Correlation Between Structural and Optical Properties of Gaas

Submitted by B.Sc. Rajat Sethi Submitted at Institute of Semiconductor and Solid State Physics Supervisor Prof. Dr. Armando Rastelli Correlation between February, 2021 Structural and Optical Properties of GaAs Quantum Dots

Master Thesis to obtain the academic degree of Diplom-Ingenieur in the Master’s Program Nanoscience and -Technology

JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, Osterreich¨ www.jku.at DVR 0093696 Eidesstattliche Erkl¨arung

Ich, Rajat Sethi, erklärean Eides statt, dass ich die vorliegende Masterarbeit selbstständig und ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die wörtlich oder sinngemäßentnommenen Stellen als solche kenntlich gemacht habe.

Die vorliegende Masterarbeit ist mit dem elektronisch ¨ubermittelten Textdokument iden- tisch.

Linz, 16.02.2021

Rajat Sethi

Abstract

The molecular beam epitaxy (MBE) is a prominent technique to fabricate self-assembled quantum dots (QDs). In this thesis we will study the structural and optical properties of GaAs/AlGaAs quantum dots grown by MBE. The characterization methods that are used in the experiment are atomic force microscopy for the structural analysis of quantum dots, and micro-PL spectroscopy for the optical analysis. The atomic force microscopy is a tool that provides us data about the morphology (especially size and shape) of the quantum dots, and micro-PL gives us the information about the optical properties of the QDs such as excitonic fine-structure-splitting, emission energy etc. Our main object in this thesis is to correlate the results from both characterization methods to achieve highly symmetrical quantum dots which can further be used in the field of quantum entanglement as they serve a good source of entangled photons. Four such samples with four different growth protocols are investigated. These samples are grown on a GaAs(001) substrate. To fabricate the quantum dots, we used droplet etching method with Al-droplets on an Al0.4Ga0.6As barrier. The samples are then characterized by AFM and micro-PL spectroscopy.

After analyzing the data gathered from both characterization methods, a correlation appears between the physical features of QDs and its optical properties. The size and shape of QDs have a clear eﬀect on their light-emitting properties. More asymmetric QDs show a higher amount of excitonic ﬁne-structure-splitting. The samples A and B show higher asymmetry in their shape, and as we move on to sample C, the asymmetry reduces, so does its excitonic-FSS. Sample D has the most symmetrical QDs, and consequently, it shows the lowest excitonic-FSS. The results from the micro-PL agrees well with the results from AFM, which demonstrates a correlation between symmetry of the quantum dots and their optical properties. The optimized growth protocol with the lowest excitonic-FSS will then be used as a source of entangled photons. The work in this thesis is conducted at the Institute of semiconductor and solid state physics of Johannes Kepler University, under the supervision of Prof. Dr. Armando Rastelli.

Acknowledgment

I would like to express my immense gratitude and immeasurable appreciation to the following persons who had contributed one way or another to make this thesis possible with their help and support.

First and foremost, I would like to thank my thesis supervisor Prof. Dr. Armando Rastelli for his advice, guidance, valuable suggestions that beneﬁted me a lot in the completion and success of the study.

I would like to express sincere thanks to my colleagues Dr. Saimon Filipe Covre da Silva and M.Sc. Huiying Huang for their support throughout the thesis.

I want to thank our great technical staﬀ Ms. Alma Halilovic, Ms. Ursula Kainz, Mr. Albin Schwarz, and Mr. Stephan Br¨auer for guiding me and giving me the introductions to the clean-room labs, equipments, and various setups that I used in my experiments.

A sincere gratitude to my family (Mom, Dad, Kiran and Dinesh). I would like to thank my sister Diksha who has always been morally supportive to me and has given me emotional encouragement whenever I fell under pressure. I want to take a moment to, specially, thank my dear friends (Prince Khurana, Hubert Buchberger, Daniela Scheuchenstuhl, Joseﬁna Makowski, and Sina) for their endless love, support, and encouragement. It couldn’t have been possible without you guys.

Contents

1 Introduction 17 1.1 Semiconductors and their heterostructures...... 17 1.2 Characterization Techniques...... 18 1.3 Focus of the thesis...... 19 1.4 Outline of the thesis...... 20

2 Theoretical Background 21 2.1 Quantum Dot...... 21 2.2 Fundamental Optical process in Quantum dots...... 23 2.3 Quantum mechanical description of quantum dots...... 25 2.4 Basics of expitaxial growth...... 27 2.4.1 Frank-van-der-Merve...... 28 2.4.2 Volmer-Weber...... 28 2.4.3 Stranski-Krastanow...... 28 2.5 Molecular beam epitaxy...... 29 2.6 Self-assembled quantum dots...... 31 2.7 Droplet formation...... 32 2.7.1 Surface preparation...... 32 2.7.2 Density and size of droplets...... 33 2.7.3 Droplet-surface interaction...... 34 2.8 Quantum dot formation...... 35 2.9 Relation between emission energy and geometry of a quantum dot..... 37 2.10 Fine structure splitting...... 40

3 Experimental Considerations 42 3.1 Atomic force microscope...... 42 3.1.1 Conﬁguration of AFM...... 43 3.1.2 Working principles of AFM...... 44

7 Contents

3.1.3 AFM probe...... 46 3.2 Micro photoluminescence spectroscopy...... 47 3.2.1 Conﬁguration of PL-spectroscopy...... 47 3.2.2 PL Measurement procedure...... 48

4 Results and Discussion 50 4.1 AFM results...... 50 4.2 PL-spectroscopy results...... 64

5 Conclusions & Outlook 70

6 Appendix A 73 6.1 Sample A...... 73 6.2 Sample B...... 74 6.3 Sample C...... 75 6.4 Sample D...... 76 6.5 Important things to remember...... 77

Bibliography 80

8 List of Figures

1.1 Schematic diagram of bulk material and three diﬀerent nanostructures, i.e. well(2D), wire(1D), and dot(0D). Blue indicates the active material, while yellow stands for shell material, which is usually a larger bandgap semiconductor. Yellow axes in the coordinate system show the directions of conﬁnement [1]...... 18 1.2 Density of states for an electron in 3D (Bulk), 2D (Quantum well), 1D (Quantum wire), and 0D (Quantum dot) [2]...... 18

2.1 Scanning transmission electron microscopy of a self-assembled quantum dot [3][12]...... 22 2.2 AFM image of nanoholes etched by droplet epitaxy in 2D and 3D; the side view shows the depth profile of the hole...... 23 2.3 Schematic diagram of CB, VB and processes in a quantum dot...... 24 2.4 This schematic diagram shows the relation between the electronic structure and the size of the QDs [4]...... 25 2.5 Geometrical cross-section of a QD...... 26 2.6 Schematic illustration of primary modes of growth (a) FM, (b) VW and (c) SK where θ is a representative thickness of the layer...... 28 2.7 Schematic diagram of MBE growth chamber with all the components.... 30 2.8 An example of how RHEED monitors the growth of layers and islands [5]. 31 2.9 A schematic diagram showing droplet-surface interaction with the dependence of contact angle [30]...... 35 2.10 A schematic diagram showing Al-droplet interaction with AlGaAs surface and etching of the nano-holes...... 36 2.11 A schematic diagram showing the formation of a quantum dot by filling the nano-hole with GaAs material...... 36 2.12 Diagram showing Energy levels in a semiconductor QD with infinitely high potential walls...... 39

9 List of Figures

2.13 Model geometry of a lens-shaped self-assembled QD [6]...... 39 2.14 Fine-structure-splitting of the neutral exciton conﬁned in a QD, visible in polarization-resolved PL spectra. An image from sample B (See appendix A). 41

3.1 A schematic diagram of AFM and its components [7]...... 43 3.2 A simpliﬁed image of a probe tip scanning the surface [8]...... 44 3.3 A diagram showing the contact (static) mode of AFM where the tip is in constant contact with the sample [8]...... 45 3.4 A diagram showing Non-contact (dynamic) mode [8]...... 45 3.5 A diagram showing Tapping mode [8]...... 46 3.6 AFM probe tip as seen under the SEM [7]...... 46 3.7 Schematic of the experimental setup with essential elements for Micro- Photoluminescence measurements. The sample within the cryostat is illuminated by laser light through a confocal microscope and the emission from single QDs spectrally resolved and detected by a spectrometer [9]... 48 3.8 A power-dependent PL spectra showing a QD’s emission peaks on various excitation powers ﬁtted by Gausian functions...... 49

4.1 5 µm x 5 µm and 2 µm x 2 µm images of sample A...... 50 4.2 A 3-dimensional side view image of the same nanohole from figure 4.1 showing the mound like structure...... 51 4.3 Line-scan showing profiles 1 and 2 in both [1-10] and [110] directions respectively...... 52 4.4 A nanohole’s width measured in [1-10] and [110] directions respectively shown as profile 1 and 2...... 52 4.5 5 µm x 5 µm and 2 µm x 2 µm images of sample B...... 53 4.6 Width of a nanohole on Sample B shown as profile 1 in [1-10] direction and profile 2 in [110] direction...... 54 4.7 6 µm x 6 µm and 2 µm x 2 µm images of sample C...... 54 4.8 Line-scans of the width of a nanohole in sample C showing the overlap of both line scans in [1-10] and [110] direction...... 55 4.9 A 3-dimensional side view image of the same nanohole from figure 4.8 showing the roughness of the surface...... 55

10 List of Figures

4.10 3 µm x 3 µm and 2 µm x 2 µm images of sample D...... 56

4.11 Line scans of the width of a nanohole in sample D showing the complete overlap of both line scans in [1-10] and [110] directions...... 56

4.12 A scatter plot between depth and base-area of sample A showing various other parameters in the table...... 57

4.13 A scatter plot showing depth and base-area of nanoholes on sample B and other parameters related to depth shown in the table...... 57

4.14 A scatter plot showing depth and base-area of nanoholes on sample C and other parameters related to depth shown in the table...... 58

4.15 A scatter plot showing depth and base-area of nanoholes on sample D with other depth related parameters shown in the table...... 58

4.16 An image showing the depth proﬁle of a nanohole...... 59

4.17 An image showing the depth of the same nanohole with two diﬀerent scan-sizes. 61

4.18 A scatter plot showing asymmetry of the nanoholes in sample A along with a table showing standard deviations and mean width in [1-10] and [110] directions...... 61

4.19 A scatter plot showing asymmetry of the nanoholes in sample B along with a table showing standard deviations and mean width in [1-10] and [110] directions...... 62

4.20 A scatter plot showing asymmetry of the nanoholes in sample C along with a table showing standard deviations and mean width in [1-10] and [110] directions...... 63

4.21 A scatter plot showing asymmetry of the nanoholes in sample D along with a table showing standard deviations and mean width in [1-10] and [110] directions...... 63

4.22 An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample A showing the excitonic-FSS...... 66

4.23 An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample B showing the excitonic-FSS...... 67

4.24 An Image of cosine-ﬁt of a quantum dot peak from sample C showing the excitonic-FSS...... 68

11 List of Figures

4.25 An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample D showing the excitonic-FSS...... 69 4.26 FSS vs Emission energy for all the samples...... 70 4.27 A scatter plot showing the depth and asymmetry of all the samples..... 70

6.1 The layer sequence of sample A along with other important parameters... 73 6.2 The layer sequence of sample B along with other important parameters... 74 6.3 The layer sequence of sample C along with other important parameters... 75 6.4 The layer sequence of sample D along with other important parameters... 76 6.5 An example of how to measure depth and width of a nanohole/island.... 78 6.6 Another way how to measure depth and width the same nanohole from ﬁgure 6.5...... 79

12 List of Tables

4.1 Depth (in nm) of selected nanoholes in all four samples, determined from the linescans as those shown in ﬁg. 4.3, 4.6 4.8 and 4.11...... 59 4.2 A comparison table of data analyzed and calculated by Gwyddion and XIM; here BA¯ is the mean base-area and V¯ is the mean volume of nanoholes... 64 4.3 A table showing some of the important growth parameters...... 68

List of Symbols

This list describes several symbols which will later be used in this thesis.

