Site control and optical characterization of

InAs quantum dots grown in GaAs nanoholes

DISSERTATION

zur

Erlangung des Grades

„Doktor der Naturwissenschafen“

an der Fakultät für Physik und Astronomie

der Ruhr-Universität Bochum

von

Yu-Ying Hu

aus

New Taipei, Taiwan

Bochum 2013

1. Gutachter Prof. Dr. Andreas D. Wieck

2. Gutachter Prof. Dr. Ulrich Köhler

Datum der Disputation 19.11.2013

I

Contents

Contents ..................................................................................................................................... I

List of Abbreviations .............................................................................................................. III

List of Symbols........................................................................................................................ V

Chapter 1 Introduction ......................................................................................................... 1

Chapter 2 Semiconductor Quantum Dots ............................................................................ 5

2.1 Low-Dimensional Structures ..................................................................................... 5

2.2 Characterizations of Quantum Dots ........................................................................... 8

2.3 Energy Level Structure of Quantum Dots ................................................................ 10

Chapter 3 Epitaxial Growth of III-V Semiconductor Nanostructures ............................... 13

3.1 III-V Semiconductor Properties ............................................................................... 13

3.2 Growth Modes in Heteroepitaxy .............................................................................. 16

3.3 Molecular Beam Epitaxy System ............................................................................. 18

3.3.1 Solid source cells and shutters .......................................................................... 22

3.3.2 Substrate heating and manipulation .................................................................. 23

3.3.3 Growth parameters ............................................................................................ 23

3.3.4 Reflection high-energy electron diffraction ...................................................... 25

3.4 Self-Assembled 3D Nanostructures ......................................................................... 26

3.4.1 Strain-induced quantum dots (SK) ................................................................... 26

3.4.2 Nanostructures by droplet epitaxy (VW) .......................................................... 29

Chapter 4 Surface Patterning Techniques for Site-Selective Growth ............................... 33

4.1 Introduction to Site-Selective Growth ..................................................................... 33

4.2 Self-Assembled Nanohole Patterning ...................................................................... 36

4.3 Focused Ion Beam Patterning .................................................................................. 39

4.3.1 Equipment ......................................................................................................... 40

4.3.2 Process .............................................................................................................. 42

4.3.3 Patterning parameters ....................................................................................... 45

II

Chapter 5 Experimental Details and Characterization Methods ....................................... 49

5.1 Sample Fabrication ................................................................................................... 49

5.2 Scanning Electron Microscopy ................................................................................ 53

5.3 Atomic Force Microscopy ........................................................................................ 55

5.4 Photoluminescence Spectroscopy ............................................................................ 57

Chapter 6 Characterizations of Self-assembled/Self-patterned GaAs Nanoholes ............. 61

6.1 Randomly-distributed Nanoholes ............................................................................. 61

6.2 Arrayed Nanoholes ................................................................................................... 67

Chapter 7 Characterizations of Site-selected InAs Quantum Dots in GaAs Nanoholes ... 79

7.1 Topography .............................................................................................................. 79

7.1.1 Quantum dots in randomly-distributed nanoholes ............................................ 79

7.1.2 Quantum dots in arrayed nanoholes .................................................................. 84

7.2 Optical Properties of Quantum Dots in Randomly-distributed Nanoholes .............. 88

7.2.1 Quantum dot ensembles .................................................................................... 88

7.2.2 Single quantum dots .......................................................................................... 95

7.3 Optical properties of Quantum Dots in Arrayed Nanoholes .................................. 100

7.3.1 Quantum dot ensembles .................................................................................. 100

7.3.2 Single quantum dots ........................................................................................ 103

Chapter 8 Summary ......................................................................................................... 107

Bibliography ......................................................................................................................... 111

Appendix............................................................................................................................... 119

A.1 Index for Sample Number .......................................................................................... 119

A.2 Mask for Photolithography ........................................................................................ 120

A.3 Ion fluence for Planes and Lines ................................................................................ 121

Acknowledgements............................................................................................................... 123

Curriculum Vitae .................................................................................................................. 125

III

List of Abbreviations

1D, 2D and 3D One-, Two- and Three- Dimensional

2DEG Two-Dimensional Electron Gas

AFM Atomic Force Microscopy

BEP Beam Equivalent Pressure

BSE Backscattered Electron

CB Conduction Band

CL Cathodoluminescence

CVD Chemical Vapor Deposition

DE Droplet Epitaxy

DOS Density of States

EDX Energy Dispersive X-ray spectroscopy

FIB Focused Ion Beam

FM Frank-van der Merwe

FWHM Full Width at Half Maximum

IC Integrated Circuits

K-cell Knudsen effusion cell

LED Light Emitting Diode

LMIS Liquid Metal Ion Source

LPE Liquid Phase Epitaxy

MBE Molecular Beam Epitaxy

MEMS Micro-Electro-Mechanical System

ML Monolayer

MOCVD Metal-Organic Chemical Vapor Deposition

MOVPE Metal-Organic Vapor Phase Epitaxy

NH Nanohole

PBN Pyrolytic Boron Nitride

PL Photoluminescence

QD Quantum Dot

QDk Quantum Disk

QDM Quantum Dot Molecule

QR Quantum Ring

QW Quantum Well

QWR Quantum Wire

IV

RHEED Reflection High-Energy Electron Diffraction

SAQD Self-assembled Quantum Dot

SE Secondary Electron

SEM Scanning Electron Microscopy

SK Stranski-Krastanov

SNOM Scanning Near Field Optical Microscopy

SPM Scanning Probe Microscope

SRIM Stopping and Range of Ions in Matter

STM Scanning Tunneling Microscopy

TEM Transmission Electron Microscope

UHV Ultra-High Vacuum

VB Valence Band

VPE Vapor Phase Epitaxy

VW Volmer-Weber

WL Wetting Layer

AFP Lehrstuhl für Angewandte Festkörperphysik

MPI Max Planck Institute

V

List of Symbols

ao lattice constant

exciton Bohr radius

B magnetic field

C0 ion concentration

D ion dose

d thickness

E electrical field

e electron charge

E energy

Eg band gaps

ħ Dirac constant

h Planck’s constant

I ion beam current

J current density

k (kx, ky, kz) wave vector

kB Boltzmann’s constant

l, m, n quantum numbers

li width of facet

lspot spacing of FIB spots

Lx, Ly, Lz quantum confining dimensions

m*

effective mass

m0 free electron mass

p momentum

P vapor pressure

Q amount of deposited material

r (x, y) in-plane dimension

r radius

R⊥ perpendicular range

rn probability of single, double, or multiple nanoholes

Rp projected range

rsum occupancy rate of FIB spots by nanoholes

Tc congruent evaporation temperature

U voltage

VI

potential distribution

δ (x) Dirac function

ε eigen energy

εr permittivity

θ monolayer coverage

θ (x) Heaviside function

λdB de Broglie wavelength

μ chemical potential

µ*

reduced effective mass

ρ density

ρ(E) density of states

ρFIB nominal density of GaAs nanoholes

Φ ion fluence

φ lateral component of wavefunction Ψ

ψ vertical component of wavefunction Ψ

Ψ wavefunction

angular frequency

1

Chapter 1 Introduction

In semiconductor physics, low-dimensional heterostructures have been intensively studied in

the past decades, e.g. quantum wells (QW), quantum wires (QWR) and quantum dots (QD). The

major motivation for these studies originates from the quantum confinement effect in such low-

dimensional systems allowing the devices to represent interesting physical properties. Among

these low-dimensional heterostructures, QDs provide a complete three-dimensional (3D)

confinement for the charge carriers resulting in discrete densities of states which are in analogy

with atoms. Therefore, QDs are also known as “artificial atoms”. Due to their remarkable atom-

like properties, QDs are interesting to fundamental research and as well as applied technologies

[1, 2].

The tasks of QD studies and applications are mainly involved with the fabrication,

characterization and manipulation of the systems at a nanometer level. The common methods

for manufacturing semiconductor QDs are chemical synthesis [3, 4], lithography [5] and self-

assembly [6, 7]. The self-assembly method is carried out by an epitaxial growth, e.g., molecular

beam epitaxy (MBE), which has been considered as a promising technique to implement QDs

into atomic level semiconductor devices through a simple and effective process. For self-

assembled quantum dots (SAQD), InAs/GaAs system is one of the most widely studied material

systems due to its outstanding physical properties in points of preparations and applications. The

strain caused by the lattice mismatch between these two materials leads to the formation of 3D

islands, i.e., strain-induced QDs, over the surface of a 2D wetting layer on a substrate in a

Stranski-Krastanov (SK) growth mode [8–10]. Typically, strain-induced QDs have a defect-free

crystal quality, similar shapes, small sizes and narrow size-distributions. The line-up band gaps of

InAs and GaAs lead to a large potential well for both electrons and holes, which make the system

a good optical emitter with the wavelength in the near infrared range [11, 12]. Besides, the direct

band gap of InAs allows efficient optical transitions between the confined states of QDs [13].

Due to these advantages, InAs/GaAs SAQDs have become one of the most feasible objects for

exploring the fundamental physics and manipulating the applied devices of 3D quantum confined

systems.

With a conventional SK growth on a planar substrate, a great quantity of SAQDs can be

generated with a high density above the order of 1010

cm-2

which is required for the efficient

optoelectronic devices such as QD lasers, light emitting diodes (LED) and high performance

2

infrared photodetectors [14–16]. QD lasers using QDs as an active medium in the light emitting

region have the superior properties of lower threshold current and better temperature insensitivity

than bulk or QW lasers. Semiconductor QDs are also desirable for the novel quantum devices

used for transferring and processing information, i.e., quantum information processing. In

particular, single QDs and QD molecules have been considered as the potential candidates for the

implementation of single photon sources for quantum cryptography [17, 18] and the building

blocks for quantum computers, such as qubits and quantum gates [19, 20]. Using quantum-

mechanical phenomena, solid-state quantum computers which are scalable up to a large number

of qubits, are expected to comprehend massive data processing of special algorithmic calculations

with a higher resulting efficiency than digital computers [21]. However, with conventional strain-

induced QDs, the high density and random distribution make it difficult to address QDs

individually for the prospect single QD appliances. In addition, the size variety of strain-induced

QDs is restricted due to the self-limiting growth which narrows the range of the emission

wavelength for possible applications [22]. Therefore, the art of the site and size control with

SAQDs becomes one of the challenges for single QD researches.

Recently, an alternative self-assembly method with MBE has been developed, called droplet

epitaxy (DE). Droplet epitaxy is a two-steps growth method with the formation of metal droplets

by Volmer-Weber (VW) growth and the subsequent crystallization of the metal droplets [23].

Contrary to the approach of SK growth, DE provides a way with more flexibility in respect of

material systems, spatial densities and nanostructure configurations. For example, apart from

lattice-mismatched systems, lattice-matched systems are allowed with DE, e.g., GaAs/AlGaAs

for heteroepitaxy and GaAs/GaAs for homoepitaxy, because strains are not essential for VW

growth. Moreover, the densities can be altered from the order of 108 cm

-2 down to 10

6 cm

-2 which

are suitable for the study of single nanostructure spectroscopy. However, the crystal quality of

droplet epitaxy grown QDs is generally lower than that of SK grown QDs, which is affected by

the process of crystallization. In addition to QDs, various productions such as quantum rings

(QR), double quantum rings and nanoholes (NH) are also possible by DE [24–39]. Besides being

major studies, the ring-like structures and nanoholes formed by droplet epitaxy have been used

for nano-scale self-patterning in order to modulate the properties of overgrown nanostructures.

For example, they are useful to produce low-density QDs for single QD investigation by refilling

them with proper materials [40–46].

Owed to the progress of epitaxial growth techniques, the foundation of quantum hetero-

structure realization has been established in a more controllable and creative way. This thesis

presents a successful development combining the advantages of SK growth and droplet epitaxy to

fabricate high-quality InAs QDs inside low-density GaAs nanoholes via a site-selective growth

by MBE. With this development, GaAs nanoholes are self-patterned on GaAs (100) substrates by

droplet epitaxy, which can provide preferential nucleation sites for the overgrown InAs QDs

through a SK growth mode. The spatial distribution of the preferentially grown QDs, i.e., site-

selected QDs, is therefore determined by that of the nanoholes controlled by the formation of

metal droplets. This development provides an in-situ process to achieve a site-selective growth

3

without additional treatments since the SK growth for QDs and the droplet epitaxy for nanoholes

are fully compatible with MBE. Nevertheless, the locations of the site-selected QDs are randomly

distributed over the surface due to the nature of self-assembled nanoholes formed by droplet

epitaxy. In order to enhance the potential of the site-selected QDs grown in self-assembled

nanoholes for novel quantum devices which require QDs being integrated into intentional

positions, an artificial surface pre-patterning technique is commonly introduced. In this thesis, an

in-situ focused ion beam (FIB) patterning is used to overcome the random distribution of self-

assembled nanoholes into arbitrarily designed orders under an ultra-high vacuum (UHV)

environment. The FIB pre-patterning technique can locally modify a substrate surface so that

the overgrown nanostructures can be carried out in a site-controlled manner according to the

arrangement of designed patterns [47–50]. Therefore, positioned self-assembled nanoholes can be

produced by combining FIB pre-patterning and droplet epitaxy, which can be further used as

templates for the re-growth of QDs. Finally, with FIB-positioned GaAs nanoholes, the site-

control of InAs QDs can be obtained with a planned arrangement via a subsequent MBE growth.

The structure of this thesis after the present introduction is as follows. In chapter 2, the

fundamental background about semiconductor QDs is introduced. It starts with the theoretical

background and the physical properties of low-dimensional quantum confined structures. Then,

the important characteristics and different fabrication methods of semiconductor QDs are

described. A theoretical model used to deduce the energy level structure of self-assembled QDs is

also explained. Chapter 3 regarding the epitaxial growth begins with a brief overview of

the physical properties of III-V compound semiconductors which are commonly used for the

realization of low-dimensional systems. The typical crystal growth modes are described in the

second section including the general mechanisms and also that in practical cases of epitaxial

growth. Then, a description about the MBE system used in this work is addressed in detail.

Finally, the formation mechanisms of various self-assembled 3D nanostructures by two MBE

growth methods are described, especially in the cases of strain-induced InAs QDs and GaAs

nanoholes formed by droplet epitaxy. In chapter 4, the surface patterning techniques used for the

complementation of a site-selective growth are addressed. First, a literature survey about the site-

selective growth of SAQDs is described. Then, the particular approach to site-selected InAs QDs

applied in this work is introduced and explained, which is developed with self-patterned GaAs

nanoholes combining with or without FIB pre-patterning. A detailed description of the in-situ FIB

system and the patterning parameters used in this work are given in the last section of this chapter.

The details about sample fabrication and experimental characterization methods are opened and

described in chapter 5. The sample fabrication is provided with MBE growth, FIB pre-patterning

and sample processing. The structural characterizations are studied by scanning electron

microscopy (SEM) and atomic force microscopy (AFM), while the optical characterizations are

measured by photoluminescence (PL) spectroscopy and scanning near field optical microscopy

(SNOM). The experimental results and discussions are shown in chapter 6 and chapter 7. In

chapter 6, the results concerning the self-assembled/self-patterned GaAs nanoholes generated by

droplet epitaxy are reported along with the studies of their structures and distributions on a bare

4

GaAs surface (without FIB pre-patterning) and on a FIB-patterned GaAs surface. In the cases of

FIB pre-patterning, Ga+ and In

+ focused beams are applied to create square arrays of spots on a

nanometer scale prior to the fabrication of GaAs nanoholes. The influence of the FIB-patterning

parameters including ion fluence and spot spacing are studied experimentally to achieve the

optimum conditions for positioning the self-assembled nanoholes. On the other hand, the results

regarding the site-selected InAs QDs in the self-assembled GaAs nanoholes on a bare GaAs

surface and on a FIB-patterned GaAs surface are reported in chapter 7. This includes the growth

evolution of QDs with various amounts of InAs coverage and the influence of different FIB-

patterning parameters on the variation of sizes and densities. The optical properties of the QDs

are also addressed in this chapter for ensembles and single ones. In the end, a summary of the

results and concluding remarks of this work are given in chapter 8.

5

Chapter 2 Semiconductor Quantum Dots

The main purpose behind this work is to study the characteristics and the optical properties of the

semiconductor quantum dots (QDs). In this chapter, the general concepts related to QDs are

described. It starts with the theoretical background of quantum confinement in low-dimensional

semiconductor structures with respect to their physical properties. Then, the basic physical

properties and the fabrication methods of semiconductor quantum dots are addressed in particular.

In order to gain an insight of the optical properties, an adiabatic approximation employed to

deduce the energy level structure of the QDs is explained in the last section.

2.1 Low-Dimensional Structures

Charge carriers, i.e., electrons and holes, behave like free carriers in a bulk semiconductor

material where all three dimensions are much larger than the wavelength of their wavefunction,

i.e., de Broglie wavelength. If any of the dimensions is reduced to the order of the wavelength,

the charge carriers are squeezed with their motions confined in the corresponding direction

resulting in quantum confinement effect [51]. In general, the de Broglie wavelength of the charge

carriers is on the nanometer scale for semiconductors.

When quantum confinement is introduced in one, two or three dimensions, the energy band

structures and the density of states (DOS) of the charge carriers can deviate substantially from

that of a bulk semiconductor. As a result, the electronic and optical properties of the materials can

change dramatically. The carrier energy levels in semiconductors can be determined by solving

the Schrödinger equation in the effective mass approximation [52]:

* ħ

( )+Ψ ( ) Ψ ( ) .

where Ψ ( ) is the carrier wavefunction, * is the effective mass of the carrier, ħ is the Dirac

constant, ( ) is the potential distribution, and E is the energy of the system. Considering

the simple case of an infinitely deep, rectangular potential well, the Schrödinger equation can be

solved by the separation of variables method giving the confinement energies for one-, two- and

three- dimensional (1D, 2D and 3D) confinement.

In a bulk where there is no potential confinement for the carriers, i.e., 0D confinement, the

energy is quadratic in the wave vector ( ) as in the case of free particles:

6

u ħ

.

For 1D confinement, one dimension of the system, e.g., Lz, is strongly reduced. Therefore, the

carriers are confined in the direction z while they can move in a plane of (x, y). This kind of 1D

confinement can be realized by heterostructures in semiconductor called quantum wells (QW)

with the energy:

ħ

**

(

)

+ .

With 2D confinement, the system is confined along two directions, e.g., y and z, with the

dimensions of and as small as the de Broglie wavelengths. The carriers are allowed to move

only along one dimension of the structure which is known as a quantum wire (QWR). Its energy

has the form:

ħ

[

(

)

(

)

] .

In the case of 3D confinement, all three dimensions of , and are reduced so that there are

no free carries in the system. The carriers are confined to a box, called a quantum dot (QD). The

energy of a QD is written as:

ħ

[(

)

(

)

(

)

] .

In the above expressions of the energies, 1, 2, … are the quantum numbers. The

structures, QW, QWR and QD, are also known as 2D, 1D and 0D potential wells, respectively.

The corresponding density of states ρ( ) as a function of the energy is represented as

ρ u

( *)

⁄

ħ ⁄ .

ρ

ħ

∑ θ

( ) .

ρ

( )

⁄

∑( )

- ⁄

.

ρ

∑ δ

( ) .

where θ( ) is the Heaviside function with θ( ) as , and θ( ) as , and

δ( ) is the Dirac function.

With a decrease of the confining dimensional degree from 3D to 0D, the confinement

potential changes the density of states tremendously. According to the equations described above,

the density of states and the confinement energy of the electronic carriers can be plotted as

Figure 2.1 with respect to the confined and unconfined structures. The unconfined bulk material

has a continuous density of states in a proportion to √ . Quantum wells have a step-like density

7

of states. In quantum wires, the density of states has a relationship inversely proportional to √ .

Finally, quantum dots have discrete energy levels. These discrete energy levels can hold electrons

or holes of opposite spin direction following Pauli’s exclusion principle. These levels can be

filled sequentially starting from the lowest levels, i.e., the ground state, equivalently to the shell

filling in the orbitals of atoms [53]. Because of the analogies to the real atoms, the quantum dots

are often referred to as “artificia atoms” [1, 2]. However, the confinement potential of real atoms

is due to the Coulomb interaction between electrons and nucleus. Furthermore, the size of the

quantum dots is typically in the range of nanometers which is much larger than real atoms, e.g.,

0.53 Å for the Bohr radius of a hydrogen atom. Thus, the features of quantum dots in energy level

structures and optical properties are qualitatively different from those of atoms [54]. The

experimental results on different types of quantum dots revealed that the inter-subband energies

of QDs are of the order of several tens of meV. Compared to these value, the inter-subband

energies of atoms are three orders magnitude higher. Due to this fact, quantum dots are very

sensitive to temperature fluctuations, e.g., at room temperature kBT ≈ 26 meV. Therefore, we

need low temperatures to resolve the energy splitting of QDs.

Figure 2.1 The illustration for three-, two-, one-, and zero-dimensional

quantum confined structures and their corresponding densities of states ρ( ) as

a function of energy E. (courtesy of F. Tinjod [55])

8

2.2 Characterizations of Quantum Dots

As described in the previous section, a quantum dot is a nanostructure that confines the

motion of the charge carriers in all three spatial directions leading to discrete quantized energy

levels due to quantum confinement effects. The first experimental evidence and theoretical

description of 3D quantum confinement was published in the early 1980s with semiconductor

nanocrystals [56, 57]. The confinement in this case is formed by the presence of the interface

between different semiconductor materials. The semiconductor quantum dot is buried in another

semiconductor matrix while the band gap of the matrix material is larger than that of the quantum

dot material. Consequently, the electron energy level and the heavy-hole energy level are

quantized and lifted relative to the band edge of the bulk material [58]. Here, the heavy-hole

energy level is considered because it is the lowest level in the valence band in most common

semiconductors used for the realization of quantum dots. A quantum dot has electronic properties

intermediate between those of bulk materials and discrete molecules. The energy quantization of

both electrons and heavy holes depends on the size, shape and composition of QDs, as well as the

intrinsic properties of QD and matrix materials. In particular, the energy band gap of QDs is size-

dependent.

For an ideal quantum dot, the quantum confining dimensions Lx, Ly and Lz should be

comparable to the de Broglie wavelengths, λ , of carriers which depends on the effective mass

m* and temperature T following the relation of

λ

√ * .

where h is Planck’s constant and kB is Boltzmann’s constant. Comparing with the mass of a free

electron m0, the effective masses of electrons and holes in semiconductor materials are typically

smaller, e.g., a s* = 0.067 m0 and hh a s

* = 0.5 m0. As a result, the de Broglie wavelengths are

in the order of 10 nm to 100 nm for semiconductors at low temperatures. However, the de Broglie

wavelength is a soft criterion. The quantization effects are for example smeared out by thermal

broadening (~ kBT) resulting in fluctuations in the potential dimensions. If the thermal energy kBT

is smaller than the binding energy resulted from Coulomb attraction between the electron and the

hole confined in a QD, the bound electron-hole pair can be described as a quasi-particle, i.e., an

exciton. The spatial extension of an exciton is defined by the exciton Bohr radius, * .

*

ε

μ* .

where εr is the permittivity of the material, µ* is the reduced effective mass ( *⁄

*⁄

hh*⁄ ) and e is the electron charge of 1.602 × 10

-19 C. In typical semiconductor materials with

large εr and small µ*, the exciton Bohr radius is usually much larger than the hydrogen Bohr

radius and the lattice constant of the host material as well. Therefore, the corresponding

wavefunctions are spatially localized within the quantum dot, and extend over many periods of

9

the crystal lattice. Alternatively, the exciton Bohr radius is a convenient parameter to describe the

dimension of the QD instead of the de Broglie wavelength which has to be considered for

electrons and holes separately [58]. For example, the exciton Bohr radius for InAs is about 35 nm

[59]. Depending on the coupling degree between the electron and the hole in an exciton, there can

be strong or weak confinements which result in different energy state equations [60, 61].

There are many different ways to obtain 3D confinement, which results in different types of

semiconductor quantum dots. Here, three different types of QDs will be described in the

following. The first one is called colloidal quantum dots, which has been demonstrated since the

mid-1980s. Colloidal quantum dots are fabricated by chemical synthesis allowing manufactures

with large quantities and different sizes of quantum dots [3, 4]. Due to their special optical

properties, these quantum dots have been widely used as biological imaging tags [62] and also as

emitters in light emitting diodes (LED) [63]. The colloidal synthesis method is a low-cost and fast

technique to fabricate quantum dots. The second type of quantum dots is realized by lateral

electrostatic potential confinement of electrons in a two-dimensional electron gas (2DEG) or by

lateral lithographic patterning of a quantum well with vertical etching [5]. The method with

patterning has attracted much attention since the end of 1980s due to its many advantages. For

example, the quantum dots can be fabricated with various lateral shapes depending on the

resolution of lithographic techniques, e.g., photolithography, electron beam or focused ion beam

(FIB) lithography and scanning tunneling microscopy (STM). The etching techniques are reliable,

while some of them are easily available. Especially, it is compatible with large-scale modern

integrated semiconductor technology [1]. The fabrication for the third type of QDs is a self-

assembly process with a heteroepitaxial growth by molecular beam epitaxy (MBE) or metal-

organic chemical vapor deposition (MOCVD). This type of QDs is called self-assembled

quantum dots (SAQD) which are widely used in quantum research nowadays. With MBE,

SAQDs can be realized either in the Stranski-Krastanov (SK) growth mode or by droplet epitaxy

(DE) inherited by Volmer-Weber (VW) growth [6, 7]. In general, SAQDs have small and

uniform sizes and similar shapes. The size is usually a few tens of nanometers for the base

diameter and a few nanometers for the height, which can result in pronounced quantum size

effects. This method can easily integrate quantum dots into semiconductor heterostructures

without complicated and time-consuming patterning steps for QD devices, e.g., quantum dot

lasers with ensembles of QDs and single photon sources based on single QDs. For QD lasers, SK

grown QD ensembles have shown a good performance with high densities of the order from

109 to 10

11 cm

-2 [11, 14]. On the other hand, DE grown QDs representing low densities of the

order of 108 cm

-2 or lower, have become promising objects for single QD spectroscopy [17, 18].

Self-assembly also allows the generation of vertical quantum dot molecules (QDMs) by the

stacking of QD layers [5], or lateral QDMs by droplet epitaxy under specific growth conditions

[24]. Several heteroepitaxy material systems have been successfully employed, such as

InAs/GaAs, InAs/InP, InAlAs/AlGaAs, InP/GaAs, Ge/Si, GaN/AlGaN for strained systems and

GaAs/AlGaAs and GaAs/AlAs for un-strained systems [1, 7]. Among them, the most studied one

10

is InAs/GaAs system which is also used in this work. More details related to InAs/GaAs QDs will

be described in the next chapter.

2.3 Energy Level Structure of Quantum Dots

An artificial atom, i.e., a quantum dot, contains a finite number of conduction band electrons

and valence band holes or excitons of the order of 1 to 100, which means a finite number of

elementary electric charges. Because of this fact, the properties of quantum dots will be changed

even with the addition or removal of only one single electron. Small quantum dots like colloidal

semiconductor nanocrystals can be as small as 2 nm to 10 nm which corresponds to 10 to

50 atoms in diameter and a total number of 100 to 100,000 atoms within the volume of a QD. For

self-assembled quantum dots, the size is typically between 10 nm and 100 nm corresponding to

approximately 1,000 to 1,000,000 lattice atoms [64].

In order to study the properties of the quantum dots composed of a certain amount of atoms,

different theoretical models have been used to deduce their energy level structure [65, 66]. The

simplest model used to realize the energy eigenstates in a quantum dot is the calculation of a

particle in a sphere potential considering the case of an infinite barrier and a finite barrier with

different inner and outer materials (different masses). This model is mostly sufficient for a large

class of dots with the shape close to a spherical form [67]. However, depending on different

growth methods and parameters, QDs with different shapes have been reported, such as lens

shape [10], facets [68] and pyramidal shape [6]. For those QDs with the shapes different from

spherical, the potential is not separable and the Schrödinger equation has to be solved

numerically in most of the cases. However, there is a semi-classical approach including the

effective mass approximation which has been applied for such QD systems [66, 69]. In this work,

the lens-shaped dots are studied which are usually considered in self-assembled quantum dots.

Lens-shaped dots were first reported by D. Leonard et al., which are described as a part of a

sphere with a given base and a height with the ratio of 1/2 to the base diameter [10, 70]. Based on

the geometry, it is suggested that the carrier confinement in the growth-direction (vertical-,

z-direction) is stronger than that in the lateral directions (in-plane-, x, y-direction). In an adiabatic

approximation, the single particle wavefunction was derived in the envelope function formalism

by effective mass approximation [71]. With this approximation, the vertical ψ( ) component of

the wavefunction can be separated from the lateral φ( ) one. Therefore, the wavefunction can

be represented as

Ψ( ) φ( ) ψ( ) φ( ) ψ( ) .

which obeys the following time-independent 3D Schrödinger wave equation:

[ ( )

]Ψ Ψ , wh r ( ) .

The potential ( ) can be decomposed into two parts:

( ) ( ) ( ) .

11

where ( ) corresponds to the potential at the center of the dot with respect to x-y plane and

is the potential difference.

Due to the strong confinement in vertical direction for lens-shaped quantum dots, the vertical

component ψ( ) can be approximated by ψ ( ) of the 1D Schrödinger wave equation at the

lateral center, :

[ ( )

] ψ ( ) ε

ψ ( ) .

Because higher excited states (n > 0) are only weakly bound and their eigen energies are larger

compared with the observed quantum dot states, the mixing of such states is not taken into

account. Within the adiabatic approximation, the ground state energy ε can be identified with the

undisturbed sub-band edge while the perturbation is constituted by the potential difference of

( ).

A 2D Schrödinger wave equation for the lateral component φ( ) can be obtained by

inserting equations 2.12, 2.14 and 2.15 into 2.13:

[⟨ψ | |ψ

⟩

] φ ( ) ( ε

) φ ( ) .

