Study of correlations in the stacking sequence of a NW 

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Polytypism in III-V nanowires

Bulk III-V semiconductors crystallize in the cubic zincblende (ZB) form, except for nitrides, which adopt the hexagonal wurtzite (WZ) structure. Along the <111> direction (which is also the typical NW growth direction), the two structures differ only for the stacking sequence, the ZB sequence being ABCABCA… and the WZ being ABABA…, where each letter indexes one of the three possible lateral positions of the ML (Fig. 1.5). Alternatively, the two structures can be distinguished by the relative orientations of the III-V bonds. In the ZB structure the III-V bonds are parallel to each other, while in WZ they are arranged in a staggered configuration (using the language of chemistry, we would say that they are in « trans » and « cis » configuration, respectively). Interestingly, materials that are ZB in their bulk form are often found to crystallize as WZ in NWs. This behavior has been observed in a number of III-V materials grown by different techniques, especially in arsenides [62, 99, 112, 113, 125, 128, 135]. For many III-V materials the energy difference between the two crystal structures is only a few meV/atom [146], and theoretical calculations predict that the WZ structure is thermodynamically favorable for very thin NWs (diameters <10 nm) because of the lower number of dangling bonds on the NW sidewalls and edges compared to ZB [1, 46, 90]. However, this cannot explain the observation of the WZ phase in the works cited above, where the diameters are much larger.

Self-catalyzed GaAs NWs: a model system

We saw that gold is commonly used to induce the growth of both elemental and III-V NWs. In fact, the vast majority of works on VLS NWs use Au, which is quite surprising given the variety of materials and growth techniques, but means that Au is suitable to seed NW growth in a very broad material and temperature window ranges. An interesting discussion of why gold is probably the most effective metal to induce NW growth can be found in Ref. [98]. On the other hand, the presence of Au in Si is extremely detrimental even at dopant concentrations. It has long been known that Au introduces both acceptor and donor states in the band gap, causing a significant reduction of carrier lifetimes, an effect detectable at concentrations as low as 1012 cm−3 [26]. While III-V NWs grown with gold still exhibit excellent electronic properties, use of Au must be avoided if integration with silicon is sought. Because of its low chemical reactivity, removal of Au surface contamination is difficult. This incompatibility with the Si platform stimulated the research for alternatives to gold. One alternative is to avoid the catalyst droplet altogether, which usually involves selective area growth, with long and expensive substrate preparation procedures. Furthermore, compared to VLS growth, the temperature/flux rate growth window is reduced and high aspect ratios are more difficult to obtain (with some notable exceptions [100]). Growth of III-V NWs using alternative foreign catalysts was explored, with examples including noble metals (Pd, Pt, Ag) and other metals (Ni, Mn, Cu and Fe) [32] each of them with unique advantages and drawbacks. For example, Mn has been exploited to grow spontaneously Mn-doped GaAs NWs [94]. The interested reader may refer to a recent review by Dick and Caroff on gold-free NW growth [32].
Finally, a third option is to exploit the VLS mechanism using a group III metal as catalyst e.g. In for InAs [57]. In this case we speak of a self-catalyzed growth mechanism. Galliumassisted GaAs NWs is, by far, the most investigated system for self-catalyzed growth. The first report of GaAs whiskers grown using liquid gallium dates back to 1965 [11] and the first example of Ga-catalyzed GaAs growth by MBE was reported by Arthur and LePore in 1969 [8] when MBE was still in its infancy. In the attempt of achieving perfect two-dimensional growth, the authors described whisker growth as a parasitic effect induced by the presence of scratches and other surface defects. Since MBE was developed with the objective of realizing high-quality epitaxial films, the formation of such peculiar structures did not stimulate much interest.
The interest revamped in recent years, when the synthesis of epitaxial high purity Gaseeded GaAs NWs was achieved [43, 71]. Ga-assisted growth has been reported first on GaAs [4, 43] and shortly afterwards on cleaved Si(100) [71] and Si(111) [103]. In both cases, a thin layer of Si oxide was deposited or spontaneously formed on the substrate. However, the role of the oxide is not yet completely clarified: Plissard et al. [114] found that NW growth can occur on both oxidized and oxide-free Si, although with different growth conditions. On one hand, the presence of oxide enhances the NW yield and reduces the formation of parasitic crystallites, but it reduces NW verticality [114]. In another paper, Plissard et al. [115] showed that a SiO2 mask with oxide-free openings can provide a high degree of verticality and suppress the growth of parasitic structures.