αe Eﬀective mass of electron

αh Eﬀective mass of hole

r Relative permitivity of the material

λDB De Broglie’s wavelength

µ∗ Reduced eﬀective mass of electron-hole

ωx Width along x-axis

ωy Width along y-axis

ψ Wave function c Speed of light h Planck’s constant

kB Boltzmann’s constant m∗ Eﬀective mass of electron-hole pair

mo Free electron mass

15 List of abbreviations

Al Aluminium AlAs Aluminium arsenide AlGaAs Aluminium galium arsenide GaAs Galium arsenide PL Photoluminescence SPM Scanning probe microscopy AFM Atomic force microscope SEM Scanning electron microscope TEM Transmission electron microscope STM Scanning tunneling microscope QD Quantum dot MBE Molecular beam epitaxy ML Monolayer VB Valence band CB Conduction band FM Frank-van-der-Merve VW Volmer-Weber SK Stranski-Krastanov UHV Ultra-high vacuum RHEED Reﬂection high-energy electron diﬀraction MOCVD Metalorganic chemical vapour deposition NC Non contact CW Continuous wave FSS Fine structure splitting BA Base-area

16 Chapter 1

Introduction

This Chapter gives a brief introduction to the types of semiconductors, their heterostructures with diﬀerent dimensionalities, and the characterization techniques which have been used to characterize the quantum dots (0D semiconductor heterostructures), the focus and the outline of the thesis and description of samples used in the research of this thesis.

1.1 Semiconductors and their heterostructures Materials can be divided into three categories according to their electronic properties i.e. conductors, semiconductors, and insulators. In the ﬁrst type of materials, the Fermi level falls in the conduction band. They possess, therefore, free electrons (so-called Fermi gas), which gives rise to a relatively high electrical conductivity. In insulators, the energy band gap between conduction and valence band is so large that it requires energy much larger than the thermal energy kBT (with kB the Boltzmann constant and T the absolute temperature) for electrons to get excited into the conduction band. That is why insulators have extremely poor conductivity. In semiconductors, the band gap is typically between 0.5 to 5 eV. Semiconductors are arguably the most researched materials in the ﬁeld of physics since the 1950s. In this section of the introduction, low dimensional semiconductors will be discussed which are the focus of this thesis.

Semiconductors can be classified into 4 types depending on their dimensionalities: 3D, 2D, 1D, and 0D (see fig. 1.1). Bulk-semiconductors (3D) have quasi-continuum bands, and the charge carriers freely move without any confinement effects. On the other hand, heterostructures (i.e. structures obtained by combining different semiconductors) enable the creation of low dimensional electronic systems. If the dimensions of the semiconductor regions are in the nanometer scale, they show quantization of energy levels, and are able

17 Chapter 1. Introduction to conﬁne electrons and holes (quasi-particles corresponding to the absence of electrons in the valence band), thus yielding interesting quantum mechanical properties [2]. Figure 1.2 shows a schematic diagram of the density of states functions for diﬀerent structures assuming parabolic dispersion of the particle energy as a function of wave-vector.

Figure 1.1: Schematic diagram of bulk material and three diﬀerent nanostructures, i.e. well(2D), wire(1D), and dot(0D). Blue indicates the active material, while yellow stands for shell material, which is usually a larger bandgap semiconductor. Yellow axes in the coordinate system show the directions of conﬁnement [1].

Figure 1.2: Density of states for an electron in 3D (Bulk), 2D (Quantum well), 1D (Quan- tum wire), and 0D (Quantum dot) [2].

1.2 Characterization Techniques Nanoscience and technology is one of the fastest growing ﬁelds of research. Over the last three decades quantum dots (0D) have become a prominent topic of research in

18 1.3. Focus of the thesis semiconductor physics. To understand the quantum properties of these semiconductor heterostructures, appropriate characterization tools are required. Scanning Probe Microscopy (SPM) is one of the most prominent tools, which is used to characterize the objects and the surfaces at the nanoscale. The SPM was invented in 1981, and since then it has gone through many changes and further developments [10]. The atomic force microscopy (AFM) is a speciﬁc type of SPM, which uses inter-atomic forces between a tip attached to a cantilever and the surface of the object to obtain images of the surface topography as well as other information.

Over the last three decades, much research effort has been devoted in fabrication of nanostructures like quantum dots, nanotubes, nanocrystals, and nanofilms. The reason behind this is to find possible applications of nonostructures in various fields e.g. data storage, quantum computing, health care, biomedical and pharmaceutical industries, coat- ing and textiles [11]. A quantum dot is a semiconductor nanostructure that exhibits unique optical properties due to the quantum confinement effect [12]. Because of its very small size, on the order of a few nanometers, the behavior of the quantum dot is similar to a three-dimensional quantum well. The semiconductor quantum dots, investigated in this thesis, are epitaxially grown nanostructures with the help of Molecular Beam Epitaxy (MBE).

Now, another technique to characterize the optical properties of quantum dots is micro-Photoluminescence spectroscopy (micro-PL). Photoluminescence spectroscopy is a contactless and non-destructive technique of probing the electronic structure of materials [13]. In this spectroscopic process, light of a certain frequency is directed upon the sample and absorbed. The illuminated region goes through a process called photo-excitation. The excess energy is partly dissipated in form of lattice vibrations and partly emitted in form of light, which is called luminescence. In the case of photo-excitation, this luminescence is called photo-luminescence, in contrast to, e.g., catodoluminescence where luminescence is produced by electron irradiation [14].

1.3 Focus of the thesis This thesis is focused on the growth and characterization of quantum dots by the above mentioned techniques. The samples which are used in these experiments are self-

19 Chapter 1. Introduction assembled unstrained GaAs quantum dots which will be discussed in full details in the next chapters. In short, on a GaAs substrate, an AlGaAs epilayer is grown and further locally etched with Aluminium droplets. These etched structures are called nano-holes. The Nanoholes are optically and electronically inactive. To activate the nanoholes into quantum dots, a GaAs layer is grown to fill these holes, followed by an AlGaAs top barrier layer. The nanohole fabrication procedure is repeated on the sample surface so that these nanoholes can be characterized by AFM to know the size, depth, width, and symmetry of the quantum dots then further characterize the quantum dots by photo-luminescence spectroscopy to correlate the emission data to its physical features (size, shape, and depth). Because of the confinement, electrons in a quantum dots occupy discrete energy levels, in a similar fashion as they do in atoms. That is why they are also called artificial atoms [15]. The objective of the thesis is to correlate the structural characterization of quantum dots with the optical characterization; so that the quality of the quantum dot samples can further be improved and optimized to match specific requirements, such as a high symmetry for the generation of polarization entangled photon pairs [16][17].

1.4 Outline of the thesis In this thesis, there are six chapters including the introduction. In these chapters I have covered all the aspects of quantum dots from fabrication to the characterization one by one. In chapter 2, the theoretical background of QDs has been explained where we discuss the physics behind the QDs. chapter 3 describes the whole experimental set-up of the research, how the QDs are grown via MBE, and how they are characterized with AFM and micro-PL spectroscopy. In the following chapters 4 and 5 we discuss the results of the previous chapter 3 and conclude the ﬁndings of the research respectively. In the last chapter 6, I will provide some additional information about the growth protocols of original samples which are used in the thesis, and some important things to remember while performing these types of experiments. Some of the material used in this thesis has been taken from already published research papers, books or online articles; in those cases, the references have been cited in the bibliography at the end of the thesis.

20 Chapter 2

Theoretical Background

In this chapter, general information about semiconductor quantum dots will be presented, as well as the quantum mechanical model to describe their behavior and the growth of quantum dots will be discussed.

2.1 Quantum Dot A quantum dot is a semiconductor nanostructure in which the motion of charge carriers is confined in a three-dimensional region of space of a few nanometer size (comparable to the extent of the electron’s wave-function, typically from 2 nm to 50 nm). The charge carriers in a quantum dot are confined in such a small space that they behave in the same fashion as they do in a single atom, where the electron motion is confined by the Coulomb attraction to the nucleus. That’s why they are also called Artificial atoms, and the phenomenon is called the Quantum confinement effect. The confinement of the charge carriers produces discrete energy levels just like it does in an atom.

There are many ways to grow quantum dots. They can be synthesized chemically by mixing some compounds into the a solution (Colliodal) or they can also be grown epitaxially from clusters of atoms obtained by using MBE. If it’s a colloidal semiconductor nanocrystal, the confinement is due to the presence of semiconductor surfaces. Colloidal nanocrystals can be as small as from 2 to 10 nm i.e. about 10 to 50 atoms in diameter. If it’s an epitaxially grown self-assembled quantum dot, the confinement of charge carriers is due to the potential produced by the difference in band gap between the quantum dot material and the surrounding barrier material [18]. Self-assembled semiconductor quantum dots are typically between 5 and 50 nm in size and have a width to height ratio of about 3 to 1. The samples which are used in this thesis contain self-assembled semiconductor

21 Chapter 2. Theoretical Background quantum dots.

Quantum dots (also called as ”artificial atoms”) have a bigger advantage over atoms because of their fixed position and rigidity in space. They can easily be embedded in a solid state matrix and are easy to integrate in optoelectronic systems [19, 20]. Semiconductor industry is well established in today’s world and there are so many applications of Quantum dots such as light-emitting-diode(LED), a field-effect device, optical micro-cavity etc. The size and shape of the epitaxially grown QDs are tunable and according to their shape and size their electronic and optical properties can also be controlled [21].

One of the most studied quantum dots are epitaxially grown self-assembled QDs, by using different semiconductor materials with different band gaps and possibly different lattice constants. Epitaxially grown quantum dots are the primary topic of discussion in this chapter. There are mainly two types of epitaxially grown self-assembled QDs, and they are called strained quantum dots, and unstrained quantum dots. If the difference between lattice constant of QD material and the matrix is large, the QD will be strained i.e. InAs/GaAs quantum dot. The following figure 2.1 shows a transmission electron microscopy image of an InAs quantum dot embedded into GaAs matrix is an example of strained quantum dot [12] and figure 2.2 is an example of unstrained quantum dot. Specifically, the image shows surface characterization of nanoholes etched by using droplet etching technique which will be discussed later in this chapter.

Figure 2.1: Scanning transmission electron microscopy of a self-assembled quantum dot [3] [12]

22 2.2. Fundamental Optical process in Quantum dots

Figure 2.2: AFM image of nanoholes etched by droplet epitaxy in 2D and 3D; the side view shows the depth proﬁle of the hole.

2.2 Fundamental Optical process in Quantum dots Photoluminescence is a form of light emission (luminescence) from a material after absorbing a photon of certain energy. The energy from the absorbed photon is transferred to an electron in the valence band which promotes it to a higher energy level in conduction band. After relaxation, the electron undergoes a transition back to its ground state by emitting a photon, this light emission is called photoluminescence (PL), as sketched in ﬁgure 2.3. Electrons occupy discrete energy levels in a quantum dot, so the energy of the emitted photon is also discrete and characteristic of that quantum dot.

The figure 2.3 shows electrons in valence bands of the barrier material initially. Then by a high energy laser, they can be promoted to conduction band which leaves a vacancy in the valence band also known as hole. This electron-hole pair, bound together by the Coulomb attraction, is called exciton. After the relaxation of electrons within the conduction band, it recombines with the hole at the minima of CB by emitting a photon. If the potential barrier outside the QD is sufficiently high, the charge carriers stay confined. As a result of confinement, the energy levels of these charge carriers are quantized, hence the energy of emitted photon is also quantized.

The Quantization eﬀect becomes more apparent when the De Broglie wavelength (as

23 Chapter 2. Theoretical Background

Figure 2.3: Schematic diagram of CB, VB and processes in a quantum dot. shown in ﬁg. 2.4) of these charge carriers is comparable to the dimensions of the conﬁning

√ h region: λDB ∼ ∗ , where h and kB are Planck’s and Boltzmann’s constants, T is 2m kB T absolute temperature and m∗ is the eﬀective mass of electron/hole pair (exciton) in the semiconductor structure [22]. Since m∗ is usually much smaller than the free-electron mass, the λDB is the order of 10-100 nm at lower temperatures. The gaps between the energy levels in this rage of size can be smaller than the thermal energy.

Electrons and holes bind together to form exciton due to Coulomb attraction when kBT is smaller than the binding energy of electron-hole pair. The spacial extent of an exciton in a semiconductor, can be quantiﬁed by the Bohr Radius:

4π 2 a = 0 r~ (2.1) µ∗e2

∗ where r is the relative permitivity of the material and µ is the reduced eﬀective mass of electron-hole.