The “undisturbed sub-band edge” ε can be considered as the “zero energy” for these states. The

integral term ⟨ψ | |ψ

⟩ can be referred to as a lateral effective potential, ( ):

( ) ⟨ψ | |ψ

⟩ ∫ψ

( ) ψ

*( , ) ( , ) .

In a semiclassical approach, this potential ( ) describes the lateral modulation of sub-band

edges. Applying an adiabatic approximation, the local sub-band edge ε ( ) depending on the

lateral position (the ground state eigen energy value of the 1D Schrödinger wave equation solved

at position r = (x,y)) can be assumed as a lateral effective potential:

( ) ε ( ) .

A scheme representing the adiabatic approximation for electrons in a lens-shaped dot is

shown in Figure 2.2. In this case, the xy-dependent ground state energy with respect to the

z-quantization determines the lateral confinement potential. For such a confinement, the 2D

harmonic oscillator potential is a good approximation as the example of a particle with the

effective mass of * bound laterally in a quantum well (in x-y plane) by a parabolic potential of

( )

( ) .

The quantum level energies can then be approximated by the simple formula:

ħ ( ) .

where is the angular frequency. ħ is represented as the lateral confinement energy. n and l

are the quantum numbers corresponding to the eigenstates of a 2D harmonic oscillator [72]. In

analogy to atomic physics, the energy levels of a QD with their quantum number adding up to

2n + l = 0, 1, 2…. correspond to the s, p, d shells, respectively. On the other hand, the vertical

12

potential ( ) can also be considered as a 1D-harmonic oscillator potential used for describing

the structure of spherical quantum dots [73]:

( )

*

.

The quantum energy levels of a 1D-harmonic oscillator potential can be represented as:

ħ (

) .

where and n are the angular frequency and the quantum number corresponding to the 1D

harmonic oscillator, respectively. ħ is represented as the vertical confinement energy. However,

the observable level structure of lens-shaped QDs is mainly determined by the in-plane

confinement [53]. The energy eigen states for a 3D lens-shaped quantum dot has been computed

by A. Wojs et al. [69]. With a finite potential barrier in an effective mass approximation, the

resulting particle for such dots resembles well to the case of a 2D harmonic oscillator.

The above approach shows the characteristic quantization of the energy levels resulting from

the lateral confinement, and also the dependency of these energy levels on the effective mass of

carriers and the size of dots. In other words, the properties of quantum dots can be controlled by

changing the size and/or the shape of the fabricated potential [74]. Many experimental electronic

and optical properties of self-assembled InAs quantum dots had been explained based on the

theoretical model of 2D harmonic oscillators [75, 76]. The detailed knowledge of the energy level

structure helps for determining the physical properties of quantum dots, which is very interesting

from a fundamental point of view as well as to possible applications. However, it is important to

note that the approach considers only single quantum dots. For QD ensembles containing dots

with various radii, the size distribution has to be considered. The optical resonance energies

strongly depend on the radius of QDs. This leads to a resonance distribution which manifests

itself as an inhomogeneous broadening in optical spectra [77].

Figure 2.2 Schematic illustration of the adiabatic approximation for electrons in a lens-

shaped quantum dot. Assuming that the vertical confinement (along z) is so strong that only

the ground state is occupied, the ground state energy can be assumed as the lateral effective

potential resulting in the lateral confinement of the quantum dot being parabolic. The

widths of the potential wells of vertical confinement are the same with the heights of the

quantum dot, z1, z2 and z3, with respect to the position of (x,y).

13

Chapter 3 Epitaxial Growth of III-V Semiconductor

Nanostructures

Owed to the development of molecular beam epitaxy in the 1970s, the quantized properties of

low-dimensional nanostructures have been largely investigated and manipulated. This chapter

begins with an introduction of III-V compound semiconductors which are widely used for the

realization of such quantum confined structures due to their unique properties. These properties

determine the electric and optical properties of the semiconductor devices as well as whether

an epitaxial growth is allowed with the materials. Three different crystal growth modes are

introduced in the second section, including the general mechanisms and also those in the practical

cases of epitaxy. The molecular beam epitaxy system used in this work and its working principle

are described in the third section. In the end, two different MBE growth methods for 3D self-

assembled nanostructures are introduced and described in detail.

3.1 III-V Semiconductor Properties

It has been proposed in the beginning of the 1950s that the semiconducting properties of

III-V compounds are obtained by combining group III elements, essentially Al, Ga and In, with

group V elements, essentially N, P, As and Sb, in the periodic table [78]. These III-V compound

semiconductors crystallize either in a zinc-blende lattice structure (GaAs, AlAs, InAs, GaSb,

InSb, GaP and InP) or in a wurtzite lattice structure (GaN, AlN and InN). A zinc-blende structure

is made up of two interpenetrating face centered cubic sub-lattices, while a wurtzite structure is

based on hexagonal lattices. Both of them have partly ionic and covalent bonding characters [79].

In the following, the properties of zinc-blende III-V compound semiconductors will be stressed,

especially GaAs and InAs, which are the materials used for the quantum dot structures in this

work. A scheme of the zinc-blende lattice structure is shown in Figure 3.1(a).

One of the most important properties of III-V compound semiconductors is the energy band

gap Eg, an energy interval without allowed states for the charge carriers. It is defined as the

smallest energetic distance between the top of the valence band and the bottom of the conduction

band. Figure 3.1 (b) shows a simplified band diagram for GaAs or InAs. The minimum of

the conduction band and the maximum of the valence band are both at the Γ-point (k = 0)

in reciprocal space. Semiconductors with this feature are referred to as direct bandgap

14

semiconductors. A direct band gap is essential for optical applications like light emitting diodes

(LED), because the exciton, i.e., the electron-hole pair can recombine to emit a photon directly

without requiring phonon interaction to ensure momentum conservation. It makes the generation

of light faster and more effective, since only then electrons and holes meet simultaneously in real

and in momentum space in the same moment. In this context, the recombination wavelength

defined by the band gap is an important property for specific applications. For example, in the

case of telecommunication applications, the commonly used wavelength of 1.55 µm is highly

desired because the losses of optical glass fibers are minimal at this wavelength. The most

commonly used III-V semiconductors have a direct band gap, e.g., GaAs, InAs, GaN and InP.

The band gap is often plotted versus the lattice constant ao as shown in Figure 3.2 because these

two are the most important parameters to determine the optoelectronic properties and the

fabrication processes of these III-V compound semiconductor devices. Both band gap energies

and lattice constants are temperature dependent. The lattice constant increases with increasing

temperature due to inharmonicity of the binding potential, while the band gap decreases because

of the atomic vibrations. The relations of temperature dependence for GaAs and InAs are listed in

Table 3.1. At 300 K, the direct band gaps are Eg,GaAs = 1.42 eV and Eg,InAs = 0.35 eV, and the

lattice constants are ao,GaAs = 5.6533 Å and ao,InAs = 6.0583 Å for GaAs and InAs, respectively.

III-V semiconductors can completely dissolve into each other. Therefore, the lines in

Figure 3.2 connecting the circles of specific binary compounds represent the energy band gaps

and lattice constants for ternary alloys depending on the mole fractions of the materials, e.g.,

AlxGa1-xAs, with x ranging continuously from 0 to 1. Furthermore, quaternary alloys are also

possible, e.g., GaxIn1-xAsyP1-y, with x and y ranging continuously from 0 to 1. Due to this fact, it

is possible to tailor the properties of the compounds for the desired applications by choosing

different elements and their compositions in a certain arbitrary ratio. This technique is referred to

as band gap engineering or band gap tailoring which makes III-V compound semiconductors

technically more flexible than elemental semiconductors like Si or Ge. Nowadays, a wide range

of bulk III-V compound semiconductors like GaAs and AlxGa1-xAs is used for traditional

semiconductor devices like transistors and lasers. However, due to the advances of epitaxial

techniques such as MBE [80, 81], liquid phase epitaxy (LPE) [82], metal-organic vapor phase

epitaxy (MOVPE) [83] and chemical vapor deposition (CVD) [84], III-V compound

semiconductors are being employed in new science and technology fields in the recent decades.

In other words, III-V compound semiconductors can be carried out not only for novel

optoelectronic devices with layered structures of different materials, but also for fundamental

investigation of low-dimensional solid-state nanostructures. More details about the epitaxial

techniques and the growth methods will be discussed in the next sections.

15

Temperature

dependency GaAs InAs

lattice constant

ao (Å) ao = 5.65325 + 3.88×10

-5·(T - 300) ao = 6.0583 + 2.74×10

-5·(T - 300)

direct band gap

Eg(Γ) (eV)

Eg = 1.519 - 5.405×10-4

·T 2

/ ( T + 204 )

(0 < T (K) < 103)

Eg = 0.415 - 2.76×10-4

·T 2

/ ( T + 83 )

(0 < T (K) < 300)

Table 3.1 Temperature dependences for the lattice constants and direct band gaps of GaAs and

InAs [13, 85].

(a) (b)

Figure 3.1 (a) The zinc-blende structure of the III-V compound semiconductor, GaAs. Dark

spheres correspond to Ga atoms. Light spheres correspond to As atoms. The lattice constant ao is

defined by the edge length of the cube. (b) The band structure of GaAs or InAs with a direct band

gap Eg at the Γ-point with k = 0. At 300 K, the band gaps are 1.42 eV for GaAs and 0.35 eV for

InAs, respectively [86].

Figure 3.2 Band gap energy versus lattice constant for zinc-blende III-V

compound semiconductors at room temperature. (courtesy of P. Tien [87])

16

3.2 Growth Modes in Heteroepitaxy

Th wor “ pitaxy” consists of two Greek words, “έπι” (epi) and “τάξ” (taxis), which mean

“on” an “arrang m nt”, r sp ctiv y. Epitaxial growth refers to a crystalline layer arranged on a

crystalline substrate in a way that one or more preferred orientations of the layer are aligned with

respect to the substrate. These kind of well-ordered layers are called epitaxial layers or epitaxial

films. In epitaxy, there are two different types of growth depending on the material systems. One

is homoepitaxy, where the substrate and the deposited materials are the same, e.g., the deposition

of Si on Si substrates or GaAs on GaAs substrates, which can be used to produce a highly pure

epitaxial layer based on the substrate. The other one is heteroepitaxy, where different materials

are deposited on the substrate, e.g., AlAs on GaAs substrates, which allows the fabrication of

heterostructures like quantum wells, quantum wires and quantum dots with the technique of band

structure engineering [88].

Generally, there are three crystal growth modes as shown in the schematic illustration of

Figure 3.3. The first one, (1) Frank-van der Merwe (FM) growth, is also called layer by layer

growth where adatoms are more strongly bound to the substrate than to each other. The adatoms

initially condense to form a complete monolayer on the substrate. The first layer is then covered

by the second layer which is a little less tightly bound. This kind of mode is observed in some

metal on metal systems, and also in semiconductor on semiconductor systems, e.g., GaAs on

GaAs or AlxGa1-xAs on GaAs. The second, (2) Volmer-Weber (VW) growth, is also named island

growth where adatom-adatom interactions are stronger than those of adatom-substrate. Therefore,

the adatoms are preferentially bound to each other rather than to the substrate, leading to the

formation of three-dimensional clusters [89]. These clusters which are nucleated directly on the

surface merge into each other forming an island of the condensed phase. This mode is displayed

by many systems of metal on insulators, including alkali halides, graphite and mica. The last one,

(3) Stranski-Krastanov (SK) growth, is an intermediate case of the two growth modes above.

Therefore, it is also known as layer plus island growth. After forming the first monolayer or a few

monolayers, subsequent layer growth is unfavorable and islands are formed on top of this

intermediate layer. This kind of heteroepitaxy growth is observed in the case with strained

systems containing small interface energies, e.g., InAs/GaAs, In(Ga)As/InP, SiGe/Si and

CdSe/ZnSe.

The heterostructures embedded in the samples of this work consist of layers with different

III-V semiconductor materials such as GaAs, AlAs and InAs. The different materials with

different structures and chemical properties at the growth interface lead to different growth

modes. An important factor for the growth in heteroepitaxy is the lattice mismatch between two

materials, i.e., the difference in their lattice constants, which determines whether layers of

different alloys can be grown epitaxially. The presence of lattice mismatch gives rise to internal

strains so that only limited combinations of materials can form strain-free heterostructures.

17

However, if the thin layers in heterostructures are allowed to contain strain, a much wider range

of materials becomes available. For instance, the lattice constants of GaAs, InAs and AlAs are

5.6533 Å, 6.0583Å and 5.6611 Å, respectively. The lattice mismatch between GaAs and InAs is

about 7 %, while that between GaAs and AlAs is only 0.1 %. Therefore, AlAs can be grown

epitaxially on GaAs even in thick layers. On the contrary, only thin epitaxial InAs strained layers

can be grown on GaAs. Strains resulting from lattice mismatches contribute to the interface

energy as a key parameter for determining the growth mode in an epitaxial growth. However, the

surface free energies for the substrate and deposited materials also influence the growth mode. In

the case of strained epitaxial layer systems, the initial growth may occur layer by layer. The sum

of the layer surface energy and the interface energy must be less than the surface energy of the

substrate in order to make wetting occur. Therefore, the FM growth is expected if +

,

where and

are the surface energies of the adsorbate and the substrate respectively, and

is

the interface energy which depends on the strain and the strength of chemical interactions

between the adsorbate and substrate at the interface [90]. This layer-by-layer growth becomes

favorable if the surface energy of the substrate increases. However, the strain energy is a term

within , which increases linearly with the number of strained layers. At certain thickness,

exceeds and the growth mode transforms from FM to SK resulting in 3D islands formed on the

2D layer. Alternatively, may be sufficiently in excess of

such that the equation

is no longer fulfilled even for a strong attractive interaction between the adsorbate and the

substrate along with a little strain. In this case, 3D islands nucleate from the onset of a VW

growth, while

[91].

Figure 3.3 Schematic representation for the three primary modes of thin-film growth.

(1) Frank-van der Merwe (FM), (2) Volmer-Weber (VW) and (3) Stranski-Krastanov

(SK). Every mode is shown with different amounts of surface overage θ.

18

3.3 Molecular Beam Epitaxy System

Molecular beam epitaxy (MBE) was developed in the late 1960s at Bell Telephone

Laboratories by J. Arthur and A. Cho [92, 93], primarily for the growth of semiconductor

compounds, such as GaAs and GaAs/AlxGa1-xAs structures [94]. Subsequently, it has been

widely extended to a variety of fields including metal, insulator, and superconductor materials

[95]. Compared with other epitaxial deposition techniques, MBE has its unique advantages, such

as the precise control of the growth in atomic monolayer dimensions, producing high quality

epitaxial structures with tailored compositions and doping, monitoring the growth dynamically in

real time and providing predictable and reproducible growth processes. Because of these

outstanding features, MBE is often called “the king discipline in epitaxy” which has become a

valuable tool in developing sophisticated electronic and optoelectronic structures in both research

and industry [96, 97].

The principle of the MBE process is based on the fact that the thermal-driven (by

evaporation or sublimation) atoms or molecules of constituent elements for the epitaxial layer

react on a heated crystalline substrate to form an ordered overlayer in ultra-high vacuum

conditions (UHV). The reaction is governed mainly by the kinetics of the surface process via

mass transfer from the impinging atomic or molecular constituents to the outermost atomic layers

of the substrate crystal. In contrast, the growth of LPE and VPE is most frequently controlled by

diffusion processes under the condition near a thermodynamic equilibrium [81]. The elemental

constituents in vapor phases generated by heating the solid sources are termed as atomic or

molecular beams. Due to the long mean free paths under UHV conditions, the atoms and

molecules do not interact with each other or with background impurities before they reach the

substrate. The composition of the epitaxial overlayer depends on the arrival ratio of the

constituent elements at the substrate, which in turn depends on the fluxes of the respective atomic

and molecular beams.

The most important aspect of MBE is the precision in the range of single atomic layers,

which is attributed to a very slow epitaxial process with growth rates typically in the order of

1 μm/h, i.e., ~1 monolayer (ML)/s, or even lower. The atomically abrupt feature of different

layers can be achieved by combining the small beam fluxes, modulated by the evaporation or

sublimation conditions of the constitute elements, together with the physical interruption of the

beams executed by rapid-action mechanical shutters. Slow growth rates also ensure an epitaxial

growth of the crystal. Because of the slow growth rates, the atoms or molecules have enough time

for diffusion to take on the crystalline orientation of the substrate. To maintain high purity and

integrity of the deposition, stringent vacuum conditions are needed to minimize contaminations

that lead to undesired background doping and impurities. Especially under such low deposition

rates with MBE, a better vacuum is required in order to achieve the same quality levels of other

deposition techniques. Furthermore, the UHV growth environment in MBE makes it possible to

study the growth process using in-situ diagnosis and analysis techniques. Concluding the above,

19

an extreme control regarding the dimensionality, composition and impurity incorporation can be

achievable by an MBE system [98].

A Riber Epineat III-V solid source MBE (SS MBE) system, equipped at the laboratory of

Lehrstuhl für Angewandte Festkörperphysik (AFP), Bochum, is used to fabricate the samples in

this work. It consists of a growth chamber, a transfer chamber (also known as a buffer chamber)

and a load-lock chamber. The growth chamber is the main chamber for MBE where the epitaxial

growth takes place. The transfer chamber is used to place or store samples and transfer samples to

neighboring chambers. The load-lock chamber is used to load or unload samples between the air

and the vacuum environment without disturbing the vacuum condition of the other chambers. In

addition, this MBE system is directly connected to a focused ion beam system and a hydrogen

cleaning chamber via a sample rotation chamber. This is a unique feature that allows additional

in-situ processing and structuring of the epitaxy grown samples all in UHV conditions. In the

following, this system is also named as MBE-FIB system. In the rotation chamber, it is possible

to flip a sample by 180° to face upwards for FIB structuring or downwards for MBE growth. A

detailed description of the FIB system will be given in section 4.3. A scheme of the MBE system

combined with the FIB system is shown in Figure 3.4. Each chamber is made of stainless steel,

connected with separate primary pumping stacks and isolated by gate valves. Transfer rods are

used to take, transport and deposit samples in and between the chambers. All components

withstand baking temperatures up to 250 °C in order to remove the physisorbed water-rich layer

and chemisorbed gases on the surface after exposure to atmospheric air [96]. The load-lock

chamber is evacuated by a turbo molecular pump and an ion getter pump for the working pressure

of 1 × 10-8

Torr. All the other chambers are under a UHV in the order of 1 × 10-10

Torr. The UHV

in the growth chamber is maintained by the combination of two ion getter pumps, a titanium

sublimation pump and liquid-nitrogen cooled cryo-shroud [99]. A schematic diagram of the

growth chamber is presented in Figure 3.5. Reduced to its essentials, the MBE growth chamber

comprises three parts as following. A UHV system allows to keep the undesired residual

impurities as low as possible so that there is no gas reaction before the constituent beams reach

the substrate. Solid source cells with shutters can provide atomic or molecular beams with a

precise control. A substrate heating support is used to heat up and maintain the substrate

temperature and also to keep a steady rotation speed during growth. Commonly, a reflection high-

energy electron diffraction (RHEED) system and a mass spectrometer are additionally fitted in.

RHEED is applied for diagnosis and analysis of the growth process. A quadrupole mass

spectrometer is used as a true element-specific detector for monitoring the background gas

composition, analyzing the species emerging from the sources, and checking for an eventual air

leak of the system [80].

20

Figure 3.4 Scheme of the MBE-FIB system at AFP. The MBE system consists of a

growth chamber, a transfer chamber and a load-lock chamber. It is furthermore

connected to a hydrogen cleaning chamber and a FIB chamber through a sample

rotation chamber. The transfer rods are used for transporting samples from one

chamber to a neighboring one. Each chamber contains vacuum and is separated by

gate valves.

21

Figure 3.5 Scheme of the III-V SS MBE growth chamber. It is fitted with thermal

effusion cells and an e-beam evaporator with rapid-action shutters to alter the flux of

the atomic or molecular beams. The substrate is placed with its face towards the cells

on a substrate rotation support, and heated up by a substrate heater closely above. An

incident high-energy electron beam to the sample surface with a glancing angle

smaller than 3° generates RHEED patterns on the screen at the opposite side.

22

3.3.1 Solid source cells and shutters

The solid source MBE is equipped with Al, Ga and In cells of group III elements, C and Si

cells of group IV elements, and an As valved-cracker cell of group V elements. The cells are used

to produce directed atomic beams, or a molecular beam in the case of arsenic (which give rise to

the name “mo cu ar” am pitaxy). Th group IV m nts ar us for oping, i.e., the C cell

for p-type doping and the Si cell for n-type doping. The C cell is made of an electron beam

evaporator with a pyrolytic graphite bar heated directly from its side by an accelerated electron

beam [100]. All the other cells are Knudsen effusion cells (K-cells) made of pyrolytic boron

nitride (PBN) crucibles, filled with ultra-pure ingots or pellets of desired materials inside. Each

K-cells is heated by a meander shaped tungsten filament. The operation temperature for K-cells is

in the range of 200 °C to 1400 °C. The temperatures of the cells are measured by thermocouples,

and the heating power is regulated by a PID-feedback loop according to the readout data from the

thermocouples. Every solid source is independently heated until the desired beam flux is reached

for growth.

However, the evaporation of the materials should ideally take place when the condensed

phase and its vapor are in thermodynamic equilibrium. The flux is mainly regulated by the vapor

pressure which essentially increases exponentially with the temperature of the cell. Therefore, the

flux basically follows Arrhenius’ law in a thermodynamic process with an activation energy Ea:

⁄

where P is the vapor pressure of the source material, P0 is a constant of the vapor pressure, kB is

the Boltzmann constant and T is the temperature of the cell. Usually, the group III elements are

supplied as monomers, while the group V elements are generated as tetramers or dimers. The As

valved-cracker cell has a two-zones furnace called cracker zone to dissociate As4 into As2, and

also a valve to control the flux [80]. The flux is monitored by measuring the beam equivalent

pressures (BEP) of constituent elements by a moveable ionization gauge. A Bayard-Alpert

ionization gauge is used in this case with a measuring range down to 1 × 10-11

Torr. The ion

gauge can be moved mechanically either to the position close to the substrate for measuring the

BEP directly from the cell towards the substrate, or outside of the beam to determine the

background pressure.

Every cell is equipped with a computer controlled shutter positioned in front of it which

allows for switching the supply of the beam toward the substrate on and off within a fraction of

one second (about 300 ms). Thus, together with the beam impinging rate about 1 ML/s on the

substrate, the growth control with a monolayer precision is achieved. The temperature of the cells

and the switching of the shutters are both controlled by the Riber Crystal Eyes software which is

also capable of programming growth recipes.

23

3.3.2 Substrate heating and manipulation

Quartered GaAs (100) epi-ready wafers of 3 inches in diameter are used as substrates for

epitaxial growth in this work. Before loading to the growth chamber, a substrate is first degassed

at 150 °C for 45 minutes in the load-lock chamber under vacuum. After that, it is transferred into

the growth chamber via the transfer chamber using a magnetically coupled transfer rod as shown

in Figure 3.4. The substrate is placed onto a rotatable support in the close proximity (a few

millimeters) of a heater, facing the effusion cells. The substrate is heated during growth to

increase the mobility of adatoms or molecules on the surface and consequently reducing the

formation of lattice defects. The substrate is heated only by radiation. The heater is made of a

meandered tantalum filament with a PBN diffusor. The substrate support is made of refractory

materials, such as Mo and Ta, which do not decompose or give out gas impurities even when

heated up to 1,400 °C.

A thermocouple measures from the back side of the heater while the heating current is

regulated by a feedback loop. From the construction, the heater is not set in direct contact with

the substrate so there is a difference between the set temperature of the heater and the actual

substrate temperature. To be sure about the precise substrate temperature, an infrared pyrometer

is used to measure indirectly through a view port of a transparent window. A dual wavelength,

emissivity-independent pyrometer is the best option for this purpose [96]. In the following, the

thermocouple temperature and the pyrometer temperatures are registered as Tset and Tpyro,

respectively. For producing uniform and reproducible layers, it is very important to maintain

uniform temperature across the substrate with a maximum deviation of 5 °C. The substrate is thus

kept rotating by a rotation assembly during the growth process in order to have a high degree of

temperature uniformity on the substrate, which is also beneficial for the homogeneous growth of

the layer sequences as all the cells are tilted with respect to the substrate normal direction by the

same angle about 20°.

3.3.3 Growth parameters

During the epitaxial growth, there are numerous competing processes for the growth kinetics

of adatoms on a heated substrate as shown schematically in Figure 3.6. The adatoms or

molecules impinging on the substrate surface can be adsorbed on the surface. They can then

migrate on the surface until they incorporate into either the crystal surface lattice of the substrate

or the overgrown epitaxial layer. They can also aggregate with other adatoms to form nucleation

seeds which can grow further into islands or layers. Meanwhile, the interdiffusion or intermixing

can occur inside the crystal lattice. However, when the substrate temperature is sufficiently high,

the thermally desorbed atoms will not be incorporated into the crystal lattice. In the case of III-V

semiconductor compounds, group V elements are preferentially desorbed above the congruent

evaporation temperature Tc [96]. On the other hand, group III elements also tend to evaporate at

even higher temperatures. In order to avoid the re-evaporation, the substrate temperature should

24

not exceed a certain temperature. The congruent temperatures of different compounds are listed

below in Table 3.2.

With the temperature and surface conditions for MBE growth in this work, the sticking

coefficient of the group III elements, i.e., Al, Ga and In, on a GaAs substrate surface is unity,

which means that all the atoms stick onto the surface. In contrast, the sticking coefficient of the

group V elements, As4 and As2, all alone is zero. As4 or As2 can be incorporated on the surface

only if the adatoms of group III elements are present. This gives the advantage that the

stoichiometry is self-regulated as long as the system is under arsenic-rich conditions. For this

reason, the growth rate is then controlled by the flux of group III elements when an arsenic

overpressure is maintained during the growth. For GaAs growth, the ratio of III/V elements is

about 1/30, while for InAs growth, the ratio is about 1/190. These flux ratios are determined by

the BEPs measured from the ionization gauge multiplied with the gauge sensitivity factor for the

elements as listed in Table 3.3.

Figure 3.6 Schematic illustration

of the surface processes occurring

during the growth by MBE [97].

III-V Compound AlAs GaAs InAs AlP GaP InP

Tc (°C) 850 650 380 700 670 363

Table 3.2 List of approximate congruent sublimation temperature (Tc) for Langmuir

evaporation of III-V semiconductor compounds [96].

Element Al Ga In As

Sensitivity factor 0.92 1.68 2.44 1.76

Table 3.3 The ion gauge sensitivity factors for different elements [99]

25

3.3.4 Reflection high-energy electron diffraction

The surface crystallography and growth kinetics are monitored by reflection high-energy

electron diffraction (RHEED) [101]. In practical, it can be used to ensure the reproducibility of

growth, to calculate the growth rate, and also to determine the surface crystal structure,

cleanliness and smoothness. This technique employs a high-energy electron beam (up to 25 keV

with this system) emitted from an electron beam source directed onto the substrate surface at a

glancing angle of about 0.5° to 2°. The image of the diffraction pattern is shown on a fluorescent

screen symmetrically placed opposite the electron beam source. Due to the small glancing

incident angle, RHEED is very surface-sensitive as the electron beam is only scattered in the

first few atomic layers, not in the bulk crystal. The scattering results in diffraction patterns

which can be used to monitor the surface reconstruction. In the case of GaAs, numerous surface

reconstructions exist depending on the arsenic pressure and the substrate temperature [98]. The

appearance of the diffraction patterns can be used to provide qualitative feedback on the surface

morphology. If the sample surface is smooth, the diffraction pattern appears streaky, i.e.,

elongated spots. With increasing surface roughness, the diffraction pattern becomes more and

more hazy.

RHEED can provide an accurate, quick and direct method to determine the growth rate by

monitoring the intensity of the pattern by a camera from the screen. During layer by layer growth,

the intensity of the RHEED pattern, most prominently the specular spots, oscillates because the

roughness of the newly forming layers is larger than that of the closed ones. Each period of the

oscillations corresponds to the time needed for the growth of one monolayer. A scheme of the

relation between different monolayer growth stages and RHEED intensity oscillations is shown in

Figure 3.7. Furthermore, with RHEED patterns, it is also possible to identify the growth

transition from layer to island structures like quantum dots when the pattern changes from streaky

to spotty.

Figure 3.7 RHEED intensity

oscillations with the period of

the growth of one monolayer on

a GaAs (001) surface [102]. The

signal assumes a maximum for

the surface coverage = 0 and

= 1, e.g., a completed Ga plane

or a completed As plane for the

growth of GaAs layers.

26

3.4 Self-Assembled 3D Nanostructures

Self-assembled semiconductor nanostructures have been the focus for rigorous research

efforts in terms of basic physics and solid-state devices due to their unique optoelectronic- and

physical properties. As already discussed in the previous section, 3D islands can occur if the

growth system obeys the relation of

for either strained or unstrained systems by SK

or VW growth mode, respectively. In the following, two different self-assembly growth methods

to generate 3D nanostructures with lattice-mismatch and lattice-match will be discussed. The first

approach based on SK growth mode can result in strain-induced quantum dots. The second one

following VW growth is called droplet epitaxy (DE) which allows both strained and unstrained

systems to produce various nanostructures such as QDs, quantum rings (QR) and nanoholes (NH).

3.4.1 Strain-induced quantum dots (SK)

The SK growth mode used for producing quantum dots takes the advantage from the natural

tendency of strained systems, e.g., InAs/GaAs, InAs/InP, InAlAs/AlGaAs, InP/GaAs, Ge/Si,

GaN/AlGaN and GaAs/AlGaAs [1]. As illustrated in Figure 3.8, the basic mechanism is

presented for an InAs/GaAs system with a quite considerable lattice mismatch of 7 % which

leads to the formation of InAs QDs on a GaAs (100) substrate. (a) The GaAs substrate has a

lattice constant of aGaAs ~ 5.66 Å. (b) The initial InAs growth occurs layer by layer on the GaAs

substrate because of the small interface energy between the substrate and the grown material.

