Site control and optical characterization of InAs quantum dots grown in GaAs nanoholes

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1 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

2 1. Gutachter Prof. Dr. Andreas D. Wieck 2. Gutachter Prof. Dr. Ulrich Köhler Datum der Disputation

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5 Contents Contents... I List of Abbreviations... III List of Symbols... V Chapter 1 Introduction... 1 Chapter 2 Semiconductor Quantum Dots Low-Dimensional Structures Characterizations of Quantum Dots Energy Level Structure of Quantum Dots Chapter 3 Epitaxial Growth of III-V Semiconductor Nanostructures III-V Semiconductor Properties Growth Modes in Heteroepitaxy Molecular Beam Epitaxy System Solid source cells and shutters Substrate heating and manipulation Growth parameters Reflection high-energy electron diffraction Self-Assembled 3D Nanostructures Strain-induced quantum dots (SK) Nanostructures by droplet epitaxy (VW) Chapter 4 Surface Patterning Techniques for Site-Selective Growth Introduction to Site-Selective Growth Self-Assembled Nanohole Patterning Focused Ion Beam Patterning Equipment Process Patterning parameters I

6 Chapter 5 Experimental Details and Characterization Methods Sample Fabrication Scanning Electron Microscopy Atomic Force Microscopy Photoluminescence Spectroscopy Chapter 6 Characterizations of Self-assembled/Self-patterned GaAs Nanoholes Randomly-distributed Nanoholes Arrayed Nanoholes Chapter 7 Characterizations of Site-selected InAs Quantum Dots in GaAs Nanoholes Topography Quantum dots in randomly-distributed nanoholes Quantum dots in arrayed nanoholes Optical Properties of Quantum Dots in Randomly-distributed Nanoholes Quantum dot ensembles Single quantum dots Optical properties of Quantum Dots in Arrayed Nanoholes Quantum dot ensembles Single quantum dots Chapter 8 Summary Bibliography Appendix A.1 Index for Sample Number A.2 Mask for Photolithography A.3 Ion fluence for Planes and Lines Acknowledgements Curriculum Vitae II

7 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 III

8 RHEED SAQD SE SEM SK SNOM SPM SRIM STM TEM UHV VB VPE VW WL AFP MPI Reflection High-Energy Electron Diffraction Self-assembled Quantum Dot Secondary Electron Scanning Electron Microscopy Stranski-Krastanov Scanning Near Field Optical Microscopy Scanning Probe Microscope Stopping and Range of Ions in Matter Scanning Tunneling Microscopy Transmission Electron Microscope Ultra-High Vacuum Valence Band Vapor Phase Epitaxy Volmer-Weber Wetting Layer Lehrstuhl für Angewandte Festkörperphysik Max Planck Institute IV

9 List of Symbols a o B C 0 D d E e E E g ħ h I J k (k x, k y, k z ) k B lattice constant exciton Bohr radius magnetic field ion concentration ion dose thickness electrical field electron charge energy band gaps Dirac constant Planck s constant ion beam current current density wave vector Boltzmann s constant l, m, n quantum numbers l i l spot L x, L y, L z m * m 0 p P Q r (x, y) r R r n R p r sum T c U width of facet spacing of FIB spots quantum confining dimensions effective mass free electron mass momentum vapor pressure amount of deposited material in-plane dimension radius perpendicular range probability of single, double, or multiple nanoholes projected range occupancy rate of FIB spots by nanoholes congruent evaporation temperature voltage V

10 potential distribution δ (x) Dirac function ε eigen energy ε r θ θ (x) λ db μ permittivity monolayer coverage Heaviside function de Broglie wavelength chemical potential µ * reduced effective mass ρ density ρ(e) density of states ρ FIB Φ φ ψ Ψ nominal density of GaAs nanoholes ion fluence lateral component of wavefunction Ψ vertical component of wavefunction Ψ wavefunction angular frequency VI

11 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 lowdimensional 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 atomlike 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 selfassembly [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 selfassembled 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 cm -2 which is required for the efficient optoelectronic devices such as QD lasers, light emitting diodes (LED) and high performance 1

12 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 quantummechanical 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 straininduced 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 10 8 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 heterostructure 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., siteselected 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 2

13 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 selfassembled 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 sitecontrol 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 siteselective 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 3

14 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 FIBpatterning 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. 4

15 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: 5

16 u ħ. For 1D confinement, one dimension of the system, e.g., L z, 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 6

17 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 k B T 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]) 7

18 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 sizedependent. For an ideal quantum dot, the quantum confining dimensions L x, L y and L z 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 k B is Boltzmann s constant. Comparing with the mass of a free electron m 0, the effective masses of electrons and holes in semiconductor materials are typically * * smaller, e.g., a s= m 0 and hh a s= 0.5 m 0. 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 (~ k B T) resulting in fluctuations in the potential dimensions. If the thermal energy k B T 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 where ε r is the permittivity of the material, µ * * is the reduced effective mass ( * μ * * hh) and e is the electron charge of C. In typical semiconductor materials with large ε r 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 8..

19 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 selfassembly process with a heteroepitaxial growth by molecular beam epitaxy (MBE) or metalorganic 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 10 9 to cm -2 [11, 14]. On the other hand, DE grown QDs representing low densities of the order of 10 8 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 9

20 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: ( ) ( ) ( ). 10

21 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 ( lateral center, : ) of the 1D Schrödinger wave equation at the [ ( ) ] 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, ( ): In a semiclassical approach, this potential ( ) ψ ψ ψ ( ) ψ * (, ) (, ). ( ) 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 11

22 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 lensshaped 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, z 1, z 2 and z 3, with respect to the position of (x,y). 12

23 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 selfassembled 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 E g, 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 13

24 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 a o 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 E g,gaas = 1.42 ev and E g,inas = 0.35 ev, and the lattice constants are a o,gaas = Å and a o,inas = 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., Al x Ga 1-x As, with x ranging continuously from 0 to 1. Furthermore, quaternary alloys are also possible, e.g., Ga x In 1-x As y P 1-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 Al x Ga 1-x As 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. 14

25 Temperature dependency lattice constant a o (Å) direct band gap E g (Γ) (ev) GaAs InAs a o = (T - 300) a o = (T - 300) E g = T 2 / ( T ) (0 < T (K) < 10 3 ) E g = 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 a o is defined by the edge length of the cube. (b) The band structure of GaAs or InAs with a direct band gap E g 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]) 15

26 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 Al x Ga 1-x As 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. 16