Since the value of µ∗ is usually very small as compared to the free electron mass, and

r is large for typical semiconductor materials, a is signiﬁcantly larger than the Bohr’s radius for a hydrogen atom. Instead of considering λDB for electrons and holes separately, it is usually more convenient to describe a QD as a region of space with size comparable

24 2.3. Quantum mechanical description of quantum dots

Figure 2.4: This schematic diagram shows the relation between the electronic structure and the size of the QDs [4].

to the exciton’s Bohr radius a [23][22].

2.3 Quantum mechanical description of quantum dots To understand how a charge carrier behaves in a quantum dot, the Schr¨odinger’s equation can be taken into consideration and solved for a Quantum dot potential:

2 − ~ ∇2ψ(r) + V (r)ψ(r) = Eψ(r) (2.2) 2m

Since a quantum dot conﬁnes the charge in three dimensions, the particle in the box model can be applied and the Schr¨odinger’sequation’s can be solved with the following potential:

 0 if 0 < z < L (x, y)  z  V(x,y,z) =   ∞ if otherwise

25 Chapter 2. Theoretical Background

Figure 2.5: Geometrical cross-section of a QD.

In this model, the local height of the quantum dot, Lz, depends on the in-plane coordinates x and y (ﬁg. 2.5). Since the motion along z axis dominates the kinetic energy, we can try to separate the vertical and lateral motion.

ψ(x, y, z) = ψ(x, y)ψ(z) (2.3)

The potential V(x,y,z) disappears inside the dot. By substituting 2.3 into Schr¨odinger’s equation 2.2:

2 2 − ψ(z) ~ ∇2ψ(x, y) − ψ(x, y) ~ ∇2ψ(z) = Eψ(x, y)ψ(z) (2.4) 2m 2m

2 2 ~ ∇2ψ(x, y) ~ ∇2ψ(z) − 2m − 2m = E (2.5) ψ(x, y) ψ(z)

Since the potential along the z direction is known, as seen in figure 2.5, the Schrödinger’s equation can be solved along the vertical motion, and the values of Ez can be obtained by ∗ using me as the effective mass of an electron.

2 ~ 2 − ∗ ∇ ψ(z) = Ezψ(z) (2.6) 2me

2 2 2 ~ π nz Ez(x, y) = ∗ 2 (2.7) 2me Lz(x, y)

We assume nz = 1 because energy levels with nz > 1 are much higher, and therefore, negligible when photoluminescence spectra from a quantum dot is measured at moder- ate excitation power. In this case, only the lowest lying energy levels are occupied and

26 2.4. Basics of expitaxial growth contribute to the spectra. The vertical conﬁnement behaves like potential for the lateral motion; so we set Ez = Vxy and we get the Schr¨odingerequation:

~2 − ∗ ∇ψ(x, y) + Vxyψ(x, y) = Eψ(x, y) (2.8) 2me

The solution of this equation depends on the details of the conﬁnement potential. Under the assumption of a lens-shape quantum dot, the potential can be replaced with a parabolic potential, and the lateral conﬁnement produces a spectrum of equally spaced levels as in a harmonic oscillator.

2.4 Basics of expitaxial growth To understand how quantum dots are grown, first, it is important to understand the modes of growth. There are three primary modes of thin film growth in nanofabrication. All three of them are used prominently to grow thin-films, islands and epitaxially grown quantum dots. The following steps and the growth modes are important to understand before studying the growth of a quantum dot. There are a few fundamental steps in the process of thin film growth [24].

1. When a material A is transferred to a substrate B, the interaction between two material takes place and the atoms of material A becomes weakly attached to the substrate. 2. The atoms which lie on the crystalline surface of the substrate are called adatoms. The adatoms diffuse over the substrate towards the low energy sites and depending on their affinity to the material of the substrate, chemical bonds between the adatoms and substrate are formed. 3. A cluster of adatoms starts to form on several locations over the substrate in order to minimize the energy of the system. This process is called Nucleation. 4. As these clusters grow bigger into islands and approach each other, they merge together to form continuous structure. This process is called Coalescence. 5. The islands continue to grow against each other until the entire substrate is covered. 6. After deposition, in the end, the processes such as grain growth and diffusion take place depending on the substrate temperature and environment.

27 Chapter 2. Theoretical Background

Now, depending on a material’s aﬃnity and environmental conditions, a simple description of these modes of growth are as following [25].

2.4.1 Frank-van-der-Merve

In this mode of growth, the adatoms are very compatible with the substrate material. They directly attach to the surface hindering the growth of clusters and islands. This type of growth mode creates smooth and conformal layers covering the substrate. This type of growth is also called layer by layer growth.

2.4.2 Volmer-Weber

Volmer-Weber (VW) growth is the opposite to the previous. In this mode of growth, the interaction between the adatoms of the deposited material is stronger than the interaction between the adatoms and substrate. Hence, islands of deposited material are formed all over the substrate. In the following ﬁgure 2.6, schematics of these modes of growth are graphically shown.

Figure 2.6: Schematic illustration of primary modes of growth (a) FM, (b) VW and (c) SK where θ is a representative thickness of the layer.

2.4.3 Stranski-Krastanow

The Stranski-Krastanow (SK) mode is the combination of both of the growth modes described above. In this mode, the growth follows the Frank-van-der-Merve pattern until it reaches a critical thickness. When the interaction between the adatoms and the substrate

28 2.5. Molecular beam epitaxy material weakens, the Volmer-Weber growth takes over the further growth process by creating three dimensional islands. This mode of growth is the most commonly used mode in QD growth.

In the following section, an introduction to MBE is given to better extrapolate the growth and characterization of quantum dots.

2.5 Molecular beam epitaxy ”Molecluar beam” is a ﬂow of unidirectional kinematic atoms without any collision among them; and ”epitaxy” made up of two Greek words epi meaning upon or akin and taxis which means an order or arrangment. Therefore, epitaxy means an ordered growth of one crystalline layer upon another [26]. The MBE is very unique and diﬀerent from other types of growth techniques like MOCVD because it takes place in UHV (ultra- high-vacuum). It relies upon the reaction between the atoms/molecules of the deposition material and the surface of the starting crytal (substrate); this reaction relies upon kinetic processes such as migration, adsorption, desorption, dissociation etc.

This technique is used to grow thin epitaxial films of a wide variety of materials, ranging from semiconductors to oxides to metals. Molecular beam epitaxy and the related technologies were first developed in 1970-71 by J. R. Arthur and Alfred Y. Cho at Bell Telephone Laboratories [27]. Up to now, it is considered to be the fundamental tool in nanotechnology and semiconductor industry. It was first used to grow a compound semiconductor, and still is widely used in large part because of high technological value of such materials in electronics industry [28].

In figure 2.7, all the main components of an MBE machine can be seen. There is a growth chamber which is kept under ultra-high vacuum of about 10−9 mbar to achieve the highest level of purity in thin film samples. There’s a mechanical arm that holds the substrate inside the chamber. The UHV is maintained in the growth chamber by pumps (typically cryopumps and/or ion getter pumps) and crypanels, cooled by using liquid Nitrogen at a very low temperature of around −196 ◦C[27]. The surface of the substrate is typically cleaned in-situ by heating the substrate to desorb the oxide layer or through hydrogen irradiation. There are multiple effusion cells filled with source materials

29 Chapter 2. Theoretical Background

Figure 2.7: Schematic diagram of MBE growth chamber with all the components.

like Ga, As and Al. These elements are in their ultra-pure form and heated until they slowly start to sublimate or evaporate. The effusion cells have shutters which can be opened or closed anytime when needed. These shutters are controlled by a computer software for MBE. When the shutter of one cell is opened, the gaseous element is condensed onto the substrate. The adatoms of that element migrate to the positions of lowest energy on the surface of the substrate. They may also react with other adatoms, for example Ga and As react on the surface of the substrate to form Gallium Arsenide (GaAs) crystal. A Reflection high-energy electron diffraction (RHEED) gun is also a part of the MBE, which monitors the growth of the crystalline layers. The RHEED signals are shown in figure 2.8 in which bright lines indicate a planar surface and layer-by-layer growth, and bright spots indicate the presence of three dimensional islands. In MBE, the thickness of the layers can be controlled down to the single atomic layer with high precision. The growth rate is typically from 0.01 µm/hour - 0.3 µm/hour.

To further explain the growth of quantum dots, it is crucial to talk about an alternative growth mechanism which is a little diﬀerent from SK-growth mode. In this growth method, instead of growing islands, the surface of the substrate is etched by droplets of a certain material, which form on the substrate following the Volmer-Weber growth. It is called droplet etching method [29].

30 2.6. Self-assembled quantum dots

Figure 2.8: An example of how RHEED monitors the growth of layers and islands [5].

2.6 Self-assembled quantum dots Self-assembled quantum dots can be divided into two categories on behalf of the lattice mismatch between materials of the quantum dot and the material on which it is grown(the substrate).

1. Strain-induced quantum dots When the material of the quantum dot is lattice mismatched with the substrate, it results into strain-induced quantum dots. Strain-induced quantum dots follow the SK-growth mode. The InAs/GaAs quantum dot is the most common example and widely studied. It starts oﬀ with two dimensional FW growth mode until it reaches a critical thickness (in this case 1.7 ML) and then InAs strained islands begin to form on top of the two-dimensional layer (wetting layer) in order to minimize the strain energy at the expense of an increased surface. These islands are formed wherever they ﬁnd the minimum elastic energy to minimize the total surface energy. Eventually the islands are buried under a GaAs layer to form strain-induced quantum dots. In this case, the method is called droplet epitaxy since the droplets are epitaxially arranged onto the substrate layer.

2. Unstrained quantum dots When there is a very small or no diﬀerence between the lattice constants of the quantum dot material and the substrate, it usually results into a layer by layer growth. Therefore, to remedy the situation, there has to be another way to fabricate quantum dots. The droplet etching method is used in this case eg. GaAs/AlGaAs (in which the lattice mismatch is at most 0.14% for pure AlAs). Droplet etching

31 Chapter 2. Theoretical Background

mechanism is further explained in details because the QDs grown by this method are the main focus of this thesis.

Droplet etching method is used to fabricate unstrained quantum dots and many other types of quantum heterostructures. In addition, unconventional ring like QDs, other special nano-heterostructures, QDs with unconventional shape and sizes etc. can be created with this approach [30]. In this method, which is usually employed for III-V semiconductors, droplets are created by exposing the surface to a a ﬂux of group-III elements without supply of group-V elements. In the droplet-etching method, nanoholes are created by the droplets upon exposure to a relatively low ﬂux of group-V elements [31].

2.7 Droplet formation There are a few steps to droplet etching which give a detailed description of what materials can be used for droplet formation, how droplets are formed and how they interact with the surface of the substrate. In this thesis, the samples are obtained by using aluminium droplets to etch the nanoholes on an AlGaAs surface. These steps are as following.

2.7.1 Surface preparation

It is important to know the initial status of the surface before formation of the droplets. Molecular beam epitaxy is a technique which is compatible with droplet epitaxy/etching. In MBE process, it is also very important to know that surface reconstruction aﬀects the growing layers, and it highly depends on the temperature of the substrate in the MBE chamber and the ambient environment[29]. Since the MBE setups usually have an integrated RHEED, the growth of layers can be continuously monitored to ascertain the status of the substrate surface. Before the substrate is introduced into the UHV chamber, the substrate is outgassed i.e. it is heated up to 300 ◦C for a few hours to remove all the water and other gases absorbed by it. After that the sample is introduced into the UHV chamber and heated again up to 300 ◦C and the As cell is opened to balance the rate of desorption and adsorption. Since the substrate was exposed to the air before introducing it into the UHV, It is covered with an oxide layer. For an epitaxial growth, it is important to remove these oxide layers in advance. There are diﬀerent methods to remove the oxide layers like hydrogen cleaning [32] or thermal deoxidation. In our case we

32 2.7. Droplet formation use thermal deoxidation. The substrate wafer is heated up to 580 ◦C to desorb the oxides present on the substrate surface. At around 580 ◦C the rate of desorption saturates and by using RHEED data, the Tdeox can be calculated. After this whole process of removing the impurities and oxides, the surface of the substrate becomes rough. To make the surface smooth, the substrate is further annealed for about 15 minutes at 620 ◦C.