However, due to the lattice mismatch, the strain energy will increase with the InAs layer

thickness d. At a certain thickness, the strain energy is beyond the limit that the system can afford

to remain in the 2D growth mode. Thus, it will be energetically favorable to release the strain by

forming the subsequent InAs into 3D islands on the already-grown 2D layer. This process is also

known as lattice relaxation. The thickness at which this occurs is defined as the critical layer

thickness dc, and the underlying layer is called the wetting layer (WL) following the GaAs lattice

constants, i.e., epitaxially. The InAs islands form randomly in an attempt to recover the bulk InAs

lattice constants of aInAs ~ 6.06 Å. These self-assembled quantum dots grown by an SK approach

are therefore referred to as the strain-induced quantum dots.

During the SK growth, the strain relaxation is elastic and free of dislocations, leading to the

formation of an ensemble of coherent (defect-free) 3D islands. The growth mechanism

responsible for the coherent islands has been theoretically analyzed in the strained system [103].

A phase diagram corresponding to the analysis results is shown in Figure 3.9. Λ is the ratio of

the energy of the dislocated interface to the change of the surface energy. According to this phase

diagram, the formation of the coherent islands occurs with a sufficient amount of material while

the ratio Λ is larger than a critical value of Λ0, i.e., a small change of the surface energy or a large

energy of the dislocated interface. Meanwhile, such considerations indicate that a coherent 3D

island is in thermodynamic equilibrium when it is smaller than a certain size. Moreover, in such

semiconductor systems, one remarkable property is that these strained 3D islands do not undergo

27

Ostwald ripening (small islands rearranged into few large islands) after being formed, and display

a narrow size distribution. Thus, in principle, an ensemble of coherent islands is energetically

more favorable than a single large island in the system.

Figure 3.8 Schematic drawing showing the growth of the InAs quantum dots by the

SK growth method. (a) GaAs substrate (orange color); (b) growth of the strained InAs

(blue color) wetting layer on GaAs (100); (c) with increasing InAs coverage above a

critical thickness, the strained layer relaxes to minimize the surface energy by the

spontaneous formation of randomly distributed islands. (courtesy of R. Roescu [104])

Figure 3.9 A phase diagram for three

different morphologies. UF: Uniform Film,

CI: Coherent Island, DI: Dislocated Island,

Q: the amount of the deposited material, Λ:

the ratio between the energy of dislocated

interfaces and the change of the surface

energy. (adapted from [8, 103])

28

The phenomena of the island density, size distribution and the absence of ripening have been

explained by theoretical kinetic and thermodynamic models. In the kinetic models, the evolution

of island growth is predicted by various processes such as diffusion, deposition, attachment and

detachment under strong non-equilibrium conditions, which result in self-limiting growth to the

size and density of the coherent islands with respect to the growth rate and coverage [22]. For

example, a preferential migration of adatoms towards smaller islands due to kinetic barriers limits

the attachment to the strained islands [105], while the competition between the bonding energy

and the strain energy leads to the enhancement of adatom detachment from large islands [106]. In

the thermodynamic models, an ensemble of 3D islands with ordered size, shape and relative

arrangement is described as a new class of equilibrium surface structures [107]. When the

formation of a single 3D island is introduced on such surface structures, the total energy of the

system will be changed. According to this change, there exists an optimum island size

corresponding to the absolute minimum of the energy for the mismatched systems. In this model,

the change of the surface energy is mainly due to the appearance of side facets and the

disappearance of certain areas of the wetting layer. The shape and size of the islands then appear

to be strongly interdependent. However, there is no driving force for ripening in this case.

According to the thermodynamic and kinetic mechanisms, the growth parameters appear

crucial in the final surface morphology of the 3D islands. Experimentally, the dependence of the

density ρ

of islands has been described as a function of the deposited amount by the relation

similar to a first order phase transition as ρ ρ

( )

, where d > dc. dc is the critical

thickness. is the exponent. ρ

is the normalization density of islands. Processing the

experimental data, the fitting parameters = 1.76, ρ = 2 × 10

11 cm

-2, and dc = 1.5 ML has been

found for the InAs islands deposited on GaAs (100) at a substrate temperature of 530 °C [70].

However, the value of the critical thickness strongly depends on the growth conditions.

From previous works, the value of dc for InAs/GaAs system is found to be 1.5 ML to 1.8 ML

[68, 108–110]. Moreover, when the thickness exceeds another feature thickness dd, dislocations

start to emerge in the structure, i.e., dislocated islands, while the quality of the QDs reduces. In

order to obtain high quality QDs, it is therefore important to keep the layer thickness d within a

range dc < d < dd, which has been suggested to be in the interval of 1.7 ML < d < 3.0 ML [111]. If

further materials are deposited, the system can have a tendency to ripening which would induce

certain disadvantages for the quantum dot fabrication such as reducing the density, broadening

the size distribution and resulting in defects in the large islands [112].

29

3.4.2 Nanostructures by droplet epitaxy (VW)

Contrary to the SK growth mode, another self-assembly method for 3D nanostructures called

droplet epitaxy (DE) has emerged recently. This method was first proposed by N. Koguchi and

K. Ishige used for the growth of GaAs microcrystals on an S/GaAs substrate [23]. Subsequently,

self-assembled GaAs quantum dots were successfully fabricated on an AlGaAs surface using

droplet epitaxy [7]. In MBE growth, droplet epitaxy is an alternative method which can make up

the deficiency of the SK approach to fabricate various self-assembled nanostructures. For

example, the SK growth method is limited by the presence of lattice mismatch, which is not

essential in droplet epitaxy. Therefore, DE allows the growth of lattice-matched systems, e.g.,

GaAs/GaAs, inefficient lattice-mismatched systems, e.g., GaAs/AlxGa1-xAs, as well as lattice-

mismatched systems. Furthermore, droplet epitaxy can offer a higher degree of freedom in

controlling the size and density of nanostructures because the transition process of liquid phase

metal droplets into solid semiconductors is not limited to the native strain or the material system.

Additionally, for the study of single nanostructures, either a super-low density or a subsequent

process to focus on only one singular nanostructure is required. A DE approach can provide a low

density of the order of 105 to 10

7 cm

-2 which is several orders of magnitude lower compared to

that of the SK method [27].

Droplet epitaxy is based on the incorporation of group V elements into the group III element

droplets formed on the substrate to obtain the growth of III-V nanocrystals [23]. In practical, the

growth of droplet epitaxy contains two processes which are the metal droplet formation and the

crystallization. For example, in the case of a GaAs/AlGaAs heterostructure, Ga is supplied on an

AlGaAs substrate with the absence or the presence of only small quantities of arsenic flux. After

the deposition of Ga atoms on the AlGaAs surface, a part of the deposited Ga atoms will combine

with the remaining arsenic atoms on the AlGaAs surface and the rest will form Ga droplets by

atomic migration. The formation of droplets is based on the VW growth mode because the

binding energy of Ga adatoms is larger than that between Ga adatoms and the AlGaAs surface

atoms. This process is subject to the phenomenon of Ostwald ripening (the small droplets

incorporate into the large ones) when the amount of the deposition material is sufficiently high

[112]. The size and density of droplets depend on the substrate temperature applied in this

process, e.g., smaller droplets with a high density are obtained at a lower temperature. On the

other hand, the size of the droplets can simply be changed by the coverage of the deposited metal

material, i.e., a higher monolayer coverage leads to larger droplets [113].

After forming Ga metal droplets, an As flux is applied to crystallize the droplets into

semiconductor nanostructures, i.e., GaAs. In general, crystallization is immediately executed after

the formation of droplets in order to prevent further Ostwald ripening. Because of the high

surface energy density of the metal droplets, the crystallization starts at the interface of three

phases, i.e., the skirt of the droplet (the circular line of the interface between Ga droplets and the

AlGaAs substrate), as shown in Figure 3.10 (a) [114–116]. Therefore, the crystalline

30

nanostructures are pinned on the substrate surface with their density basically consistent with that

of the droplets. Meanwhile, the growth process of the crystalline nanostructures is determined by

the atomic diffusion of Ga atoms and the incorporation of As atoms which can be changed under

different growth conditions. In other words, higher temperature leads to higher Ga atomic

mobility on the substrate surface, while higher arsenic flux enhances the crystallization resulting

in a reduction of the diffusion regions of the Ga atoms (Ga atoms are captured by arsenic atoms).

Therefore, the final morphology of the crystalline nanostructures can be controlled by the

substrate temperature and the arsenic flux applied in the process of crystallization. For example,

at a low temperature (200 °C ~ 300 °C), the metal droplets will be crystallized into

semiconductor quantum dots under a high arsenic pressure (~10-4

Torr) [30] when the region of

the Ga atomic migration is smaller than the dimension of the droplets as shown in Figure 3.10 (b).

Alternatively, single QRs or double QRs will be obtained under a medium arsenic pressure

(~8×10-6

Torr) [29] or a low arsenic pressure (~2×10-6

Torr) [37], when the Ga atomic diffusion

region is comparable with or larger than the droplet dimensions as shown in Figure 3.10 (c) and

(d), respectively. Furthermore, at a high temperature (~ 500 °C), the droplets can generate deep

nanoholes by the thermal solution of the crystalline substrate underneath the liquid droplets. This

process is also called local droplet etching or nanodrilling [34, 36]. More unique nanostructures

have been created in different conditions, such as quantum dot molecules and ensembles,

transition structures between single and double quantum rings, and QDs with ultra-low density

[24–27, 44–46]. All in all, owed to the flexibility of liquid phase metal droplets in droplet epitaxy,

the realization of these various self-assembled nanostructures becomes possible.

Two kinds of productions, shallow and deep nanoholes, are fabricated with low As pressure

and high substrate temperature in this work. Figure 3.11 illustrates the mechanisms regarding the

crystallization processes for nanohole structures with a GaAs/GaAs system under these growth

conditions. After a Ga droplet is formed on a GaAs surface by VW growth, a low As flux is

supplied on the Ga droplet. Ga atoms of the droplet react with arsenic atoms into GaAs molecules.

Meanwhile, thermal etching takes place at the GaAs surface in a contact with the Ga liquid where

there is a Ga-rich condition at high temperature [34]. The Ga liquid droplet solves the GaAs

crystalline substrate into GaAs molecules. Due to the driving force induced by the surface energy

differences at the interfaces of three phases, the nucleation of GaAs crystals first starts at the skirt

of the droplet and then along the edge of the droplet. The crystal growth is carried out by the

thermal diffusion of the GaAs molecules from the internal thermal solution and from the

external arsenic-flux reaction toward the edges of the droplet resulting in a downhill material

transportation [33]. After all, the crystallization is effective at the droplet edge leading to the

formation of a circular nanostructure, i.e., a ring-like structure [42]. During the crystallization, the

amount of Ga atoms in the droplet decreases as does the droplet size. Finally, all the Ga atoms are

solidified, i.e., fixed in the crystal. A nanohole is then left on the surface. The shallow nanohole is

constructed by the ring-like crystalline structure. On the other hand, the deep nanohole is formed

with a significant thermal etching. In general, a larger and deeper nanohole can be developed

with a larger droplet due to sufficient materials for growing and etching [34, 39].

31

Figure 3.10 Schematic illustration of the morphology evolution during the crystallization of the

Ga droplets under different sizes of the Ga diffusion region [115]. (a) The preferential

crystallization occurs at the skirt of the droplet. The formation process for (b) QD, (c) QR and

(d) double QR. The red and green hemispheres represent the Ga droplet and the GaAs

nanostructure. The red and blue spheres represent the Ga atoms and the As atoms. The orange

arrows point to the Ga diffusion region boundary.

Figure 3.11 The crystallization process for a nanohole structure by droplet epitaxy

(adapted from [39]). (a) the formation of a Ga droplet (b) the material transportation

of the GaAs molecules originated partly from the reaction between Ga droplet and As

flux, and partly from the solution of the GaAs substrate towards the edge of the

droplet (c) the growth of the ring-like structure at the edge of the droplet with the

reduction of the droplet volume (d) a nanohole structure formed after the

solidification

33

Chapter 4 Surface Patterning Techniques for Site-

Selective Growth

This chapter begins with an introduction which includes the concept related to the site-selective

growth of strain-induced QDs and a review of previous works with various patterning approaches.

The site-selective growth is mostly obtained with the help of templates which can provide

preferential nucleation sites. In this work, the templates were made of self-patterned GaAs

nanoholes generated by droplet epitaxy for the site-control of QDs. The GaAs nanohole templates

can be realized with either a random distribution or an organized arrangement. The randomly-

distributed GaAs nanoholes on a GaAs surface are formed due to the nature of droplet epitaxy.

On the other hand, the achievement of arranged GaAs nanoholes relies on the pre-patterning of a

GaAs surface with an in-situ focused ion beam (FIB) in the way that Ga droplets can nucleate

preferentially depending on the patterns and then be transformed into GaAs nanoholes through

crystallization. The ideas of using self-patterned nanohole templates for the site-selective growth

of QDs, and combining a FIB pre-patterning technique to control the sites of self-patterned

nanoholes, are explained and demonstrated in the second section. A detailed description of the

focused ion beam system used in this work is shown in the last section, including the features,

working principle and the equipment. The essential FIB parameters and the pattern design applied

for pre-patterning in this work are given in this part as well.

4.1 Introduction to Site-Selective Growth

0D semiconductor quantum dots with a sharper density of states have superior transport and

optical properties with respect to higher dimensional structures. Therefore, intense research with

the subject of semiconductor quantum dots has been done for their possible use. The ensembles

of self-assembled quantum dots have been used in optoelectronic devices such as quantum dot

lasers [11, 14]. On the other hand, single semiconductor quantum dots have attracted a lot of

interests for their applications in future novel nanoelectronic devices used for solid-state quantum

information processing, e.g., single photon sources for quantum cryptography [17, 18, 117] and

the building blocks for quantum computing [19, 20, 118]. In particular, the success of all these

new quantum devices based on single QDs or QDMs requires the ability to fabricate

nanostructures with control of size and spatial location. However, the growth of self-assembled

QDs, by either Stranski-Krastanov growth mode or droplet epitaxy, tends to cover the surface in a

34

near-random fashion with some preferences for nucleation at underlying step edges [9]. This

random nucleation makes it difficult to address each individual self-assembled QD separately.

Therefore, it is necessary to combine strategies that would permit the precise location of

nanostructures carrying high optical quality, i.e., the site-control and the site-selective growth of

QDs.

For the purpose of a site-selective growth, a commonly utilized strategy to overcome the

random positioning of self-assembled nanostructures is based on the pre-patterning of substrates.

The aim of pre-patterning is to create templates with well-ordered arrays of preferential

nucleation sites for island overgrowth. Through a re-growth on such templates, the site-selective

growth of self-assembled quantum dots can then be achieved. The preferential nucleation sites are

derived from the atomic diffusion differences between different faceted surfaces on the template.

For example, the selective nucleation of InGaAs QDs was found at or near the multistep edge of

the GaAs epilayer grown on GaAs (001) substrates with a misorientation of 2° along the [010],

[110] and [1 0] directions, resulting in the self-alignment of quantum dots along the step edges

by MOCVD [119]. Another example of the self-alignment of self-assembled InAs islands was

achieved by using wet chemical etching with grating pitches from 0.28 µm to 5 µm on GaAs

surface with MBE [120]. It was observed on the samples with the smallest pitch of 0.28 µm that

the islands are located at the sidewalls or at the bottom of the valleys. However, with larger

spacings, island nucleation occurred at the sidewalls of the ridges along the [ ] direction, while

the islands were found on the (100) planes and at the foot of the mesa-structure with the ridges

along the [ ] direction. The preferential nucleation of self-assembled QDs has been found at

multistep edges, on top of ridges, in the bottom of valleys and at the sidewall of mesa-structures

where there are different faceted surfaces. It is suggested that the surface with appropriate

modification can provide an influence to QD positioning [120].

In terms of surface pre-patterning, except creating preferential nucleation sites, it also

ensures the reproducibility of those nucleation sites with an exact position control. For instance, a

lateral site-control of strain-induced InAs QDs in arrays has been established using lithography

combined with etching. Trenches patterned on the GaAs (100) surface were employed as

preferential nucleation sites for the InAs QDs to grow in chains by chemical beam epitaxy [121].

Later, the selectively grown InAs QDs on the top of the (100) faceted mesa stripes of the GaAs

substrate have also been demonstrated [122, 123]. Extended from the pre-patterning method, an

idea of surface strain engineering was obtained through the combination of stressors with

patterning, which created a lattice of nucleation sites for QDs [124, 125]. During an MBE

re-growth of InAs, the thermodynamic and diffusion kinetics of the In atoms were modified by

the sub-surface strain fields introduced by growing a strained In(Ga)As film below the surface.

As a result, the InAs layers grow more rapidly on the top of the mesas, forming a preferential

growth of InAs islands on the top of sub-surface stressors.

In order to address single dots individually, it is important to reduce the field of preferential

nucleation sites allowing limited number of QDs grown within demanded dimension. For

35

example, the approach by e-beam lithography has often been used for the realization of site-

selected QDs due to its good resolution. The template patterned by e-beam lithography allows a

range of preferential nucleation down to the nanometer scale forcing QDs into the designed

lateral positions, resulting in single or double dots in arrays with a good optical quality

[126, 127]. The QDs array grown on the patterned surface can be further capped by spacer layers,

serving as a strain template for controlling the formation site of QDs in the second layer [128].

The growth approach of long range ordered and homogeneous InAs QD arrays with periodicities

ranging from 160 nm to 200 nm on patterned GaAs substrates along with their optical properties

has been studied, which makes such QDs promising for single QD device application [129, 130].

Besides e-beam lithography, focused ion beam lithography is also a potential technique to

achieve positioning of nanostructures by pre-patterning the substrate [47–50]. Earlier, focused ion

beam has been used to generate arrays of FIB spots directly on the epitaxial GaAs surface.

Combining in-situ annealing and GaAs re-evaporation, shallow holes then were created based on

the arrays of FIB spots. These shallow holes which contain a high density of surface steps can

provide a suitable template for the site-selective growth of InAs QDs [47]. Compared to e-beam

lithography, the focused ion beam technique has the advantages of direct patterning in UHV

conditions without additional lithography steps and time-effective processing benefited from the

heavy mass of ions. In addition, there are also other techniques using scanning probes like atomic

force microscopy (AFM) and scanning tunneling microscopy (STM) to generate a modified

surface for QD positioning [131, 132]. Nevertheless, an in-situ technique is always preferable to

attain high quality semiconductor nanostructures for either research investigations or industrial

applications. Due to its outstanding advantages, an in-situ FIB technique has been employed as

the surface patterning method in this work. More details about focused ion beam will be

described in section 4.3.

The mechanism of strain-induced QDs grown selectively on patterned holes has been

described as a result of directed atomic diffusion and nucleation towards the patterned holes as

shown in Figure 4.1 [125]. It is suggested that introducing patterned holes on the substrate can

create a periodic array of localized centers where the adatoms will be driven in due to the surface

chemical potential gradient of these holes [133–135]. The geometry of the patterned holes can be

considered as a bottom facet, i, surrounded by two sidewalls, s, with the same misorientation

angle, θ, with respect to the horizontal direction. For a binary alloy, e.g., InAs, the chemical

potential of the facet can be represented as

μ μ

, with (

csc θ

cot θ ).

Here, and

are the surface free energy of sidewalls and facet, respectively. µ0 is the chemical

potential for a uniform surface. 0 is the atomic volume. li is the width of the facet. The minus

sign refers to surface profile. Under the associated driving force given by the potential gradient,

InAs will preferentially accumulate at the bottom of the hole. Once the critical thickness is

achieved in the patterned region, an island or islands will nucleate to relieve local build-up of

36

strain according to the SK growth mode. As a result, the site-control of self-assembled QDs is

obtained.

Figure 4.1 Schematic of the periodic surface patterning process using electron beam

lithography for producing site-selected strain-induced QDs [125]. (A) Developing

patterns by electron-beam lithography on a GaAs substrate (B) Transferring patterns

using wet chemical etching. (C) Introducing the patterned GaAs substrate into the

MBE chamber for re-growth of a GaAs epitaxial buffer layer followed by InAs

deposition. (D) InAs QDs are formed in the hole after the critical thickness for 3D

islands growth is reached in the depression following the SK growth mode.

4.2 Self-Assembled Nanohole Patterning

Alternative to artificial pre-patterning, self-assembly patterning (self-patterning) by droplet

epitaxy has been revealed as a potential technique to produce nanoholes as templates for the site-

selective growth of QDs without the need of any lithographic steps [40–46]. In this work, the

self-patterned nanohole templates were developed in GaAs/GaAs systems by droplet epitaxy. The

description about droplet epitaxy can be found in subsection 3.4.2. These nanoholes fabricated by

droplet epitaxy having high densities of monolayer steps (high-index surface) can provide

preferential nucleation sites for the further nucleation of deposited InAs, resulting in the

formation of strain-induced InAs QDs following the SK growth within the same series of MBE

growth, i.e., an in-situ process. The density of these strain-induced QDs is therefore

corresponding to that of the GaAs nanoholes formed by droplet epitaxy so that the value possible

to be obtained is as low as 107

cm−2

[38]. The size of the QDs is related to the amount of InAs

deposited in the GaAs nanoholes with the independence of their density, which is opposed to the

QD formation by the SK growth method [43]. This fact is especially interesting for the

applications based on single QDs. Particularly, a different number of QDs per nanohole can also

be obtained resulting in QD pairs or QDMs, which is coincidentally the same with other

37

lithographic techniques [41, 136]. Moreover, in the self-assembly growth, the strain-induced

approach can provide defect-free QDs whose crystal qualities are generally better than that of the

QDs carried out by the crystallization in droplet epitaxy. Combining the advantages from droplet

epitaxy and the strain-induced approach in the MBE growth, this technique is therefore becoming

a promising method to achieve site-selected QDs or QDMs with low densities and high optical

qualities for their potential applications e.g., single QD devices. In this work, this combination

was used for realizing the site-selective growth with InAs QDs in GaAs nanoholes.

Nevertheless, the nanoholes formed by droplet epitaxy are randomly distributed, which in

turn leads to randomly-distributed QDs on the sample. In order to further control the location as

well as to design the arrangement of the quantum dots arbitrarily, an in-situ focused ion beam

pre-patterning was applied before the fabrication of self-assembled/self-patterned nanoholes in

this work. It has been found that using the FIB technique can locally modify the surface in a way

that the site-selective growth of crystals can be achieved based on the FIB patterns with various

FIB parameters [137]. In addition, due to the difference of surface energies on the FIB modified

surface, the preferential nucleation of metal droplets is expected via a site-selective growth by the

VW growth mode [138]. With crystallization under certain growth conditions by droplet epitaxy,

these site-selected metal droplets can be transformed into crystalline nanoholes resulting in well-

organized self-assembled nanoholes on the surface depending on the FIB patterning parameters.

By using these FIB-arranged nanoholes as templates, the arrayed QDs with an arbitrarily defined

distribution can then be realized via a site-selective growth by MBE. This serial approach,

involving two subsequent site-selective growths with two different surface patterning techniques,

can be developed by the MBE-FIB system at AFP via an in-situ process. For the two subsequent

site-selective growths, first, the Ga droplets are preferentially nucleated on the FIB-patterned

surface, which can be crystallized into GaAs nanoholes through droplet epitaxy. Secondly, the

strain-induced InAs QDs are preferentially formed in these GaAs nanoholes which are self-

patterned on the FIB-patterned surface. In other words, the droplet epitaxy method plays a role in

the site-selective growth as well as in the surface patterning, in a self-assembly way. The

schematic illustration shown in Figure 4.2 serves to explain the development processes used in

this work.

At beginning, the growth of the GaAs epitaxial layer was carried out by MBE with a GaAs

substrate. Then, the sample is transferred into the FIB system under the vacuum conditions. An

in-situ focused ion beam is employed to generate several FIB-patterned areas on the GaAs

surface. The applied patterns in this work are designed with square arrays of spots within an area

of 60 × 60 μm2. According to this pattern design, several small locally modified spots of the order

of nanometers are therefore generated on the surface by a focused beam, which are called the

“FIB spots”. Each FIB-patterned area, consisting of the square arrays of FIB spots, can be created

with different FIB parameters which will be given in subsection 4.3.3. After FIB patterning, the

surface modified sample is transferred back into MBE for the fabrications of self-patterned

nanoholes and strain-induced QDs in sequence.

38

Figure 4.2 Schematic illustration of the site-selective growth processes for QDs grown in GaAs

nanoholes with or without FIB pre-patterning by a MBE-FIB system (not in scale). (a) Using

MBE, a GaAs layer is grown on a GaAs (100) substrate. Then, the sample is transferred to the

FIB system under vacuum conditions. (b) in-situ FIB patterning is carried out by a Ga+ or an In

+

ion beam to create FIB spots on the surface. The sample containing the FIB-patterned area and

the bare GaAs surface (without FIB-patterning) is then transferred back to the MBE system under

vacuum conditions. (c) MBE re-growth is executed for the formation of GaAs nanoholes by

droplet epitaxy and InAs QDs by SK growth in sequence. GaAs nanoholes are formed on the

FIB-patterned area and also on the bare GaAs surface, resulting in arrayed or randomly-

distributed nanoholes. Then, the deposited InAs is preferentially nucleated inside both types of

GaAs nanoholes resulting in site-selected QDs with an arrayed arrangement or a random

distribution embedded in the sample.

GaAs nanoholes self-assembly by droplet epitaxy via homoepitaxy are generated with the

conditions of a low As pressure and a high substrate temperature for this work. The mechanism

of the nanoholes generated by droplet epitaxy can be found in subsection 3.4.2. Due to the nature

of self-assembly, GaAs nanoholes are spread all over the sample, i.e., on the FIB-patterned areas

and also on the bare GaAs surface outside the FIB-patterned areas at the same time. However, on

the FIB-patterned areas, the GaAs nanoholes are formed site-selectively due to the surface energy

difference induced by FIB pre-patterning represented as well-arranged “arrayed nanoholes”

depending on the arrays of FIB spots. On the other hand, the formation of the GaAs nanoholes on

the bare GaAs surface without FIB pre-patterning does not occur site-selectively but in a

randomly-distributed manner resulting in “randomly-distributed nanoholes”. The deposition of

InAs is then executed in the MBE system directly after the formation of the nanoholes. Due to the

chemical potential gradients as a result of the high-index surfaces of the nanoholes, the nucleation

of the InAs deposition will occur preferentially in these nanoholes (both arrayed and randomly-

distributed ones). When the critical thickness of the deposited InAs inside the GaAs nanoholes is

reached for the 2D-3D transition, the strain-induced InAs QDs are then formed by SK growth

with site-selection. These site-selected QDs follow the distribution of GaAs nanoholes resulting

in arrayed or randomly-distributed QDs generated on the FIB-patterned area or the bare GaAs

surface, respectively. The growth mechanism of strain-induced QDs by SK growth is addressed

39

in subsection 3.4.1. Finally, the in-situ site-selective growth of QDs with a controllable

distribution is therefore demonstrated owed to the combination of two compatible MBE growths,

FIB direct writing techniques, as well as the facility of the MBE-FIB system. More details about

the parameters and process of FIB patterning will be given in subsection 4.3.3. The sample

fabrication concerning the details of MBE growth will be given in section 5.1.

4.3 Focused Ion Beam Patterning

The technique of focused ion beam (FIB) is particularly used for the fabrication of

nanostructures in semiconductor industries and material science researches, which was mainly

developed during the late 1970s and the early 1980s. With the increasing circuit density and

decreasing feature dimensions in the semiconductor industry during that time, this technology has

been used as offline equipment for repairing masks, modifying and analyzing electronic devices,

debugging integrated circuits (IC) and preparing the transmission electron microscope (TEM)

specimens [139, 140]. Since the increasing demand for micro- and nano-structures in the 1990s,

FIB has been used in research as a powerful tool allowing the fabrication of high quality and high

precision nanostructures which can be applied for micro-electro-mechanical systems (MEMS),

photonic devices and sensors, scanning probe microscope (SPM) tips, magneto resistive head

trimming and micro-tools [141–144].

The art of using FI for nanofa rication is a so ca “ ir ct writing”, which transfers

patterns by removing or adding materials using a small FIB spot directly impinging on the

substrate, offering a maskless process [48]. The approaches to remove and add materials include

milling, ion-assisted etching, implantation, and ion-induced deposition, based on the phenomena

resulting from the ion-solid interactions. The key to the direct-writing technology is the ability of

FIB to operate a fine beam size with proper current and energy which is used to remove or add a

required amount of material with high precision in two dimensions. These FIB features are

enabled due to the invention of the liquid metal ion source (LMIS) which provides high current

density and a variety of ion species [145]. Due to the heavier masses of ions compared to those of

electrons or photons, larger energies and shorter wavelengths allow direct writing on hard

materials (such as semiconductors, metals or ceramics) without major forward and backward

scattering resulting in shorter penetration length in solid [146]. Thus, the feature size of the

pattern is only dictated largely by the beam size and the interaction of the beam with the target

material. In contrast, electrons or photons can mainly be applied for writing on soft materials

(such as polymers or resists) and the corresponding feature sizes are determined by the proximity

of backscattered electrons (BSE) or the wave diffraction limit [147]. Moreover, the lateral

straggling of the implanted ions in FIB technology is very low. Therefore, the proximity effect

40

can be reduced [148]. By controlling these well-focused ion beams, nanoscale patterning on

target materials with a high accuracy and complicated 3D structures can be achieved.

4.3.1 Equipment

The basic components of a FIB system consist of an ion source, an ion optics column, a

substrate stage, and a vacuum chamber in the range of UHV. An Orsay Canion 31 Plus FIB

column is used to define the pattern for site-selected QDs in this work. The FIB column is

interconnected to an MBE system as shown in Figure 3.4. A schematic diagram of the FIB ion

column is shown in Figure 4.3 which serves to introduce the basics of the FIB system.

Figure 4.3 The schematic diagram of a focused ion beam column.

