where there is

no parabolic structure.

As is shown in Fig 4-15 (a) and (c), the average of emission brightness of QDs with a parabolic structure is nearly twice of average brightness of QDs at the reference area in the sample No. 8227. It shows that parabolic structure can be an effective method to enhance the emission brightness of QDs.

5 Conclusions and Future work

Single photon sources based on semiconductor quantum dots are a crucial component for developments of quantum applications such as long-distance quantum communication and quantum information processes. This thesis measured the emission of InAs-based and InAsP-based QDs at telecom C-band and observed the micro-photoluminescence of these semiconductor QDs. Besides, samples with different structures consisting of a DBR structure,

0 500 1000 1500 2000 2500 30000

2

4

6

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10

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14

16

18

20

# of

QD

s

Brightness (counts)

8227 with parabolic

(28 QDs)

countsBrightness 821=

a1530 1540 1550 1560 1570

0

2

4

6

8

10

12

bEmitting Wavelength of QDs (nm)

(28 QDs)

B

8227 with parabolicnmEW 85.1547=l

0 200 400 600 800 1000 12000

5

10

c

countsBrightness 458=

(24 QDs)

# of

QD

s

Brightness (counts)

8227 Reference

1530 1540 1550 1560 15700

2

4

6

d

nmEW 82.1552=l

# of

QD

s

Emitting Wavelength of QDs (nm)

8227 Reference

(24 QDs)

44 |

a top DBR structure, a nanowire structure and a parabolic structure are compared with each other to explore the most effective way to enhance the brightness of QDs and lower the fine structure splitting of QDs for entanglement measurements. A micro-photoluminescence spectroscopy setup was used to observe the emission of measured QDs in the samples at the telecom C-band (~ 1550 nm). Measurements on samples No. 8334, No. 8335, No. 336 and No. 8343 grown by MOVPE shows that the average values of the fine structure splitting of measured QDs grown in these four samples are 19.88 µeV, 10.62 µeV, 24.15 µeV and 16.79 µeV, respectively. The fine structure splitting of QDs grown at 545 °C was the lowest in the samples without a DBR structure or nanowire structure which implies that the best growth temperature of InAs-based QDs is 545 °C. More enhancement structures for improving the brightness of the QDs were fabricated. Compared to a DBR structure grown under the QDs layer and the parabolic mirror reflector structure, nanowire structure plays best performance on enhancement on the emission brightness of QDs. The DBR structure under QD layers contains 20 pairs in total where one pair is formed up with one layer of GaAs followed by one layer of AlAs. Also, the control of the target thickness of the DBR layers should be explored more. Moreover, the enhancement on the brightness of QDs may benefit from the parabolic structures. In this thesis, the delay-lines, one of the essential components of HOM measurement, was built and aligned for the preparation of measurements. Besides, one crucial part of this thesis work is that the stability measurement was undertaken in the quantum communication network connected between Ericsson research lab in Kista and KTH QNP Lab in downtown Stockholm, spanning a total distance of 36 km. We demonstrated a stability measurement experimental setup in KTH QNP Lab. The light was originally sent from Albanova to Ericsson Lab in Kista. The stability of the polarizations of light sent back from Kista was expected. Humidity and some other factors may have influence on the stability of the power and polarizations of the light. Besides, the fiber used in the network was not polarization-maintaining, leading to the fluctuation of stability of polarizations and power of light. More measurements have been carried out for exploring the factors relevant to the stability of polarizations of photons. For the future experiments, more new approaches to lowering the FSS and improving the brightness of QDs will be explored. There will be continual evolution process about more stable quantum communication in the coming future.

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