◦ Tanneal = Tdeox + 40 C (2.9) where Tdeox is our growth temperature.

Before the growth of the quantum dots, a buffer layer is grown to recover a planar surface. In our case GaAs is the buffer layer in all the samples (see appendix A for sample protocols), since the substrates consist of GaAs(001). Because this layer is grown under arsenic ambient environment, therefore, initial surface status is terminated by arsenic. After the buffer layer growth, the temperature of the substrate can be changed depending upon the type of the next layer or shape of the desired nanostructure. In our case the next layer is a layer of AlGaAs which acts as the bottom barrier for our GaAs quantum dots since AlGaAs has a larger energy bandgap compared to GaAs. After the AlGaAs layer, a 0.5 ML of aluminium is grown in the absence of Arsenic in the background. The growth takes place in Volmer-Weber mode and creates droplets, which further etches the surface and creates nanoholes. The composition of the walls around the nonohole opening is an optically inactive material AlAs as As from the AlGaAs layer diffuses into the Al droplet during etching process (see fig. 2.10). The temperature also plays an important role in droplet etching process.

2.7.2 Density and size of droplets

The second most important factor is the size and density of the droplets, which is directly linked to the size and density of the QDs in a sample. The size and density of the droplets depend on the deposited amount of material, and the temperature of the substrate [33]. The cluster formation begins at a certain temperature depending on the type of metallic dorplets (Al or Ga). For example, below 200 ◦C in case of Ga, the clusters starts to coalesce, which reduces the number of clusters. This drastic decrease in the

33 Chapter 2. Theoretical Background number of clusters is due to the phenomenon called Oswald ripening [34, 35, 36]. Oswald ripening is a type of interaction between two neighbouring clusters. It can be described as a determining factor for the size distribution of the clusters on a sample surface. It is easy for atoms to detach from the smaller clusters and condense to a larger cluster. So, the larger clusters expand at the expense of smaller clusters [37, 38].

2.7.3 Droplet-surface interaction

In this section, the interaction between droplets and the surface of the substrate is discussed. The thermal etching (also called droplet etching or local droplet etching) depends on the growth conditions such as: substrate temperature, growth rate of Al- deposition or the amount of Al to form the droplets. The shape of the droplets onto the surface of the substrate is deﬁned by the wettability of the surface. Furthermore, the property to wet the surface is described by the angle of contact of the droplet onto the surface. Three types of situations arise here: No wetting, partial and complete wetting [30]. The status of the substrate surface, temperature in the growth chamber, and the size of the droplets are some of the key factors that the contact angle depends on. When a droplet forms on the substrate surface, it increases the overall free energy of the system. As seen in the ﬁgure 2.9, at contact angle 0◦, the deposition material spreads perfectly onto the surface of the substrate to the maximum. For all the other cases where the contact angle θ is bigger than 0◦, the partial wetting case occurs which is:

γs = γi + γc cos θ (2.10) where γc and γs are the free energies of the cluster and the substrate respectively and γi is the interfacial free energy[30].

On high temperatures of more than 600 ◦C, the thermal etching is considerable when the droplets are annealed for some time in As atmosphere. After annealing, as seen in the ﬁgure 2.10 the droplet takes a form of a nanohole with a ring-like lobe surrounding it on top.

34 2.8. Quantum dot formation

Figure 2.9: A schematic diagram showing droplet-surface interaction with the dependence of contact angle [30].

2.8 Quantum dot formation Once the nanoholes are created after annealing the substrate surface, the nanoholes have to be filled with a certain type of compound semiconductor material in order to make them optically active and transform them into quantum dots. In our case, after the hole formation, the holes on the AlGaAs surface are filled with GaAs to form strain-free quantum dots. The figures 2.10 and 2.11 show the process of etching and formation of a QD. In part a) of the fig. 2.10, a layer of Al is deposited onto the AlGaAs surface. This deposition takes place in VW mode of growth and Al droplets are formed. In part b) it shows the interaction of Al droplets with the surface under annealing process, the As from the surface diffuses into the Al droplet and forms crater like structures all over the surface. These craters are called nanoholes as seen in c) of figure 2.10. Also an AFM image of nanoholes is shown both 2D and 3D in part d) and e) respectively. Figure 2.11(f) shows the formation of a QD by growing a layer of GaAs on top and filling the nanoholes. Subsequently, a capping or a barrier layer of AlGaAs is grown on top.

35 Chapter 2. Theoretical Background

Figure 2.10: A schematic diagram showing Al-droplet interaction with AlGaAs surface and etching of the nano-holes.

Figure 2.11: A schematic diagram showing the formation of a quantum dot by ﬁlling the nano-hole with GaAs material.

36 2.9. Relation between emission energy and geometry of a quantum dot

2.9 Relation between emission energy and geometry of a quantum dot The unique properties of QDs enable an impressive and illustrative demonstration of quantum mechanics. A quantum dot is a system which conﬁne the motion of charge carriers in all directions to a region of space small enough to render quantization eﬀects observable. The resulting quantization of energy levels can be easily studied by PL imaging and spectroscopy since the energy of the discrete emission lines is related to the energy levels of the QD system.

A simple QD can be modeled by Schr¨odinger’s equation for a particle in a box with inﬁnitely high potential walls:

2 − ~ ∇2ψ(r) + V (r)ψ(r) = Eψ(r) (2.11) 2m

where the potential for a particle of mass m is in Cartesian coordinates V(x,y,z)=0 inside the box and V(x,y,z)= ∞ outside the box. After separation of variables and solving the equation with suitable wave functions ψ, the energy E of the particle takes the form:

π2 2 n n n E = ~ ( x )2 + ( y )2 + ( z )2 (2.12) 2m Lx Ly Lz with the quantum numbers nx,ny,nz=1,2,. . . and the dimensions of the box Lx,Ly,Lz.

This implies an increase of energy for higher quantum numbers and a decrease for larger masses, meaning that smaller masses cause stronger quantization effects. The ground-state energy E0 for nx,ny,nz=1 is dominated by the shortest side length of the box whereas the energy difference between the first excited state E1 (nx=2 for Lx>Ly>Lz) and the ground-state depends on the longest side length:

π2~2 ∆E = E1 − E0 = 3 2 (2.13) 2mLx

37 Chapter 2. Theoretical Background

To estimate for which dimensions a system behaves differently than a bulk box at thermal energy 3kBT and thus can be considered a QD, we demand the ground-state energy and the energy difference to the first excited state to be larger than the thermal energy[6]. This leads to the constraint that all dimensions must be smaller than:

π~ Lx < √ (2.14) 2mkBT With realistic numbers for a free carrier with eﬀective mass (in units of the free electron

3.√8nm mass m0) m = αm0 in a semiconductor at room temperature, this dimension is ≈ α . Thus, QDs must have sizes of a few nanometers to observe quantum eﬀects at room temperature.

When certain energy states of such a semiconductor QD are populated, e.g. by il- lumination with appropriate laser light, the QD system can emit light of photon energies that depend on the involved energy levels. Figure 2.12 illustrates this emission process between ground-states in a QD with inﬁnitely high potential walls and an energy gap Eg between valence and conduction band of the bulk semiconductor. For a cube-shaped QD of dimension L, the energy of emitted photons is calculated with the eﬀective masses αe and αh of the involved electrons and holes as follows:

2 2 π ~ 1 1 Elight ≈ Eg + 3 + (2.15) 2m0 αe αh

A refined model for self-assembled QDs considers the more realistic shape of a flat, round, inverted lens-shaped structure as exemplified in figure 2.13 [6]. The potential still is approximated to be V(x,y,z) = ∞ outside and V(x,y,z) = 0 inside the QD, but now the boundary of the QD is described by a parabola:

4x2 4y2 Lz(x, y) = h 1 − 2 + 2 (2.16) wx wy where h is the central height of the QD and wx, wy the width in the respective direction.

Under the condition of a ﬂat QD (h < wx,wy), the Schr¨odingerequation can be

38 2.9. Relation between emission energy and geometry of a quantum dot

Figure 2.12: Diagram showing Energy levels in a semiconductor QD with inﬁnitely high potential walls.

Figure 2.13: Model geometry of a lens-shaped self-assembled QD [6]. formulated with a potential for a lateral motion in (x,y) that depends on the conﬁnement along z and can be approximated by a harmonic oscillator potential [22]. The solution of the Schr¨odingerequation for a lens-shaped dot then yields energies of √ √ 2 2 2 2 π ~ 1 2 2~ π 1 2 2~ π E(nx, ny) = + + nx + + ny (2.17) 2mh 2 mhwx 2 mhwy

with the quantum numbers nx,ny= 0,1,2,. . . .

The energy of emitted photons from a round, symmetric (wx=wy=wz) QD with quantum number N = nx+ny=1,2,. . . is consequently derived as:

39 Chapter 2. Theoretical Background

√ 2 2 2 ~ π 1 1 2 2~ π 1 1 Elight(N) ≈ Eg + 2 + + (1 + N) + (2.18) 2m0h αe αh m0hw αe αh

As it is seen in equation 2.18, the main contribution to the ground-state emission energy comes from the height conﬁnement in the dot. Furthermore, the level splitting between excited states is found to be constant and inversely proportional to hw, which means that the higher or wider the dot is, the closer are the energy levels. The band gap energy of GaAs as well as the eﬀective masses of electrons and holes at the experimental conditions can be found in literature, leaving the equation dependent only on the dimensions of the QD. Thus, the size and the symmetry of a QD can be deduced by measuring the energy of its emitted light via PL spectra, and symmetry in size and shape plays a huge role in optical behaviour of a quantum dot which will be discussed further with more details in the chapter 4.

2.10 Fine structure splitting Fine structure splitting is phenomenon in which the neutral exciton emission in a QD (the main spectral line in the QDs studied here) splits into two or more components [39]. Each of these lines have a slightly different wavelength. This phenomenon occurs because of electronic transitions from one energy state to another. The split lines, which are called the fine structure, arise from the exchange interaction in presence of an in-plane asymmetry. In turn, the exchange interaction arises from the interaction between spins of electrons and holes. In the case of singly charged excitons, we have either two electrons (for the X−) or two holes (for the X+) in the lowest-lying energy state confined in the conduction band or valence band. Because of the Pauli exclusion principle, the two particles must have opposite spin so that the overall spin is zero. The radiative recombination gives rise to two lines, depending on the spin of the other carrier (electron in the case of X+ or hole in the case of X−. Those two lines have the same energy which means the spectral line observed by photoluminescence is actually two-fold degenerate [40]. The figure 2.14 shows gray-scale-coded polarization-resolved spectra of a neutral exciton confined in a GaAs QD. Due to the energy splitting, which is below the resolution of the used spectrometer, the line central position appears to follow a sinusoidal function. As seen in the section 2.9, the

40 2.10. Fine structure splitting

Figure 2.14: Fine-structure-splitting of the neutral exciton confined in a QD, visible in polarization-resolved PL spectra. An image from sample B (See appendix A). emission energy depends on the depth and width of a quantum dot, in other words the geometry of a QD. The geometry of the a QD has an important effect on the FSS as well. It is well known from the theory that the FSS arises from anisotropy present in the quantum dot’s confinement potential [40]. In Stransky-Krastanov (SK) epitaxially grown QDs, the anisotropy can come from multiple sources such as shape, strain and piezoelectricity [41]. To reduce the impact of strain and material intermixing on the FSS, unstrained GaAs QDs in AlGaAs matrix have been used to study the relation between anisotropy and FSS [42]. Several papers have found that an increasing elongation and decreasing size produce a larger FSS [43][40]. In this thesis we verify this correlation using GaAs QDs grown for the first time at Institute of semiconductor and solid state physics, JKU, as discussed in chapter 4.

41 Chapter 3

Experimental Considerations

This chapter is dedicated to the experimental setup for the characterization of nanoholes and quantum dots by atomic force microscopy and micro-photoluminescence spectroscopy, respectively. The functionality of these setups will also be discussed in this chapter. The atomic force microscope (AFM) is a very useful technique to characterize the physical and structural properties such as size, shape, symmetry, width, and depth of the quantum dots [44], and photoluminescence spectroscopy is used to characterize the electronic and optical properties of quantum dots. There is a correlation between the structural and optical properties of a quantum dot because the geometry (size and shape) of a QD aﬀects the electronic properties which will be proved consequently, in the next chapter. Due to this correlation, these two techniques together make the best characterization combination for quantum dots.