(courtesy of S. Shvarkov)

The basic components of the ion optics column consist of an extraction electrode, condenser

lenses, an E × B filter, a beam blanker, a Faraday cup, a scanning and stigmation octupole,

objective lenses, two sets of selection apertures and a mechanical vacuum separation valve to

isolate the source chamber from the column (for changing LMIS). The lenses are made of biased

ring or cylinder shaped metal plates. Their focal length can be adjusted by varying the

electrostatic potentials. After extracted from a LMIS, ions are accelerated through the column by

the acceleration voltage, Uacc, which is adjustable between 5 kV and 30 kV with intervals of 5 kV.

These ions are focused and collimated into a parallel or crossover beam by the condenser lens.

Then, the ion beam is passed through a mass separator called an E × B filter or a Wien-filter. A

Wien filter is only used when the system is equipped with an alloy source. It is used to separate

41

the ion species emitted from the alloy source by applying an electrical field (E) and a magnetic

field (B). Both fields are orthogonal to the ion beam and to each other, so that the Coulomb and

Lorentz forces are anti-parallel. These two opposite forces acting on the accelerated ions

compensate each other only if the velocity of the ions is equivalent to the ratio of E/B. Because of

different mass to charge ratios, only the selected ions can pass through the mass selection

apertures toward the target while the other unwanted species are filtered out. Below the E × B

filter, there is the deflection and stigmator octupole. The deflector is capable of controlling the

final trajectory of the ions as well as performing the scanning of the beam over the sample. The

stigmator is used for correcting astigmatism and collimation to eliminate the ions that are not

directed vertically. The objective lens located below the stigmator helps to reduce the beam size

and also to improve the focusing of the beam. With a two-lens optical system, the diverging mode

has an advantage to form a small beam size at any beam currents among the four typical beam

operation modes, i.e., the crossover mode, the diverging mode, the parallel mode and the

converging mode [149]. The current selection apertures are applied to regulate the beam current

in a range from few nA to the order of pA. The beam blanker permits quickly switching off the

beam or deflecting the beam into an internal Faraday cup by which the beam current can be

measured. With this system, the ion beam can scan within a working area of 505 by 505 μm2, and

thereby write patterns via the lithography system called “Elitha”. These patterns are designed and

generated by a computer aided design program, e.g., AutoCad. A sample is placed on a computer

controlled x-y table which allows the displacement up to 50 mm in both directions perpendicular

to the FIB column. In this way, more than one area can be operated by step-and-repeat within the

quarter of a 3-inches wafer used in this work.

Liquid metal ion sources (LMIS) are the most common source for FIB techniques. They are

high brightness ion sources, which generate a beam of ions by the use of field emission. The ion

beam can then be focused to a nano-spot with an adequate current density for FIB direct writing

or imaging. These sources are made of metals which have relatively low melting temperatures

and low reactivity [150]. Currently, the available elements of LMIS made by the AFP group

include As, Au, B, Be, Bi, C, Co, Cr, Cu, Dy, Er, Fe, Ga, Ge, Gd, Ho, In, Mn, Ni, P, Pd, Pt, Si,

Sn and Tb [151]. In order to lower the melting point and to control the reactivity or to have

alternative elements from one LMIS, the elements are often prepared in a eutectic alloy, e.g.,

AuSiBe, AuErSi or GaIn. However, Bi, Ga, In and Sn can be prepared either in alloys or in

elemental LMIS. Among these elements, As, B, Be, P and Si are important for III-V

semiconductor technology because they are potential dopant elements. Ga- and In-LMIS are easy

in handling because of the low melting temperatures (29.8 °C for Ga and 156.6 °C for In), low

volatility and their long lifetime. Due to their high beam stability, good focusing properties

together with small energy spread and enough mass for high milling rates, Ga- and In-LMIS have

been used in FIB very frequently. For this work, Ga- and In-LMIS are employed for direct

writing in the nanoscale regime on the GaAs surfaces in order to locally modify the surface such

that the GaAs nanoholes can preferentially be formed along the FIB patterns by droplet epitaxy.

These FIB-arranged nanoholes can then serve as templates to establish site-selected InAs QDs

42

spatially following the pattern design. Moreover, Ga and In ions have the properties of high

sputter yield, small longitudinal ion range and that they are electrically almost neutral in GaAs,

which makes them suitable for patterning on GaAs surfaces [137].

A typical LMIS consists of a cylindrical spiral with a tungsten needle through it and a

tungsten filament, as shown in Figure 4.4. The spiral tube acts as a reservoir for the metal or

eutectic alloy. The spiral reservoir can be heated up through the filament to melt the metal or

alloy, and then feed the liquid metal to the tip of the needle. To extract the ions from the LMIS, a

high positive voltage of a few kV is applied to the needle relative to the extraction electrode,

which causes an electrostatic force at the tip. Depending on the balance between the electrostatic

force and the surface tension of the liquid metal at the tip, a sharp peaked cone called the Taylor

cone is formed [152]. Due to the extremely small radius at the apex of the Taylor cone (about

2 nm), a huge electric field (above 1 × 108 V/cm) is formed by the extraction voltage resulting in

ionization and thermally assisted field emission of metal atoms in the vapor phase. Finally, the

positively charged ions are accelerated towards the extraction electrode with typical operation ion

currents about 2 µA to 10 µA. Most of the ions that run into the electrode are lost. Only a small

fraction transverses the central electrode aperture hole along or close to the optical axis of the ion

column. These extracted ions can then be condensed into a focused beam by the lens and ground

electrodes in the ion optics column.

(a) (b)

Figure 4.4 (a) An emitting HoNi alloyed

LMIS. (photo by A. Melnikov) (b) A Ga

LMIS consists of a spiral tube, a tungsten

needle and a tungsten filament.

4.3.2 Process

When ions hit a target material, they will collide with both the nuclei and electrons of the

target. The ion-solid interactions can be classified in two main distinct processes. One is the

elastic interactions with nuclei, which cause the displacement of lattice atoms, surface sputtering

and the generation of defects. Another one is the inelastic interactions with electrons, which

produce secondary electrons, X-rays and optical photon emission. Therefore, when ions strike on

a solid material, the events of sputtering, implantation, surface amorphization, swelling,

deposition, backscattering and nuclear reactions can take place [150, 153]. The trajectory of ions

is only changed as the result of a collision with an atom. Although between successive

43

interactions with nuclei, ions interact with the electrons as well, the ions will nearly not change

their trajectory which can be considered linear due to the big discrepancy between ion and

electron masses. The distance from the position where the ion enters the target to the position

where it stops is called “range”. The projection of the range along the incident direction of the

ions is called the projected range, Rp, while the distance traveled along a perpendicular axis is the

perpendicular range R⊥. The standard deviation in a projected range is called projected straggle,

ΔRp, while the statistical fluctuation of a perpendicular range is called lateral straggle, ΔR⊥. The

spatial distribution of the implanted ion is known as an implantation profile. The range and the

spatial distribution of an ion in an amorphous solid were studied theoretically by J. Lindhard et al.

[154]. According to their theory, the projected range of implanted ions can be described in first

approximation by a Gaussian function:

( )

√

[ ( )

( )

]

where D is the ion dose defined by the impinging ion charges per unit area. The maximum ion

concentration is at Rp. A software package called SRIM (Stopping and Range of Ions in Matter)

has been widely used for predicting the projected range and the sputter yield of many different

ions at a wide energy range hitting on the matters which in general could be gases, liquids or

solids with only their mass density being the distinguishing parameter. SRIM uses three

dimensional Monte-Carlo simulation of the ion-atom collision to calculate the stopping range of

ions in matter [155]. Despite of the distribution, it can also predict the kinetic phenomena

attributed from the energy loss of the ions, not only sputtering and implantation but also the target

damage, phonon production, ionization and ion reflection. The implantation profiles for Ga+ and

In+ ions incident perpendicularly into a GaAs substrate with an ion energy of 30 keV are shown

in Figure 4.5 using SRIM simulations. The calculated parameters for these cases of Ga+ and In

+

ions are listed in Table 4.1.

Applied for the sample processing in this work, the FIB writing is associated with sputtering,

redeposition, amorphization (swelling) and implantation. Among them, sputtering is the major

mechanism for material removal characterized by its efficiency which is normally represented by

the so-called sputter yield defined as the number of atoms ejected from the target surface per

incident ion. The sputter yield depends mainly on the ion energy, the incidence angle and the

substrate material. Normally, sputtered atoms ejected from the solid surface into the gas phase are

not under thermodynamic equilibrium. Therefore, they tend to condense back upon the solid

surface nearby so that a portion of the ejected atoms may absorb on or close to the sputtered

surface, resulting in redeposition. However, if the ion energy or dose is not sufficient for

sputtering, amorphization may take place, causing the bombarded area of the substrate to swell.

The effective sputtering dose should be at least two orders of magnitude higher than the

amorphization dose [156, 157]. Contrary to these processes which are normally executed by a

high energy FIB, an alternative technique reducing the ion energy by a retarding field can locally

deposit low-energy ions onto the surface of a sample via a soft-landing method.

44

Figure 4.5 SRIM simulation

for the ion implantation profile

by the injection of the Ga+ and

In+ ions into a GaAs substrate

at the ion energy of 30 keV.

Range (nm) Rp ΔRp R⊥ ΔR⊥

Ga+ 18.3 9.6 6.5 8.5

In+ 14.7 6.7 4.4 5.7

Table 4.1 The ion ranges for Ga+ and In

+ ions of 30 keV incident perpendicularly

into a GaAs substrate. Rp: projected range (longitudinal), R⊥: perpendicular range

(lateral), ΔRp: projected straggle, ΔR⊥: lateral straggle.

It is known that the focused ion beam generated from liquid metal ion sources is typically

composed of a core with a Gaussian distribution of ion current density and a long-range tail with

an exponential distribution of ion current density, decaying with the radial distance from the

beam center [158, 159]. In other words, the ion current intensity at the fringe (tail) of the beam is

much smaller than that at the center (core) [146], but finite and higher than it were with a pure

Gaussian beam-shape. R. Kubena et al. have reported the current density profile of focused Ga+

ion beams of 50 keV fitted with a double Gaussian and double exponential distribution of the

form:

( )

ρ

- ( ⁄ )

⁄ ＋ ρ

- ( ⁄ )

⁄ ＋ ρ

- ⁄ ＋ ρ

- ⁄

where J0 is the peak current density. Although the FWHM (full width at half maximum)

of an ion beam is less than 100 nm, the profiles change from a Gaussian distribution to

exponential with the coefficients, 32 nm < 3 < 67.5 nm for ρ3 = 0.02, and 4 = 160 nm for

1.6 × 10-3

< ρ4 < 1.3 × 10-4

. In other words, the tail has a long range from the beam center with

the intensity falling by at least two orders of magnitude lower than the peak intensity [159]. As a

result, amorphization quite far away from the beam center can occur by the exposure of the beam

tail during the milling process. The range and the decay intensity of the tail can be changed due to

different operating parameters, e.g., the ion source current. The outer radius of the tail can be

45

orders of magnitude larger than the FWHM of the current density distribution, i.e., a few µm or

even mm [160, 161].

In addition to direct writing, FIB is capable of imaging by collecting the secondary electrons

generated by impinging ions through the photomultiplier in a secondary electron detector with the

ion beams scanning over the substrate, which allows surface characterization of the materials.

Figure 4.6 shows the FIB image of a testing sample with the holes milled by a Ga-LMIS. The

shape of the holes is determined by the form of the focused ion beam which can be adjusted by

the stigmators. The advantage of FIB imaging over scanning electron microscopy (SEM) is a

higher material contrast. However, due to the higher mass of ions compared to electrons, the

damage to the samples is larger. Nevertheless, this imaging method helps to examine the focus on

the sample surface and to find the position marks on the sample. However, secondary electron

imaging has to be used carefully because the ion beam always damages the depicted areas. For

this reason, adjusting focus and alignment are done on dedicated areas, far away from the area

needed to be patterned. After that, the sample is mechanically moved to a scheduled position with

the ion beam blanked, i.e., in a “blind manner”, to ensure that only intentional writing is done on

the area of interest.

Figure 4.6 FIB imaging of a testing sample

with the holes milled by a Ga-LMIS with an

ion current of approximately of 100 pA and a

duration time of about 5 seconds.

4.3.3 Patterning parameters

In order to control the locations of single QDs in this work, two different FIB patterns are

designed as shown in Figure 4.7. The pattern (a) is composed of square arrays of spots with

equidistance for positioning nano-scale objects with micro-scale distances in between. The

equidistant spot spacings, lspot, are varied with 0.5 µm, 1 µm and 2 µm within a square area of

60 × 60 µm2. Another pattern (b) is used as the marker for defining the coordination, which is

made of a cross with a length of 100 µm and a width of 20 µm. The coordination markers are

46

useful for determining the location of desired FIB-patterned areas embedded in the sample during

an ex-situ structure characterization or optical measurements.

Figure 4.7 (a) The pattern of square arrays of spots in an area of 60×60 µm2. The

spacing between the spots, lspot, is varying from 0.5 µm to 2 µm resulting in different

densities of arrays in the FIB-patterned areas. (b) The cross-shaped pattern designed

for the coordination markers.

In this work, the FIB patterns were executed using a Ga+ or an In

+ ion beam with an ion

energy of 30 keV controlled in a diverging mode. With the Ga- and In-LMIS, the ion source

currents were operated individually at about 3.0 µA and 1.8 µA, while the target currents were

measured with about 50 pA and 80 pA, respectively. Such high target currents were intentionally

chosen to reduce the interruption time between the MBE growths. The FIB spots patterned on the

sample surface corresponded to the pattern design of square arrays. The whole square area of the

FIB spots is named as the FIB-patterned area of 60 × 60 µm2. The FIB-patterned areas were

aligned in a line with a fixed interval of 300 µm in between realized by step-and-repeat in order

to avoid the interaction between each other. In order to optimize the parameters for positioning

self-assembled GaAs nanoholes, different FIB parameters were applied to the FIB-patterned areas,

including the ion fluence Φion of Ga+ or In

+ and the spot spacing.

The ion fluence Φion is defined by the number of impinging ions Nion per unit area A, i.e.,

Φ ⁄ . The number of impinging ions onto one spot can be expressed as ⁄ .

Here, I is the ion beam current measured by the Faraday cup. t is the dwell time on a spot

calculated from the frequency f. q is the charge number of ion species, e.g., q = 1 for Ga+ or In

+.

e is the elementary charge of 1.6×10-19

C. i is the number of repeating times. For patterning spots,

the area is in fact the cross-section area of the beam focused on the substrate. As a result, the ion

fluence on one spot with the radius r can be calculated as follows,

Φ Φ

( )

which is used for the ion fluence calculation with arrays of FIB spots in this work.

The spot ion fluences used in this work were ranging from 3 × 104 to 1 × 10

7 ions/spot with

the beam size in the scale of 100 nm. As the ion fluences above 1 × 106 ions/spot, a significant

47

sputtering process can occur resulting in the depths of the sputtered holes ranging from 2.5 nm to

14 nm under the substrate surface as shown in Figure 4.8. On the other hand, the coordination

markers were executed at very high ion fluences by a target current of above 2 nA with a large

beam size in order to perform an efficient milling process producing a clear step which can be

visible under an optical microscope or even bare eyes after overgrown with capping layers.

Therefore, a further ex-situ lithographical processing can be achieved with the help of these

coordination markers.

Figure 4.8 (a), (b) and (c) are the SEM images of the FIB spots fabricated with the

spacing of 1 µm and the In+ ion fluences of 1 × 10

6 ions/spot, 3 × 10

6 ions/spot and

1 × 107 ions/spot, respectively. (d), (e) and (f) are the depth profiles of the FIB spots

with the corresponding patterning parameters measured by AFM.

49

Chapter 5 Experimental Details and Characterization

Methods

The experimental details about the sample fabrication and the characterization methods for site-

selected QDs are introduced in this chapter. The fabrication involves the combination of FIB

patterning and MBE growth, where the parameters of FIB patterning have been addressed in the

previous chapter. The essential parameters for the fabrications of self-assembled GaAs nanoholes

and InAs QDs are described in the first section. Two structure characterization techniques, i.e.,

scanning electron microscopy (SEM) and atomic force microscopy (AFM), were employed to

study the topography and morphology of the sample surfaces associated with the nanoholes and

the QDs. The optical characterization of the QDs was obtained from the photoluminescence (PL)

spectra measured by two different techniques, PL spectroscopy and scanning near field optical

microscopy (SNOM).

5.1 Sample Fabrication

As described in section 4.2, the fabrication of the samples includes several processes. The

first step is the growth of an epitaxial GaAs matrix layer with a high purity and a smooth surface

by MBE. The second step is patterning arrays of spots on the sample surface by in-situ FIB

writing. The third one is the formation of GaAs nanoholes by droplet epitaxy in the MBE system.

The last step is the deposition of InAs using different amounts of coverage in order to investigate

the evolution of strain-induced QDs in the GaAs nanoholes by SK growth with MBE. An

illustrated scheme of these processes can be found in Figure 4.2. The MBE growth was executed

by a solid source MBE system of the type Riber Epineat III-V SS. The FIB writing was done by

an Orsay Canion 31 Plus FIB column with a Ga or In LMIS. The experimental setup of these two

systems can be found in section 3.3 and 4.3, respectively. The MBE system is connected with the

FIB column through vacuum valves, i.e., the MBE-FIB system, as illustrated in Figure 3.4. Due

to this advantage, all transport procedures between the processes were performed under UHV

conditions to ensure that the whole fabrication is surface clean.

A quartered 3-inches GaAs (100) epi-ready wafer was first degassed at 150 °C for at least

45 minutes in the load-lock chamber in a vacuum. After degassing, the wafer was transferred into

the growth chamber via the transfer chamber using the transfer rods. Prior to the epitaxial growth,

50

the wafer was thermally cleaned by two steps in the main chamber of the MBE system. First,

the substrate temperature was raised up to Tpyro = 550 °C (Tpyro, pyrometer temperatures) and

maintained for at least 15 minutes to remove the impurities from the substrate in the absence of

arsenic atmosphere. Secondly, the temperature was increased to Tpyro = 600 °C (Tset ~ 660 °C,

depending on the substrate conditions; Tset, thermocouple temperature) to desorb the oxides from

the surface. In order to prevent the dissociation of arsenic from the GaAs substrate, the As valve

has to be opened during the second step. After achieving a stable substrate temperature at 600 °C

and a homogeneous arsenic atmosphere inside the growth chamber with the arsenic BEP, PAs, of

1.3 × 10-5

Torr, the MBE growth process of the sample fabrication began. It started with the

growth of a 50 nm GaAs epitaxial layer followed by 30 periods of the short-period superlattice

(SPS) with 2 nm AlAs / 2 nm GaAs. The SPS in this case was used to smooth the surface

roughness caused by the impurities from the substrate. From RHEED, a clear reconstruction of

(2×4) along [ ] indicated a smooth GaAs surface. After smoothing, another 150 nm or 200 nm

thick GaAs epilayer was grown as the matrix layer for the subsequent formations of nanoholes

and QDs.

After the growth of a GaAs matrix, the substrate temperature was decreased to a standby

value at Tset = 400 °C. The As valve was then closed and the growth was interrupted to transfer

the sample into the FIB chamber for the process of FIB patterning at room temperature. Two

types of FIB patterns were generated in a sequence. The first one was composed of square arrays

of FIB spots with the variable spacing lspot in an area of 60 × 60 µm2. The second one was made

of a cross-shaped coordination marker. The details about the FIB patterning parameters and the

pattern design can be found in subsection 4.3.3. During the preparation for FIB patterning, the

whole interruption time of growth was about one hour, which includes transferring the sample,

defining the coordination of the sample and fine tuning the ion beam focus, FIB spot patterning

(about 5 minutes for 10 areas) and coordination markers carving (about 30 minutes for 3 markers).

After FIB patterning, the sample was transferred back to the MBE chamber for the generation of

GaAs nanoholes and the deposition of InAs.

During this one hour interruption time, the As valve was fully closed, leading to a decrease

of the background pressure in the growth chamber down to the order of 10-9

Torr. Such low

pressure is essential for the formation of metal droplets during droplet epitaxy. After reloading

the sample in the growth chamber, the substrate temperature was raised up to Tpyro = 545 °C for

the growth in the mode of droplet epitaxy. The deposition of Ga with a nominal coverage θGa of

3 ML or 5 ML was supplied (equivalent to the standard growth of GaAs with the growth rate of

0.70 ML/s calculated by RHEED). During the deposition of Ga, the As BEP was maintained at

around 6.0 × 10-7

Torr which is the minimum controllable value in the MBE system of this work.

This process is a kind of arsenic-debt atomic layer MBE growth, resulting in the formation of Ga

droplets on the surface by VW growth mode. The slight As pressure could suppress additional

Ostwald ripening during the droplet formation. The nucleation of the deposited Ga atoms on the

FIB-patterned areas was site-selective depending on the arrayed FIB spots, yielding arrayed Ga

metal droplets. Meanwhile, the Ga droplets could be formed on the bare GaAs surface outside the

51

FIB-patterned areas as well, however, in a random distribution. Both of these Ga droplets were

then crystallized by arsenic resulting in GaAs semiconductor nanostructures. With the conditions

of low As pressure and high substrate temperature, a transformation from hemisphere-like

droplets into hole-like nanostructures is favored. The mechanism of nanoholes generated by

droplet epitaxy, including the droplet formation and crystallization, can be found in subsection

3.4.2. The sample was then annealed under the same BEP of As with the temperature rapidly

raised up to Tpyro = 610 °C ~ 620 °C within 2 minutes in order to evaporate the rest of the liquid

Ga droplets [36]. The small amount of As maintained during the annealing process could prevent

possible desorption of As from the crystalline GaAs at this temperature. The fabrication of GaAs

nanoholes was thus achieved. Then, the substrate was cooled down. For the structure

characterization of the GaAs nanoholes, the substrate temperature was cooled down to the

standby temperature, i.e., Tset = 400 °C, for the subsequent ex-situ analyses.

Moreover, GaAs nanoholes formed by droplet epitaxy can be further used as templates for

the site-selective growth of strain-induced QDs. For the overgrowth of these site-selected

QDs after the formation of GaAs nanoholes, the substrate temperature was decreased to

Tpyro = (525 ± 2) °C to allow the deposition of InAs. In meanwhile, the BEP of As was increased

up to 6.8 × 10-6

Torr for the growth of QDs. The growth rate of InAs was chosen to be

~ 0.04 ML/s in this condition. The total InAs coverage was delivered in consecutive cycles, each

consisting of 4 seconds of In deposition followed by 4 seconds of growth interruption. This

interruption allows the diffusion of In atoms on the surface until they find a suitable location for

binding in order to make up epitaxial layers. The number of In cycles is calculated by using the

RHEED-oscillation data which has previously been gained at a particular substrate temperature.

For the conventional strain-induced QDs grown by the same MBE system of this work, the

standard InAs coverage θInAs is 2.1 ML for InAs QDs grown on a planar GaAs (100) surface.

However, in this work, the InAs coverage θInAs was varied from 1.40 ML to 1.75 ML in order to

study the growth evolution for the site-selectively grown QDs in the GaAs nanoholes. The site-

selected QDs grown in the arrayed GaAs nanoholes on the FIB-patterned areas can follow the

position of the nanoholes, resulting in arrayed QDs. On the other hand, on the bare GaAs surface

outside the FIB-patterned area, the site-selected QDs were reproduced, depending on the

distribution and the density of the GaAs nanoholes, resulting in randomly-distributed QDs.

After the InAs deposition, the sample was either cooled down directly to the standby

temperature and then taken out without capping for ex-situ structure characterization, or the

growth was continued by providing the samples with capping layers to complete the confinement

of QDs for ex-situ optical investigation [1]. The capping layer, an 8 nm or 10 nm GaAs layer, was

grown with the temperature decreased to Tpyro = 510 °C, followed by a 7 nm to 22 nm GaAs layer

growth with the substrate temperature raised to Tpyro = 600 °C. After that, the short period

superlattice with 3 nm AlAs / 1 nm GaAs and/or the GaAs top layer were grown with an arsenic

BEP of 1.3 × 10-5

Torr. After capping, the sample was cooled down to the standby temperature of

Tset = 400 °C and was then ready for the subsequent ex-situ processes and analyses.

52

In order to define the position of the FIB-patterned areas and also to unite the quantity of the

QDs participating in their ensemble optical properties, an ex-situ photolithography technique was

employed for providing orientation and for segmenting the sample into several regions in terms

of optical measurements. In practical, the quartered 3-inches sample was first cut into a piece of

5 × 5 mm2 including the whole region which has undergone FIB patterning. Then, the square

shaped mesas with an active area of 40 × μm2 were fabricated by photolithography and wet

chemical etching. The alignment of the mesas and the FIB-patterned areas (with the area of

60 × 60 μm2) was achieved by aligning the coordination markers cleaved by FIB with the

markers on the mesa. After etching, an Au metal layer was coated by thermal evaporation in

order to conceal the optical luminescence from the undesired area during the optical measurement.

At the same time, the Au coating layer also makes th m sa structur s com ”visi ”, which

helps for a coarse position tuning in the measurement setups with naked eyes. After these

preparations, the well-defined areas of the sample were ready for the ensemble or single QD

spectroscopy analyses.

Several samples were fabricated with different growth parameters in order to understand the

relation between the structure of GaAs nanoholes and droplet coverage, as well as the growth

evolution of strain-induced QDs in the nanoholes. For the case of nanohole structures, sample A0

and B0 were generated respectively with nominal Ga coverages θGa of 3 ML and 5 ML without

InAs deposition. For the case of InAs QDs in GaAs nanoholes, sample A75 was fabricated with

the GaAs nanoholes formed with θGa of 3 ML followed by the InAs deposition with an InAs

coverage θInAs of 1.75 ML. Also, sample B40, B58 and B75 were fabricated with GaAs nanoholes

formed with θGa of 5 ML followed by InAs deposition with θInAs of 1.40 ML, 1.58 ML and

1.75 ML, respectively. For the optical measurements, the capped samples, C40, C46, C58, C65

and C75, were produced with GaAs nanohole formed with θGa of 5 ML followed by the InAs

deposition with θInAs of 1.40 ML, 1.46 ML, 1.58 ML, 1.65 ML and 1.75 ML, respectively. The

characterization methods used in this work will be introduced in the following sections. The

experimental results of both the randomly-distributed and arrayed GaAs nanoholes will be given

and discussed in Chapter 6, while those of the site-selected InAs QDs grown in both types of

GaAs nanoholes will be shown and discussed in Chapter 7.

53

5.2 Scanning Electron Microscopy

A scanning electron microscope (SEM) is mainly used to observe the topography of a

sample by scanning the surface with a high-energy focused electron beam. The signals derived

from the beam-sample interactions provide the information about external morphology, chemical

composition and the texture of crystalline materials, which can be detected by a variety of

detectors and then converted into images.

All SEMs are essentially composed of a vacuum system, an electron optics column,

detectors and an image processor. The vacuum system generally includes two vacuum chambers

and vacuum pumps. One chamber, which houses the electron optics column, is maintained in

UHV conditions about 1 × 10-10

mbar. Another chamber consists of a sample stage and detectors

usually in a lower vacuum in the order of 10-5

to 10-8

mbar, which is located below the electron

optics column and separated by a valve. The electron optics column is accomplished with the

electron source (gun) and the electromagnetic lenses in order to produce an electron beam with

narrow energy dispersion and precise kinetic energy for scanning the sample. The electron gun is

used to eject electrons by field emission or thermal emission processes. The electromagnetic

lenses include the condenser lenses to condense the electron beam, and the objective lens to focus

the electron beam on the sample surface. After travelling through the electromagnetic lenses, the

accelerated electron beam is incident on the sample. The kinetic energy is dissipated and parts of

this energy result in the ejection of secondary electrons (SE), backscattered electrons, Auger

electrons, X-rays and light. These signals are detected by the appropriate detectors e.g., the

secondary electron detector, the backscatter electron detector, the X-ray detector and the

cathodoluminescence (CL) detector. In an SEM, the secondary electrons provide information of

the morphology and the topography of the sample. The backscattered electrons can be used to

illustrate contrast in composition of multiphase materials. These two signals are the most

commonly used signals for composing SEM images. Furthermore, the X-ray spectra collected for

energy dispersive X-ray spectroscopy (EDX) are characteristic of the atoms, allowing the

chemical composition of the materials to be determined. Finally, the CL spectroscopy collecting

the light emission from the sample has the ability to investigate the optical properties of the

samples.

As in any microscope, the main objective of SEM is for magnification and focus of clarity.

The amount of information which a micrograph can provide is dependent on the resolution of a

microscope. The resolution in a microscope means the smallest interval that one can distinguish

between two adjacent points. With an SEM, the resolution mainly depends on the size of the

electron spot, which in turn depends on the wavelength of electrons and the electron optics

system. When the electron beam enters the lens and aperture system in the microscope, it

produces overlapping diffraction patterns for each point of objects. The distance r between two

diffraction maxima corresponding to the limit of resolution can be determined by:

54

. λ

. λ

sin

where λ is the wavelength of the beam, NA is the numerical aperture, n is the refractive index of

surrounding medium and is the angle between the optical axis and the beam edge. The formula

was developed by E. Abbe [162] and Lord Rayleigh [163] based on light optical microscopes.

For a normal light optical microscope, the maximum resolution is limited to about 200 nm which

corresponds to the wavelength of visible light ranging from 400 nm to 760 nm. However, much

smaller wavelengths can be achieved by using the electron beam in an SEM. The wavelength of

an electron beam can be varied depending on its acceleration voltage, U, with the dependence

derived from the de Broglie relation, λ ⁄ , as given by the formula:

λ

√

where h is Planck’s constant; p is the momentum; me is the electron mass; and e is the electronic

charge. For an electron microscope with the acceleration voltage of 20 kV, the wavelength is

about 0.008 nm which has the potential to increase the resolution by a factor of 104 to 10

5 over

the light optical microscope. When the electron velocity approaches the speed of light, i.e.,

c = 3 × 1010

cm/s, at a high voltage, e.g., 50 kV, v = 1.326 × 1010

cm/s, the relativistic correction

of the mass has to be taken into account. However, the maximum resolution is actually not

attainable in SEM because the theoretical wavelength is still limited by lens aberrations,

vibrations, noise and stray fields. The magnification of SEM imaging can range largely to that of

optical microscopy up to a nanometer scale. In a SEM, the magnification is carried out by the

ratio of the dimensions of the raster on a sample and the raster on a display device. Therefore,

unlike light optical microscopes and transmission electron microscopes, where the magnification

is a function of the power of the objective lens, the magnification of SEM is controlled by the

power of scanning coils or deflector. With a fixed display size, higher magnification can be

achieved simply by reducing the size of the raster on the sample.