27 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 Å, Å and 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. 17

28 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/Al x Ga 1-x As 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, 18

29 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 Torr. All the other chambers are under a UHV in the order of 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 highenergy 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]. 19

30 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. 20

31 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. 21

32 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 E a : where P is the vapor pressure of the source material, P 0 is a constant of the vapor pressure, k B 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 As 4 into As 2, 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 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. 22

33 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 T set and T pyro, 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 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 T c [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 23

34 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, As 4 and As 2, all alone is zero. As 4 or As 2 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 T c ( C) Table 3.2 List of approximate congruent sublimation temperature (T c ) for Langmuir evaporation of III-V semiconductor compounds [96]. Element Al Ga In As Sensitivity factor Table 3.3 The ion gauge sensitivity factors for different elements [99] 24

35 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. 25

36 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) 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 a GaAs ~ 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 d c, 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 a InAs ~ 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 Λ 0, 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 26

37 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]) 27

38 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 > d c. d c is the critical thickness. is the exponent. ρ is the normalization density of islands. Processing the experimental data, the fitting parameters = 1.76, ρ = cm -2, and d c = 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 d c for InAs/GaAs system is found to be 1.5 ML to 1.8 ML [68, ]. Moreover, when the thickness exceeds another feature thickness d d, 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 d c < d < d d, 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]. 28

39 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/Al x Ga 1-x As, as well as latticemismatched 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 10 5 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) [ ]. Therefore, the crystalline 29

40 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 (~ Torr) [29] or a low arsenic pressure (~ 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]. 30

41 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 31

42

43 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 randomlydistributed 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 33

44 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 34

45 example, the approach by e-beam lithography has often been used for the realization of siteselected 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 [ ]. 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. µ 0 is the chemical potential for a uniform surface. 0 is the atomic volume. l i 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 35

46 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 siteselective 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 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 10 7 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 36

47 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 wellorganized 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 selfpatterned 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 μm 2. 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 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. 37

48 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 randomlydistributed 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 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 randomlydistributed 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 38

49 in subsection 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 The sample fabrication concerning the details of MBE growth will be given in section 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 [ ]. 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 39

50 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 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, U acc, 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 40

51 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 μm 2, 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 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 41

52 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 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 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 42

53 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, R p, while the distance traveled along a perpendicular axis is the perpendicular range R. The standard deviation in a projected range is called projected straggle, ΔR p, 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: ( ) 43 [ ( ) ( ) where D is the ion dose defined by the impinging ion charges per unit area. The maximum ion concentration is at R p. 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. ]

54 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) R p ΔR p R ΔR Ga In Table 4.1 The ion ranges for Ga + and In + ions of 30 kev incident perpendicularly into a GaAs substrate. R p : projected range (longitudinal), R : perpendicular range (lateral), ΔR p : 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 - ( ) where J 0 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 ρ 3 = 0.02, and 4 = 160 nm for < ρ 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 + ρ - + ρ - 44

55 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 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, l spot, are varied with 0.5 µm, 1 µm and 2 µm within a square area of µm 2. 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 45

56 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 µm 2. The spacing between the spots, l spot, 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 µm 2. 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 Φ ion of Ga + or In + and the spot spacing. The ion fluence Φ ion is defined by the number of impinging ions N ion 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 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 to ions/spot with the beam size in the scale of 100 nm. As the ion fluences above ions/spot, a significant 46

57 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 ions/spot, ions/spot and ions/spot, respectively. (d), (e) and (f) are the depth profiles of the FIB spots with the corresponding patterning parameters measured by AFM. 47

58

59 Chapter 5 Experimental Details and Characterization Methods The experimental details about the sample fabrication and the characterization methods for siteselected 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, 49

60 the wafer was thermally cleaned by two steps in the main chamber of the MBE system. First, the substrate temperature was raised up to T pyro = 550 C (T pyro, 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 T pyro = 600 C (T set ~ 660 C, depending on the substrate conditions; T set, 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, P As, of 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 T set = 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 l spot in an area of µm 2. 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 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 T pyro = 545 C for the growth in the mode of droplet epitaxy. The deposition of Ga with a nominal coverage θ Ga 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 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 50

61 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 The sample was then annealed under the same BEP of As with the temperature rapidly raised up to T pyro = 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., T set = 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 T pyro = (525 ± 2) C to allow the deposition of InAs. In meanwhile, the BEP of As was increased up to 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 θ InAs is 2.1 ML for InAs QDs grown on a planar GaAs (100) surface. However, in this work, the InAs coverage θ InAs 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 siteselected 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 T pyro = 510 C, followed by a 7 nm to 22 nm GaAs layer growth with the substrate temperature raised to T pyro = 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 Torr. After capping, the sample was cooled down to the standby temperature of T set = 400 C and was then ready for the subsequent ex-situ processes and analyses. 51

62 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 mm 2 including the whole region which has undergone FIB patterning. Then, the square shaped mesas with an active area of 40 μm 2 were fabricated by photolithography and wet chemical etching. The alignment of the mesas and the FIB-patterned areas (with the area of μm 2 ) 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 θ Ga 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 θ Ga of 3 ML followed by the InAs deposition with an InAs coverage θ InAs of 1.75 ML. Also, sample B40, B58 and B75 were fabricated with GaAs nanoholes formed with θ Ga of 5 ML followed by InAs deposition with θ InAs 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 θ Ga of 5 ML followed by the InAs deposition with θ InAs 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. 52

63 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 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: 53

64 . 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; m e 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 nm which has the potential to increase the resolution by a factor of 10 4 to 10 5 over the light optical microscope. When the electron velocity approaches the speed of light, i.e., c = cm/s, at a high voltage, e.g., 50 kv, v = 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 (~ 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 cm -2 grown by the same MBE system of this work. 54

65 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 Si 3 N 4. 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 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 55

66 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) 56

67 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 straininduced 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 E 0 is about ev for the s shell, while the excited-state transition energies E 1 and E 2 are ev 57

68 and 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 k B T 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 electronhole 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 selfassembled 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 (e 1 for electrons; hh 1 for heavy holes, corresponding to the s shell of the QD), or to the lowest unoccupied excited state (e 2 and e 3 ; hh 2 and hh 3, corresponding to the p and d shells of the QD, respectively) (4) the recombination with the emission of photons carrying characteristic energies E 0, E 1 and E 2 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. 58

69 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 cm 2 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 LN 2 -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 59

70 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 LN 2 -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) 60