3.1 Atomic force microscope Atomic force microscope also known as AFM, is a type of scanning probe microscope. This technique was developed by scientists from IBM-research Zurich, Dr. Gerd Binning and Heinrich Rohrer. And the ﬁrst experimental implementation was introduced by Dr. Binning, Christoph Gerber and Calvin Quate in 1986 which earned them the Nobel Prize in physics of that year. It is a prominent characterization tool in semiconductor physics for surface topography. It scans the surface of the object and processes into a high quality image with atomic resolution and high accuracy. The advantage of AFM over other types of SPM is that the object doesn’t have to be electronically conductive which means that it can scan all types of solid surfaces regardless of their electronic conductivity.

42 3.1. Atomic force microscope

3.1.1 Conﬁguration of AFM

To understand the functionality and the working principle of AFM in detail, the body of AFM and its components should be discussed. The following diagram in ﬁg. 3.1 shows the main components of an atomic force microscope.

Figure 3.1: A schematic diagram of AFM and its components [7]

As seen in figure 3.1, a cantilever is connected to a piezoelectric element which is used to drive its oscillations. The sharp tip is on the free end of the cantilever. The detector records the movement and deflection of the cantilever (mechanical signal) and converts it into an electrical signal, and then sends the data to a feedback electronics connected to the AFM [7]. The sample and/or tip are mounted on a piezoelectrically-driven stage which can move in x, y, and z direction to locate the tip apex with respect to the sample [7]. The sample or tip is raster scanned along the x-y direction (see fig. 3.2) after the tip is brought into proximity to its surface. A feedback loop helps to keep the probe-sample force constant during the scan. This feedback loop takes deflection of the cantilever as an input and gives an output to adjust the z distance between the tip apex and the sample [45]. The variation in height on the sample changes the deflection of the cantilever. The

43 Chapter 3. Experimental Considerations height of the probe is adjusted according to the predeﬁned values in the feedback, which restores the deﬂection in the cantilever. A well adjusted feedback loop always adjusts the probe-sample separation, and keeps it constant to give the best quality images [46].

Figure 3.2: A simpliﬁed image of a probe tip scanning the surface [8].

3.1.2 Working principles of AFM

The atomic force microscopy technique has gone under many developments since 1982, and during the last three decades, scientists have established three main modes of scanning. These modes of scanning are as following.

Contact mode (static mode)

In this mode, the tip is in constant contact with the sample at all times while scanning [47]. The static deﬂection of the cantilever is measured which determines the topography in this mode. A strong repulsive interaction between the tip and the sample occurs, which gives rise to the friction between them which makes this mode very harsh for delicate samples especially biological and organic samples.

Non-contact mode (dynamic mode)

In this mode, the tip is never in contact with the surface [47]. The cantilever oscillates just above the surface where the oscillation amplitude is from a few nanometers (< 10nm) to a few angstrom or it oscillates with its resonance frequency. The topography in this mode is determined by the Van der Waals forces which act for tip-surface distances from 1 nm to 10 nm, and above the surface, where other long range forces act to reduce the

44 3.1. Atomic force microscope

Figure 3.3: A diagram showing the contact (static) mode of AFM where the tip is in constant contact with the sample [8]. resonance frequency of the cantilever [48]. In this mode of AFM, the tip does not go through an abrasive erosion after a few scans like it does in contact mode and the sample surface also stays untouched [7]. This is why this mode of scanning is ideal for measuring biological samples and soft organic thin ﬁlms [49].

Figure 3.4: A diagram showing Non-contact (dynamic) mode [8].

Tapping mode

This mode is a combination of contact and non-contact operation modes of AFM. In ambient conditions, some types of samples tend to develop layers of moisture. In these conditions, it is hard to keep the probe tip in close contact to the surface to detect the short- range forces while trying not to stick the tip into these layers. In this case, the contact mode presents a major challenge [50]. To bypass this problem, the tapping mode was developed. It is also called dynamic contact mode. In this mode, the cantilever oscillates up and down near or at its resonance frequency.

Only tapping mode operation has been used to measure all the samples in this thesis

45 Chapter 3. Experimental Considerations

Figure 3.5: A diagram showing Tapping mode [8]. to achieve the best quality images. All the images taken are shown in Chapter 4 in the results.

3.1.3 AFM probe

In AFM, the probe is a very sharp tip at the end of a cantilever which is sticking out of the holder. There are many types of probe tips, which are available according to the type of sample (eg: rigid, organic, semi-soft etc) and the scan-mode. The size and shape of these tips varies but typically for semiconductor materials the radius of the tip is a few nanometers in size, which is ideal to achieve high quality images at atomic resolution. In the ﬁgure 3.6, images of a typical NC/tapping mode AFM probe tips are shown under the scanning electron microscope (SEM).

Figure 3.6: AFM probe tip as seen under the SEM [7].

There are a few characteristics of a typical AFM probe:

46 3.2. Micro photoluminescence spectroscopy

1. Vertical spring constant- The spring constant of the cantilever always requires to be in the 10−2 to 102 N/m range. The spring constant in this range can measure deﬂection caused by small forces (1/10 of a pN in NC-mode). 2. Lateral spring constant- The Lateral spring constant is always higher to minimize the lateral shift error in topography and to avoid lateral bending. 3. Resonance frequency- The cantilever requires to have a resonance frequency higher than the 10 kHz to achieve a large imaging bandwidth [8]. Thermal drifts during a slow scan are a main cause which disturbs the measurements at low frequency bandwidth. To eliminate this eﬀect high resonance frequency is required. 4. Quality factor- A high quality factor of cantilever increases the detection sensitivity of AFM in NC or tapping mode. The quality factor is typically between 10 to 1000 but in contact mode.

3.2 Micro photoluminescence spectroscopy As mentioned in the previous chapter, photoluminescence is a process in which photons are emitted by a material after having absorbed light, usually from a laser [51]. The emitted photons have lower energy than the one absorbed because the excited electrons in a semiconductor hetero-structure will lose some energy in form of vibrational energy. PL- spectroscopy is an outstanding and non-destructive technique to study the energy levels and electronic structure of a semiconductor hetero-structure, doping material and excitonic complexes [52]. There are also a few limitations to this technique which only probes the energetically lowest transitions.

3.2.1 Conﬁguration of PL-spectroscopy

A continuous wave (CW) laser is used as a light source. A sample is mounted into the cryostat that is connected with a vacuum pump to isolate the sample thermally from the environment. The cryostat as seen in the ﬁgure 3.7 is connected to a liquid Helium can to cool down the sample. The cryostat is mounted on a stage that can be moved in xy-plane to position the sample relative to a laser beam. The detector is also cooled down by pouring liquid Nitrogen into the CCD camera. A dichroic beamsplitter is used to split the emitted beam from the incident beam. The whole setup is connected with a computer and controlled by a software. A lens is used after the PL-ﬁlter to focus the

47 Chapter 3. Experimental Considerations

PL-signal onto the entrance slit of the monochromator. In the computer software, a few parameters are important to fill in before starting the experiment such as entrance slit size, grating, central spectral wavelength, acquisition time etc. By moving the microscope’s objective to find the focus onto the sample surface and the maximum PL-signal onto the monochromator entrance slit, can the experiment be started. The following figure 3.7 shows a schematic diagram illustrating a typical PL experimental setup (also known as continuous wave photoluminescence spectroscopy).

Figure 3.7: Schematic of the experimental setup with essential elements for Micro- Photoluminescence measurements. The sample within the cryostat is illuminated by laser light through a confocal microscope and the emission from single QDs spectrally resolved and detected by a spectrometer [9].

3.2.2 PL Measurement procedure

In this experiment, ﬁrst a single QD on the sample is located by randomly moving the motorized stages holding the cryostat with a coarse step size of 1 µm. While looking at the continuously acquired emission spectrum at relatively low excitation power of 5 µW, as soon as a QD is positioned within the excitation spot, a characteristic PL spectrum is observed. After that the emission intensity is maximized by optimizing the position with a ﬁne step size of 0.25 µm. Under the assumption of a low enough concentration of GaAs

48 3.2. Micro photoluminescence spectroscopy

QDs on the sample, It is reckoned that only a single QD is addressed within the excitation spot. During the measurement, the laser is always blocked through the long-pass ﬁlter placed in front of the spectrometer. The spectra at various excitation powers in the range of 5 µW-650 µW are recorded, before locating several other single QDs and repeating the power-dependent measurements. In the ﬁgure 3.8 a spectrum of intensity vs energy for one quantum dot is shown as an example on various excitation powers; more emission peaks emerge as the power is increased. Here, N is the number of excited state (Quantum number).

Figure 3.8: A power-dependent PL spectra showing a QD’s emission peaks on various excitation powers ﬁtted by Gausian functions.

49 Chapter 4

Results and Discussion

In this chapter, the results based upon the data collected and analyzed from AFM and micro-PL are shown and discussed to see if there is a correlation between them. The data provided by these two techniques can be correlated since the electronic and optical properties, obtained from PL measurements, depend on the physical composition and structural properties of a quantum dot sample. I have used four samples (A, B, C and D). All the sample protocols and their original names are given in appendix A.

4.1 AFM results For each sample, several AFM images with different scan-size and from different locations are collected. For each sample, 10 nanoholes on different locations are measured by AFM to have a statistical analysis of their structural properties. Every sample has a slightly different growth protocol, hence, the nanoholes are different in shape and size for each sample. The results are shown from sample A to D in increasing order of the nanohole symmetry. Figure 4.1 shows the images of sample A. The first image is of scan-size 5 µm x

Figure 4.1: 5 µm x 5 µm and 2 µm x 2 µm images of sample A.

50 4.1. AFM results

Figure 4.2: A 3-dimensional side view image of the same nanohole from ﬁgure 4.1 showing the mound like structure.

5 µm and the second image is the magnification of the first image at 2 µm x 2 µm. The surface of the sample A was obtained by depositing 0.6 ML of Al at a substrate temperature of 610 ◦C followed by annealing in As with the background pressure of 4.5x10−7 mbar. The nanoholes have an average depth of about 7.7±0.7 nm and a width of 105±9 nm along the [1-10] direction (horizontal) and about 79±3.4 nm along [110] direction (vertical). The surface also shows in figure 4.2, some shallow mounds which stem from buried QDs obtained by infilling of nanoholes with GaAs. These QDs are nominally identical to the nanoholes seen in the figure 4.1. The average anisotropy of QDs in sample A is around 0.15 which arises from the high difference between the width measured in [1-10] and [110] direction. The QDs in sample A are visibly asymmetric. As seen in figures 4.3, the width of nanohole is measured with a line scan by using a AFM analysis tool called Gwyddion. Figure 4.3 is just an example of how the width of rest of the nanoholes is measured. In figure 4.4, profile 1 shows the width measured in [1-10] direction which is equal to 103 nm and profile 2 is the width measured in [110] direction which is 88 nm. The nanoholes in sample A look elliptical and have a high anisotropy. The width of the nanoholes in sample A, as seen in figure 4.4, is measured from first peak to the second peak. These peaks represent the ring like ridges around the nanohole.

51 Chapter 4. Results and Discussion

Figure 4.3: Line-scan showing proﬁles 1 and 2 in both [1-10] and [110] directions respectively.

Figure 4.4: A nanohole’s width measured in [1-10] and [110] directions respectively shown as proﬁle 1 and 2.