A Quanta 200 FEG SEM system from FEI has been used for imaging in this work, which is

capable of magnifying from 12× to 1,000,000×. The SEM working with a hot field emission gun

and the acceleration voltage can be operated from 200 V to 30 kV. The maximum resolution in

the high-vacuum mode (~ 6 × 10-4

Pa) is about 1.2 nm and 3.0 nm at the acceleration voltage of

30 kV and 1 kV, respectively. A SEM has advantages including a high degree of magnification

and an excellent depth of field resulting in its remarkable abilities for imaging a comparatively

large area and showing 3D structure. Moreover, it allows to image bulk materials and not just thin

films or foils, which makes it easy for sample preparation. Owed to the advantages above, SEM

has been considered as a suitable and efficient technique for imaging small 3D nanostructures,

e.g., quantum dots with a great quality. Figure 5.1 shows images with different magnifications by

the Quanta 200 FEG SEM system. The image (a) displays a FIB-sputtered coordination marker

used in this work, while the image (b) illustrates the strain-induced InAs quantum dots on a

planar (100) GaAs surface with a density of the order of 1010

cm-2

grown by the same MBE

system of this work.

55

Figure 5.1 SEM images from the Quanta 200 FEG. (a) A cross-shaped coordination

marker after the growth of droplet epitaxy in MBE, produced by In+ FIB patterning

on a GaAs substrate. (b) The InAs quantum dots grown on the planar (100) GaAs

surface at AFP.

5.3 Atomic Force Microscopy

Atomic force microscopy (AFM) is a scanning probe microscopy technique providing high

resolution topography images on the atomic scale [164]. The working principle is based on

measuring the force between a probing tip and the sample during lateral scanning (x-y). The

sample surfaces can be insulating, semiconducting or conductive, which makes AFM a

complementary technique to scanning tunneling microscope (STM) which is limited to a

conductive or semiconducting sample surface. Moreover, since the measurement can be carried

out in ambient air and no special sample preparation is needed, AFM has been considered as a

versatile and convenient technique to investigate the surface topography of nanostructures made

up of both solid and soft matter.

The key component of an AFM is the cantilever, i.e., a flexible arm, with an atomically

sharp tip set at the end for scanning the sample surface. The cantilevers are usually made of Si

and Si3N4. The small curvature radius of the tip is of the order of nanometers, leading to high

lateral resolution. The working principle of the AFM is illustrated schematically in Figure 5.2 (a).

When the tip is brought into close proximity of the sample surface, the forces between the tip and

the surface will result in a deflection of the cantilever. The relation between the force and the

deflection follows Hook’s law. The potential energy can then be described by

,

where k is the spring constant of the tip of the order of 1 N/m while d is the shortest vertical

displacement. With of the order of 4 × 10-21

J at room temperature, the smallest observable

vertical displacement (z) is 0.5 nm. The force between the tip and the sample is of the order of a

nano Newton [165]. The deflection is monitored by the reflection of an incident laser beam upon

the cantilever into a position sensitive detector which consists of an array of photodiodes. The

output signal from the detector is calculated by normalizing the signal difference between the

56

photodiodes with their sum which is proportional to the total deflection of the cantilever. During

scanning, the force is kept constant by a feedback loop, i.e., keeping a constant distance between

the tip and the surface by moving the cantilever (or the sample) up and down promptly. This

delicate vertical movement can be carried out by piezoelectric actuators which results in a

resolution on the atomic scale. Similar actuators are also used to move the cantilever laterally to

scan a topographic map of the surface features.

The AFM equipment used for this work is a scanning probe microscope from Digital

Instruments equipped with a Si cantilever having a tip with a nominal curvature radius of 5 nm to

10 nm with the angle of 20°. Since the resolution is affected by the tip geometry, the resolution

which can be obtained in this case is in the order of a few nanometers. A tapping mode is

performed to study the surface morphological properties of the samples in order to prevent the

destruction of the surface and the tip as well. In the tapping mode of operation, the tip is

oscillated at its resonant frequency by an actuator. The decrease of the amplitude of the

oscillation generated when the cantilever approaches the sample is used to measure the force

between the tip and the sample [165]. An AFM can provide the information from lateral and

vertical dimensions of the nanostructures present on the sample surface with a high magnification.

Contrary to optical or electron microscopes, e.g., an SEM, which provide a two-dimensional

projection of the surface, AFM can study the information in all three dimensions of the sample.

The resolution of this system is appropriate to study nanostructures such as self-assembled

quantum dots and nanoholes. Figure 5.2 (b) shows an AFM image with the strain-induced InAs

quantum dots grown on a planar (100) GaAs surface by the same MBE system of this work. The

measured base diameter of the dots is about 50 nm while the dot height is around 11.5 nm.

(b)

Figure 5.2 (a) The working principles of AFM. A

sharp tip is mounted on a cantilever for scanning the

surface of the sample. The deflections of the

cantilever are reported by a reflected laser beam into

an array of photodiodes. Photoelectric circuitry of the

detector then converts the deflections into height

information recorded as a digital image [166]. (b)

The AFM topography image of strain-induced InAs

quantum dots grown on a planar GaAs (100) surface.

(courtesy of S. Valentin)

57

However, this method has certain limits which should be taken into account. For example,

AFM characterization requires uncapped quantum dots, while it has been observed that the QD

structural characteristics changes before and after the growth of the capping layer. AFM is

therefore more valuable for a comparative analysis than for quantitative measurement of the QD

dimensions. Furthermore, because the physical resolution is limited by the shape of the tip, the

dimensions of the nanostructures can be distorted by a blunted tip. Also, steep steps normally

cannot be measured because of the nature of AFM tips. Compared to SEM, the size of the AFM

scan image is much smaller in the order of a few tens to hundred micrometers. Moreover, due to

the low scanning speed, the thermal heating of the cantilever by the laser beam can lead to

thermal drift in the image.

5.4 Photoluminescence Spectroscopy

Photoluminescence (PL) spectroscopy is a powerful and non-destructive optical technique

for providing information about the optical properties of semiconductor materials with rapid and

sensitive ability. It is capable of investigating the information involving the intrinsic optical

processes corresponding to host semiconductors, and also the extrinsic optical processes related

to impurities or defects which affect material qualities and device performances [167]. PL

spectroscopy is an efficient technique which has been widely applied for the characterization of

quantum wells, superlattices, and also quantum dots [1].

Photoluminescence is the radiation emitted from semiconductor crystals after the excitation

by an incident light source, e.g., a laser beam. In particular, it reflects the recombination paths of

the photogenerated electron-hole pairs. For example, in a self-assembled quantum dot system, the

electron-hole pairs are obtained by exciting electrons from the valence band (VB) to the

conduction band (CB) using a laser beam with a higher energy than the band gap of the matrix

material, i.e., above-band excitation. In this case, many electron-hole pairs are created in the

matrix surrounding the dot. A fraction of these electrons and holes can be captured by the

quantum dot and then relax nonradiatively to the ground state (s shell) or weakly excited sates

(p, d and f shell) of the quantum dot over a sub-ps-timescale. The electron-hole pairs in the

confined levels of the quantum dot can then recombine radiatively with the typical life time about

1 ns. The radiative recombination is accompanied with the emission of a photon which carries a

characteristic energy. A schematic representation of the photoluminescence process in a quantum

dot is shown in Figure 5.3. A typical PL spectrum from the ensembles of conventional strain-

induced InAs quantum dots embedded in a GaAs matrix is also shown, which was measured at

77 K. The peaks present in the spectrum are associated with the transitions from the s, p and d

shells of the QDs, the wetting layer (WL) and the GaAs. The ground-state transition energy E0 is

about 1.054 eV for the s shell, while the excited-state transition energies E1 and E2 are 1.124 eV

58

and 1.178 eV from the p, and d shells, respectively. The PL spectra of QDs are mainly attributed

to the photon emission following the selection rules which allow the recombination of the

electrons and the holes belonging to the levels of same quantum numbers and whose

wavefunctions are sufficiently overlapped [168]. In other words, an electron in an s shell will

recombine with a hole in the s shell, a p electron with a p hole, and so on. When the temperature

is low enough such that kBT is smaller than the quantum dot energy level spacing, the quantized

properties of the energy levels become apparent in the PL spectra. The number of the electron-

hole pairs present in the system can be adjusted by the excitation power density. Since the

relaxation times to the ground states are much shorter than the life-time of the radiative

recombination, the emission from the s shell can be observed at a low excitation power. As the

excitation power density is increased, more carriers are present in the QD system and the higher

shells are filled subsequently. This phenomenon is known as level-filling represented as the

typical behavior of self-assembled InAs QDs [53]. More information can be obtained by

analyzing the luminescence spectrum as a function of different parameters, e.g., temperature and

excitation wavelength.

(a) (b)

Figure 5.3 (a) The schematic illustration of the photoluminescence processes (1) to (4) for a self-

assembled InAs/GaAs QD system (adapted from [104]). (1) the formation of electron-hole pairs

in the GaAs bulk by a laser excitation (2) the capture of the carriers into the QD (3) the relaxation

to the ground state (e1 for electrons; hh1 for heavy holes, corresponding to the s shell of the QD),

or to the lowest unoccupied excited state (e2 and e3; hh2 and hh3, corresponding to the p and d

shells of the QD, respectively) (4) the recombination with the emission of photons carrying

characteristic energies E0, E1 and E2 from the transition of s, p, and d shells, respectively.

(b) A typical PL spectrum measured at 77 K from the ensembles of conventional strain-induced

InAs QDs in a GaAs matrix grown by the same MBE system of this work at AFP (provided by

A. Rai). The PL peaks are attributed to the transitions of the discrete energy states, s, p and d

shells, of the QDs. The transition peaks of the InAs wetting layer (WL) and the GaAs are also

present.

59

Figure 5.4 shows a schematic for the experimental apparatus of the PL setup used for

measuring the optical properties from the ensembles of QDs in this work. The excitation source is

a diode laser with a wavelength of 635 nm, i.e., 1.95 eV, operating with an excitation power of

5 mW. The energy of the laser is higher than the band gap of the semiconductor under study, e.g.,

~ 1.51 eV for GaAs at 77 K. The samples are fixed on a finger cryostat for low temperature

measurements. The cryostat is capable of cooling down to 4.2 K. A resistance thermometer, i.e., a

PT 100 resistor, is capable of measuring the temperature from room temperature down to 70 K.

An Allen-Bradley resistor is used for measuring temperatures down to 4 K. The cryostat is

equipped with a high purity quartz window, which allows the excitation as well as the

luminescence light to pass through. The cryostat is mounted on a movable table which allows

sample movement in all three dimensions in order to make an intersection of the laser beam and

the optical axis and also to realize sample mapping. The associated optics includes a mirror and a

lens to reflect and focus the excitation light to a small spot in the order of 10-5

cm2 on the sample,

and two other lenses to focus the luminescence signals on the entrance slit to a high resolution

monochromator. A SPEX 500M monochromator is capable of dispersing the luminescence

signals spectrally by a diffraction grating with a blaze optimized to a wavelength of 750 nm or

1000 nm. The dispersed signals are then detected by a LN2-cooled InGaAs detector with a lock-in

amplifier measuring the detector signal in modulating the frequency of the laser with 133 Hz in

“internal oscillator made” to bandpass-filter the signal for noise suppression. Finally, the signal

from the lock-in amplifier is digitally read out with the help of an IEEE-488 interface and a

Lab-View computer program which is also used to control the monochromator and also for data

processing and storage.

In contrary to the PL spectroscopy, a scanning near field optical microscope (SNOM) is used

to distinguish the single QDs both spectrally and spatially. Because of the sub-wavelength

aperture diameter of the probe, the resolution limit of a typical optical microscope can be

overcome with this technique which results in high resolution images [165, 169, 170]. A

schematic illustration is shown in Figure 5.5 with the layout of the aperture-type SNOM at

Max Planck Institute (MPI) of Microstructure Physics, Halle. The microscope setup is mounted

inside a vacuum chamber under ultra-high vacuum conditions. The sample is attached to the cold

finger of a cryostat which is capable of stabilizing the temperature in the range between 8 K and

300 K by a liquid helium flow. The SNOM scan head consists of a near-field fiber probe, a tuning

fork shear-force setup to regulate the distance between the probe and the sample surface,

piezoelectric actuators for fine positioning on a nanometer scale, and a motorized translation

stage for coarse positioning on a micrometer scale. The near-field fiber probe is made by pulling

an optical fiber to a sharp tip modified from an AFM tip with a thin metal coating layer and an

aperture with a diameter of about 300 nm at the end of the tip. The fiber tip is glued along one

side of the arms of the quartz crystal tuning fork. The distance between the sample and the tip is

kept very small by the use of a feedback mechanism based on the regulation of the quartz tuning

fork. The sample or the tip is scanned so as to construct an image of the sample. A microscope

objective allows for visual inspection of the tip-sample region by collecting the reflected light

60

from the illumination with an LED. The light is then routed onto a camera outside the vacuum

chamber. The microscope objective can also be used for far-field illumination and illumination

collection of the sample. A green He-Ne laser source with the wavelength of 543 nm is coupled

to the SNOM via an optica fi r coupler. In spectroscopic experiments, the luminescence emitted

from the sample is also guided by the optical fiber and then spectrally dispersed in a

monochromator SP2560 on the grating of 150 lines/mm with a blaze optimized for a wavelength

of 800 nm and a slit width of 150 μm, and finally detected by an InGaAs detector.

Figure 5.4 The experimental setup for the PL spectroscopy with a laser diode at the

wavelength of 635 nm, the lenses and a mirror, a monochromator, a LN2-cooled

InGaAs photodetector, a lock-in amplifier and the computer control unit. (adapted

from [104])

Figure 5.5 Schematic diagram of the SNOM setup at Max Planck Institute of

Microstructure Physics, Halle. (courtesy of A. Senichev)

61

Chapter 6 Characterizations of Self-assembled/Self-

patterned GaAs Nanoholes

Site-control has been considered as a promising pathway to integrate self-assembled QDs into

single QD based devices for the implementation of solid-state quantum information. In this work,

the site-control was realized by using self-assembled/self-patterned GaAs nanoholes as templates

for the subsequent site-selective growth of QDs by MBE. To study the properties of these site-

selected QDs formed on the nanohole templates, it is important to first understand the structures

of the nanoholes which may influence the performance of the quantum systems directly. The self-

assembled/self-patterned GaAs nanoholes of this work were generated by droplet epitaxy. In

order to study the influence of the Ga coverage on the topography of nanoholes, two different

amounts were applied. For each sample, the GaAs nanoholes were formed on the bare GaAs

surface (without FIB pre-patterning) and also on the FIB-modified surface, i.e., the FIB-patterned

areas. The FIB-patterned areas composed of square arrays of FIB spots were created by an in-situ

FIB technique with different patterning parameters on a GaAs surface. In this chapter, the

characteristics of the GaAs nanoholes formed on both types of surfaces are shown and discussed

in two subsequent sections. In the first section, the nanoholes on the bare GaAs surface are

addressed with their shapes and distributions. Then, the impact of FIB patterning on the

arrangements and the structures of the nanoholes is discussed in the second section with several

different FIB-patterned areas. A comparison between the GaAs nanoholes on the bare GaAs

surface and on the FIB-patterned area is also included.

6.1 Randomly-distributed Nanoholes

For the site-selective growth of QDs with surface-patterned templates, the geometry of the

templates is one of decisive parameters leading to the preferential nucleation of the overgrown

materials. For GaAs nanostructures generated by droplet epitaxy, the morphology depends on the

diffusion region of Ga atoms or GaAs molecules (before being solidified into GaAs crystals)

together with initial preferential nucleation at the skirts of Ga droplets. The preferential

nucleation at the skirt is driven by the surface energy difference of three phases. The diffusion

region is determined by the competition between Ga atomic migration and As incorporation

[115, 116]. Meanwhile, high substrate temperatures can lead to thermal melting of liquid Ga

droplets resulting in local concaves on the surface [36, 39, 114]. Therefore, the shape of the

62

nanoholes is mainly influenced by substrate temperature, arsenic pressure and the size of metal

droplets [27, 28, 113]. In order to optimize the structures of nanoholes for the site-selective

growth of QDs, two GaAs nanohole samples, A0 and B0, were fabricated with nominal Ga

coverages θGa of 3 ML and 5 ML, respectively, at high temperature and low As pressure by

droplet epitaxy. For studying the morphology of these nanoholes, no InAs was deposited on the

samples. The details about the sample fabrications are described in section 5.1. These two GaAs

nanohole samples were characterized by SEM and AFM for a full inspection of the

nanostructures.

Figure 6.1 The GaAs nanoholes on the bare

GaAs surface of sample A0 fabricated with

θGa = 3 ML by droplet epitaxy. (a) The SEM

image (30,000×) (b) The AFM 3D topography

of a typical nanohole with the lateral distances

of x along [ ] and y along [ ], and the

height, z. (c) The profiles corresponding to the

AFM topography. L is the outer diameter of the

nanohole. l is the diameter of the wall. H and h

are the (higher and lower) heights of the wall

along x or y. is the inner width of the

nanohole with respect to the half maximum of h

along the corresponding direction. The red

horizontal dotted line corresponds to the

substrate surface, while the black one to the

bottom of the hole.

Figure 6.1 presents the SEM image of GaAs nanoholes formed on sample A0 with a

nominal Ga coverage of 3 ML and the AFM topography of one typical GaAs nanohole on this

sample. These self-assembled GaAs nanoholes are randomly-distributed on the GaAs surface

with a density of ~ 8.0 × 107 cm

-2. In the SEM image (a), the nanoholes represent an inner

63

diameter of ~ 25 nm along the crystal direction of [ ]. In the AFM 3D image (b), the typical

GaAs nanohole has an asymmetric wall elongated along [ ] which surrounds the inner hole. In

droplet epitaxy, this kind of walls from the nanoholes is also known as a ring-like structure which

is usually transformed from a droplet crystallized with low arsenic pressure. The formation of a

ring-like structure is due to a faster solidification rate at the edge of a metal droplet resulting from

preferential nucleation at the interface of three phases which starts at the skirt of the droplet [115]

and a downhill material transportation from the droplet by diffusion [29, 31]. Because the atomic

diffusion rates depend on the crystal directions of the substrate, the differences of the material

transportations toward different directions lead to the asymmetric structure of the nanohole. The

profiles in (c) corresponding to the cross-sections of the typical GaAs nanohole along [ ] and

[ ] directions feature the dimensions which are denoted as follows. The outer diameter of the

whole nanohole structure is indicated as L. The diameter of the wall surrounding the inner hole is

labeled as l measured from the tops of the wall. The heights of the wall along each crystal

direction are indicated as H and h for the higher and lower ones, respectively. The inner width of

the nanohole, represented by , is measured at the half maximum of the lower height h along a

corresponding direction. The average values of these dimensions measured by AFM from sample

A0 are listed in Table 6.1 for [ ] and [ ] directions, respectively.

θGa = 3 ML L l H H

[ ] 315 ± 15 127 ± 5 2.1 ± 0.3 0.9 ± 0.3 33 ± 6

[ ] 240 ± 13 106 ± 10 1.1 ± 0.2 0.9 ± 0.1 45 ± 9

Table 6.1 The dimensions of GaAs nanoholes on the bare GaAs surface of sample A0

along [ ] and [ ] directions in units of nanometers. The nanoholes were formed with a

nominal Ga coverage of 3 ML. L is the outer diameter of the nanohole. l is the diameter of

the wall. H (higher) and h (lower) are the heights of the wall. is the inner width of the

nanohole with respect to the half maximum of h.

Because of the faster crystal growth at the edge of droplets and the initial preferential

nucleation occurring at the skirts [29, 31], the diameter of walls l and the heights of walls, H and

h, are suggested to be dependent on the dimensions of the original metal droplets [32]. Moreover,

the outer diameter of the nanoholes L depends on the diffusion region of Ga atoms or GaAs

molecules which is determined by the substrate temperature and the As pressure during

crystallization [32]. From the ratio of the outer diameters of nanoholes between two directions,

, which is about 1.3, a faster atomic migration along [ ] is substantiated compared

to [ ]. This ratio is slightly larger than the ratio for the diameters of the walls with

corresponding directions, , which is about 1.2. Meanwhile, the outer diameters of

nanoholes are more than twice larger than the diameters of walls for each direction. These results

all validate a significant lateral diffusion of atoms or molecules from droplets under this growth

condition. Moreover, the wall of a nanohole has different heights along the direction of [ ]

with a ratio of about 2 by . This height difference reveals an asymmetrical atomic

64

migration along this direction, i.e., different diffusion rates towards two opposite orientations of

[ ] and [ ]. The lower side of the wall was proposed to be originated along the direction

with a faster Ga diffusion rate [32]. However, the heights of the wall along another direction, i.e.,

[ ], are nearly equivalent. These observations suggest that the asymmetrical atomic migration

is more pronounced in the direction with a faster atomic diffusion, i.e., [ ]. It is noticed that

although the whole nanohole structure is larger in the lateral dimension along [ ], the inner

width of the nanohole is wider along [ ] with a ratio of about 1.4 by . For

convenience, GaAs nanoholes formed with a nominal Ga coverage of 3 ML on a bare GaAs

surface are simplified as A-type nanoholes in the following.

Figure 6.2 The GaAs nanoholes on the bare

GaAs surface of sample B0 fabricated with

θGa = 5 ML by droplet epitaxy. (a) The SEM

image (30,000×) (b) The AFM 3D topography

of a typical nanohole with the height of z and the

lateral distances of x and y along [ ] and

[ ], respectively (c) The profiles of the typical

nanohole corresponding to the AFM topography.

L is the outer diameter of the nanohole. l is the

diameter of the wall. H and h are the (higher and

lower) heights of the wall along one direction.

is the inner width of the nanohole with respect to

the half maximum of h along the corresponding

direction. The red horizontal dotted line relates

to the substrate surface, and the black one to the

bottom of the hole.

Figure 6.2 shows the SEM and the AFM image of GaAs nanoholes on sample B0 which was

fabricated with a nominal Ga coverage of 5 ML. Compared with those of sample A0, these GaAs

nanoholes on the bare GaAs surface of sample B0 are also randomly distributed, but with a

65

slightly lower density of 7.0 × 107 cm

-2. This reduction of density along with an increase of Ga

coverage can be proposed as the evidence of Ostwald ripening involved in the formation of metal

droplets. In the SEM image (a), the nanoholes have an inner diameter of about 33 nm along the

crystal direction of [ ]. An asymmetric ring-like structure surrounding the inner hole is

observed with a higher brightness in the image. This ring-like structure corresponds to the wall

structure shown in the AFM image (b) which illustrates the topography of a typical GaAs

nanohole of this sample. As mentioned earlier, the lateral asymmetric structure of the wall was

caused by the difference of atomic migration between [ ] and [ ] directions. The topography

of this typical nanohole is similar to that on sample A0. However, with sample B0, the wall of the

nanohole can be viewed as an integration of two adjacent hills with different heights. The

difference of the heights is due to asymmetric atomic migration along opposite crystal directions.

These two hills are represented as the asymmetric peaks in the profile (c) according to the cross-

sections of the nanohole along [ ] and [ ]. Especially for the direction of ], the higher

hill has a higher degree of asymmetry than the lower one. The designated dimensions of the

nanohole are illustrated in the profile in the way similar to those of the A-type nanoholes on

sample A0. As a matter of convenience, GaAs nanoholes formed with a nominal Ga coverage of

5 ML on a bare GaAs surface are simplified as B-type nanoholes in the following. In Table 6.2,

the average values of the dimensions of the B-type nanoholes on sample B0 are listed with both

[ ] and [ ] directions.

θGa = 5 ML L l H h

[ ] 321 ± 19 143 ± 10 4.2 ± 0.4 2.9 ± 0.5 34 ± 8

[ ] 222 ± 7 127 ± 9 2.3 ± 0.5 2.0 ± 0.4 60 ± 11

Table 6.2 The dimensions of GaAs nanoholes on the bare GaAs surface of sample B0

along [ ] and [ ] directions in units of nanometers. The nanoholes were formed with a

nominal Ga coverage of 5 ML. L is the outer diameter of the nanohole. l is the diameter of

the wall. H (higher) and h (lower) are the heights of the wall. is the inner width of the

nanohole with respect to the half maximum of h.

Due to a larger Ga atomic migration along [ ] than along [ ], the B-type nanoholes of

sample B0 are represented with an elongated outer diameter which is similar to the A-type

nanoholes of sample A0. However, unlike the A-type nanoholes, the asymmetric heights of walls

are present not only along [ ] but also along [ ] for the B-type nanoholes. The ratio of the

heights, H to h, is about 1.4 along [ ], and 1.2 along [ ]. This reveals that the asymmetric

atomic diffusions in these two directions are both significant under the growth conditions of this

sample. The diameters of the walls along these two directions for the B-type nanoholes are larger

than those along corresponding directions for the A-type nanoholes, respectively. Since the

diameters of walls depend on the size of original droplets, the walls with broader diameters can

be suggested as the productions transformed from larger droplets generated with a higher material

supply by VW growth [113]. Compared with those of the A-type nanoholes along corresponding

66

directions, the wall heights, H and h, of the B-type nanoholes generated with a higher Ga

coverage are more than twice higher, respectively. It has been found that a larger droplet

consisting of a longer interface area (the skirt of a droplet) can result in a stronger crystallization

leading to an increase of wall heights [32]. These results concerning the dimensions are all

consistent with the relation that larger droplets lead to broader nanoholes together with higher and

wider walls. However, the ratio of two heights along [ ], , decreased from 2 to 1.4,

as the Ga coverage increased from 3 ML to 5 ML. In other words, these two hills of the walls

both become higher with an increase of Ga coverage, but the contrast between them becomes

smaller. Compared with the A-type nanoholes, the B-type nanoholes have a larger outer diameter

along [ ], but a slightly shorter outer diameter along [ ], resulting in a higher ratio of 1.4 by

. In these growth conditions, the outer diameters of the nanoholes are determined by

the atomic diffusion along with a downhill material transportation. Therefore, it can be assumed

that the paths for the material to reach the surface are longer in the case of larger and higher

droplets generated by a higher Ga coverage. With the direction of [ ] displaying a slower

diffusion rate, the material supply for growing the outer diameters of nanoholes might thus be

less sufficient, resulting in the smaller outer diameters. Finally, compared with those of the

A-type nanoholes, the widths of the B-type nanoholes are generally wider together with a larger

ratio of .

Concluding this section, self-assembled/self-patterned GaAs nanoholes were successfully

fabricated under the conditions of low As pressure and high substrate temperature by droplet

epitaxy. These nanoholes are constructed by the asymmetric walls surrounding the inner holes

with the bottoms slightly below the sample surface due to thermal etching. These kinds of

structures are generally referred to as ring-like structures or holed nanostructures represented as

valleys [33]. The asymmetry structures result from the different atomic diffusion rates along the

different crystal directions of the substrate. Due to a fast crystal growth at the edge of droplets

and a downhill material transport, higher and broader walls can be transformed from larger Ga

droplets which are formed with a higher Ga coverage [42]. According to the experimental results,

Figure 6.3 shows two similar proportional relations between the wall heights, , and the wall

diameter, , along [ ] for the A-type and the B-type nanoholes formed with nominal Ga

coverages of 3 ML or 5 ML, respectively. These nanoholes are composed of high densities of

monolayer steps (high-index surface) which can be the preferential nucleation sites for the

overgrowth of QDs. Compared to the A-type nanoholes, the B-type nanoholes with a larger

valley which is wider along the crystal direction of [ ] have a broader field of preferential

nucleation sites. With ideal surface-patterned templates for site-selective growth, the densities of

overgrown QDs should be consistent with those of patterned nanoholes. Here, the densities of

these two types of self-patterned nanoholes are both less than one nanohole per µm2. This value is

suitable for the study of single nanostructure spectroscopy which is useful to realize the

properties of individual quantum dots for single QD devices.

67

Figure 6.3 The plot with the higher

heights of the walls H as a function of

the diameters of the walls l along for the GaAs nanoholes on the bare

GaAs surfaces of sample A0 and B0

fabricated with nominal Ga coverages

of 3 ML and 5 ML, respectively.

6.2 Arrayed Nanoholes

In the previous section, the GaAs nanoholes formed on the bare GaAs surface of sample A0

and B0 by droplet epitaxy have been represented with a random distribution. At the same time,

the GaAs nanoholes were also formed on the FIB-patterned areas of these two samples. These

FIB-patterned areas were created by an In+ or Ga

+ ion beam with an ion energy of 30 keV. Each

FIB-patterned area was composed of square arrays of FIB spots within an area of 60 × 60 µm2.

For different FIB-patterned areas, the ion fluence of the FIB spots, Φion where ion denotes In or

Ga, was varied from 3 × 104 ions/spot to 1 × 10

7 ions/spot, while the spacing between the FIB

spots (the pitch), lspot, was designed as 0.5 µm, 1 µm or 2 µm. The details about FIB parameters

and pattern designs can be found in subsection 4.3.3.