71 Chapter 6 Characterizations of Self-assembled/Selfpatterned 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 siteselected 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 selfassembled/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 61

72 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 θ Ga 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 θ Ga = 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 ~ cm -2. In the SEM image (a), the nanoholes represent an inner 62

73 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. θ Ga = 3 ML L l H H [ ] 315 ± ± ± ± ± 6 [ ] 240 ± ± ± ± ± 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, to [, which is about 1.3, a faster atomic migration along [ ] is substantiated compared ]. 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 63

74 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 θ Ga = 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 64

75 slightly lower density of 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 crosssections 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. θ Ga = 5 ML L l H h [ ] 321 ± ± ± ± ± 8 [ ] 222 ± ± ± ± ± 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 65

76 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 µm 2. 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. 66

77 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 µm 2. For different FIB-patterned areas, the ion fluence of the FIB spots, Φ ion where ion denotes In or Ga, was varied from ions/spot to ions/spot, while the spacing between the FIB spots (the pitch), l spot, was designed as 0.5 µm, 1 µm or 2 µm. The details about FIB parameters and pattern designs can be found in subsection 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 selfassembled 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 Φ Ga are varied from ions/spot to 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 ions/spot (a). With Ga + ion fluences above 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 ions/spot at these conditions. With the Ga + ion fluence of ions/spot (b), each FIB spot is occupied by one GaAs nanohole, i.e., a single nanohole. For the higher Ga + ion fluences of ions/spot (c) and 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 67

78 fluence of 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 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) ions/spot, (b) ions/spot, (c) ions/spot, (d) ions/spot, and (e) ions/spot. 68

79 Figure 6.5 The FIB-patterned areas of sample B0 with different Ga + ion fluences Φ Ga and spot spacings l spot. (a) l spot = 0.5 µm and Φ Ga = ions/spot, (b) l spot = 1 µm and Φ Ga = ions/spot, (c) l spot = 1 µm and Φ Ga = ions/spot, and (d) l spot = 1 µm and Φ Ga = 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 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 69

80 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) ions/spot, (b) ions/spot, (c) ions/spot, and (d) ions/spot. The In + ion beam was employed for pre-patterning sample A0 before the formation of GaAs nanoholes. The In + ion fluences Φ In were applied in a higher range from ions/spot to 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 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 ions/spot (b) and ions/spot (c), the probability of double 70

81 GaAs nanoholes becomes higher. Furthermore, with the In + ion fluence of 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 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) ions/spot, (b) ions/spot, (c) ions/spot, and (d) ions/spot. With the spot spacing of 1µm and the In + ion fluence of 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 71

82 exhibits the formation of GaAs nanoholes. With the higher In + ion fluences of ions/spot (b) and 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 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 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 C 0. 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 ions/spot and ions/spot. This suggests that the surface chemical potential gradients were only sufficient at the center along with the ion concentration of C 0 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 C 0, 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 ions/spot, a strong sputtering process can lead to damages of the substrate, resulting in sputtered holes with the depth in the order of 72

83 nanometers as shown in subsection 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 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 ions/spot to 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 ions/spot to ions/spot, resulting in single, double or multiple nanoholes. To summarize, the probabilities 1 of single, double and multiple GaAs nanoholes are registered as r n, where n is the amount of nanoholes in one FIB spot. Therefore, r 1, r 2, r 3 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, r sum = r 1 + r 2 + r 3 +. Figure 6.8 (a) shows r n as a function of n and the value of r sum 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 ions/spot to ions/spot, the probability of single nanoholes r 1 is dominated along with an increase of the probability of double nanoholes r 2. At the same time, the occupancy rate r sum increases from 87 % to 97 %. Similar results are also observed for the FIBpatterned 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 r sum 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 ions/spot. Furthermore, with the spacing of 2 µm, when the In + ion fluences are high at ions/spot and ions/spot, the probabilities of double and triple nanoholes, r 2 and r 3, become dominant in sequence. With corresponding FIB patterning parameters, the occupancy rate r sum 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. 73

84 Figure 6.8 The probability of single, double or multiple GaAs nanoholes, r 1, r 2, r 3 = r n, from different FIB-patterned areas. The sum of the probabilities equals to the occupancy rate of FIB spots, r sum = r 1 + r 2 + r 3. (a) The FIB-patterned areas of sample B0 with a spot spacing l spot of 2 µm and Ga + fluences Φ Ga from ions/spot to ions/spot. For sample A0, (b) the FIB-patterned areas with a spot spacing of 2 µm and In + fluences Φ In from ions/spot to ions/spot, and (c) with a spacing of 1 µm and In + fluences from ions/spot to 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 densities 2 of GaAs nanoholes, ρ FIB, 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. 74

85 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 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 ions/spot to ions/spot. However, a relatively high nominal density is observed with the lowest ion fluence of 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 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 ions/spot to 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 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 (r sum ) together with the increase of double nanoholes (r 2 ). 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 (r 2, r 3...) since all the FIB spots were occupied (r sum ~ 100 %). These various nominal densities suggest that the GaAs nanoholes transformed from Ga droplets formed on different FIBpatterned areas may have different dimensions depending on different patterning parameters. Figure 6.9 The nominal densities ρ FIB of GaAs nanoholes as a function of ion fluences, Φ Ga or Φ In, with different spot spacings l spot for (a) sample B0 and (b) sample A0 with Ga + and In + ion pattering, respectively. 75

86 Figure 6.10 AFM images and the corresponding profiles of the GaAs nanoholes formed with (a) θ Ga = 3 ML and (b) θ Ga = 5 ML on the FIB spots with l spot = 2 µm created with Φ In = ions/spot and Φ Ga = ions/spot on sample A0 and sample B0, respectively. θ Ga /ion species D 3 ML/ In + (A0) 268 ± ± ± ± ± ± ML/ Ga + (B0) 341 ± ± ± ± ± ± ML/ In + (A0) 243 ± ± ± ± ± 9 5 ML/ Ga + (B0) 269 ± ± ± ± ± 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 θ Ga of 3 ML or 5 ML by droplet epitaxy. The FIB-patterned areas were created with Φ ion = ions/spot and l spot = 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. 76

87 Figure 6.10 shows the topography of the typical GaAs nanoholes formed on the FIBpatterned areas generated with the optimum parameters, an ion fluence of 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 FIBpatterned 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 ions/spot and a spot spacing of 2 µm, leading to the achievement of 77

88 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 FIBpatterned 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. 78