52 4.1. AFM results

Similarly in all the samples, the width is measure in both horizontal and vertical directions by taking the measurements from peak to peak elimination the outer parts of the circular ridges around the nanoholes. For each sample, 15 of such nanoholes are measured to have a statistical analysis of shape and size anisotropy. Likewise, in ﬁgure 4.5

Figure 4.5: 5 µm x 5 µm and 2 µm x 2 µm images of sample B. topographical images of sample B are shown with a scan-size of 5 µm x 5 µm and 2.5 µm x 2.5 µm. The second image of figure 4.5 shows the magnification of the sample surface. The nanoholes in sample B are obtained by depositing 0.6 ML of Al at a substrate temperature of 574 ◦C and the sample afterwards, is annealed in As at a background pressure of 4.6x10−7 mbar. The nanoholes in sample B have an average depth of about 4.6±0.5 nm and a width along [1-10] direction is 60±3.7 nm and 65.5±3.0 nm along [110] direction. The surface, in figure 4.5 together with the other images of sample B which are obtained and analyzed, doesn’t show any visible mounds which means the surface of sample B is smoother than that of sample A. The average anisotropy of QDs in sample B is around −0.04. The nanoholes in the sample B visibly look less asymmetric than sample A. As seen in figure 4.6, the width measured in [1-10] and [110] directions are 67 nm and 61 nm respectively. The average difference of width measured in both directions of all 15 nanoholes is around 6 nm which is much less than that of sample A (where it is 26 nm). In figure 4.7, the images from sample C are shown with a scan-size of 6 µm x 6 µm and 2 µm x 2 µm. The nanoholes in sample C are obtained by depositing 0.6 ML of Al at a substrate temperature of 569 ◦C. The sample is annealed in As with a background pressure of 2.32x10−7 mbar. In sample C, the surface reconstruction looks better than the previous samples. The average nanohole depth is around 5.1±0.6 nm and the average width along horizontal and vertical

53 Chapter 4. Results and Discussion

Figure 4.6: Width of a nanohole on Sample B shown as proﬁle 1 in [1-10] direction and proﬁle 2 in [110] direction.

Figure 4.7: 6 µm x 6 µm and 2 µm x 2 µm images of sample C. direction is 58±3.5 nm and 56.3±2.7 nm. The average anisotropy is about 0.015 which is less than sample A and B. Our goal is to reduce the anisotropy factor as low as possible to achieve the highest quality symmetrical quantum dots. In ﬁgure 4.8, we can see that the line-scans in both direction almost overlap each other showing better symmetry of QDs in sample C. The ﬁgure 4.9 shows that the mounds on the surface are not as abrupt as in sample A.

Figure 4.10 shows the nanoholes of sample D which are obtained by depositing 0.55 ML of Al at a substrate temperature of 569 ◦C. The sample is annealed in As with a background pressure of 2.32x10−7 mbar. The average depth of nanoholes in sample D is 6.8±0.8 nm and average width along [1-10] and [110] are 60.5±5.6 nm and 60±6 nm

54 4.1. AFM results

Figure 4.8: Line-scans of the width of a nanohole in sample C showing the overlap of both line scans in [1-10] and [110] direction.

Figure 4.9: A 3-dimensional side view image of the same nanohole from figure 4.8 showing the roughness of the surface. respectively which makes sample D the sample with the most symmetric QDs out of all four. The average anisotropy in sample D is around 0.005. At some locations on the sample surface, mounds can be seen which are buried QDs after infilling of GaAs in the nanoholes. In figure 4.11, we can see both line-scans in [1-10] and [110] overlaps perfectly which means the QDs in sample D are very high quality and the most symmetrical of all the four samples. It makes sample D the best contender for the further research in order to obtain strongly entangled photons because higher symmetry in a quantum dot

55 Chapter 4. Results and Discussion means very low excitonic ﬁne-structure-splitting which we will see in section 4.2 under the results of micro-PL spectroscopy. Based on the high-resolution AFM images, the

Figure 4.10: 3 µm x 3 µm and 2 µm x 2 µm images of sample D.

Figure 4.11: Line scans of the width of a nanohole in sample D showing the complete overlap of both line scans in [1-10] and [110] directions. structural properties of the nanoholes were analysed via a software. For each nanohole, the depth, the base area and volume were determined. The results of the four samples are shown with scatter plots in ﬁgures 4.12, 4.13, 4.14 and 4.15. In each plot the average depth, average base-area (BA), mean volume and standard deviation of depth (σx) are also shown. According to these plots, sample A has the largest quantum dots by volume. Sample D has the second largest QDs while sample B and C are quite similar.

Figure 4.16 shows (as an example) how the depth of a nanohole is measured manually

56 4.1. AFM results

Figure 4.12: A scatter plot between depth and base-area of sample A showing various other parameters in the table.

Figure 4.13: A scatter plot showing depth and base-area of nanoholes on sample B and other parameters related to depth shown in the table. by taking a line-scan with the help of Gwyddion. The peaks on the top of the linescan represent the ring like ridges surrounding the nanoholes as seen in the image (ﬁg. 4.16) and these ring like ridges are excluded from the depth, but they can also be included

57 Chapter 4. Results and Discussion

Figure 4.14: A scatter plot showing depth and base-area of nanoholes on sample C and other parameters related to depth shown in the table.

Figure 4.15: A scatter plot showing depth and base-area of nanoholes on sample D with other depth related parameters shown in the table. depending on how you measure the width. If we include these peaks into the actual depth, then we have to measure the width of the nanoholes according to where the depth lines intersects these peaks. A more detailed explanation of measuring the width-depth is given

58 4.1. AFM results in appendix B.

Figure 4.16: An image showing the depth proﬁle of a nanohole.

Dot Sample A Sample B Sample C Sample D 1. 7.8 4.7 5.4 6.8 2. 7.5 4.2 5.3 6.9 3. 7.4 5.0 5.9 7.1 4. 6.8 5.4 4.9 6.3 5. 7.3 4.2 5.8 6.7 6. 9.1 4.1 5.2 8.6 7. 7.9 4.0 4.8 8.2 8. 7.7 5.1 4.5 6.4 9. 9.3 4.0 5.5 7.4 10. 8.2 4.1 4.5 7.3 11. 7.5 4.5 4.1 6.3 12. 7.4 4.7 4.3 6.2 13. 8.3 5.1 6.4 6.4 14. 7.4 5.7 5.5 6.2 15. 7.3 4.4 4.8 5.9 d¯ 7.7 4.6 5.1 6.8 σd 0.7 0.5 0.6 0.8 Table 4.1: Depth (in nm) of selected nanoholes in all four samples, determined from the linescans as those shown in ﬁg. 4.3, 4.6 4.8 and 4.11.

In the table 4.1, The depth of nanoholes of each sample is shown. For each sample, 15 random nanoholes at diﬀerent locations have been measured by taking a linescan with the help of Gwyddion analysis tool. All measurements are in nanometer. An average depth is shown for each sample on the bottom of the table as d¯together with the standard deviation

59 Chapter 4. Results and Discussion

σd. We used two types of analysis tools to measure the depth. One of which is called Gwyddion which is generally a standard tool used for analyzing the AFM data and the other tool is called XIM which is provided and developed by Prof. Dr. Armando Rastelli. XIM is better for analyzing large amount of data at once and it detects islands/holes automatically after you set certain commands, depth and height parameters while in Gwyddion the data analysis is done manually by selecting each nanohole and performing line-scans. We see a difference in results from both analyzing techniques. The data analyzed by XIM is larger in size (about 20-25 nanoholes on each sample); while via Gwyddion, we analyzed depth and width of 15 nanoholes per sample (see table 4.1, and fig. 4.18 to 4.21). The data analyzed by XIM is shown in figures 4.12, 4.13, 4.14, and 4.15 for each sample. For example, sample A shows a mean depth of 7.6±1.0 nm according to plot fig. 4.12 but the manual line-scans of 15 different nanoholes on sample A shows a mean depth of 7.7±0.7 nm which are almost equal. Similarly, samples B, C, and D show a non-significant difference in data (mean depth) measured by Gwyddion and XIM.

We can conclude that the data analysis by XIM and Gwyddion is both reliable in this case, and shows little to no significant difference. It depends on the goal of the experiment. XIM has a little more advantage over Gwyddion because it can process large amount of data at once on one command while Gwyddion is more labor intensive because we have to manually select the data points in our case. There are other factors that may contribute in erroneous results. For example, an error of about 1 nm has also been seen when we measure the depth of the same nanohole on two different images with different scan-sizes. In figure 4.17, we can see that a smaller scan-size of 2.5 µm x 2.5 µm of a nanohole provides more detailed and accurate depth profile than a larger scan-size of 5 µm x 5 µm of the same nanohole. As it is known that the fine-structure-splitting occurs because of the elongation of the quantum dots. To see the size asymmetry, the width of the nanoholes is measured both along the x and y axes as seen in figures 4.3 and 4.4. It is observed that in some samples the difference is high and in others it is not significant.

W − W = x y , (4.1) Wx + Wy where Wx and Wy are the widths measured along x and y directions respectively. Smaller the shape anisotropy, the more symmetrical the dots are. A scatter plot for each sample

60 4.1. AFM results

Figure 4.17: An image showing the depth of the same nanohole with two diﬀerent scan- sizes.

showing the relation between Wx and Wy is presented in ﬁgures 4.18, 4.19, 4.20, and 4.21. A mean width in both direction is also shown in a small table together with a standard deviation σx and σy in each direction and anisotropic ratio . Black squared dots represent the nanoholes and their respective widths along x and y directions, while red circular dots represent their respective anisotropy .

Figure 4.18: A scatter plot showing asymmetry of the nanoholes in sample A along with a table showing standard deviations and mean width in [1-10] and [110] directions.

61 Chapter 4. Results and Discussion

Figure 4.18 shows that the sample A has highly elongated nanoholes hence asymmetric QDs. The anisotropy is around 0.15 as compare to sample B (see ﬁg. 4.19) where the value of is −0.04; here −ve sign represents the direction of elongation (Wy > Wx) in sample B. The scatter plot in ﬁgure 4.20 shows that the value of is 0.01 in sample C which means in sample C, the quantum dots are structurally more symmetric than sample A and B.

Figure 4.19: A scatter plot showing asymmetry of the nanoholes in sample B along with a table showing standard deviations and mean width in [1-10] and [110] directions.

The anisotropic value of nanoholes in sample D is 0.005 which is less than all the other sample and indicates that the quantum dots in sample D are the most symmetrical.

The mean width Wx is 60.5 ± 5.6 nm and value of Wy is 60.0 ± 6 nm which means that, theoretically, sample D has symmetrical quantum dots.

Now, we can further compare the data analyzed by Gwyddion and XIM to have an overview of compatibility of both tool. In ﬁgure 4.18, mean Wx and Wy of sample A

(by Gwyddion) are given in the table included in the plot, and the values of mean Wx/2 and Wy/2 are approximately 43 nm and 38 nm respectively after reducing their relevant standard deviations. Now, if we assume the base of the elongated nanohole as an ellipse and apply them into πab (which is area of ellipse); where a and b are the values of Wx/2

62 4.1. AFM results

Figure 4.20: A scatter plot showing asymmetry of the nanoholes in sample C along with a table showing standard deviations and mean width in [1-10] and [110] directions.

Figure 4.21: A scatter plot showing asymmetry of the nanoholes in sample D along with a table showing standard deviations and mean width in [1-10] and [110] directions.

and Wy/2 (also known as major and minor axes). After calculation, it gives an average base-area of about 5119.8 nm2 which is comparable to the mean BA 4630.3 nm2 (shown in ﬁgure 4.12) of sample A analyzed by XIM. The average depth of nanoholes in sample

63 Chapter 4. Results and Discussion

A which is manually calculated by taking 15 diﬀerent line-scans, is around 7.0 nm after π(BA¯ )d¯ reducing the standard deviation (see table 4.1). The volume of the nanoholes is 3 ; which, after our calculations, is around 11946 nm3. It is also comparable to the data processed by XIM where the value of mean volume of nanoholes on sample A is 11730 nm3 (see ﬁg. 4.12). Similarly, we can compare the results from Gwyddion and XIM for all the other samples (see table 4.2).

Therefore, we can say that Gwyddion and XIM, when used together, are both very promising tools to analyze AFM data only if we process images that are high in quality and have the same scan-size (5 µm x 5 µm or smaller). Table 4.2, shows a brief comparison between data analyzed by Gwyddion and XIM. The data from Gwyddion is manually calculated by taking line-scans of 15 diﬀerent nanoholes while data from XIM is automatically processed and have a larger sample size (about 20-25 nanoholes).