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Heterostructure formation in nanowires: advantages and challenges

Epitaxy refers to the growth of a single crystal on top of another (usually semiconductors) with the same or fixed relative crystal orientation. We speak of homoepitaxy if the two crystals are of the same material and of heteroepitaxy if they are not. Epitaxial layers of two different materials are referred to as heterostructures. Heterostructures widely expand the range of application of semiconductor materials beyond simple doping. High quality heterostructures allowed for major developments, such as quantum wells and superlattices. Nevertheless, as mentioned previously, the quality of NW heterostructures obtained by top-down methods may be limited by the degradation of the starting bulk material (or thin film) upon etching. Actually, the advantage of bottom-up NWs is to grow structures that cannot be obtained in planar form. In the two-dimensional case (except for homoepitaxy), the epilayer and its substrate have generally different lattice parameters. Let as and ae be the lattice parameters of the relaxed substrate and epilayer, respectively, the lattice mismatch is: f = ae−as ae .

Scanning electron microscopy

The scanning electron microscope (SEM) exploits electrons to produce images of a sample. A focused electron beam (with a diameter of about 1 nm) is scanned over the sample surface, where it interacts with matter, producing electrons and radiation that are collected by suitable detectors. A typical SEM column is composed by a cathode (either a hot filament or a field emission cathode) and by focusing magnetic lenses. Coils are used to deflect the beam to produce a scan in the directions perpendicular to the beam. The column is usually operated at between 1 and 40 kV. Because of the high electron kinetic energy, a large number of signals are produced in an SEM: backscattered electrons, secondary electrons, Auger electrons, Bremsstrahlung X-rays, characteristic X-rays and cathodoluminescence. However, most SEM are only equipped with detectors for backscattered and secondary electrons. The energy spectrum of the outgoing electrons contains an intense component made of elastically backscattered electrons, a component at slightly lower energy of electrons inelastically scattered by plasmons or interband transitions, followed by a long, flat region that extends to energies down to 50 eV. The last region, at low energies, is that of the so-called « true » secondary electrons. These electrons underwent multiple scattering, thus they do not have any particular directionality and they are not material-sensitive, and for this reason are suitable for sample topography.

Table of contents :

Thesis overview
List of figures
List of tables
1 Vapor-liquid-solid growth of III-V nanowires 
1.1 What are nanowires?
1.2 The vapor-liquid-solid mechanism of nanowire growth
1.2.1 Growth directions
1.2.2 Nanowire growth dynamics
1.3 Understanding NW growth with nucleation theory
1.3.1 Calculation of the 2D nucleation barrier
1.3.2 The classical nucleation rate
1.3.3 Polytypism in III-V nanowires
1.4 Self-catalyzed GaAs NWs: a model system
1.4.1 Crystal structure
1.5 Heterostructure formation in nanowires: advantages and challenges
1.5.1 The reservoir effect
2 Experimental methods 
2.1 Molecular beam epitaxy
2.1.1 Effusion cells and flux measurements
2.1.2 RHEED
2.1.3 Absolute calibration of the vapor fluxes
2.2 Electron microscopy characterization
2.2.1 Scanning electron microscopy
2.2.2 Transmission electron microscopy
2.2.3 Quantification of composition using medium and high-resolution HAADF contrast in scanning transmission microscopy
3 Study of correlations in the stacking sequence of a NW 
3.1 Introduction
3.2 NW synthesis and data collection
3.3 Probabilistic analysis of the stacking sequence: conditional probabilities .
3.4 Distribution of cubic and hexagonal segments
3.5 The pair correlation function
3.6 Including correlations in the classical nucleation theory
3.6.1 Standard choice
3.6.2 ANNNI for the nucleus interface energy
3.6.3 Extending the ANNNI model to the step energy
3.7 Conclusions
4 Development of self-catalyzed Ga(As,P) axial heterostructures 
4.1 Introduction
4.2 Growth of pure, self-catalyzed GaP nanowires
4.3 Growth of GaAs (GaP) insertions in GaP (GaAs)
4.4 Behavior of As and P fluxes
4.5 Morphology of the growth front
4.6 Conclusions
5 (Al,Ga)As axial heterostructures 
5.1 (Al,Ga)As insertions in self-catalyzed GaAs NWs
5.2 Experimental details
5.3 Abruptness of interfaces
5.3.1 Estimation of Al fraction in the liquid
5.3.2 The effect of As flux and Al diffusion
5.3.3 Improving interface abruptness with droplet pre-filling
5.4 Modeling the interface composition
5.4.1 Liquid-solid equilibrium of the Al-Ga-As alloy
5.4.2 Predicting the composition profile
5.4.3 An analytical solution for the interface profile
5.5 Conclusions
6 On thin nanowires and the ultimate control of nucleation events 
6.1 Nucleation statistics in time
6.1.1 Growth rate diagram of self-catalyzed GaAs nanowires
6.1.2 Depleting the droplet: growth versus evaporation
6.1.3 Difficulties of the steady-state approach
6.1.4 Pulsing the As supply
6.1.5 First experimental demonstrations
6.1.6 Conclusions
6.2 Growth of thin NWs
General conclusions and perspectives
References 

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