89 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 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 θ InAs 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 79

90 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 h D of (8.2 ± 0.1) nm, has larger base diameters d D 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 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. 80

91 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. 81

92 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 selfpatterned 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 82

93 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 10 7 cm -2. The sizes of the QDs depend on the InAs coverages inside the nanoholes where the deposited InAs were preferentially accumulated, while 83

94 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 siteselective 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 siteselected QDs grown with 1.75 ML of InAs comprise larger dimensions. Because of the sizedependent energy band gap for QDs, it is interesting to investigate the optical properties of these QDs with various sizes 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 FIBpatterned 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 84

95 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 Φ In of ions/spot and a spot spacing l spot of 1 µm, (b) Φ In = ions/spot and l spot = 2 µm, (c) Φ In = ions/spot and l spot = 1 µm, and (d) Φ In = ions/spot and l spot = 2 µm. QD pairs of sample B58 grown in the arrayed B -type nanoholes with a Ga + ion fluence of 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 85

96 in previous section 6.2. Comparing these arrayed QDs with those QDs grown in the randomlydistributed 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 ions/spot and 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 86

97 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 FIBpositioned GaAs nanoholes on different FIBpatterned areas of sample B58. (a) The FIBpatterned area with a Ga + ion fluence Φ Ga of ions/spot and a spot spacing l spot of 1 µm, (b), (c) Φ Ga = ions/spot and l spot = 2 µm, and (d) Φ Ga = ions/spot and l spot = 2 µm. The profiles correspond to the QD pair shown in image (c) along [ ] and [ ] directions. 87

98 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 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 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 88

99 InAs coverage of 1.40 ML, the peak center at 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 ev (918 nm). According to SK growth, these two emerging lowenergy shoulders indicate the growth of new structures inside the GaAs nanoholes, i.e., the straininduced 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 ev (980 nm) and 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 ev (1092 nm), ev (1058 nm), ev (1030 nm) and 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. 89

100 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 powerdependence 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 ev (987 nm) and 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 lowerenergy peak at ev (E 0 ) 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 E 1 = ev (965 nm) appeared representing the firstexcited-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 E 0 of 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 E 1 of ev (986 nm) and E 2 of 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. 90

101 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 E 0 of ev (1068 nm), E 1 of ev (1027 nm), E 2 of ev (994 nm) and E 3 of 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. I 0 denotes the maximum intensity with an excitation power of 5 mw. E 0 and E 1 represent the energies corresponding to the ground-state (s-shell) and the firstexcited-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. 91

102 Figure 7.8 Power-dependent PL spectra at measured 77 K for sample C58 with an InAs coverage of 1.58 ML. I 0 denotes the maximum intensity with an excitation power of 5 mw. E 0, E 1 and E 2 represent the energies corresponding to the ground-state (s-shell), the firstexcited-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 E 0, E 1, E 2 and E 3 of ev, ev, ev and 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 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. 92

103 Figure 7.9 Power-dependent PL spectra at 77 K for sample C65 with an InAs coverage of 1.65 ML. I 0 denotes the intensity with an excitation power of 5 mw. E 0, E 1, E 2 and E 3 represent the energies corresponding to the ground-state (s-shell), the first-excited-state (pshell), 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 As the InAs coverage increases, the ground-state-transition energies from the QDs represent a red-shift from ev to 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 ev (E 0 ) 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 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 93

104 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 (E 0 and ), the first, second, and third excited states (E 1, E 2 and E 3 ) 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. 94

105 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 μm 2 with a pixel size of 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 μm 2 with a pixel size of nm 2. The excitation power is 113 W/cm 2. (provided by A. Senichev, MPI of Microstructure Physics, Halle). 95

106 Figure 7.12 The spectrally-integrated PL mapping image of a bright spot and its crosssection 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 μm 2 with a pixel size of nm 2. The arrow is only a guide for showing the direction of the cross-section image. E 00, E 10, E 01, and E A 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 μm 2 together with a fine pixel size of nm 2 was applied for spectrally-integrated PL mapping, as shown in Figure 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 E 00 = ev, two high-energy peaks with E 10 = ev and E 01 = ev, and also one small peak with E A = 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 E 00 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 E 00 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 E 10 and E 01 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 E A 96

107 might originate from the transitions between the ground-state (s-shell) electrons and the secondexcited-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/cm 2 to 379 W/cm 2. E 00 is the transition energy of the ground states. E 10, E 01, E 20, E 11 and E 02 are the transition energies of the excited states corresponding to, where x and y are the in-plane directions, n x and n y are the quantum numbers of the confinements. For example, E 10 is the recombination energy of the first excited states from the quantum confinement along the x direction. E A 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 n x and n y and oscillator frequencies x and y [177]. With a low power density, the peak present with the energy E 00 of 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 97

108 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 E A of ev, E 10 of ev, E 01 of ev, E 20 of ev, E 11 of ev, and E 02 of 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 (E 10 E 00 ) / (E A E 00 ) 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 E 00 of these single QDs are in the range from ev to ev. The first-excited-state-transition energies E 10 range from ev to ev, while the energies E 01 from ev to 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 E 10, E 01 and E A with respect to E 00 are shown in the plot (c), as a function of the ground-statetransition energy. With the increasing ground-state energies, the energy separation between E 01 and E 00, i.e. E 01 E 00, shows a stronger decreasing tendency than that with E 10 E 00. The energy separations for E A E 00 only change in a small range of 13 mev to 16 mev. The ground-statetransition energy E 00 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 selfpatterned 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. 98

109 (a) 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. E 00 is the transition energy of the ground states (s shell). E 10 and E 01 are the transition energies of the first excited states (p shell) with the confinements along the in-plane directions, x and y, respectively. E A is considered to be the transition energy between the groundstate (s-shell) electrons and secondexcited-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 E 00. The black dotted lines is calculated assuming the ratio h/ e of The blue and green dashed lines are only a guide to the eyes. (b) (c) 99

110 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 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 siteselectively 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 ions/spot, ions/spot and 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 μm 2. 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 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 ρ FIB of the arrayed B -type nanoholes are both of the order of 10 7 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 μm 2. 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 100

111 the un-patterned area (Φ In = 0 ions/spot) is found with an energy of 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 ions/spot to 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 ions/spot, ions/spot and 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 (Φ In = 0) is shown in each graph for comparison. 101

112 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 ions/spot to 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 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 102