Tools Sample A Sample B Sample C Sample D Gwyddion BA¯ [nm2] 5120 2784 2299 2367 XIM BA¯ [nm2] 4630 1917 1736 2171 Tools Sample A Sample B Sample C Sample D Gwyddion V¯ [nm3] 11946 3804 3448 4812 XIM V¯ [nm3] 11730 3130 2836 4776

Table 4.2: A comparison table of data analyzed and calculated by Gwyddion and XIM; here BA¯ is the mean base-area and V¯ is the mean volume of nanoholes.

The results from the AFM only prove the structural symmetry of quantum dots in sample D. To prove that quantum dots are truly symmetrical, we also need to measure their optical properties and analyze the value of excitonic FSS. For a quantum dot to be perfectly symmetric, its FSS should also be very low. In another words, it should be able to provide highly entangled photons. From previous works [44], we expect the most anisotropy to correlate with the excitonic ﬁne-structure-splitting. We will explore this point in the next section.

4.2 PL-spectroscopy results In this section, the results from photolumenescence spectroscopy are analyzed and discussed. According to the results, the progress towards achieving symmetrical quantum dots is seen from sample A to D by changing the growth parameters. Growth protocol for

64 4.2. PL-spectroscopy results each sample is shown in appendix A. After looking at the layer sequence of each sample, we can say that they all have a very similar layer sequence and composition but there are a few key parameters which are diﬀerent such as substrate temperature during Al-etching, background pressure (beam ﬂux), annealing temperature, annealing time etc. We will compare these parameters further in this section.

The data from PL-spectroscopy is analyzed by a spectra analysis tool XRSP3, provided and developed by Pr. Dr. Armando Rastelli. The XRSP3 works on some basic commands such as select, zoom, fit, and plot. To give an overview of how the PL-data is analyzed, figure 4.22 is shown as an example. Here, a sharp spectral peak is selected (zoomed in) and fitted by Gausian fit. Since the excitonic-FSS has sinusoidal pattern, we give a command to plot a ’cosine’ of this spectral peak. Afterwards, the cosine is fitted as well. All the spectral parameters related to that particular selected peak (QD) such as energy offset, FSS, polarization and FWHM are automatically processed and shown in a ’fit’ window. This is how we find out the value of FSS and energy offset which are two of the most important parameters to correlate the structural and optical properties of a QD [53]. To have a statistical analysis about 10 quantum dot peaks are measured for each sample except sample C. Unfortunately, due to an apparatus malfunction, we could not collect more than 4 data points for sample C. In figure 4.22, a sinusoidal pattern of a quantum dot peak is apparent which indicates towards a high excitonic-FSS in sample A. The average value of excitonic-FSS in sample A is about 22.43 ±3.4 µeV with an average emission energy of 1.57313 eV. The correlation between the structural and optical properties seem to be established here as the nanoholes on sample A have high structural asymmetry (see fig. 4.27).

In ﬁgure 4.23 a spectra of a single quantum dot is shown in sample B. Sample B has an average excitonic-FSS of about 17.68 ±1.57 µeV and the average emission energy of about 1.58487 eV. And the spectral line in the polarization spectra of the peak appears to follow a sinusoidal function with a high amplitude. Sample C has an average excitonic-FSS of about 11 ±3.5 µeV and the average emission energy of about 1.5725 eV.

As we move from ﬁgure 4.22 to 4.25, a gradual decrease in excitonic-FSS is seen, where sample D has the lowest average FSS value of about 3.23 ±0.85 µeV with an average

65 Chapter 4. Results and Discussion

Figure 4.22: An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample A showing the excitonic-FSS. emission energy of 1.55344 eV. A low emission energy indicates that the QDs in sample D are larger in size than sample B and C which is true according to table 4.1. Also the sinusoidal pattern of the spectral peak in the polarization-resolved spectra shown in ﬁgure 4.25 seems to disappear indicating that QDs in sample D have very low excitonic-FSS.

In ﬁgure 4.26, a scattered plot of excitonic-FSS of all the samples and their related emission energies is shown. As predicted, sample A shows the highest FSS out of all the samples because of high asymmetry present in the nanoholes (see ﬁg. 4.27) while sample D shows the lowest FSS due to higher structural symmetry. Figure 4.27 is a scatter plot obtained from the AFM data, here the +ve anisotropy indicates the elongation of a QD in [1-10] direction and −ve indicated the elongation of a QD in [110] direction. Only sample B shows a −ve asymmetry. For a quantum dot to be symmetric, the must be close to zero.

As we compare ﬁgure 4.26 and 4.27, we see that sample B and C have a higher emission energy than sample D which means the quantum dots in sample B and C are smaller than sample D. But, sample A seems not to follow this rule of physics from our calculations. The AFM measurement of sample A shows that it has the deepest nanholes hence the largest quantum dots but PL-data indicates that the emission energy of sample A is much higher

66 4.2. PL-spectroscopy results

Figure 4.23: An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample B showing the excitonic-FSS..

than sample D which contradicts the laws of physics (size quantization). If the quantum dots in sample A are the deepest, they must show the lowest emission energies. There can be several explanations to this type of odd behavior but the most plausible explanation is that quantum dots in sample A are in fact small in size while nanoholes on the top layer are larger. This can happen sometimes if there was an error during the growth of the sample. It is plausible that the nanoholes that were ﬁlled with GaAs to create QDS in sample A, couldn’t etch as deep as the nanoholes present on the top layer of the sample. So, we might be comparing the structural properties of the larger nanoholes to the optical properties of

67 Chapter 4. Results and Discussion

Figure 4.24: An Image of cosine-ﬁt of a quantum dot peak from sample C showing the excitonic-FSS. smaller quantum dots. Therefore, our results from sample A seem to contradict the basic notion of size quantization.

Now, we discuss and comment on some of the important growth parameters which might be responsible to achieve highly symmetrical QDs because our main focus in this thesis is to not only characterize and establish a correlation between the structural and optical properties of the GaAs/AlGaAs quantum dots but to also understand the growth process in order to grow samples with highly symmetrical QDs which can further serve as a source of entangled photons. All the growth protocols for each sample are given in Appendix A. The most important parameters that aﬀect the shape and size of a nanohole are amount of Al used for droplet formation, substrate temperature during droplet etching, deposition rate of Al during droplet etching etc. As we can see from all the growth protocols, that the amount of Al used for the droplet formation is practically the same for every sample which is 0.6 ML/s. The table 4.3 to shows some important growth parameters aﬀecting

Sample Substrate tempera- Deposition rate of Al Growth interval after ture during droplet droplet droplet etching formation A 610 ◦C 0.3 ML/s 10 sec B 574 ◦C 0.5 ML/s 20 sec Pyrolysis C 569 ◦C 0.5 ML/s 20 sec (Pyrolysis) D 569 ◦C 0.5 ML/s 20 sec (Pyrolysis)

Table 4.3: A table showing some of the important growth parameters. the size and shape of the nanoholes. According the growth protocol, sample A has the higher substrate temperature of about 610 ◦C during the droplet formation and a lower Al

68 4.2. PL-spectroscopy results

Figure 4.25: An Image of a grey-scale-coded polarization-resolved spectra of a QD and the cosine-ﬁt of its peak in sample D showing the excitonic-FSS. deposition rate than the other samples which is a plausible reason of a high asymmetry in nanohole size and shape. According to the growth protocol (ﬁg. 6.4), Sample D has the substrate temperature of about 569 ◦C and a lower background pressure during the Al droplet formation which can be a reason of symmetrical quantum dots in sample D.

69 Figure 4.26: FSS vs Emission energy for all the samples.

Figure 4.27: A scatter plot showing the depth and asymmetry of all the samples.

70 Chapter 5

Conclusions & Outlook

In this work, I have performed a combined structural and optical investigation of GaAs/Al- GaAs QDs obtained by the droplet etching method via MBE by varying the growth parameters, in particular the substrate temperature during droplet etching. This work shows that there is a correlation between the structural and optical properties of quantum dots. In sample A, the elongation of the quantum dot is very high with an asymmetry of about 0.15 which subsequently gives a very high excitonic ﬁne-structure-splitting when examined under PL-spectroscopy. In sample B, the elongation of the quantum dot is much less than sample A, and here we see the FSS associated with it decreases gradually because the value of asymmetry in sample B is around −0.04. In sample C, the quantum dots are almost symmetrical with a very small elongation of about 0.01 but due to an apparatus malfunction we could not perform a detailed investigation on its optical properties. We could only examine four quantum dots in sample C with an average FSS of about 11 ±3.5 µeV.

The most symmetrical quantum dots were found in sample D, with an almost non significant size asymmetry of about 0.005 with an average FSS of 3.23 ±0.85 µeV which makes it a good contender for the further research in the field of quantum entanglement. Although sample C and D have almost the same composition and growth parameters except the droplet size, sample C shows some structural asymmetry as compared to sample D, which could arise from surface reconstruction after droplet etching. In Sample C the droplet size is 0.6 ML while in sample D it is 0.55 ML, which theoretically does not affect the quantum dot size or shape. It only means that sample D has a lower QD density. The QD density of sample C is around 3QD/µm2 and in sample D it is 2QD/µm2. The main object of this thesis has been established after analyzing the results from AFM and PL-spectroscopy which is to characterize the GaAs/AlGaAs quantum dots and correlate

71 Chapter 5. Conclusions & Outlook their structural and optical properties.

After the execution of this thesis, the optimized protocol to obtain small FSS was employed to create sources of highly entangled photons which were recently used also for quantum key distribution purposes [16][54]. In the future it will be interesting to investigate how the size and shape of QDs aﬀect also the lifetime of the conﬁned excitons, as this parameter determines the maximum photon generation rate of a certain QD.

72 Chapter 6

Appendix A

In this chapter, the growth protocol of each sample is presented.

6.1 Sample A

Original name As132; Growth parameters : GaAs QDs in Al0.4Ga0.6As barriers at Tave ◦ ◦ ◦ + 140 C; Droplets at Tave + 140 C = 650 C; Al 0.6ML; Increased anneal time during hole ◦ etching; Al2 kept 0.35 ML/s during etching at a substrate temperature of 610 C; Tdeox= 548 ◦C. This sample is grown by PhD. Huiying Huang.

Figure 6.1: The layer sequence of sample A along with other important parameters.

73 Chapter 6. Appendix A

6.2 Sample B

Original name As138; Growth parameters : GaAs QDs in Al0.4Ga0.6As barriers at ◦ ◦ ◦ Tdeox + 80 C; Droplets at Tave + 130 C = 634 C; Al 0.6 ML; Al2 during droplet etching ◦ ◦ 0.5 ML/s at a substrate temperature of 574 C; Tdeox= 554 C. This sample is grown by Post Doc. Saimon Da Silva.

Figure 6.2: The layer sequence of sample B along with other important parameters.

74 6.3. Sample C

6.3 Sample C

Original name As146; Growth parameters : GaAs QDs in Al0.4Ga0.6As barriers at ◦ Tdeox= 569 C; Al droplet 0.6 ML; Al2 during droplet etching 0.5 ML/s at a substrate temperature of 569 ◦C. Grown by Saimon.

Figure 6.3: The layer sequence of sample C along with other important parameters.

75 Chapter 6. Appendix A

6.4 Sample D

Original name As163; Growth parameters : GaAs QDs in Al0.4Ga0.6As barriers at ◦ Tdeox=569 C; Al droplets at Tdeox with Al 0.55 ML using GI of 20 sec after Al droplet; Al2 during droplet etching 0.5 ML/s at a substrate temperature of 569 ◦C. Grown by Saimon.

Figure 6.4: The layer sequence of sample D along with other important parameters.

76 Appendix B

6.5 Important things to remember This chapter is mainly for masters students who will do similar experiments and use similar methods for fabrication and characterization as presented in this work. Here is a list of things that can go wrong and are almost never found in any publication. May the things described in the list be helpful for the future master students and save their time and eﬀorts.