For sample B0, the Ga+ ion beam was employed for pre-patterning before the formation of

GaAs nanoholes by droplet epitaxy. Figure 6.4 and Figure 6.5 show the SEM images of self-

assembled GaAs nanoholes formed on the FIB-patterned areas composed of square arrays of FIB

spots with different spot spacings (only a part of each FIB-patterned area is shown). The Ga+ ion

fluences ΦGa are varied from 3 × 104 ions/spot to 3 × 10

6 ions/spot for different FIB-patterned

areas. As shown in Figure 6.4 with a spot spacing of 2 µm, the GaAs nanoholes are not arranged

by the FIB spots and represent a random distribution on the surface with the lowest Ga+ ion

fluence of 3 × 104 ions/spot (a). With Ga

+ ion fluences above 1 × 10

5 ions/spot, the GaAs

nanoholes were formed preferentially and well-organized by the square arrays of FIB spots.

These results reveal the limit of Ga+ ion fluence for ordering the GaAs nanoholes with a

minimum of 1 × 105 ions/spot at these conditions. With the Ga

+ ion fluence of 1 × 10

5 ions/spot

(b), each FIB spot is occupied by one GaAs nanohole, i.e., a single nanohole. For the higher Ga+

ion fluences of 3 × 105 ions/spot (c) and 1 × 10

6 ions/spot (d), there are one or two GaAs

nanoholes present in one FIB spot, i.e., single or double nanoholes. With an even higher Ga+ ion

68

fluence of 3 × 106 ions/spot (e), triple nanoholes are observed. In other words, the amount of

GaAs nanoholes can be increased to exceed the number of the FIB spots, as long as the ion

fluence is sufficiently high. However, with the highest Ga+ ion fluence of 3 × 10

6 ions/spot, the

GaAs nanoholes tended to form at the edges of the FIB spots instead of the center.

Figure 6.4 The FIB-patterned areas of

sample B0 with the spot spacing of

2 µm and different Ga+ ion fluences of

(a) 3 × 104 ions/spot,

(b) 1 × 105 ions/spot,

(c) 3 × 105 ions/spot,

(d) 1 × 106 ions/spot, and

(e) 3 × 106 ions/spot.

69

Figure 6.5 The FIB-patterned areas of sample B0 with different Ga+ ion fluences ΦGa

and spot spacings lspot. (a) lspot = 0.5 µm and ΦGa = 3 × 105 ions/spot, (b) lspot = 1 µm and

ΦGa = 1 × 105 ions/spot, (c) lspot = 1 µm and ΦGa = 3 × 10

5 ions/spot, and (d) lspot = 1 µm

and ΦGa = 1 × 106 ions/spot.

With smaller spot spacings of 0.5 µm and 1 µm, the preferential formation of self-assembled

GaAs nanoholes on the FIB spots occurred as well, as shown in Figure 6.5. However, not all the

FIB spots lead to the formation of GaAs nanoholes. For the FIB spots occupied with GaAs

nanoholes, the nanoholes are present in a single or double form on each FIB spot. Similar to the

results observed from the FIB-patterned areas with the spacing of 2 µm, the increase of the GaAs

nanoholes and the displacement of the location from the center of the FIB spots are also observed

with the increasing ion fluence for the areas with the spacing of 1 µm. With the smallest spot

spacing of 0.5 µm, the GaAs nanoholes become less-ordered, although the Ga+ ion fluence is

above the limit value of 3 × 105 ions/spot. This random-like distribution of GaAs nanoholes

indicates that the spot spacing of 0.5 µm is too close for performing a good alignment of the

nanoholes at this condition. Therefore, controlling the spacing between the FIB spots is one of the

70

key aspects to arrange the distribution of the nanoholes. On the other hand, the number of the

nanoholes present in each FIB spot is determined by the ion fluence in these cases.

Figure 6.6 The FIB-patterned areas of sample A0 with a spot spacing of 2 µm and different

In+ ion fluences of (a) 3 × 10

5 ions/spot, (b) 1 × 10

6 ions/spot, (c) 3 × 10

6 ions/spot, and

(d) 1 × 107 ions/spot.

The In+ ion beam was employed for pre-patterning sample A0 before the formation of GaAs

nanoholes. The In+ ion fluences ΦIn were applied in a higher range from 3 × 10

5 ions/spot to

1 × 107 ions/spot compared to those of the Ga

+ ion fluences used for sample B0. Figure 6.6 and

Figure 6.7 show the GaAs nanoholes preferentially formed on the square-arrayed FIB spots with

spot spacings of 1 µm and 2 µm, respectively (only a part of each FIB-patterned area is shown).

For the spot spacing of 2 µm with an In+ ion fluence of 3 × 10

5 ions/spot, most of the GaAs

nanoholes were preferentially formed on the FIB spots in an ordered manner, as shown in

Figure 6.6 (a). Each FIB spot is occupied with either single or double GaAs nanoholes. For

higher In+ ion fluences of 1 × 10

6 ions/spot (b) and 3 × 10

6 ions/spot (c), the probability of double

71

GaAs nanoholes becomes higher. Furthermore, with the In+ ion fluence of 3 × 10

6 ions/spot, there

are triple or even quadruple nanoholes present in one FIB spot. However, as the ion fluence

increased, the location of the GaAs nanoholes shifted from the center towards the edges of the

FIB spots. These observations are similar to the results of sample B0 patterned by the Ga+ ion

beam. Finally, with the highest In+ ion fluence of 1 × 10

7 ions/spot (d), multiple GaAs nanoholes

are located not only at the edges of FIB spots but also at the positions further away from the spots.

However, because the spot spacing of 2 µm is larger than the displacement, the arrangement of

the GaAs nanoholes is still distinguishable, which is dependent on the FIB pattern.

Figure 6.7 The FIB-patterned areas of sample A0 with a spot spacing of 1 µm and different

In+ ion fluences of (a) 3 × 10

5 ions/spot, (b) 1 × 10

6 ions/spot, (c) 3 × 10

6 ions/spot, and

(d) 1 × 107 ions/spot.

With the spot spacing of 1µm and the In+ ion fluence of 3 × 10

5 ions/spot, the nucleation of

GaAs nanoholes was well located on the FIB spots, as shown in Figure 6.7 (a). Similar to the

results of Ga+ ion patterning with corresponding parameters on sample B0, not every FIB spot

72

exhibits the formation of GaAs nanoholes. With the higher In+ ion fluences of 1 × 10

6 ions/spot

(b) and 3 × 106 ions/spot (c), single or double GaAs nanoholes are present on each occupied FIB

spot. Even though there are still empty FIB spots, the probability of double GaAs nanoholes

increases with the increasing ion fluence. The displacement of the nucleation location relative to

the center of the FIB spots is also observed with high ion fluences. For the highest In+ ion fluence

of 1 × 107 ions/spot (d), the amount of the occupied FIB spots decreases significantly, although

the amount of the GaAs nanoholes increases. In other words, the preferential formation of the

GaAs nanoholes at the FIB spots is no longer favored. Furthermore, the location of the GaAs

nanoholes occurred at the edges and also between the FIB spots, resulting in a random

distribution. This result reveals the limit of In+ ion patterning for positioning self-assembled

GaAs nanoholes at the ion fluence around 3 × 106 ions/spot and the spot spacing of 1 µm.

As described in subsection 4.3.2, a focused ion beam is typically composed of a core and a

long-range tail. The ion current intensity of the ion beam is much smaller at the tail than that at

the center with at least two orders of magnitude lower than the peak intensity [146, 158, 159].

The range of the tail can vary in a range of a few µm [160]. Thus, for the FIB writing process of

spot arrays with a high ion current density, the exposed areas are in a much wider region beyond

the size of the FIB spots. Therefore, an unintentional exposure is created with the ion

concentration decreasing with the distance from the center of the FIB spots [171]. From the

experimental results above, it can be deduced that the Ga adatoms were drawn to the FIB spots

and then preferentially nucleated at the sites containing sufficient surface chemical potential

gradients induced by FIB sputtering and a certain ion concentration C0. In the cases of this work,

either by Ga+ or In

+ beams, single GaAs nanoholes were formed at the center of the FIB spots

with the ion fluences of 1 × 105

ions/spot and 3 × 105 ions/spot. This suggests that the surface

chemical potential gradients were only sufficient at the center along with the ion concentration of

C0 with these cases. When the ion fluence further increased, the preferential nucleation became

unfavorable at the center of the FIB spots, but took place at the position away from the center

where the ion concentration was much lower due to the exposure from the beam tail. Because the

ion current density decreases monotonically with the distance from the beam center, ion beams

with higher ion current densities can create broader circular regions featured with C0, providing

more preferential nucleation sites for the overgrown Ga droplets by droplet epitaxy. Multiple

GaAs nanoholes crystalized from the droplets were therefore generated together with the

displacement from the center of FIB spots.

However, the arrangement of the GaAs nanoholes can become disordered if the ion fluence

is too high. Also, the ion fluence can be integrated if the spot spacing is as small as the range of

the beam tail, resulting in an undesired high ion concentration between the spots. As a result, FIB

pre-patterning can loose the function of positioning self-assembled GaAs nanoholes. In order to

achieve the alignment of the GaAs nanoholes with a high accuracy, it is necessary to maintain a

regular ion concentration profile on the substrate surface by controlling ion fluence and spot

spacing. Furthermore, with an ion fluence above 1 × 106 ions/spot, a strong sputtering process

can lead to damages of the substrate, resulting in sputtered holes with the depth in the order of

73

nanometers as shown in subsection 4.3.3. These sputtered holes remaining on the surface may

affect the crystal qualities, resulting in the reduction of the optical properties. Therefore, the

selection with a low but sufficient ion fluence is required to produce arrayed nanohole templates

for overgrown site-selected quantum structures, e.g., QDs, and to ensure the optical or electrical

performance of the quantum systems as well. In this work, the optimum parameters of FIB

patterning are found to be an ion fluence of 3 × 105 ions/spot and a spot spacing of 2 µm for the

positioning of GaAs nanoholes formed by droplet epitaxy. Comparing In+ and Ga

+ ion patterning

regarding to the distribution of GaAs nanoholes of sample A0 and B0, similar results are found

with the corresponding FIB parameters of ion fluences from 3 × 105 ions/spot to 3 × 10

6 ions/spot

and spot spacings of 1 µm and 2 µm. Therefore, it can be concluded that In+ and Ga

+ ion beams

have the comparable abilities for controlling the sites of self-assembled GaAs nanoholes under

these conditions.

From the above results, the number of GaAs nanoholes in each FIB spot depends on the ion

fluence ranging from 1 × 105 ions/spot to 3 × 10

7 ions/spot, resulting in single, double or multiple

nanoholes. To summarize, the probabilities1 of single, double and multiple GaAs nanoholes are

registered as rn, where n is the amount of nanoholes in one FIB spot. Therefore, r1, r2, r3··· are the

probabilities of single, double, triple… nanoholes. The sum of these nanohole probabilities is

then equal to the occupancy rate of the FIB spots, rsum = r1 + r2 + r3 +···. Figure 6.8 (a) shows rn

as a function of n and the value of rsum with different ion fluences applied on the FIB-patterned

areas of sample B0 with a spot spacing of 2 µm by Ga+ ion patterning. Increasing the Ga

+ ion

fluence from 1 × 105 ions/spot to 3 × 10

6 ions/spot, the probability of single nanoholes r1 is

dominated along with an increase of the probability of double nanoholes r2. At the same time, the

occupancy rate rsum increases from 87 % to 97 %. Similar results are also observed for the FIB-

patterned areas of sample A0 generated by In+ ion patterning with spot spacings of 2 µm and

1 µm and different ion fluences, as shown in Figure 6.8 (b) and (c). With the spacing of 1 µm,

the occupancy rate rsum increases from 59 % to 82 % with the increase of In+ ion fluence, while

with the spacing of 2 µm, it is nearly 100 % for all the range of the ion fluence except

3 × 106 ions/spot. Furthermore, with the spacing of 2 µm, when the In

+ ion fluences are high at

1 × 107 ions/spot and 3 × 10

7 ions/spot, the probabilities of double and triple nanoholes, r2 and r3,

become dominant in sequence. With corresponding FIB patterning parameters, the occupancy

rate rsum for sample A0 with In+ ion patterning is found higher than that for sample B0 with Ga

+

ion patterning. Therefore, In+ ion patterning can be considered more reliable than Ga

+ ion

patterning in terms of representing a higher probability of the occurrence of GaAs nanoholes in

these conditions.

1 The probability is calculated by the amount of the FIB spots occupied by single, double or multiple GaAs

nanoholes divided by the total amount of the patterned FIB spots. The calculation was done with the SEM

images showing larger fields of the FIB-patterned areas with smaller magnification than the images shown in

this thesis.

74

Figure 6.8 The probability of single, double or multiple GaAs nanoholes, r1, r2, r3··· = rn,

from different FIB-patterned areas. The sum of the probabilities equals to the occupancy

rate of FIB spots, rsum = r1 + r2 + r3 ···. (a) The FIB-patterned areas of sample B0 with a

spot spacing lspot of 2 µm and Ga+ fluences ΦGa from 1 × 10

5 ions/spot to 3 × 10

6 ions/spot.

For sample A0, (b) the FIB-patterned areas with a spot spacing of 2 µm and In+ fluences

ΦIn from 3 × 105 ions/spot to 3 × 10

7 ions/spot, and (c) with a spacing of 1 µm and In

+

fluences from 3 × 105 ions/spot to 3 × 10

6 ions/spot.

As mentioned in the previous section 6.1, the dimensions of self-patterned nanoholes formed

by droplet epitaxy depend on the sizes of the original metal droplets, which may influence the

properties of the overgrown nanostructures. With the same supply of materials, i.e., the amount of

nominal Ga coverage, larger Ga droplets are generated with a lower density following Ostwald

ripening, leading to larger GaAs nanoholes. In order to estimate the relative dimensions of the Ga

droplets and the GaAs nanoholes formed on different FIB-patterned areas, the nominal densities2

of GaAs nanoholes, ρFIB, are plotted as a function of ion fluence with different spot spacings in

2 The nominal density is calculated from the SEM images showing larger fields of the FIB-patterned areas with

smaller magnification than the images shown in this thesis.

75

Figure 6.9. The nominal density is defined by the amount of GaAs nanoholes per unit area (cm-2

).

The intrinsic density is the density of the GaAs nanoholes randomly formed on the bare GaAs

surface of the sample, i.e., the A-type and B-type nanoholes, as introduced in section 6.1. For

sample B0 with a nominal Ga coverage of 5 ML, the nominal densities with spacings of 1 µm and

2 µm are all below the intrinsic density of 7.0 × 107 cm

-2 in the full range of Ga

+ ion fluence, as

shown in (a). In general, the nominal densities increase with increasing ion fluence from

1 × 105 ions/spot to 3 × 10

6 ions/spot. However, a relatively high nominal density is observed

with the lowest ion fluence of 3 × 104 ions/spot together with the spacing of 2 µm. Furthermore,

with the smallest spacing of 0.5 µm together with the Ga+ ion fluence of 3 × 10

5 ions/spot, the

nominal density can be even higher than the intrinsic density. In the earlier discussion, it has been

found that the number of the GaAs nanoholes in each FIB spot can be increased by increasing the

ion fluence in the range from 1 × 105 ions/spot to 3 × 10

7 ions/spot. Here, it shows that reducing

the ion fluence to a certain value or decreasing the spacing with sufficient ion fluence can

increase the nominal density close to or even above the intrinsic density of the nanoholes.

A similar increase is also found for sample A0 using In+ ion patterning with a higher range

of ion fluence, as shown in Figure 6.9 (b). For sample A0 with a nominal Ga coverage of 3 ML,

the intrinsic density of the GaAs nanoholes on the bare GaAs surface is 8.0 × 107 cm

-2. It is

observed that even with the higher ion fluence range, the nominal densities are still lower than the

intrinsic density with a spacing of 2 µm. However, with a spacing of 1 µm, the nominal density

can be increased above the intrinsic density by using high ion fluences. This increase observed

with the spacing of 1 µm is consistent with the increase of the occupied FIB spots (rsum) together

with the increase of double nanoholes (r2). On the other hand, with the spacing of 2 µm, the

increase of the nominal densities is contributed from the rise of the double and multiple

nanoholes (r2, r3...) since all the FIB spots were occupied (rsum ~ 100 %). These various nominal

densities suggest that the GaAs nanoholes transformed from Ga droplets formed on different FIB-

patterned areas may have different dimensions depending on different patterning parameters.

Figure 6.9 The nominal densities ρFIB of GaAs nanoholes as a function of ion fluences, ΦGa

or ΦIn, with different spot spacings lspot for (a) sample B0 and (b) sample A0 with Ga+ and

In+

ion pattering, respectively.

76

Figure 6.10 AFM images and the corresponding profiles of the GaAs nanoholes

formed with (a) θGa = 3 ML and (b) θGa = 5 ML on the FIB spots with lspot = 2 µm

created with ΦIn = 3 × 105 ions/spot and ΦGa = 3 × 10

5 ions/spot on sample A0 and

sample B0, respectively.

θGa /ion species D

3 ML/ In+ (A0) 268 ± 18 157 ± 7 5.6 ± 1.1 2.8 ± 0.6 72 ± 10 2.5 ± 0.1

5 ML/ Ga+ (B0) 341 ± 10 185 ± 4 7.6 ± 0.3 5.7 ± 0.5 89 ± 6 10.4 ± 0.7

3 ML/ In+ (A0) 243 ± 8 141 ± 4 3.0 ± 1.0 1.1 ± 0.7 92 ± 9

5 ML/ Ga+ (B0) 269 ± 4 175 ± 7 3.1 ± 0.6 2.3 ± 0.4 117 ± 8

Table 6.3 The dimensions of the GaAs nanoholes on the FIB-patterned areas of sample A0

and B0 along [ ] and [ ], in units of nanometers. The nanoholes were formed with a

nominal Ga coverage θGa of 3 ML or 5 ML by droplet epitaxy. The FIB-patterned areas were

created with Φion = 3 × 105 ions/spot and lspot = 2 µm by In

+ or Ga

+ beams. L is the outer

diameter of the nanohole. l is the diameter of the wall. H (higher) and h (lower) are the heights

of the wall. w is the width of the nanohole. D is the depth of the nanohole against the substrate

surface.

77

Figure 6.10 shows the topography of the typical GaAs nanoholes formed on the FIB-

patterned areas generated with the optimum parameters, an ion fluence of 3 × 105 ions/spot and

a spacing of 2 µm, by In+ and Ga

+ ion patterning for sample A0 (a) and sample B0 (b),

respectively. The structures of these nanoholes are composed of a high wall above the substrate

surface and a deep hole below the surface. The dimensions of these nanoholes along [ ] and

[ ] directions are listed in Table 6.3. L is the outer diameter of the whole nanohole structure.

l is the diameter of the wall surrounding the inner hole, measured at the tops. The heights of the

wall are indicated as H and h for the higher and lower ones, respectively. The width w and the

depth D of the inner hole are measured with respect to the substrate surface. For convenience,

GaAs nanoholes formed with nominal Ga coverages of 3 ML and 5 ML on FIB-patterned areas

are named as A’-type and B’-type nanoholes, respectively. Similar to those of the A-type

nanoholes on sample A0 and the B-type nanoholes on sample B0, the asymmetric wall structures

of these nanoholes are due to the different atomic diffusion rates depending on the crystal

directions. However, compared to the A-type and B-type nanoholes, these A’-type and B’-type

nanoholes have larger diameters, higher walls, and greater depths.

Due to the local surface modification on the FIB-patterned area, the accumulation of Ga

adatoms was enhanced at the FIB spots, leading to the formation of Ga droplets by VW growth. It

can thus be presumed that the droplets formed on the FIB-patterned area were larger than those

on the bare GaAs surface. Moreover, the nominal densities of the nanoholes on the FIB-patterned

areas with the optimum patterning parameters are lower than the intrinsic densities for sample A0

and sample B0, respectively. With the same amount of materials, larger Ga droplets on the FIB-

patterned area are therefore confirmed with respect to those on the bare GaAs surface. Under the

growth conditions with low As pressure and high substrate temperature in this work, the

formation of nanoholes was due to preferential crystallization at the edge of droplets along with

downhill material transportation from the droplets and thermal etching toward the substrate under

the droplets [32]. Therefore, the dimensions of the nanoholes depend on the sizes of the droplets.

In other words, with larger Ga droplets accumulated on the FIB-patterned areas, larger and deeper

GaAs nanoholes can be generated. The significant depths under the substrate surface of these

A’-type and B’-type nanoholes reveals the evidence of strong thermal etching processes on the

FIB-patterned areas. Since the nominal densities are almost the same for the A’-type and B’-type

nanoholes with optimum patterning parameters, larger depths would be expected for the

nanoholes crystallized from larger droplets formed with a higher Ga coverage. This is found

consistent with the observed result in the AFM images that the B’-type nanohole is deeper than

the A’-type nanohole.

To conclude, arrayed GaAs nanoholes are successfully produced with their locations

depending on the designed patterns generated by a FIB technique via a site-selective growth by

droplet epitaxy. The distribution of the GaAs nanoholes on the FIB-patterned areas depends on

the ion fluence and the spacing between FIB spots. The optimum FIB parameters are found to be

an ion fluence of 3 × 105 ions/spot and a spot spacing of 2 µm, leading to the achievement of

78

nearly 100 % probability with GaAs nanoholes formed on the FIB spots. Both In+ and Ga

+ ion

beams are capable of positioning GaAs nanoholes, while the In+ ion beam has represented a

better performance in the conditions of this work. The Ga droplets formed on the optimum FIB-

patterned area are suggested to be larger than those on the bare GaAs surface, which leads to

GaAs nanoholes with larger dimensions, especially the depths. These arrayed GaAs nanoholes

containing great surface chemical potential gradients are promising for providing preferential

nucleation sites for site-selected QDs with a distribution corresponding to the arrangement of the

nanoholes. This approach aided by the flexibility of droplet epitaxy and the abilities of FIB

writing provides designable features to position arrays of nanoholes in an efficient way, which

can be useful for both research and industry.

79

Chapter 7 Characterizations of Site-selected InAs

Quantum Dots in GaAs Nanoholes

The implementation of single QD based devices for quantum information relies on the technique

with site-control. In the previous chapter, two types of GaAs nanoholes formed by droplet epitaxy

have been successfully demonstrated. Randomly-distributed GaAs nanoholes were formed on the

bare GaAs surface with a low density, while arrayed GaAs nanoholes were realized with the help

of FIB pre-patterning. These GaAs nanoholes can be used as templates providing preferential

nucleation sites for subsequent InAs deposition, leading to a site-selective growth for QDs

following SK growth by MBE. The QDs grown site-selectively on both types of GaAs nanoholes

reproduce the spatial distribution of the GaAs nanoholes, representing either a random

distribution along with a low density, or an intentional arrangement on the substrate. In this

chapter, the experimental results of the topography characteristics and the optical properties of

these two types of site-selected InAs quantum dots grown in the GaAs nanoholes are shown and

discussed.

7.1 Topography

The site-selected QDs were overgrown with various amounts of InAs coverage ranging from

1.40 ML to 1.75 ML on both types of GaAs nanoholes. The topography and the distribution of

these InAs QDs were investigated by AFM and SEM. In the first part of this section, the focus is

laid on the site-selected QDs grown with randomly-distributed GaAs nanoholes on a bare GaAs

surface. In the second part, the arrangement of the site-selected QDs grown in FIB-positioned

GaAs nanoholes on the FIB-patterned areas is addressed. Furthermore, a comparison between

QDs grown in these two types of nanoholes with corresponding InAs coverages is also introduced.

7.1.1 Quantum dots in randomly-distributed nanoholes

For strain-induced InAs QDs, the formation is strongly dependent on the critical thickness of

InAs on GaAs for a 2D-3D transition. In order to investigate the growth evolution of the InAs

QDs on the nanohole-patterned GaAs surface, the amounts of InAs coverage θInAs were varied

from 1.40 ML to 1.58 ML and 1.75 ML for sample B40, B58 and B75, respectively. The details

of the sample fabrication are described in section 5.1. For each sample, the GaAs surface was

patterned with GaAs nanoholes by droplet epitaxy with a nominal Ga coverage of 5 ML without

80

FIB pre-patterning, i.e., B-type nanoholes. Typical 3D nanostructures grown with different

amounts of InAs coverage are shown in Figure 7.1 and Figure 7.2 for these three samples. From

the AFM image of sample B40 with the lowest InAs coverage of 1.40 ML, there was no 3D

structure emerging from the nanoholes as shown in Figure 7.1 (a). The original GaAs nanoholes

(before overgrown by InAs) correspond to the B-type nanoholes of sample B0 without InAs

deposition as shown in Figure 6.2. Comparing the topography profiles from sample B0 and B40,

it can be observed that the hole of sample B40 is more flat, especially along [ ] direction with

a height of less than 1 nm. This observation suggests that the GaAs nanoholes were filled by the

deposited InAs material resulting in InAs nanostructures with their shapes depending on the

GaAs nanoholes. According to the comparison, the configuration of the InAs nanostructures can

be estimated with a lateral diameter of about 60 nm and a height of less than 2 nm.

For sample B58 with the InAs coverage of 1.58 ML, there are two types of quantum dots

observed in GaAs nanoholes as shown in the AFM images of Figure 7.1 (b1) and (b2). In the

image (b1), two quantum dots are adjacent to each other in one GaAs nanohole, resulting in a QD

pair. They are aligned along [ ] which is the direction with the greater widths of B-type

nanoholes as described in section 6.1. Among these two dots, the higher one with the height hD

of (8.2 ± 0.1) nm, has larger base diameters dD of (71 ± 2) nm and (49 ± 4) nm along [ ] and

[ ], respectively. For the smaller one with the height of (6.9 ± 1.0) nm, the base diameters are

smaller with (57 ± 1) nm and (40 ± 1) nm along [ ] and [ ], respectively. In the image (b2),

a single QD is observed in the GaAs nanohole having the height of (9.5 ± 0.2) nm and the base

diameters of (69 ± 1) nm and (74 ± 1) nm along [ ] and [ ], respectively. The formation of

single QDs in nanoholes is dominated by a probability about 6 times higher than that of QD pairs

in this case. In general, the sizes of QD pairs are smaller than those of single QDs of this sample.

In addition, the lateral structural asymmetry of QD pairs is found more pronounced than that of

single QDs by comparing their base diameters along [ ] and [ ] directions.

For sample B75 with an InAs coverage of 1.75 ML, large single dots (islands) formed in

GaAs nanoholes are observed by AFM as shown in Figure 7.2. From the AFM measurement, the

height of the island is shown with (10.4 ± 0.1) nm, and the base diameters are represented with

(111 ± 3) nm and (108 ± 10) nm along [ ] and [ ], respectively. However, the shape of the

islands shown in the image is distorted due to the effects from the AFM-tip. Therefore, the real

lateral diameters of the islands should be only smaller than the measured values. Nevertheless,

compared with the overview SEM image, these islands have similar sizes and shapes. Moreover,

the formation of the islands is inside the GaAs nanoholes, but not in between them. The density

of islands is about 7.0 × 107 cm

-2 which corresponds to the density of the B-type nanoholes on

sample B0 without InAs deposition. In other words, the site-control of the strain-induced QDs

was successfully obtained along with the fact that the QD distribution was consistent with that of

the self-patterned GaAs nanoholes.

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Figure 7.1 AFM images and profiles of different nanostructures grown with different

amounts of InAs coverage of 1.40 ML and 1.58 ML on the bare GaAs surfaces (without

FIB pre-patterning) of sample B40 (a) and sample B58 (b1and b2, selected from the same

image), respectively.

82

Figure 7.2 AFM images for sample B75 and

profiles for the InAs island generated in the

GaAs nanoholes with an InAs coverage of

1.75 ML. The GaAs nanoholes were formed

with a nominal Ga coverage of 5 ML on the

bare GaAs (100) surface by droplet epitaxy

without FIB pre-patterning.

For comparison, Figure 7.3 shows the AFM image of InAs quantum dots grown in the self-

patterned GaAs nanoholes generated with a nominal Ga coverage of 3 ML on the bare GaAs

surface of sample A75, i.e., A-type nanoholes. The QDs were grown with an InAs coverage of

1.75 ML which is the same for sample B75 with B-type nanoholes. However, unlike sample B75,

the absence of quantum dots is observed in some of the A-type nanoholes in this sample.

Furthermore, the dots were formed with different sizes, especially the heights. The profiles (1) to

(3) are shown as examples, which correspond to the three nanostructures labeled in the AFM

image. For the first one (1), there is no 3D island formed inside the GaAs nanohole. The second

structure (2) is composed of a dot with a height of (3.7 ± 0.5) nm, and the dot base diameters of

(65 ± 2) nm and (57 ± 3) nm along [ ] and [ ], respectively. For the last one (3), the dot

height is (8.6 ± 0.3) nm, and the dot base diameters are (73 ± 1) nm and (71 ± 3) nm along [ ]

and [ ], respectively. The same influence of the tip geometry on the AFM image which is

visible in Figure 7.2 also applies for Figure 7.3, leading to the distortion of high dots. Therefore,

the real lateral sizes of the dot (3) should be smaller than the measured values described above.

An SEM image of this sample is also shown for comparison. The difference of the dot heights

suggests that InAs was not homogeneously deposited on the template composed of A-type

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nanoholes. As described in section 6.1, the A-type nanoholes represented shorter walls compared

with the B-type nanoholes. According to the mechanisms for the site-selective growth of InAs

QDs shown in section 4.1, shorter sidewalls may lead to less surface chemical potential gradients

at the holes resulting in less driving force for the preferential accumulation of InAs. The

templates composed of the B-type nanoholes which have higher walls and are all filled by QDs

have shown a better performance to realize the site-selective growth of strain-induced QDs with a

high uniformity of the dot sizes. Therefore, the nanohole templates fabricated with a nominal Ga

coverage of 5 ML are found to be more reliable to monitor the distribution of single QDs or QD

pairs for the studies of single QD spectroscopy.

Figure 7.3 AFM and SEM images of sample A75 from the bare GaAs surface without

FIB pre-patterning, and profiles (1) to (3) for the nanostructures labeled in the AFM image

with 1, 2 and 3. The sample was fabricated with a nominal Ga coverage of 3 ML for the

formation of nanoholes by droplet epitaxy and an InAs coverage of 1.75 ML for the

overgrown of QDs by SK growth.