113 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 FIBpatterned areas. Therefore, the optical properties of QDs can be tuned with the help of FIB prepatterning 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 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 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 siteselectively 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 μm 2 and a pixel size of 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 103

114 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 Moreover, the FIB spots with the optimum condition were all occupied by single or double GaAs nanoholes with the probabilities r 1 of 93 % and r 2 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 FIBpatterned area with Φ In = ions/spot and l spot = 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 μm 2 and a pixel size of nm 2. The excitation power is 113 W/cm 2. The spectra correspond to the spot 1 and 2 in the image consist of the transition peaks with the energies E 0, E 1, E 2 and E B. E 0 is the transition energy for the ground states of the single QDs. E 1 and E 2 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 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 E 0 104

115 of 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 E 1 = ev and E 2 = 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 E 0 = 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 E 1 = ev and E 2 = ev. However, the peaks with E B from both spots having an energy separation of 8 mev with respect to their ground-state peaks, E B - E 0, are different from the peaks considered to be the recombination between ground-state electrons and second-excited-state holes with E A observed in the previous subsection In addition, the pronounced peak present with an energy of 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 prepatterning 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. 105

116

117 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 10 7 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 siteselectively 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 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 wellpositioned 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. 107

118 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 ions/spot to 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 FIBpatterned 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 108

119 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 selfassembled/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 selfassembled 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]. 109

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121 Bibliography 1. D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum dot heterostructures (John Wiley Chichester 1999). 2. A. Zrenner, J. Chem. Phys. 112, 7790 (2000). 3. M.A. Hines, P. Guyot-Sionnest, J. Phys. Chem. 100, 468 (1996). 4. Y. Cao, U. Banin, J. Am. Chem. Soc. 122, 9692 (2000). 5. L.P. Kouwenhoven, D.G. Austing, S. Tarucha, Rep. Prog. Phys. 64, 701 (2001). 6. D. Bimberg, M. Grundmann, N.N. Ledentsov, S.S. Ruvimov, P. Werner, U. Richter, J. Heydenreich, V.M. Ustinov, P.S. Kop'ev, Z.I. Alferov, Thin Solid Films 267, 32 (1995). 7. K. Watanabe, N. Koguchi, Y. Gotoh, Jpn. J. Appl. Phys. 39, L79-L81 (2000). 8. E. Pehlke, N. Moll, A. Kley, M. Scheffler, Appl. Phys. A-Mater. 65, 525 (1997). 9. D. Leonard, M. Krishnamurthy, S. Fafard, J.L. Merz, P.M. Petroff, J. Vac. Sci. Technol. B 12, 1063 (1994). 10. D. Leonard, M. Krishnamurthy, C.M. Reaves, S.P. Denbaars, P.M. Petroff, Appl. Phys. Lett. 63, 3203 (1993). 11. K. Kamath, P. Bhattacharya, T. Sosnowski, T. Norris, J. Phillips, Electron. Lett. 32, 1374 (1996). 12. R. Mirin, A. Gossard, J. Bowers, Electron. Lett. 32, 1732 (1996). 13. I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001). 14. D. Bimberg, N. Kirstaedter, N.N. Ledentsov, Z.I. Alferov, P.S. Kop'ev, V.M. Ustinov, IEEE J. Sel. Top. Quant. 3, 196 (1997). 15. A. Fiore, J.X. Chen, M. Ilegems, Appl. Phys. Lett. 81, 1756 (2002). 16. P. Bhattacharya, X.H. Su, S. Chakrabarti, G. Ariyawansa, A.G.U. Perera, Appl. Phys. Lett. 86, (2005). 17. P. Michler, A. Kiraz, C. Becher, W.V. Schoenfeld, P.M. Petroff, L. Zhang, E. Hu, A. Imamoglu, Science 290, 2282 (2000). 18. C. Santori, M. Pelton, G. Solomon, Y. Dale, Y. Yamamoto, Phys. Rev. Lett. 86, 1502 (2001). 19. D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998). 20. G. Burkard, D. Loss, Phys. Rev. B 59, 2070 (1999). 21. P.W. Shor, SIAM J. Comput. 26, 1484 (1997). 22. H.T. Dobbs, D.D. Vvedensky, A. Zangwill, J. Johansson, N. Carlsson, W. Seifert, Phys. Rev. Lett. 79, 897 (1997). 23. N. Koguchi, K. Ishige, Jpn. J. Appl. Phys. 32, 2052 (1993). 111

122 24. Z.M. Wang, K. Holmes, Y.I. Mazur, K.A. Ramsey, G.J. Salamo, Nanoscale Res. Lett. 1, 57 (2006). 25. Z. Gong, Z.C. Niu, S.S. Huang, Z.D. Fang, B.Q. Sun, J.B. Xia, Appl. Phys. Lett. 87, (2005). 26. K. Tung, H. Gao, N. Xiang, J. Cryst. Growth 371, 117 (2013). 27. J.H. Lee, Z.M. Wang, E.-S. Kim, N.Y. Kim, S.H. Park, G.J. Salamo, Nanoscale Res. Lett. 5, 308 (2010). 28. J.H. Lee, Z.M. Wang, Z.Y. Abu Waar, G.J. Salamo, Cryst. Growth Des. 9, 715 (2009). 29. T. Mano, N. Koguchi, J. Cryst. Growth 278, 108 (2005). 30. T. Mano, K. Mitsuishi, Y. Nakayama, T. Noda, K. Sakoda, Appl. Surf. Sci. 254, 7770 (2008). 31. T. Mano, K. Watanabe, S. Tsukamoto, H. Fujioka, M. Oshima, N. Koguchi, J. Cryst. Growth 209, 504 (2000). 32. A.Z. Li, Z.M. Wang, J. Wu, Y. Xie, K.A. Sablon, G.J. Salamo, Cryst. Growth Des. 9, 2941 (2009). 33. Z.M. Wang, K. Holmes, J.L. Shultz, G.J. Salamo, Phys. Status Solidi (a) 202, R85 (2005). 34. Z.M. Wang, B.L. Liang, K.A. Sablon, G.J. Salamo, Appl. Phys. Lett. 90, (2007). 35. Z.M. Wang, B.L. Liang, K.A. Sablon, J.H. Lee, Y.I. Mazur, N.W. Strom, G.J. Salamo, Small 3, 235 (2007). 36. C. Heyn, A. Stemmann, R. Eiselt, W. Hansen, J. Appl. Phys. 105, (2009). 37. S.S. Huang, Z.C. Niu, Z.D. Fang, H. Ni, Z. Gong, J.B. Xia, Appl. Phys. Lett. 89, (2006). 38. C. Zhao, Y.H. Chen, B. Xu, P. Jin, Z.G. Wang, Appl. Phys. Lett. 91, (2007). 39. Á. Nemcsics, Acta Polytech. Hung. 8, 5 (2011). 40. P. Boonpeng, S. Kiravittaya, S. Thainoi, S. Panyakeow, S. Ratanathammaphan, J. Cryst. Growth (2013). 41. J.H. Lee, Z.M. Wang, N.W. Strom, Y.I. Mazur, G.J. Salamo, Appl. Phys. Lett. 89, (2006). 42. B.L. Liang, Z.M. Wang, J.H. Lee, K.A. Sablon, Y.I. Mazur, G.J. Salamo, Appl. Phys. Lett. 89, (2006) onso- onz z,. n,. Fust r,. onz z,. onz z,. Mart n z-pastor, Appl. Phys. Lett. 91, (2007). 44. N.W. Strom, Z.M. Wang, J.H. Lee, Z.Y. Abu Waar, Y.I. Mazur, G.J. Salamo, Nanoscale Res. Lett. 2, 112 (2007) onso- onz z,. Mart n- nch z,. onz z,. n,. Fust r,. onz z, Cryst. Growth Des. 9, 2525 (2009). 46. J.H. Lee, Z.M. Wang, B.L. Liang, K.A. Sablon, N.W. Strom, G.J. Salamo, Semicond. Sci. Tech. 21, 1547 (2006). 47. M. Mehta, D. Reuter, A. Melnikov, A.D. Wieck, A. Remhof, Appl. Phys. Lett. 91, (2007). 112