1. Surface contamination Make sure the surface of the samples for AFM or any other surface topography microscopy, should be clean and dirt free. Touching the sample with bear hands can tragically change the imaging results. 2. Blunt Tip This is common after scanning for a long time with the same tip. Tips may last very long, or sometimes go blunt quickly. In order to find out if our tip is blunt, scan a well-known sample which we already know from our professor. 3. Scan-size During statistical analysis, make sure that the AFM data points are all taken from the images with same scan size and quality. Otherwise, the line-scan gives a different result for the same data point. All images should be high quality and the scan size should be 5 µmx5 µm or less. 4. Vibration AFM probes are highly sensitive to vibrations. Vibrational noises like people walking or running around the probe or doing other types of heavy work that can create vibrations, can easily lower the image quality and in most of the cases these images are useless. Micro-PL setup is also very sensitive to such vibrations. 5. Tip contamination Sometimes even if the sample is clean and other parameters are completely fine, the

77 Appendix B

image comes out either blurry or distorted; which could be a result of Tip contamination. Very seldom it happens that the tip accumulate some dirt particles from the surface. These particles can act like a secondary tip. This dirt can be away after scanning a hard vigorous surface but changing the tip is the best option. 6. Hysteresis This can occur when we are scanning the same sample from different direction, the end image shows some lines either along x or y direction. An easy fix to this problem is slow scan rate. 7. Excess light Experiments like Micro-PL are highly sensitive to the stray light sources. So make sure that the room is completely dark with all the lights turned off. It can obviously manipulate the optical results. 8. Measuring the correct depth and width While working with AFM analysis tools such as Gwyddion, there is no right or wrong way of measuring distance when we take a line-scan of an island or a nanohole (in our case) as it is a manually done. We need to just make sure if we take the depth of an object from a certain point then the width should be taken accordingly where the depth lines intersect that object on the sample. For example, the images in figures 6.5 and 6.6 show how we can measure one quantity according to after we have measured the other one. It is not going to make a significant change in our overall data analysis as long as we always adhere to the same rule and analyze the data with the same procedure. In fig. 6.6, as we include the peaks/islands into the depth, the width of

Figure 6.5: An example of how to measure depth and width of a nanohole/island.

78 6.5. Important things to remember

Figure 6.6: Another way how to measure depth and width the same nanohole from ﬁgure 6.5.

the same nanohole increases accordingly. It does not have any signiﬁcant impact on the statistical analysis as long as all the nanoholes are measured the same way.

79 Bibliography

[1] Benjamin Bruhn. Fabrication and characterization of single luminescing quantum dots from 1D silicon nanostructures. PhD thesis, KTH Royal Institute of Technology, 2012.

[2] Romain Toro. Optical Spectroscopy of Novel Quantum Dot Structures. PhD thesis, University of Sheﬃeld, 2014.

[3] AN Vamivakas and M Atat¨ure.Photons and (artiﬁcial) atoms: an overview of optical spectroscopy techniques on quantum dots. Contemporary Physics, 51(1):17–36, 2010.

[4] Stephanie M Reimann and Matti Manninen. Electronic structure of quantum dots. Reviews of modern physics, 74(4):1283, 2002.

[5] Ayahiko Ichimiya, Philip I Cohen, and Philip I Cohen. Reﬂection high-energy electron diﬀraction. Cambridge University Press, 2004.

[6] Arkadiusz Wojs, Pawel Hawrylak, Simon Fafard, and Lucjan Jacak. Electronic structure and magneto-optics of self-assembled quantum dots. Physical Review B, 54(8):5604, 1996.

[7] Wikipedia, the free encyclopedia. Atomic force microscopy, 2018. [Online; accessed April 30, 2018].

[8] Michal Hrouzek. Atomic Force Microscopy, modeling, estimation and control. PhD thesis, PhD thesis, Universit´eJoseph Fourier, 2007.

[9] Igal Bayn, Boris Meyler, Joseph Salzman, and Raﬁ Kalish. Triangular nanobeam photonic cavities in single-crystal diamond. New Journal of Physics, 13(2):025018, 2011.

[10] Roland Wiesendanger. Scanning probe microscopy and spectroscopy: methods and

80 Bibliography

applications. Cambridge University Press, 1994.

[11] Jana Drbohlavova, Vojtech Adam, Rene Kizek, and Jaromir Hubalek. Quantum dots—characterization, preparation and usage in biological systems. International journal of molecular sciences, 10(2):656–673, 2009.

[12] Wikipedia, the free encyclopedia. Quantum dot, 2018. [Online; accessed April 30, 2018].

[13] Ruquan Ye and Andrew R Barron. Photoluminescence spectroscopy and its applications. Physical methods in chemistry and nano science. OpenStax CNX, 2011.

[14] Andrew R Barron. Physical methods in chemistry and nano science. 2015.

[15] Wikipedia, the free encyclopedia. Photoluminescence Wikipedia, the free encyclopedia, 2018. [Online; accessed 31-January-2018].

[16] Daniel Huber, Marcus Reindl, Saimon Filipe Covre Da Silva, Christian Schimpf, Javier Mart´ın-S´anchez, Huiying Huang, Giovanni Piredda, Johannes Edlinger, Ar- mando Rastelli, and Rinaldo Trotta. Strain-tunable gaas quantum dot: A nearly dephasing-free source of entangled photon pairs on demand. Physical review letters, 121(3):033902, 2018.

[17] Peter Michler. Quantum dots for quantum information technologies, volume 237. Springer, 2017.

[18] BJ Riel. An introduction to self-assembled quantum dots. American Journal of Physics, 76(8):750–757, 2008.

[19] Zhiliang Yuan, Beata E Kardynal, R Mark Stevenson, Andrew J Shields, Charlene J Lobo, Ken Cooper, Neil S Beattie, David A Ritchie, and Michael Pepper. Electrically driven single-photon source. science, 295(5552):102–105, 2002.

[20] C Böckler, S Reitzenstein, C Kistner, R Debusmann, A Löffler,T Kida, S Höfling, A Forchel, L Grenouillet, J Claudon, et al. Electrically driven high-q quantum dot-

81 Bibliography

micropillar cavities. Applied Physics Letters, 92(9):091107, 2008.

[21] Andrew M Smith and Shuming Nie. Semiconductor nanocrystals: structure, properties, and band gap engineering. Accounts of chemical research, 43(2):190–200, 2009.

[22] Suwit Kiravittaya, Armando Rastelli, and Oliver G Schmidt. Advanced quantum dot conﬁgurations. Reports on Progress in Physics, 72(4):046502, 2009.

[23] William E Buhro and Vicki L Colvin. Semiconductor nanocrystals: shape matters. Nature materials, 2(3):138, 2003.

[24] Lambert Ben Freund and Subra Suresh. Thin ﬁlm materials: stress, defect formation and surface evolution. Cambridge University Press, 2004.

[25] Alberto Pimpinelli and Jacques Villain. Physics of crystal growth, volume 19. Cam- bridge university press Cambridge, 1998.

[26] Electrochemical Machining ECM. Reference module in materials science and materials engineering. 2016.

[27] Wikipedia, the free encyclopedia. Molecular beam epitaxy, 2018. [Online; accessed November 30, 2018].

[28] John R. Arthur. Molecular beam epitaxy. Surface Science, 500(1):189 – 217, 2002.

[29] Achim K¨uster,Christian Heyn, Arne Ungeheuer, Gediminas Juska, Stefano Tommaso Moroni, Emanuele Pelucchi, and Wolfgang Hansen. Droplet etching of deep nanoholes for ﬁlling with self-aligned complex quantum structures. Nanoscale research letters, 11(1):282, 2016.

[30] Akos´ Nemcsics. Quantum dots prepared by droplet epitaxial method. 2015.

[31] Massimo Gurioli, Zhiming Wang, Armando Rastelli, Takashi Kuroda, and Stefano Sanguinetti. Droplet epitaxy of semiconductor nanostructures for quantum photonic devices. Nature materials, page 1, 2019.

82 Bibliography

[32] F Bastiman and AG Cullis. Gaas (0 0 1) planarization after conventional oxide removal utilising self-governed inas qd site selection. Applied surface science, 256(13):4269– 4271, 2010.

[33] A Stemmann, Ch Heyn, T K¨oppen, T Kipp, and W Hansen. Local droplet etching of nanoholes and rings on gaas and algaas surfaces. Applied Physics Letters, 93(12):123108, 2008.

[34] Peter W Voorhees. The theory of ostwald ripening. Journal of Statistical Physics, 38(1-2):231–252, 1985.

[35] M Zinke-Allmang. M. zinke-allmang, lc feldman and s. nakahara, appl. phys. lett. 51, 975 (1987). Appl. Phys. Lett., 51:975, 1987.

[36] A Raab and G Springholz. Oswald ripening and shape transitions of self-assembled pbse quantum dots on pbte (111) during annealing. Applied Physics Letters, 77(19):2991–2993, 2000.

[37] GR Carlow. Gr carlow and m. zinke-allmang, phys. rev. lett. 78, 4601 (1997). Phys. Rev. Lett., 78:4601, 1997.

[38] VA Shchukin et al. Va shchukin and d. bimberg, rev. mod. phys. 71, 1125 (1999). Rev. Mod. Phys., 71:1125, 1999.

[39] Britannica, the free encyclopedia. Fine structure Britannica, the free encyclopedia, 2018. [Online; accessed 22-Apr-2020].

[40] M Bayer, G Ortner, O Stern, A Kuther, AA Gorbunov, A Forchel, Pawel Hawrylak, S Fafard, K Hinzer, TL Reinecke, et al. Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots. Physical Review B, 65(19):195315, 2002.

[41] R Seguin, A Schliwa, S Rodt, K P¨otschke, UW Pohl, and D Bimberg. Size-dependent ﬁne-structure splitting in self-organized inas/gaas quantum dots. Physical review letters, 95(25):257402, 2005.

83 Bibliography

[42] M Abbarchi, T Kuroda, C Mastrandrea, A Vinattieri, S Sanguinetti, T Mano, K Sakoda, and M Gurioli. Fine structure splitting of quantum dot excitons: Role of geometry and environment. Physica E: Low-dimensional Systems and Nanostruc- tures, 42(4):881–883, 2010.

[43] L´eonardMonniello, Antoine Reigue, Richard Hostein, Aristide Lemaitre, Anthony Martinez, Roger Grousson, and Valia Voliotis. Non post-selected indistinguishable single photons generated by a quantum dot under resonant excitation. arXiv preprint arXiv:1403.8001, 2014.

[44] YH Huo, A Rastelli, and OG Schmidt. Ultra-small excitonic ﬁne structure splitting in highly symmetric quantum dots on gaas (001) substrate. Applied Physics Letters, 102(15):152105, 2013.

[45] Stephen Shankland. Ibm’s 35 atoms and the rise of nanotech. CNET. http://news. cnet. com/8301-30685 3-10362747-264. html, 2009.

[46] Gerd K Bennig. Atomic force microscope and method for imaging surfaces with atomic resolution, February 9 1988. US Patent 4,724,318.

[47] Rafael Benitez and Jos´eL Toca-herrera. Looking at cell mechanics with atomic force microscopy: Experiment and theory. Microscopy research and technique, 77(11):947– 958, 2014.

[48] Leo Gross, Fabian Mohn, Nikolaj Moll, Peter Liljeroth, and Gerhard Meyer. The chemical structure of a molecule resolved by atomic force microscopy. Science, 325(5944):1110–1114, 2009.

[49] Franz J Giessibl. Advances in atomic force microscopy. Reviews of modern physics, 75(3):949, 2003.

[50] Q Zhong, D Inniss, K Kjoller, and VB Elings. Fractured polymer/silica ﬁber surface studied by tapping mode atomic force microscopy. Surface Science Letters, 290(1- 2):L688–L692, 1993.

84 Bibliography

[51] Anders Gustafsson, Mats-Erik Pistol, Lars Montelius, and Lars Samuelson. Local probe techniques for luminescence studies of low-dimensional semiconductor structures. Journal of Applied Physics, 84(4):1715–1775, 1998.

[52] Gustavo A Narvaez, Gabriel Bester, Alberto Franceschetti, and Alex Zunger. Exci- tonic exchange eﬀects on the radiative decay time of monoexcitons and biexcitons in quantum dots. Physical Review B, 74(20):205422, 2006.

[53] Oliver Stier. Theory of the electronic and optical properties of ingaas/gaas quantum dots. In Nano-Optoelectronics, pages 167–202. Springer, 2002.

[54] Christian Schimpf, Marcus Reindl, Daniel Huber, Barbara Lehner, Saimon F Covre Da Silva, Santanu Manna, Michal Vyvlecka, Philip Walther, and Armando Rastelli. Quantum cryptography with highly entangled photons from semiconductor quantum dots. arXiv preprint arXiv:2007.12726, 2020.