To conclude this subsection, the site-selected InAs QDs were successfully realized by

using the self-patterned GaAs nanoholes as templates generated by droplet epitaxy, representing

variable sizes and a low density in the order of 107 cm

-2. The sizes of the QDs depend on the InAs

coverages inside the nanoholes where the deposited InAs were preferentially accumulated, while

84

the density of the QDs depends on the distribution of the GaAs nanoholes in terms of B-type

nanoholes. For a conventional growth of strain-induced InAs QDs on a planar (100) GaAs

surface, the standard InAs coverage is about 2.1 ML by the same growth system of this work. In

the cases of using nanohole templates, the adatoms contribute to the total coverage of selective

nucleation by surface migration due to large lateral diffusivity on the nanohole-patterned surface

[125]. Therefore, although the supplies of the InAs coverage were less than the standard value in

the cases of this work, the critical thickness for the 2D-3D transition could still be achieved inside

the GaAs nanoholes by surface diffusion. At the beginning, the deposited InAs preferentially

nucleated at the bottoms of the GaAs nanoholes. Meanwhile, though the InAs thicknesses in the

nanoholes were insufficient for the 2D-3D transition, the InAs crystals filling inside the

nanoholes could be considered as individual nanostructures with their shape affected by the

dimensions of the nanoholes. When the critical thicknesses were achieved inside the GaAs

nanoholes while that on the GaAs plane in between the nanoholes was not, quantum dots or

quantum dot pairs with slightly different sizes were formed to release the strain. With a further

increase of the thicknesses inside the nanoholes, single large islands were formed. Following the

QD growth evolution of this work, the formation of the single large islands might be the result of

the coarsening of small dots and/or the coalescence of dot pairs. However, it is known that an

excess amount of deposited materials can lead to dislocated islands [8, 103]. Nevertheless, with

the amounts of InAs deposited for this work ranging from 1.40 ML to 1.75 ML, there is no

additional QD formed outside the GaAs nanoholes, resulting in a good control of the site-

selective growth. Compared with the conventional InAs QDs which generally have a height of

about 8 nm and a base diameter of about 40 nm characterized by AFM, the site-selected QDs

grown with 1.58 ML of InAs exhibit comparable or slightly larger dimensions, while the site-

selected QDs grown with 1.75 ML of InAs comprise larger dimensions. Because of the size-

dependent energy band gap for QDs, it is interesting to investigate the optical properties of these

QDs with various sizes.

7.1.2 Quantum dots in arrayed nanoholes

As shown in the previous subsection, site-selected QDs were successfully grown in the

randomly-distributed GaAs nanoholes on the bare GaAs surface outside FIB-patterned areas, i.e.,

B-type nanoholes with a nominal Ga coverage of 5 ML. The growth evolution of the site-selected

QDs was followed by filling InAs in the GaAs nanoholes, forming small dots and dot pairs, and

growing large single islands with increasing InAs coverages as those with sample B40, B58 and

B75, respectively. At the same time, the preferential growth of InAs also occurred in the arrayed

GaAs nanoholes, i.e., B’-type nanoholes with a nominal Ga coverage of 5 ML on the FIB-

patterned areas. As discussed in section 6.2, controlling FIB ion fluence and the spacing between

FIB spots can manipulate the distribution of B’-type nanoholes, which in turn determines the

location of the overgrown QDs in these nanoholes. The site-control of strain-induced QDs at

85

intentional positions is therefore realized. Figure 7.4 shows large single islands grown in the

arrayed B’-type nanoholes of sample B75. The arrayed GaAs nanoholes were well-organized

along the FIB spots which were created by In+ ion patterning with different patterning parameters.

Compared with those islands grown in the B-type nanoholes on the bare GaAs surface of sample

B75, these islands have a similar shape but a slightly larger size.

Figure 7.4 SEM images for different FIB-patterned areas on sample B75 with site-selected

InAs QDs grown with an InAs coverage of 1.75 ML in FIB-positioned GaAs nanoholes

formed with a nominal Ga coverage of 5 ML. (a) The area with an In+ ion fluence ΦIn of

1 × 105 ions/spot and a spot spacing lspot of 1 µm, (b) ΦIn = 1 × 10

5 ions/spot and lspot = 2 µm,

(c) ΦIn = 3 × 105 ions/spot and lspot = 1 µm, and (d) ΦIn = 3 × 10

5 ions/spot and lspot = 2 µm.

QD pairs of sample B58 grown in the arrayed B’-type nanoholes with a Ga+ ion fluence of

3×105 ions/spot and spacings of 1 µm and 2 µm are shown in Figure 7.5 (a) and (b), respectively.

Considering the probability of GaAs nanoholes positioned by the FIB spots using corresponding

FIB parameters, In+ ion patterning applied for sample B75 has displayed a better ability than

Ga+ ion patterning operated for this sample. This result is consistent with the observation shown

86

in previous section 6.2. Comparing these arrayed QDs with those QDs grown in the randomly-

distributed B-type nanoholes, the structural configurations are close to each other for the case of

either single dots or dot pairs. Interestingly, it is found that the probability of QD pairs is higher

on the FIB-patterned areas than that on the bare GaAs surface of this sample. The probability

ratio by QD pairs to single QDs is about 1:6 with the B-type nanoholes on the bare GaAs surface,

while it is higher than 8:1 with the B’-type nanoholes. As discussed in section 6.2, the B’-type

nanoholes formed on the optimum FIB-patterned areas have larger lateral dimensions and deeper

depths than B-type nanoholes because of the preferential accumulation of Ga droplets at the FIB

spots. The nanoholes with large lateral dimensions can provide more preferential nucleation sites

for the deposited InAs. On the other hand, the great depths suggest large surface chemical

potential gradients which can enhance the accumulation of the deposited InAs in the nanoholes

[125]. Due to sufficient material amounts and enough space inside the B’-type nanoholes, the

formation of dot pairs was preferred over that of single dots with the InAs coverage of 1.58 ML.

However, as discussed in the last subsection with a higher InAs coverage of 1.75 ML, the InAs

coverage was already beyond the amount to generate small QDs or QD pairs. Therefore, only

large single islands (no island pairs) were formed in either the B-type nanoholes or the B’-type

nanoholes of sample B75.

Figure 7.5 (c) and (d) show the topography of QD pairs grown inside the B’-type nanoholes

on two different FIB-patterned areas of sample B58 with the Ga+ ion fluences of 1 × 10

5 ions/spot

and 3 × 105 ions/spot, respectively. From these two FIB-patterned areas, the sizes of the QD pairs

are in the same range. The plot shows an example profile of the QD pairs measured along the

[ ] and [ ] directions from image (c). From the profile of the QD pair, two dots have

different heights of 4.6 nm and 4.0 nm, respectively. The dot base diameters are shown with

73 nm and 48 nm for the higher dot, and 68 nm and 57 nm for the smaller dot along [ ] and

[ ], respectively. The lateral diameters of these QD pairs are found to be comparable to or

slightly larger than those in the B-type nanoholes due to more material accumulation in these

larger B’-type nanoholes. The size of the QDs depends on the real InAs thickness deposited in the

GaAs nanoholes. Nevertheless, the original depth of the GaAs nanoholes underneath the QDs

should be taken into account for the real heights of the QDs. However, due to the self-limiting

growth in the mismatched system for coherent 3D islands, the size distribution is narrow and the

shape is uniform [22]. Therefore, coherent quantum dots with corresponding lateral dimensions

might be considered with similar configurations of the dot heights as well.

To conclude, site-selected QDs could be spatially controlled on the FIB-patterned areas with

various sizes and no additional QDs formed between the nanoholes under these conditions.

Compared to the randomly-distributed cases, a higher probability of QD pairs and larger QDs can

be generated due to more material accumulation and preferential sites at deep and large B’-type

nanoholes. Finally, the site-selected InAs QDs are not only represented in a low density but also

in a spatially designable manner. In other words, these QDs can be positioned arbitrarily with the

help of FIB writing combined with droplet epitaxy, which can be adapted for the applications

87

with specific demands in site control. With the optimized FIB pattern developed in this work,

these square arrays of QDs with a pitch of about 2 μm are suitable for the studies of single QD

spectroscopy.

Figure 7.5 SEM and AFM images for the

site-selected QD pairs grown in the FIB-

positioned GaAs nanoholes on different FIB-

patterned areas of sample B58. (a) The FIB-

patterned area with a Ga+ ion fluence ΦGa of

3 × 105 ions/spot and a spot spacing lspot of

1 µm, (b), (c) ΦGa = 3 × 105 ions/spot and

lspot = 2 µm, and (d) ΦGa = 1 × 106 ions/spot

and lspot = 2 µm. The profiles correspond to

the QD pair shown in image (c) along [ ]

and [ ] directions.

88

7.2 Optical Properties of Quantum Dots in Randomly-distributed

Nanoholes

It was shown in the previous section that the site-selective growth of the InAs QDs successfully

exploited the GaAs nanohole templates. The growth evolution of the QDs was demonstrated by

varying the InAs coverage as well. These QDs grown with different InAs coverages have shown

different dimensions and structures, which can highly influence their optical properties. This

section focuses on the optical properties of the QDs grown in randomly-distributed nanoholes.

The optical properties were investigated by photoluminescence (PL) spectroscopy and the SNOM

technique for the studies of ensembles and single QDs, respectively. In the first subsection, the

ensemble optical properties of the QDs are discussed and also compared with the conventional

strain-induced QDs grown on a planar GaAs surface. In the second subsection, the optical

properties of single QDs are addressed.

7.2.1 Quantum dot ensembles

For studying the ensemble optical properties of InAs QDs grown in GaAs nanoholes, five

QD samples, C40, C46, C58, C65 and C75, were fabricated with different amounts of InAs

coverage ranging from 1.40 ML to 1.75 ML using self-patterned GaAs nanoholes as templates

which were generated with a nominal Ga coverage of 5 ML by droplet epitaxy. For a complete

quantum confinement, these InAs QDs were covered with GaAs capping layers. This subsection

provides an investigation on the QDs grown in the randomly-distributed GaAs nanoholes, i.e., the

B-type nanoholes, which were formed without the influence of FIB pre-patterning.

The PL measurements were performed using a diode laser emitting with a wavelength of

635 nm, i.e., 1.95 eV which is well above the band gap of GaAs, and an excitation power of

5 mW. The details about the PL process for a QD system and the setup can be found in

section 5.4. Using a GaAs nanohole template, the density of the quantum dots depends on that of

the GaAs nanoholes which is about 7.0 × 107 cm

-2 for B-type nanoholes. With a spot size of the

laser of the order of 10-5

cm-2

on the sample surface, the PL spectra were thus generated from an

ensemble of few thousands of quantum dots. Due to the size fluctuations of these QDs, an

inhomogeneous broadening would be expected in the spectra. Usually, the inhomogeneous

broadening is represented by a Gaussian distribution because the sizes of self-assembled QDs are

typically in a Gaussian distribution. For the ensembles of strain-induced InAs QDs, the

experimentally observed FWHM values were typically found between 30 meV and 60 meV

[172].

Figure 7.6 shows five PL spectra (1) to (5) for the five samples with InAs coverages of

1.40 ML, 1.46 ML, 1.58 ML, 1.65 ML and 1.75 ML, respectively. These PL spectra measured at

77 K consist of several PL peaks or bands corresponding to the electron-hole transitions in the

conduction and valence bands of different semiconductor structures. The peaks with the energy

around 1.45 eV (850 nm) correspond to the transitions in wetting layers (WL) which are the 2D

InAs layers on the GaAs surface between the GaAs nanoholes. In the case with the lowest

89

InAs coverage of 1.40 ML, the peak center at 1.366 eV (908 nm) is attributed to the crystalline

nanostructures formed by filling InAs inside the GaAs nanoholes. The FWHM of this peak is

50 meV. With a higher InAs coverage of 1.46 ML, a broad PL band with two small shoulders at

the low energy side can be observed in the PL spectrum. Meanwhile, the PL spectrum maximum

shifts to a lower energy of 1.346 eV (918 nm). According to SK growth, these two emerging low-

energy shoulders indicate the growth of new structures inside the GaAs nanoholes, i.e., the strain-

induced QDs. As the InAs coverage increase further to 1.58 ML and 1.65 ML, the PL bands

broaden significantly together with multiple low- or high- energy shoulders, and move gradually

toward lower energies. The maxima of these two PL bands are at 1.265 eV (980 nm) and 1.247

eV (994 nm), respectively. With an InAs coverage of 1.75 ML, the PL spectrum shifts further to a

lower energy with four overlapping peaks with their maxima at 1.136 eV (1092 nm), 1.172 eV

(1058 nm), 1.204 eV (1030 nm) and 1.238 eV (1002 nm).

Figure 7.6 The ensemble PL

spectra of sample C40, C46,

C58, C65 and C75 with various

amounts of InAs coverage from

1.40 ML to 1.75 ML by PL

spectroscopy at 77 K with an

excitation power of 5 mW. WL

represents the recombination

from the wetting layer.

90

In order to uncover the origin of the PL broadening and the shoulders in the PL bands

following the morphology evolution of InAs QDs in GaAs nanoholes, the excitation power-

dependence measurements were employed to resolve the PL bands of sample C46, C58 and C65

as shown in Figure 7.7, Figure 7.8 and Figure 7.9, respectively. In Figure 7.7 for sample C46

with the InAs coverage of 1.46 ML, there are two peaks observed at 1.256 eV (987 nm) and

1.346 eV (921 nm) with the lowest excitation power as shown in the insert. Among them, the

source for the higher-energy peak might be the same with that observed for sample C40, which is

the transition attributed to the InAs crystalline structures filled inside GaAs nanoholes with an

insufficient InAs thickness for 2D-3D structural transition. The FWHM of this peak from

sample C46, which is about 53 meV, is comparable with the value originated from the peak of

sample C40. However, no discrete excited state originated from this kind of structures is observed

by increasing the excitation power densities. Such behavior is more like a 2D quantum well

structure with step-like densities of states, than like a QD. As described in subsection 7.1.1, these

filled InAs nanostructures which were separated by nanoholes in a layer were suggested to

have their lateral dimensions much larger than the heights. Therefore, they can be considered

as quantum disks (QDk) which have a quasi-2D quantum nature and optical properties

corresponding to those of quantum wells [173]. Therefore, this peak can be assigned to the

transition of the quantum disks with the energy labeled as . On the other hand, the lower-

energy peak at 1.256 eV (E0) is assigned to the ground-state (s-shell) transition of the QDs with

its FWHM of 40 meV which indicates a good size uniformity of the QDs. With the excitation

power increasing, the PL peak with E1 = 1.285 eV (965 nm) appeared representing the first-

excited-state (p-shell) transition of the QDs which has an energy separation of about 29 meV

from the ground-state peak. These two groups of peaks coexisting in the PL spectra of C46 reveal

that the critical InAs coverage for the 2D-3D structural transition is about 1.46 ML for this work.

With a higher InAs coverage of 1.58 ML, the PL spectrum of sample C58 consists of three

overlapping peaks which were resolved by the excitation power-dependency PL spectra as shown

in Figure 7.8. With the lowest excitation power density, the ground-state peak of QDs is resolved

with the energy E0 of 1.221 eV (1016 nm). It has a FWHM about 57 meV, which is broader than

the ground-state peak of the QDs in the previous sample C46. As described in the preceding

subsection 7.1.1, with an InAs coverage of 1.58 ML, there could be two types of QDs in the

GaAs nanoholes as observed on sample B58, which are single QDs and QD pairs with different

dimensions. Therefore, these various QD dimensions can lead to a broadening of size distribution,

and in turn to a widening of the FWHM. As the excitation power increased, the higher excited

states in the QDs were filled one by one, resulting in the presence of first-excited-state and

second-excited-state (d-shell) peaks with the energies E1 of 1.258 eV (986 nm) and E2 of

1.296 eV (957 nm), respectively. Interestingly, the signals from the 2D-like quantum disks are no

longer visible. It implies that the InAs coverage deposited inside the GaAs nanoholes is above the

critical thickness, therefore 3D QDs becomes dominating.

91

Figure 7.9 shows the excitation power-dependency PL spectra for sample C65 with the

InAs coverage of 1.65 ML. With this coverage, the PL signals are mainly attributed to the

recombination from QDs. By varying the excitation power, the peaks from the ground states, the

first, second and third excited states (f shells) of QDs were resolved with energies E0 of 1.161 eV

(1068 nm), E1 of 1.207 eV (1027 nm), E2 of 1.247 eV (994 nm) and E3 of 1.281 eV (968 nm),

respectively. The peak of the ground states was resolved as shown in the insert with the FWHM

of 34 meV for the lowest power density. Compared with sample C58, this sample shows a

smaller value for the FWHM of the ground-state peak. This reduction of the width together with

the increase of InAs coverage implies that the QDs became larger while the size uniformity

became better. Furthermore, this small value of FWHM indicates a high degree of the size

uniformity of QD ensembles, which is desired in optoelectronic applications.

Figure 7.7 Power-dependent PL spectra measured at 77 K for sample C46 with an InAs

coverage of 1.46 ML. I0 denotes the maximum intensity with an excitation power of 5 mW.

E0 and E1 represent the energies corresponding to the ground-state (s-shell) and the first-

excited-state (p-shell) recombination of QDs. represents the energy corresponding to the

recombination of QDks. WL represents the recombination from the wetting layer. The

insert is the PL spectra with the lowest intensity and its Gaussian fitting curve.

92

Figure 7.8 Power-dependent PL spectra at measured 77 K for sample C58 with an InAs

coverage of 1.58 ML. I0 denotes the maximum intensity with an excitation power of 5 mW.

E0, E1 and E2 represent the energies corresponding to the ground-state (s-shell), the first-

excited-state (p-shell) and the second-excited-state (d-shell) recombination of QDs. WL

represents the recombination from the wetting layer. The insert is the PL spectra with the

lowest intensity and its Gaussian fitting curve.

Finally, the four peaks in the PL spectrum of sample C75, which have been shown in

Figure 7.6, can be assigned to the transition from the ground states and the excited states of the

QDs with the energies E0, E1, E2 and E3 of 1.136 eV, 1.172 eV, 1.204 eV and 1.238 eV,

respectively. The FWHM of the ground-state peak is about 32 meV resolved by Gaussian fitting,

which is smaller than those of the other samples with lower InAs coverages. As mentioned in

subsection 7.1.1 for the InAs coverage of 1.75 ML, the large single islands might be originated

from the growth of small dots and/or the coalescence of dot pairs. In the conventional case, the

incorporation of dots on a planar surface usually leads to the broadening of the size-distribution.

However, it is opposite to the case with a nanohole-patterned surface in this work. The small

FWHM from this sample might suggest that the sizes of the large QDs (islands) were limited in

the GaAs nanoholes, resulting in a narrow size-distribution.

93

Figure 7.9 Power-dependent PL spectra at 77 K for sample C65 with an InAs coverage of

1.65 ML. I0 denotes the intensity with an excitation power of 5 mW. E0, E1, E2 and E3

represent the energies corresponding to the ground-state (s-shell), the first-excited-state (p-

shell), the second-excited-state (d-shell) and the third-excited-state (f-shell) recombination

of QDs. WL represents the recombination from the wetting layer. The insert is the PL

spectra with the lowest intensity and its Gaussian fitting curve.

In order to summarize the evolution of the energy structures of these QDs, the energies for

the transitions of the states are plotted versus InAs coverage as shown in Figure 7.10. As the

InAs coverage increases, the ground-state-transition energies from the QDs represent a red-shift

from 1.256 eV to 1.136 eV. This red-shift is confirmed by the size-dependent energy band gap of

the QDs. However, with the conventional InAs QDs grown on a planar GaAs surface which

comprises lateral diameters of about 40 nm and heights around 8 nm by the same growth system

of this work, the ground-state-transition peak from the ensembles was found at an energy around

1.054 eV (E0) at 77 K as shown in Figure 5.3. Compared to the conventional ones, the quantum

dots grown with nanohole templates are generally larger. Therefore, their ground-state-transition

energies should be lower than 1.054 eV. However, with respect to this energy, varying blue-shifts

from 110 meV to 230 meV are found for the ground-state transitions of these quantum dots with

decreasing sizes. This result is opposite to what would be expected from the quantum

confinement effect. This blue-shift might be attributed to the high Ga concentration in the QDs

which overweights the size dependency in the quantum confinement effect. Since GaAs

94

nanoholes were generated under the condition of arsenic deficiency by droplet epitaxy, a Ga-rich

surface formed on the nanoholes would be expected. Grown on the Ga-rich surface, QDs may

have a high Ga concentration due to the In segregation and the In-Ga intermixing during the

MBE growth of an InAs/GaAs material system [108, 174, 175]. Furthermore, for sample C58, the

energy separation between the s-shell and p-shell transitions of quantum dots is about 37 meV.

This separation is found to be almost the same with that between the next levels, p-shells and

d-shells transitions, which is 38 meV. Such equidistant energies between electron and hole levels

confirm the parabolic potential of lens-shaped QDs in this case. Similar equidistant transition

energies are also found in sample C75 with the separations between s and p, p and d, and d and

f shells of 36 meV, 32 meV and 34 meV, respectively. However, a slightly diminishing energy

separation is found for sample C65, which decreases from 46 meV to 40 meV, and then to

34 meV between the s and p, p and d, and d and f transitions, respectively. In conclusion, the

energy level structures of these QDs are incomparable with those of the conventional ones due to

the fact that the GaAs-nanohole-patterned surface leads to high Ga concentrations and different

morphologies of the QDs. Furthermore, their energy levels are influenced by the size, the

configuration and the composition varied along with the growth evolution. In order to gain more

insight into these QDs and to exclude the effect of the size distribution, an investigation of single

QDs is desired to understand their properties for further applications.

Figure 7.10 The transition energies from the ground states of QDs and QDks (E0 and

), the first, second, and third excited states (E1, E2 and E3) of QDs and wetting

layers (WL), corresponding to the PL spectra of the samples (1) C40, (2) C46, (3)

C58, (4) C65 and (5) C75 with various amounts of InAs coverage. The lines are only

a guide to the eyes.

95

7.2.2 Single quantum dots

The complex energy level structures for the InAs QDs grown in GaAs nanoholes were

proposed in the previous subsection, which was influenced by the interaction of sizes, shapes and

compositions of QDs depending on the growth process. In order to gain further insight, a SNOM

technique allowing micro-scale measurements was used to investigate the optical properties of

these QDs individually, i.e., single QD spectroscopy. For this small-scale measurement, it is

important to determine the location of detected areas precisely. In this work, the desired

areas were defined by an ex-situ photolithography technique as introduced in section 5.1.

On sample C65, one defined area containing QDs grown in the randomly-distributed GaAs

nanoholes on the bare GaAs surface is referred to as the un-patterned area for the following

paragraphs. Figure 7.11 shows the spectrally-integrated PL image measured from this

un-patterned area by a SNOM mapping technique at 10 K. The experimental SNOM settings can

be found in section 5.4. The scanning area is 4.8 × 4.8 μm2 with a pixel size of 80 × 80 nm

2.

Every pixel describes the integrated PL intensity with the energy range from 1.1 eV to 1.3 eV.

For this sample, the QDs were grown with an InAs coverage of 1.65 ML, site-selectively in the

GaAs nanoholes formed with a nominal Ga coverage of 5 ML by droplet epitaxy, i.e., B-type

nanoholes. In the mapping image, the density of these PL bright spots is consistent with that of

the B-type nanoholes on sample B0 without InAs deposition. Since the spatial distribution of the

site-selected QDs depends on that of the GaAs nanoholes, these bright spots can be attributed to

the recombination from the InAs QDs in the GaAs nanoholes individually.

Figure 7.11 The spectrally-integrated PL mapping image for the QDs embedded in

the un-patterned area of sample C65 grown with the InAs coverage of 1.65 ML,

measured at 10 K The integrated energy ranges from 1.1 eV to 1.3 eV. The scanning

area is 4.8 × 4.8 μm2 with a pixel size of 80 ×80 nm

2. The excitation power is

113 W/cm2. (provided by A. Senichev, MPI of Microstructure Physics, Halle).

96

Figure 7.12 The spectrally-integrated PL

mapping image of a bright spot and its cross-

section image, and also the PL spectrum at

10 K. The integrated energy ranges from

1.02 eV to 1.40 eV. The scanning area is

1.0 × 1.0 μm2 with a pixel size of 20 × 20 nm

2.

The arrow is only a guide for showing the

direction of the cross-section image. E00, E10,

E01, and EA are the energies of different

recombinations from the ground states and

excited states of a single QD corresponding to

the bright spot. (provided by A. Senichev, MPI

of Microstructure Physics, Halle).

In order to resolve the quantum structures contributing to the PL bright spots on this sample,

a small scanning area of 1.0 × 1.0 μm2 together with a fine pixel size of 20 × 20 nm

2 was applied

for spectrally-integrated PL mapping, as shown in Figure 7.12. The cross-section image was

extracted from the pixels along the arrow directed through the bright spot. The PL spectrum

shows one strong peak present with E00 = 1.163 eV, two high-energy peaks with E10 = 1.196 eV

and E01 = 1.212 eV, and also one small peak with EA = 1.177 eV. In the cross-section, these peaks

are coexisting at all positions along the bright spot, which indicates no distinguishable fine

structures observed in this condition. Therefore, the constituents of the bright spot can be

suggested as the signals from one uniform quantum structure. The FWHM of the strong peak

with E00 is 8 meV, which is consistent with the transition energies of neutral and charged excitons

in a single quantum dot in the range of 1 meV to 10 meV [53]. Summarizing the observations

above, it can be assumed that the PL bright spot is contributed from a single QD in a nanohole.

Therefore, the peak with E00 can be assigned to the ground-state (s-shell) transition of the QD.

With further experimental results from a power-dependent PL measurement as shown in the

following, the peaks with E10 and E01 can be supposed as the recombination signals from the first

excited states (p shells) of two different parabolic potentials attributed to the anisotropic lateral

confinement of the QD along [ ] and [ ] directions. In addition, the small peaks with EA

97

might originate from the transitions between the ground-state (s-shell) electrons and the second-

excited-state (d-shell) holes in the QD.

Figure 7.13 Power-dependent PL spectra of a single QD with different excitation

power densities from 6 W/cm2 to 379 W/cm

2. E00 is the transition energy of the

ground states. E10, E01, E20, E11 and E02 are the transition energies of the excited

states corresponding to , where x and y are the in-plane

directions, nx and ny are the quantum numbers of the confinements. For example, E10

is the recombination energy of the first excited states from the quantum confinement

along the x direction. EA is considered to be the recombination energy between the

ground-state (s-shell) electrons and second-excited-state (d-shell) holes.

Figure 7.13 shows the PL spectra of a single QD in a B-type nanohole from sample C65

with different excitation power densities. As shown in section 6.1, the B-type nanoholes formed

by droplet epitaxy have an asymmetric wall structure. For the QDs grown on this kind of

nanoholes, a slightly anisotropic QD base is then expected. Therefore, an anisotropic lateral

confinement consisting of two parabolic potentials along the in-plane directions, x and y, can be

applied for this type of asymmetric QDs [36, 176]. The discrete energy levels of QDs can then be

approximated as with the identical quantum numbers nx and ny and

oscillator frequencies x and y [177]. With a low power density, the peak present with the

energy E00 of 1.176 eV and its FWHM of ~ 6 meV is assigned to the ground-state recombination.

A slight red-shift of ~ 1.6 meV is attributed to the occurrence of additional multiexcitonic

98

transitions related to the s shell of the QD [178]. Increasing the power density, more peaks raised

corresponding to the excited states with the energies EA of 1.189 eV, E10 of 1.210 eV, E01 of

1.223 eV, E20 of 1.245 eV, E11 of 1.258 eV, and E02 of 1.276 eV. According to the parabolic

potential, the equidistant quantization energies x and y are found to be about 35 meV and

47 meV, respectively. The oscillation frequency between the electrons and holes can then be

calculated by the relation of h/ e = [2 (E10 − E00) / (EA − E00) – 1]-1

, which is about 0.23 in this

case. From the PL results, the data can be described by the approach of two parabolic potentials

very well.

Figure 7.14 (a) shows 11 individual PL spectra of single QDs that have anisotropic lateral

confinements, in the sequence according to the ground state energies of the QDs. The spectra

correspond to the signals from the bright spots shown in Figure 7.11 with maximum intensities.

The ground-state-transition energies E00 of these single QDs are in the range from 1.140 eV to

1.177 eV. The first-excited-state-transition energies E10 range from 1.184 eV to 1.214 eV, while

the energies E01 from 1.204 eV to 1.223 eV. The FWHM of the ground-state peaks are around

8 meV attributed to the transitions of excitons in a single QD [53]. The energy levels are different

from dot to dot because of the fluctuation of size, morphology and composition. In the plot (b), a

summary for the PL peaks corresponding to each single QD is shown. The energy separations of

E10, E01 and EA with respect to E00 are shown in the plot (c), as a function of the ground-state-

transition energy. With the increasing ground-state energies, the energy separation between E01

and E00, i.e. E01 – E00, shows a stronger decreasing tendency than that with E10 – E00. The energy

separations for EA – E00 only change in a small range of 13 meV to 16 meV. The ground-state-

transition energy E00 can be influenced by the size and the composition of the QD. However,

the single QDs having larger ground-state-transition energies together with smaller energy

separations might be confirmed with higher Ga concentrations. For self-assembled InAs QDs

embedded in a GaAs matrix, the high Ga concentration can be introduced through an intermixing

process in the MBE growth [108, 175, 179]. The fluctuation of the compositions might then be

the result of the diminishing energy separation described in the previous subsection for the PL

data of the QD ensembles.

Concluding the results in this subsection, with a low density benefited from the self-

patterned GaAs nanoholes formed by droplet epitaxy, the InAs QDs can be spatially revolved by

the SNOM technique for single QD investigation. With an InAs coverage of 1.65 ML,

predominant single QDs can be observed which have good optical qualities with a light emission

in the range of the near infra-red. The PL spectra reveal the anisotropic lateral confinements of

these QDs, which are explained by the asymmetric structures of B-type nanoholes where the QDs

were grown site-selectively. The fluctuation of the In-Ga concentration in the quantum dots is

also confirmed by the variation of the discrete energy levels of the QDs.