123 48. Y. Cordier, O. Tottereau, L. Nguyen, M. Ramdani, A. Soltani, M. Boucherit, D. Troadec, F. Lo, Y.Y. Hu, A. Ludwig, Phys. Status Solidi (c) 8, 1516 (2011). 49. H. Wang, J.L. Gray, J. Vac. Sci. Technol. B 29, 04D106 (2011). 50. M. Kammler, R. Hull, M.C. Reuter, F.M. Ross, Appl. Phys. Lett. 82, 1093 (2003). 51. M. Cahay (ed), Quantum confinement VI. Nanostructured materials and devices : proceedings of the international symposium (Electrochemical Society, Pennington, N.J 2001). 52. E. Kapon, Proc. IEEE 80, 398 (1992). 53. O. Gywat, H.J. Krenner, J. Berezovsky, Spins in optically active quantum dots. Concepts and methods (Wiley-VCH, Weinheim 2010). 54. B. Szafran, J. Adamowski, S. Bednarek, Physica E 5, 185 (1999). 55. F. Tinjod, Mécanismes de formation des boîtes quantiques semiconductrices, application aux nanostructures II-VI et étude de leurs propriétés optiques. PhD thesis (Université Joseph Fourier-Grenoble I 2003). 56. A.I. Ekimov, A.A. Onushchenko, JETP Lett. 34, 345 (1981). 57. A.L. Efros, Sov. Phys. Semicond.+ 16, 772 (1982). 58. S. Kiravittaya, A. Rastelli, O.G. Schmidt, Rep. Prog. Phys. 72, (2009). 59. A.L. Efros, M. Rosen, Annu. Rev. Mater. Sci. 30, 475 (2000). 60. J.I. Pankove, Optical processes in semiconductors (Courier Dover Publications 1971). 61. T.J. Bukowski, J.H. Simmons, Crit. Rev. Solid State 27, 119 (2002). 62. I.L. Medintz, H.T. Uyeda, E.R. Goldman, H. Mattoussi, Nat. Mater. 4, 435 (2005). 63. V.L. Colvin, M.C. Schlamp, A.P. Alivisatos, Nature 370, 354 (1994). 64. L. Jacak, P. Hawrylak, A. Wójs, Quantum dots (Springer, Berlin [u.a.] 1998). 65. T. Sako, J. Paldus, G.H. Diercksen, The Energy Level Structure of Low-dimensional Multielectron Quantum Dots, in: J.R. Sabin, E. Brandas (eds), Theory of confined quantum systems (Elsevier, Boston 2009). 66. J.-Y. Marzin, G. Bastard, Solid State Commun. 92, 437 (1994). 67. F. Henneberger, J. Puls, C. Spiegelberg, A. Schulzgen, H. Rossman, V. Jungnickel, A.I. Ekimov, Semicond. Sci. Tech. 6, A41 A50 (1991). 68. J.M. Moison, F. Houzay, F. Barthe, L. Leprince, E. Andre, O. Vatel, Appl. Phys. Lett. 64, 196 (1994). 69. A. Wójs, P. Hawrylak, S. Fafard, L. Jacak, Phys. Rev. B 54, 5604 (1996). 70. D. Leonard, K. Pond, P.M. Petroff, Phys. Rev. B 50, (1994). 71. O. Wolst, Electro-optical investigations of zero-dimensional nanostructures. Anisotropic Stark effect in InAs, GaAs self-assembled quantum dots (Lehrstuhl für Mikrocharakterisierung, Friedrich-Alexander-Universität, Erlangen 2003). 72. R.C. Ashoori, Nature 379, 413 (1996). 73. M. Rontani, F. Rossi, F. Manghi, E. Molinari, Phys. Rev. B 59, (1999). 74. J. R. Sabin, E. Brandas (eds), Theory of confined quantum systems (Elsevier, Boston 2009). 113

124 75. H. Drexler, D. Leonard, W. Hansen, J.P. Kotthaus, P.M. Petroff, Phys. Rev. Lett. 73, 2252 (1994). 76. M. Fricke, A. Lorke, J.P. Kotthaus, G. Medeiros-Ribeiro, P.M. Petroff, Europhys. Lett. 36, 197 (1996). 77. L. Bányai, S.W. Koch, Semiconductor quantum dots (World Scientific, Singapore, River Edge, NJ 1993). 78. H. Welker, H. Weiss, Group III-Group V Compounds, in: F. Seitz, D. Turnbull (eds), Solid state physics. Advances in research and applications (Academic press, New York 1956). 79. H.H. Wieder, J. Vac. Sci. Technol. 8, 210 (1971). 80. K. Ploog, Annu. Rev. Mater. Sci. 11, 171 (1981). 81. M.A. Herman, H. Sitter 7, Molecular beam epitaxy. Fundamentals and current status (Springer, Berlin, New York 1996). 82. E. Kuphal, Appl. Phys. A-Mater. 52, 380 (1991). 83. T.F. Kuech, Mater. Sci. Rep. 2, 1 (1987). 84. D.A. Glocker, S.I. Shah, Handbook of thin film process technology (Institute of Physics Pub., Bristol, U.K 2002). 85. J.S. Blakemore, J. Appl. Phys. 53, R123-R181 (1982). 86. M. Levinshtein, S. Rumyantsev, M. Shur, Handbook series on Semiconductor Parameters (vol 1). Si, Ge, C (Diamond), GaAs, GaP, GaSb, InAs, InP, InSb (World Scientific 1996). 87. P.K. Tien, Proc. Int. Summer School (1982). 88. F. Capasso, Science 235, 172 (1987). 89. K. Oura, V.G. Lifshits, A.A. Saranin, A.V. Zotov, Surface Science. An Introduction (Advanced Texts in Physics) (Springer 2003). 90. J.A. Venables, G.D.T. Spiller, M. Hanbucken, Rep. Prog. Phys. 47, 399 (1984). 91. S.A. Chambers, Surf. Sci. Rep. 39, 105 (2000). 92. A.Y. Cho, J. Appl. Phys. 41, 2780 (1970). 93. A.Y. Cho, J.R. Arthur, Prog. Solid State Ch. 10, Part 3, 157 (1975). 94. A.Y. Cho, Thin Solid Films 100, 291 (1983). 95. C. Webb, S.-L. Weng, J.N. Eckstein, N. Missert, K. Char, D.G. Schlom, E.S. Hellman, M.R. Beasley, A. Kapitulnik, J.S. Harris, Appl. Phys. Lett. 51, 1191 (1987). 96. E.H. Parker, The technology and physics of molecular beam epitaxy (Plenum Press 1985). 97. M.A. Herman, H. Sitter, Molecular beam epitaxy. Fundamentals and current status (Springer-Verlag, Berlin, New York 1989). 98. R.F.C. Farrow, Molecular beam epitaxy. applications to key materials (William Andrew Publishing 1995). 99. Riber, Riber MBE 32 operator's guide D. Reuter, A.D. Wieck, A. Fischer, Rev. Sci. Instrum. 70, 3435 (1999) W. Braun, Applied RHEED. Reflection high-energy electron diffraction during crystal growth (Springer, Berlin [u.a.] 1999) M. Ohring, Materials science of thin films (Academic press 2001). 114

125 103. D. Vanderbilt, L.K. Wickham, MRS Proc. 202, 555 (1990) R.M. Roescu, Wavefunctions and carrier-carrier interactions in InAs quantum dots studied by capacitance-voltage spectroscopy. PhD thesis (Ruhr-Universität Bochum 2008) N.P. Kobayashi, T.R. Ramachandran, P. Chen, A. Madhukar, Appl. Phys. Lett. 68, 3299 (1996) A.-L. Barabási, Appl. Phys. Lett. 70, 2565 (1997) V.A. Shchukin, N.N. Ledentsov, D. Bimberg, Physica E 9, 140 (2001) G. Medeiros-Ribeiro, K. Schmidt, T. Ngo, J.L. Feng, A. Lorke, J. Kotthaus, P.M. Petroff, Appl. Phys. Lett. 71, 2014 (1997) C. Heyn, Phys. Rev. B 64, (2001) L.G. Wang, P. Kratzer, N. Moll, M. Scheffler, Phys. Rev. B 62, 1897 (2000) P. Michler, Single semiconductor quantum dots (Springer 2009) I. Daruka, A.-L. Barabási, Phys. Rev. Lett. 79, 3708 (1997) J.H. Lee, Z.M. Wang, N.Y. Kim, G.J. Salamo, Nanotechnology 20, (2009) Á. Nemcsics, Óbuda University e Bulletin 2, 193 (2011) X. Li, G.W. Yang, J. Phys. Chem. C 112, 7693 (2008) X. Li, J. Cryst. Growth 377, 59 (2013) R.M. Stevenson, R.M. Thompson, A.J. Shields, I. Farrer, B.E. Kardynal, D.A. Ritchie, M. Pepper, Phys. Rev. B 66, (2002) A. Imamoglu, D.D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Sherwin, A. Small, Phys. Rev. Lett. 83, 4204 (1999) M. Kitamura, M. Nishioka, J. Oshinowo, Y. Arakawa, Appl. Phys. Lett. 66, 3663 (1995) D.S. Mui, D. Leonard, La Coldren, P.M. Petroff, Appl. Phys. Lett. 66, 1620 (1995) S. Jeppesen, M.S. Miller, D. Hessman, B. Kowalski, I. Maximov, L. Samuelson, Appl. Phys. Lett. 68, 2228 (1996) R. Tsui, R. Zhang, K. Shiralagi, H. Goronkin, Appl. Phys. Lett. 71, 3254 (1997) A. Konkar, A. Madhukar, P. Chen, Appl. Phys. Lett. 72, 220 (1998) H. Lee, J.A. Johnson, M.Y. He, J.S. Speck, P.M. Petroff, Appl. Phys. Lett. 78, 105 (2001) B.D. Gerardot, G. Subramanian, S. Minvielle, H. Lee, J.A. Johnson, W.V. Schoenfeld, D. Pine, J.S. Speck, P.M. Petroff, J. Cryst. Growth 236, 647 (2002) P. Atkinson, M.B. Ward, S.P. Bremner, D. Anderson, T. Farrow, G.A. Jones, A.J. Shields, D.A. Ritchie, Physica E 32, 21 (2006) T. Ishikawa, T. Nishimura, S. Kohmoto, K. Asakawa, Appl. Phys. Lett. 76, 167 (2000) S. Kiravittaya, H. Heidemeyer, O.G. Schmidt, Physica E 23, 253 (2004) S. Kiravittaya, A. Rastelli, O.G. Schmidt, Appl. Phys. Lett. 87, (2005) S. Kiravittaya, A. Rastelli, O.G. Schmidt, Appl. Phys. Lett. 88, (2006) S. Kohmoto, H. Nakamura, T. Ishikawa, S. Nishikawa, T. Nishimura, K. Asakawa, Mater. Sci. Eng. B-Adv. 88, 292 (2002) C.K. Hyon, S.C. Choi, S.-H. Song, S.W. Hwang, M.H. Son, D. Ahn, Y.J. Park, E.K. Kim, Appl. Phys. Lett. 77, 2607 (2000). 115