99

Figure 7.14 (a) The PL data for the

single QDs correspond to the

maximum-intensity signals from the

bright spots, 1 to 11, in Figure 7.11

measured by SNOM. E00 is the

transition energy of the ground states

(s shell). E10 and E01 are the transition

energies of the first excited states

(p shell) with the confinements along

the in-plane directions, x and y,

respectively. EA is considered to be the

transition energy between the ground-

state (s-shell) electrons and second-

excited-state (d-shell) holes. The

dotted lines are only a guide to the

eyes. The plot (b) shows the transition

energies of each QD. The plot (c)

shows the energy separation between

the excited states and the ground states,

as a function of E00. The black dotted

lines is calculated assuming the ratio

h/ e of 0.23. The blue and green

dashed lines are only a guide to the

eyes.

(b) (c)

(a)

100

7.3 Optical properties of Quantum Dots in Arrayed Nanoholes

In the previous sections, the site-selected InAs quantum dots in the randomly-distributed GaAs

nanoholes have been reported with good optical properties on the bare GaAs surface. In this work,

in order to design the distribution of quantum dots with an intentional pattern for novel quantum

devices, site-selected InAs QDs were also generated in the arrayed GaAs nanoholes positioned on

the FIB-patterned areas. However, it is known that FIB pre-patterning may influence the

properties of the sample due to FIB-induced defects. In order to investigate the influence of FIB

pre-patterning and its induced damage on the optical properties of the QDs, several FIB-patterned

areas with different FIB parameters were investigated by PL spectroscopy and the SNOM

technique for QD ensemble and single QD optical measurements, respectively. In the first part,

the experimental results from the ensembles of QDs on the arrayed GaAs nanohole templates are

discussed. In the second part, an insight to the single QDs in the GaAs nanoholes embedded in a

FIB-patterned area is given with the measurement data.

7.3.1 Quantum dot ensembles

The ensembles of site-selected QDs grown in the arrayed GaAs nanoholes of sample C65 are

studied in this subsection for their optical properties measured by PL spectroscopy. These QDs

were grown with an InAs coverage of 1.65 ML. The GaAs nanoholes were formed site-

selectively on the FIB-patterned area with a nominal Ga coverage of 5 ML by droplet epitaxy, i.e.,

B’-type nanoholes. These FIB-patterned areas consisting of square arrays of FIB spots were

created by In+ ion patterning with various ion fluences of 1×10

5 ions/spot, 3×10

5 ions/spot and

1×106 ions/spot together with different spot spacings of 0.5 µm, 1 µm and 2 µm, respectively. As

mentioned in section 5.1, an ex-situ photolithography technique was applied for defining the

position of the investigated regions and quantifying the amounts of QD ensembles participating

in the measurement within an area of 40 × μm2. An area composed of site-selected QDs grown

in the B-type nanoholes without FIB pre-patterning was defined as the un-patterned area of

sample C65. The single QD optical properties from this un-patterned area have been shown in the

previous subsection 7.2.2. In this section, the ensemble PL spectrum from this un-patterned area

is used for a comparison. The PL measurements were carried out at 77 K by a diode laser

emitting at 635 nm with an excitation power of 5 mW. The details about the PL process and the

setup are addressed in section 5.4. According to the observation in section 7.1, using B-type and

B’-type nanoholes as templates for the site-selective growth of QD, the arrangement of the QDs

was found highly dependent on the distribution of these nanoholes. The intrinsic density of the

randomly-distributed B-type nanoholes and the nominal density ρFIB of the arrayed B’-type

nanoholes are both of the order of 107 cm

-2. Therefore, the generation of the PL spectra was

obtained from an ensemble of hundreds of quantum dots in the investigated areas of 40 × μm2.

Therefore, the inhomogeneous broadening in the PL spectra should be considered due to size

fluctuations.

In Figure 7.15, the PL spectra are attributed to the recombinations from the s, p and d shells

of the QDs. The peak for the ground-state (s-shell) transition of the QD ensembles embedded in

101

the un-patterned area (ΦIn = 0 ions/spot) is found with an energy of 1.151 eV (1077 nm) and a

FWHM of about 38 meV obtained by Gaussian fitting. Comparing this un-patterned area with the

FIB-patterned areas generated with a spot spacing of 2 µm together with different ion fluences,

there is no significant difference from the ground-state energies of the QD ensembles, as shown

in the plot (a). On the other hand, for the FIB-patterned areas with a smaller spot spacing of 1 µm,

the ground-state energies are slightly blue-shifted with respect to those for the un-patterned area,

as shown in the plot (b). With an even closer spot spacing of 0.5 µm as shown in the plot (c), the

ground-state energies are blue-shifted in the range of 10 meV for the FIB-patterned areas with

respect to those for the un-patterned area. However, with corresponding spacings, the impact of

ion fluences on the energy level structures of the QDs is found insignificant with these values

from 1 × 105 ions/spot to 1 × 10

6 ions/spot.

Figure 7.15 PL spectra of the site-selected

InAs QDs grown with an InAs coverage of

1.65 ML in the arrayed GaAs nanoholes

formed with a nominal Ga coverage of 5 ML

on the FIB-patterned areas with various In+ ion

fluences of 1 × 105 ions/spot, 3 × 10

5 ions/spot

and 1 × 106 ions/spot together with different

spot spacings of (a) 2 µm, (b) 1 µm, and (c)

0.5 µm. The spectrum for the QDs in the

un-patterned area (ΦIn = 0) is shown in each

graph for comparison.

102

As mentioned in subsection 7.1.2, contrary to the B-type nanoholes on the bare GaAs surface,

the B’-type nanoholes in the optimum FIB-patterned area are larger and deeper which can lead to

a stronger preferential deposition of overgrown InAs, resulting in larger QDs or QD pairs in the

nanoholes. With larger QDs, a red-shift should thus be expected in the PL spectrum compared to

that in the un-patterned area. However, under the condition applied in this work with an arsenic

deficiency for droplet epitaxy, GaAs nanoholes would be expected to have a Ga-rich surface. As

discussed in section 6.2, due to the difference of the surface energies on a FIB-modified surface,

Ga adatoms were locally accumulated on the FIB spots resulting in the formation of Ga droplets

which are larger than those on the un-patterned area. With low arsenic pressure together with

high substrate temperature, the GaAs crystalline substrate would be melted by the liquid droplets

into GaAs molecules by thermal etching, until all the droplet materials were crystallized. With

larger Ga droplets formed on the FIB spots, deeper nanoholes containing a larger Ga-rich region

would then be produced on the FIB-patterned areas. With subsequent InAs deposition, In-Ga

intermixing can take place during the growth, resulting in a high Ga concentration in the QDs

[174, 175]. Therefore, for the QDs on the FIB-patterned areas composed of large GaAs nanoholes

with a Ga-rich surface, the absence of the red-shift might be due to the neutralization by the

increases of the QD size and the Ga concentration.

On the other hand, with the decreasing spot spacings, the blue-shifts may be due to the size

variation of the QDs on different FIB-patterned areas. As discussed in section 6.2, with the ion

fluences ranging from 1 × 105 ions/spot to 1 × 10

6 ions/spot, the nominal density of the nanohole

increased with the decreasing spot spacing. Especially, using a spot spacing of 0.5 µm with the

optimized ion fluence of 3 × 105 ions/spot, the nominal density could be created above the

intrinsic density of the GaAs nanoholes on the bare GaAs surface. With the same amount of the

deposited materials, i.e., a nominal Ga coverage of 5 ML, smaller Ga droplets would be formed

along with higher densities due to Ostwald ripening, which would be transformed into smaller

and shallower GaAs nanoholes by droplet epitaxy. With a shallower depth, the chemical potential

gradients at the nanohole are therefore smaller, which leads to less pronounced preferential

growth for the subsequent InAs deposition. Therefore, with the same supplied InAs coverage of

1.65 ML, less accumulation of the InAs in the smaller nanohole would result in smaller QDs

which in turn result in a blue shift of a PL spectrum. Besides, using the same spot spacing with

the ion fluences of this range, the deviation of the nominal densities of the B’-type nanoholes on

sample B0 is relatively small. A small size fluctuation of the QDs would thus be expected

between these FIB-patterned areas. As a result, the PL spectra of these site-selected QDs display

a dependency weakly on the FIB ion fluence, but relatively significant on the spacing between

FIB spots.

Since the density of the site-selected QD depends on that of the GaAs nanoholes, the density

of the QDs is higher with a smaller FIB spot spacing. However, when the spot spacing of the

FIB-patterned area gets closer, the PL intensities for the QD ensembles generally become weaker.

This decline could possibly resulted from the degradation in the crystal quality of the GaAs

surface due to the damages induced by the energetic ion beam through sputtering or implantation

103

which can present in the form of vacancies or interstitials in the substrate [171]. With a smaller

spot spacing, a higher amount of ion irradiation on the FIB-patterned areas was created since the

sizes of the patterned areas were fixed to be the same. Therefore, the crystal quality of the GaAs

matrix deteriorates because of a great amount of FIB-induced defects. During the PL process,

these defects could be the scattering centers for the charge carriers. The crystalline alteration

owed to FIB patterning reduced the efficiency of electron-hole recombinations, which may

explain the observed decrease in the PL intensity. Especially with dense distributed FIB spots on

the GaAs surface created by a spacing of 0.5 µm, where the ion irradiation was integrated

between the spots, the intensity may drop further when the ion fluence increases.

Concluding these ensemble PL measurements for the FIB-patterned areas, it was revealed

that the site-selected QDs in the arrayed GaAs nanoholes with FIB pre-patterning might represent

different sizes and Ga concentrations compared to those in the un-patterned area, because the

nanohole templates were formed with variations of hole sizes and densities on different FIB-

patterned areas. Therefore, the optical properties of QDs can be tuned with the help of FIB pre-

patterning and droplet epitaxy. However, the optical properties are found not only influenced by

the QD size and density, but also the crystal quality of the sample affected by FIB-induced

defects. Therefore, the controlling and damaging properties of FIB should be carefully taken into

account in order to ensure the efficiency of devices for electrical or optical applications. With a

sufficient distance between the FIB spots, the PL spectra are found less dependent on the ion

fluence in these cases.

7.3.2 Single quantum dots

As discussed in the previous subsection, the ensemble optical properties of InAs QDs in the

arrayed GaAs nanoholes were varied with different FIB parameters. In order to obtain a close

view of these QDs influenced by FIB pre-patterning, the SNOM technique was employed for the

single QD optical characterization. As mentioned in section 6.2, the optimum FIB patterning

parameters for the site control are found to be an ion fluence of 3 × 105 ions/spot with a spot

spacing of 2 µm by In+ ion patterning to achieve a high probability of GaAs nanoholes positioned

on the FIB spots. The FIB-patterned area of sample C65 created with this optimum condition was

chosen for studying single QDs in the positioned GaAs nanoholes. The QDs were grown site-

selectively in the GaAs nanoholes with an InAs coverage of 1.65 ML by SK growth, while the

GaAs nanoholes were formed site-selectively on the FIB pre-patterned area with a nominal Ga

coverage of 5 ML by droplet epitaxy, i.e., B’-type nanoholes. The spectrally-integrated PL

mapping image with a scanning area of 4.8 × 4.8 μm2 and a pixel size of 80 × 80 nm

2 is shown in

Figure 7.16, measured at 10 K. The integration of the PL intensity was made with the energy

range from 1.02 eV to 1.40 eV. The experimental settings of SNOM can be found in section 5.4.

Two bright spots are present in this scanning area. The distance between these two bright spots is

104

close to twice of the FIB spot spacing. With the nanohole template generated with arrayed

B’-type nanoholes, each GaAs nanohole was occupied by one QD or a QD pair, i.e., with the

probability of 100 %, as shown in section 7.1.2. Moreover, the FIB spots with the optimum

condition were all occupied by single or double GaAs nanoholes with the probabilities r1 of 93 %

and r2 of 7 %, respectively, as shown in section 6.2. As a result, with these arrayed nanoholes

positioned by FIB pre-patterning, only a part of the QDs has a respectable optical quality that

could be measured by the SNOM technique.

Figure 7.16 The spectrally-integrated PL

image by SNOM mapping at 10 K for the

single QDs grown with an InAs coverage of

1.65 ML in the GaAs nanoholes formed with a

nominal Ga coverage of 5 ML on the FIB-

patterned area with ΦIn = 3 × 105 ions/spot and

lspot = 2 µm. (provided by A. Senichev, MPI

of Micro-structure Physics, Halle). The

integrated energy ranges from 1.02 eV to

1.40 eV with a scanning area of 4.8 × 4.8 μm2

and a pixel size of 80 × 80 nm2. The excitation

power is 113 W/cm2. The spectra correspond

to the spot 1 and 2 in the image consist of the

transition peaks with the energies E0, E1, E2

and EB. E0 is the transition energy for the

ground states of the single QDs. E1 and E2 are

the transition energies of the excited states.

The PL spectra from these two PL spots with the maximum intensities are shown in the plots.

The FWHM of the ground-state peaks of these QDs is comparable with those of the single QDs

on the un-patterned area as shown in subsection 7.2.2. However, different from the anisotropic

lateral confinements observed in the case of the un-patterned area, the measurement results for

these single QDs embedded in the FIB-patterned area represent more like isotropic confinements.

In the PL spectrum for the first spot (1), the peak with the maximum intensity and the energy E0

105

of 1.189 eV is assigned to the ground-state transition with a FWHM of ~ 6 meV. The energies for

the first- and second-excited-state transitions are E1 = 1.216 eV and E2 = 1.241 eV, respectively.

The equidistant energy separation of 27 meV is consistent with the approach from a parabolic

potential. In the spectrum of the second spot (2), the energy of the peak for ground-state

transitions is E0 = 1.185 eV, and the FWHM amounts to 8 meV. The equidistant energy

separation between the first- and second-excited-state transition peaks is 34 meV, by the energies

E1 = 1.219 eV and E2 = 1.254 eV. However, the peaks with EB from both spots having an energy

separation of 8 meV with respect to their ground-state peaks, EB - E0, are different from the peaks

considered to be the recombination between ground-state electrons and second-excited-state holes

with EA observed in the previous subsection 7.2.2. In addition, the pronounced peak present with

an energy of 1.223 eV for the second spot (2) has a narrow FWHM less than 2 meV which is

much less than the other peaks. These two peaks might correspond to the emission from different

neutral and charged excitons in the same single quantum dot [53] or to the emission raised from a

different dot since the probability of QD pairs can become higher with B’-type nanoholes and the

formation of double GaAs nanoholes is possible in this FIB-patterned area.

Concluding the results in this subsection, the distribution, configuration and optical quality

of site-selected QDs can be changed by using a combination of droplet epitaxy and FIB pre-

patterning to produce various nanohole templates. However, in order to heal the sample crystal

quality which is reduced by the FIB-induced defects, a proper annealing process should be

considered for a future work. Nevertheless, this approach represents a potential way to modify the

distribution of strain-induced QDs, owed to the flexibility of droplet epitaxy and the variable

abilities of FIB writing.

107

Chapter 8 Summary

In order to overcome the limits of strain-induced InAs QDs with respect to their sizes and

densities, a site-selective growth has been demonstrated with an MBE system in this work by

using GaAs nanoholes as templates fabricated by droplet epitaxy with a random distribution or an

organized arrangement, where an in-situ FIB pre-patterning has been employed for the latter.

The GaAs nanoholes were formed on a GaAs epilayer, i.e., homoepitaxy, using the droplet

epitaxy as a self-assembly method, by crystallizing Ga metal droplets under the conditions of low

As pressure and a high substrate temperature. In general, these nanoholes have been represented

with a thermally etched valley surrounded by an asymmetric wall structure due to different

atomic diffusion rates depending on the crystal directions of the substrate surface. On the bare

GaAs surface without FIB pre-patterning, the GaAs nanoholes are randomly distributed with a

low density of the order of 107 cm

-2 which is desired for the studies of single nanostructure

spectroscopy. On the other hand, the GaAs nanoholes on the FIB-patterned area were site-

selectively formed, resulting in an organized order according to the pattern design and the ion

fluence. The optimum patterning parameters have been obtained with an ion fluence of

3 × 105 ions/spot together with a spot spacing of 2 μm by a focused In

+ ion beam with an energy

of 30 keV. FIB pre-patterning with these parameters allows GaAs nanoholes to be well-

positioned in the square arrays of FIB spots with a formation probability of nearly 100 %, where

single nanoholes are dominant. The formation of double, triple or multiple nanoholes can be

achieved by increasing the ion fluence, while the nucleation occurs at the edge of the FIB spots

because of the unintentional exposure from the tail of the ion beam. Moreover, decreasing the

distance of the spot spacing, the nominal density of the GaAs nanoholes on the FIB-patterned

area can be increased to even above the intrinsic density of the nanoholes on the bare GaAs

surface. Compared with the nanoholes on the bare GaAs surface (A-type or B-type nanoholes),

the GaAs nanoholes formed on the optimum FIB-patterned areas (A’-type or B’-type nanoholes)

are generally deeper and wider. This is due to a sufficient thermal etching and the crystallization

with larger Ga droplets resulting from the preferential nucleation of Ga adatoms induced by the

surface energy difference on the FIB-modified surface.

The site control of InAs QDs was realized using B-type and B’-type nanoholes as templates

together with a subsequent MBE growth following the SK mode. Therefore, these QDs are

featured with a low density or an arranged distribution consistent with that of the nanoholes.

108

However, the size and the configuration of the QDs were altered with different amounts of

deposited InAs in the GaAs nanoholes. For various amounts of InAs coverage ranging from

1.40 ML to 1.75 ML, the growth evolution of these QDs could be investigated. First, the

deposited InAs preferentially filled the GaAs nanoholes. Then, single QDs or QD pairs were

formed due to the 2D-3D transition. Finally, large single islands were generated in the nanoholes

by the growth of single dots and/or the coalescence of dot pairs. Meanwhile, the preferential

nucleation of InAs was enhanced in the deep B’-type nanoholes due to large chemical potential

gradients. Therefore, the QDs grown on the optimum FIB-patterned areas have larger dimensions

compared to those on the bare GaAs surface with corresponding amounts of InAs coverage. In

addition, the formation probability for QD pairs is higher on the FIB-patterned area with respect

to that on the bare GaAs surface because the wide B’-type nanoholes contains more preferential

nucleation sites for the deposited InAs. The formation of the QDs was well controlled inside the

nanoholes within this coverage range, so that the site-selective growth of strain-induced QDs was

successfully implemented with an arbitrary manipulation in terms of the sizes and the locations.

A good optical quality of these site-selected InAs QDs has been confirmed from the optical

characterization by photoluminescence (PL) spectroscopy, despite the interruption between the

MBE growths for FIB patterning in the approach of this work. At a low InAs coverage, the quasi-

2D quantum structures, i.e., the quantum disks, present in the PL spectra were attributed to the

filled InAs nanostructures in the GaAs nanoholes with a thickness below the critical value for the

2D-3D transition. With higher amounts of InAs coverage, the PL signals for the QD ensembles

emerged corresponding to the recombinations from the ground states and the excited states. The

red shift of the PL spectra was due to the increase of QD sizes with increasing InAs coverage,

while the narrowed FWHM of the ground-state peaks proposed the improvement of the size

homogeneity. Moreover, the emission energies have revealed a high Ga concentration in these

In(Ga)As QDs which was caused by an intermixing process during the growth with a Ga-rich

surface at the GaAs nanoholes formed under an arsenic deficiency by droplet epitaxy. Calculated

from the ground-state and excited-state energies, the equidistant energy separations are consistent

with the eigenstates of a 2D harmonic oscillator potential which describes the confinement of

lens-shaped QDs [72].

With FIB pre-patterning by In+ ion fluences from 1 × 10

5 ions/spot to 1 × 10

6 ions/spot and

a spot spacing of 2 μm, the ensemble optical properties of the InAs QDs in the positioned GaAs

nanoholes are comparable with those in the randomly-distributed GaAs nanoholes without FIB

pre-patterning. In general, the QDs grown on the FIB-patterned areas with these FIB patterning

conditions have a larger size than those on the bare GaAs surface. Therefore, the consistent

ground-state energies suggested an even higher Ga concentration of these QDs due to the

intermixing with a larger Ga-rich region induced by the deep B’-type nanoholes on the FIB-

patterned areas. However, a slight blue shift was present in the PL spectra as the spot spacing

became closer because the size of the QDs depends on the dimensions of B’-type nanoholes

which were varied with the patterning parameters. Meanwhile, the PL intensity was reduced with

109

the decreasing spot spacing due to the degradation of the crystal quality caused by the integration

of the FIB-induced defects, especially with the smallest distance of 0.5 μm in this work.

Aided by the low density of the GaAs nanoholes, the spectrum of a single QD could be

realized by the SNOM technique for these strain-induced InAs QDs. The optical characteristics of

the single QDs grown on the B-type nanoholes with predominant asymmetric walls have been

explained by the anisotropic lateral confinements. The energy levels of the single QDs can be

well described by the approach with two parabolic potentials along the in-plane directions with

different equidistant energy separations. However, the structures of the QD energy levels were

found different from dot to dot depending on the interactions of size and composition. On the

other hand, an isotropic lateral confinement was shown for the single QDs grown on the B’-type

nanoholes with pronounced valleys formed by sufficient thermal etching. In addition, because the

crystal quality can be degraded by the FIB-induced damage, a compensation of FIB patterning or

an additional annealing process should be considered in order to suppress or heal the defects.

Nevertheless, the results of the optical characterization support the approach combining MBE

growths and FIB writing as a possible pathway to modify the configuration and the distribution of

self-assembled nanoholes leading to the realization of site-selected QDs with various properties.

In conclusion, the site-selective growth for good-quality and low-density In(Ga)As QDs and

QD pairs with intentional arrangements was successfully developed and optimized with self-

assembled/self-patterned GaAs nanoholes, by using the advantages of two completely compatible

MBE growths and the in-situ FIB direct-writing techniques. In terms of confinements, emitting

wavelengths and spatial distributions, this development has broadened the potentials of self-

assembled QDs in fundamental research and also in semiconductor applications, especially for

those based on single QD devices such as single photon sources for quantum cryptography or

qubits for quantum computers [17–20].

111

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119

Appendix

A.1 Index for Sample Number

The sample numbers used in this thesis are named for the convenience of description and

understanding. Appendix 1 shows the index of these sample numbers corresponding to the

internal sample numbers at AFP. The internal sample numbers are ordered depending on the

Riber MBE growth sheets which contain the parameters of the growth process.

Sample Ga coverage

[ML]

InAs coverage

[ML]

In cycles

(cycles for normal QD)

Internal Sample

Number

A0 3 0 0 #14105

B0 5 0 0 #14236

A75 3 1.75 9 (10.75) #14108

B75 5 1.75 9 (10.75) #14115

B58 5 1.58 9 (12) #14233

B40 5 1.40 8 (12) #14240

C75 5 1.75 9 (10.75) #14116

C65 5 1.65 9 (11.5) #14203

C58 5 1.58 9 (12) #14235

C46 5 1.46 9 (13) #14297

C40 5 1.40 8 (12) #14242

Appendix 1 Index of the internal sample number at AFP

120

A.2 Mask for Photolithography

Appendix 2 shows the mask layout based on a van der Pauw mesa and a contact mask. In

this work, this mask layout was used to define the position and area of the investigated regions on

the samples for optical measurements. The investigated regions were defined corresponding to

the active regions of the mesa. The contact regions were coated with Au in order to conceal the

undesired signals and to make a visible contrast for the mesa structures.

Appendix 2 The mask layout for mesa and metal contact.

121

A.3 Ion fluence for Planes and Lines

Ion fluence, Φion, is one of the most important parameter of FIB direct writing. As mentioned

in subsection 4.3.3, the ion fluence is defined as number of impinging ions Nion per unit area A:

Φ

.

The number of impinging ions is expressed as:

.

I is the ion beam current measured by the Faraday cup. t is the dwell time calculated from the

frequency f. q is the charge number of ion species, e.g., q = 1 for Ga+ or In

+. e is the elementary

charge of 1.6×10-19

C. i is the number of repeating times.

For the patterning of planes, the writing area is a sum of lines with small distances defined

by the step size s and the increment c. The step size3 is 7.7 nm in this work, which depends on the

deflector and the working area of the FIB system. The area of the plane A is given by the number

of discrete points nx and ny between the distance of (c·s) with the relation of A = (nx c s) × (ny c s)

= nx ny c 2

s 2

. The dwell time t is given by the relation of t = nx ny / f, where f is the frequency.

The ion fluence for planes is thus expressed as follows:

Φ Φ

s

For the patterning of lines, the area is given by A = 2 r (nx c s) where r is the radius of the ion

beam, and the dwell time amounts to t = nx / f. The ion fluence for lines is expressed by following

equation:

Φ Φ

s

3 With a magnification of 1×, the working area of the FIB system used in this work is 505 × 505 µm

2 composed

of 216

×216

pixels with an inter-pixel distance of 7.7 nm which is defined as the step size here.

123

Acknowledgements

In the end, I would like to express my sincere gratitude to all the people who helped me with

the accomplishment of this thesis in various ways.

My deepest gratitude goes first and foremost to Prof. Dr. Andreas D. Wieck, my supervisor,

who offered me the opportunity to pursue my PhD degree in his group. I am grateful for his

constant encouragement and unwavering support. He has greatly inspired and motivated me in

research with his wide scientific knowledge and impressive explanations. His optimistic attitude

and positive energy have helped me overcome the depression and frustration during my study

many a time. Similarly, my heartfelt tribute shall be paid to Prof. Dr. Dirk Reuter for his

instructive guidance and wise advices. He helped me develop the strategy of the experiments with

his wealth experience and thorough deliberation. His substantial contribution to the fulfillment of

this work is ineffaceable. Furthermore, I would like to thank Prof. Dr. Ulrich Köhler for being

willing to be the second referee and providing his valuable suggestions. Without their tuitions,

this thesis could not have reached its present form.

I am greatly indebted to Prof. Dr. Achim W. Hassel who provided me the opportunity to be

a part of International Max Plank Research School for SurMat. Prof. Hassel has provided his

suggestions from a chemist’s point of view injecting different possibilities into our corporations.

I would also like to extend my gratitude to SurMat for offering the scholarship, providing

training courses and holding scientific conferences. At this point, Dr. Rebekka Loschen and

Ms. Elke Gattermann are also acknowledged for their thoughtful organization.

My highly gratitude goes to the collaborators at Max-Planck-Institut für Mikrostrukturphysik

in Halle, Mr. Alexander Senichev for putting his effort into the fruitful SNOM results, and

Dr. Peter Werner for his support of this corporation. Moreover, I would like to thank Institut für

Experimentalphysik IV of Ruhr-Universität Bochum for providing the instrument of SEM. I am

also grateful of Institut für Analytische Chemie-Elektroanalytik und Sensorik of Ruhr-Universität

Bochum for providing the access of AFM measurements and their technical supports. My

gratitude goes to the collaborators at the institute of CRHEA-CNRS in France as well for

their generous supports, especially the technical supports from Mr. Olivier Tottereau,

Mr. Yuan-Yang Xia and Ms. Monique Teisseire, and the scientific discussion with

Dr. Fabrice Semond.

My thanks would go to all the colleagues at AFP for providing a nice working atmosphere

and unconditional helps in the labs. First, I would like to thank Dr. Arne Ludwig for sharing his

knowledge and opinions concerning my work. I would also like to thank my former colleagues

Dr. Razvan Roescu, Dr. Kirill Trunov and Dr. Ashish Rai who helped me to start my first

steps in the group. A special gratitude goes to my office mate Dr. Stepan Shvarkov for his

124

delightful company and numerous helps at work and also in life. I also appreciate the supports

from Sascha Valentin, Rüdiger Sott, Patrick Labud and Markus Greff, concerning

experiments and measurements. Great acknowledgement goes to our skillful technicians,

Rolf Wernhardt, Georg Krotenbruck and Torsten Ermlich for constructing and repairing the

instruments and computer systems, Nadine Viteritti for the delicate sample processing with

photolithography, Ronna Neumann and Swetlana Mazarov for producing LMIS, and also to

our reliable secretaries, Carmen Rockensüß and Heike Büscher for the administration work.

I owe my special and sincere gratitude to my friends, Sani Noor, Nadezhda Kukharchyk,

and Shovan Pal, for putting their valuable time and effort into the comments on the draft. Their

proofreading and suggestions have improved the quality of this thesis a lot.

The financial supports from SurMat, Deutsch-Französische Hochschule (DFH/UFA CDFA

05-06), AFP and CRHEA-CNRS are gratefully acknowledged.

Last, my wholehearted appreciation would go to my beloved family for their loving

considerations and great confidence in me all through these years, and also to my dearest friends

who always listen to my problems and stand by my side without doubt.

125

Curriculum Vitae

Yu-Ying Hu, born 5th

May 1983 in New Taipei, Taiwan.

1989－1991 Sinpu Elementary School, New Taipei, Taiwan

1991－1995 Rongfu Elementary School, New Taipei, Taiwan

1995－1998 Jiangcui Junior High School, New Taipei, Taiwan

1998－2001 Zhongshan Girls High School, Taipei, Taiwan

2001－2005 Bachelor of Science

Department of Engineering and System Science (Material Science)

National Tsing Hua University, Hsinchu, Taiwan

Project: The preparation of electrochromic devices

2005－2008 Master of Science

Department of Engineering and System Science (Material Science)

National Tsing Hua University, Hsinchu, Taiwan

Thesis: Phase transition and related properties of nanocrytalline Zr(N,O)

thin films by unbalanced magnetron sputtering

2009－present PhD candidate and assistant researcher

Lehrstuhl für Angewandte Festkörperphysik,

Ruhr-Universität Bochum, Germany

Surface and Interface Engineering in Advanced Materials (2009-2012),

International Max Plank Research Schools, Germany

Thesis: Site control and optical characterization of InAs quantum dots

grown in GaAs nanoholes