126 133. G. Biasiol, K. Leifer, E. Kapon, Phys. Rev. B 61, 7223 (2000) A. Madhukar, K.C. Rajkumar, P. Chen, Appl. Phys. Lett. 62, 1547 (1993) M. Ozdemir, A. Zangwill, J. Vac. Sci. Technol. A 10, 684 (1992) R. Songmuang, S. Kiravittaya, O.G. Schmidt, Appl. Phys. Lett. 82, 2892 (2003) M. Mehta, Positioning of self-assembled InAs quantum dots by focused ion beam implantation. PhD thesis (Ruhr-Universität Bochum 2007) M.-Y. Li, J. Lee, Z. Wang, Y. Hirono, J. Wu, S. Song, S.-M. Koo, E.-S. Kim, G.J. Salamo, Phys. Status Solidi (a) 209, 1075 (2012) La Giannuzzi, F.A. Stevie, Micron 30, 197 (1999) S. Reyntjens, R. Puers, J. Micromech. Microeng. 11, 287 (2001) J.H. Daniel, D.F. Moore, J.F. Walker, J.T. Whitney, Microelectron. Eng. 35, 431 (1997) J.H. Daniel, D.F. Moore, J.F. Walker, Smart Mater. Struct. 9, 284 (2000) M.K. Miller, K.F. Russell, K. Thompson, R. Alvis, D.J. Larson, R. Anderson, S.J. Klepeis, J.M. Cairney, D.W. Saxey, D. Mcgrouther, Microsc. Microanal. 13, 428 (2007) M. Albrecht, C.T. Rettner, A. Moser, B.D. Terris, Microsyst. Technol. 13, 129 (2006) P.D. Prewett, G.L.R. Mair, Focused ion beams from liquid metal ion sources (Research Studies Press 1991) A.A. Tseng, Small 1, 924 (2005) A.A. Tseng, K. Chen, C.D. Chen, K.J. Ma, IEEE T. Electron. Pa. M. 26, 141 (2003) J. Melngailis, Nucl. Instrum. Meth. B 80, 1271 (1993) K. Sakaguchi, T. Sekine, J. Vac. Sci. Technol. B 16, 2462 (1998) J. Orloff, L. Swanson, M.W. Utlaut, High resolution focused ion beams. FIB and its applications: The physics of liquid metal ion sources and ion optics and their application to focused ion beam technology (Springer 2003) P. Mazarov, A. Melnikov, R. Wernhardt, A.D. Wieck, Appl. Surf. Sci. 254, 7401 (2008) D.R. Kingham, L.W. Swanson, Appl. Phys. A 34, 123 (1984) C.-S. Kim, S.-H. Ahn, D.-Y. Jang, Vacuum 86, 1014 (2012) J. Lindhard, M. Scharff, H.E. Schiøtt, Range concepts and heavy ion ranges (Munksgaard 1963) J.F. Ziegler, M.D. Ziegler, J.P. Biersack, Nucl. Instrum. Meth. B 268, 1818 (2010) L. Frey, C. Lehrer, H. Ryssel, Appl. Phys. A-Mater. 76, 1017 (2003) A. Lugstein, B. Basnar, J. Smoliner, E. Bertagnolli, Appl. Phys. A-Mater. 76, 545 (2003) K.D. Cummings, L.R. Harriott, G.C. Chi, Ostermayer, Jr.,F. W., P.D. Blais, Proc. SPIE 0632, 93 (1986) R.L. Kubena, J.W. Ward, Appl. Phys. Lett. 51, 1960 (1987) J. Orloff, Rev. Sci. Instrum. 64, 1105 (1993) T. v r,. g r-waldau, M. Eckberg, E.T. Heyen, H. Lage, A.D. Wieck, K. Ploog, J. Appl. Phys. 72, 1858 (1992) E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873) Rayleigh, Philos. Mag. 42, 167 (1896). 116

127 164. G. Binnig, C.F. Quate, Phys. Rev. Lett. 56, 930 (1986) T. Pradeep, Nano. The essentials : understanding nanoscience and nanotechnology (McGraw-Hill, New York, London 2008) G. Kada, F. Kienberger, P. Hinterdorfer, Nano Today 3, 12 (2008) P.J. Dean, Prog. Cryst. Growth Ch. 5, 89 (1982) J. Tulkki, A. Heinämäki, Phys. Rev. B 52, 8239 (1995) A. Rasmussen, V. Deckert, Anal. Bioanal. Chem. 381, 165 (2005) hm,. icht r, M. ptitz,. i nau, v. ci. Instrum. 68, 3458 (1997) G.B. Assayag, J. Vac. Sci. Technol. B 11, 2420 (1993) M. Grundmann, N.N. Ledentsov, O. Stier, D. Bimberg, V.M. Ustinov, P.S. Kop'ev, Z.I. Alferov, Appl. Phys. Lett. 68, 979 (1996) B.L. Liang, P.-S. Wong, T. Tran, V.G. Dorogan, Y.I. Mazur, M.E. Ware, G.J. Salamo, C.-K. Shih, D.L. Huffaker, Nano Res. 6, 235 (2013) Y. Ji, W. Lu, G. Chen, X. Chen, Q. Wang, J. Appl. Phys. 93, 1208 (2003) F. Heinrichsdorff, M. Grundmann, O. Stier, A. Krost, D. Bimberg, J. Cryst. Growth 195, 540 (1998) C. Heyn, A. Stemmann, T. Köppen, C. Strelow, T. Kipp, M. Grave, S. Mendach, W. Hansen, Appl. Phys. Lett. 94, (2009) S.-S. Li, K. Chang, J.-B. Xia, Phys. Rev. B 71, (2005) A. Rastelli, S. Stufler, A. Schliwa, R. Songmuang, C. Manzano, G. Costantini, K. Kern, A. Zrenner, D. Bimberg, O.G. Schmidt, Phys. Rev. Lett. 92, (2004) A.D.B. Maia, E.C.F. da Silva, A.A. Quivy, V. Bindilatti, V.M. de Aquino, I.F.L. Dias, J. Phys. D Appl. Phys. 45, (2012). 117

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129 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 A #14105 B #14236 A (10.75) #14108 B (10.75) #14115 B (12) #14233 B (12) #14240 C (10.75) #14116 C (11.5) #14203 C (12) #14235 C (13) #14297 C (12) #14242 Appendix 1 Index of the internal sample number at AFP 119

130 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. 120