Bruno Daudin

Julien Pernot

Nicolas Mollard

Keywords: molecular beam epitaxy, GaN, nanowires, n and p-type doping, axial p-n junction, electron beam induced current jets moléculaires, GaN, nanofils, dopage de type n et type p, jonction p

III-nitride nanostructures have been attracting increasing attention due to their peculiar properties and potential device applications as lighting LEDs. The control and evaluation of the doping in the nanostructures is a crucial, yet a challenging issue. This thesis advances the field by exploring the n and p type doping process of GaN nanowires (NWs) grown by molecular beam epitaxy (MBE). In particular, their electrical properties have been revealed through a multi-technique approach at the single NW level.

Firstly, the structural and electrical properties of a series of Si-doped (n-type) GaN NWs have been studied. High resolution energy dispersive X-ray spectroscopy measurements on single NWs have illustrated the achievement of a higher Si incorporation in NWs than in epilayers, and Si segregation at the edge of the NW with the highest doping.

Furthermore, direct transport measurements (four probes measurements from 300 K down to 5 K) on single NWs have shown a controlled doping with resistivity from 10 2 to 10 -3 Ω.cm, and a carrier concentration from 10 17 to 10 20 cm -3 . Field effect transistor measurements have evidenced the n-type nature and a high electron mobility of the nonintentionally doped NWs.

Secondly, the growth conditions of Mg-doped (p-type) and axial GaN p-n junction NWs have been determined to achieve significant Mg incorporation. Furthermore, the electrical properties of the axial GaN p-n junction NWs, dispersed on SiO 2 and contacted by ITO, have been studied using electron beam induced current (EBIC) technique. EBIC technique revealed the location of the p-n junction and clearly demonstrated its operation under reverse and forward polarization. Moreover, EBIC showed highly resistive p-GaN in accordance with the difficulties to perform direct transport measurements on p-GaN NWs.

This original study provides a nanoscale description of the electrical and doping properties of the GaN NWs, facilitating the fabrication of the future GaN nanostructures based devices.

Introduction

L'intérêt récent porté aux nanofils (NWs) de GaN résulte du développement rapide des semi-conducteurs nitrures (III-N). Grâce à leur largeur de bande directe, qui couvre une grande gamme de longueurs d'onde, allant du proche infrarouge (IR) au spectre visible jusqu'à l'ultraviolet (UV) profond, les semi-conducteurs nitrures sont les matériaux idéaux pour la fabrication de dispositifs optoélectroniques tels que les diodes électroluminescentes (LEDs), diodes laser (LDs) et photodétecteurs. Au vu de ces applications technologiques, des décennies d'activités de recherche ont été consacrées à l'amélioration de la qualité des cristaux, des propriétés optiques, structurelles et électriques des matériaux III-N par différentes méthodes de croissance et techniques de caractérisation. Dans l'histoire des nitrures, deux découvertes importantes méritent d'être mentionnées : (1) la proposition de l'utilisation d'une couche tampon d'AlN pour améliorer considérablement la qualité des cristaux de la couche planaire de GaN, par Amano et al. en 1986 [1] ; (2) la révélation de l'activation du dopage accepteur de Mg dans GaN obtenue par recuit dans une atmosphère libre d'hydrogène [START_REF] Nakamura | Thermal annealing effects on p-type Mg-doped GaN films[END_REF] ou par irradiation par faisceau électronique de faible énergie [START_REF] Amano | p-type conduction in Mgdoped GaN treated with low-energy electron beam irradiation (LEEBI)[END_REF] au début des années 90. Ces deux découvertes ont ouvert la voie à la fabrication des premières LEDs bleues [START_REF] Nakamura | Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes[END_REF], et plus tard aux premières LDs [START_REF] Nakamura | InGaN-based multi-quantum-well-structure laser diodes[END_REF], qui sont les composants technologiques de base des disques Blue-ray. Ces avancées ont démocratisé l'utilisation de matériaux à base de nitrures sur des marchés commerciaux variés. Le prix Nobel de physique 2014 a été en outre attribué aux professeurs Isamu Akasaki, Hiroshi Amano et Shuji Nakamura « pour l'invention des diodes électroluminescentes bleues efficaces qui ont permis la fabrication de sources de lumière blanche intenses et économes d'énergie», signant la reconnaissance scientifique des énormes progrès dans le domaine des nitrures.

Cependant, l'un des problèmes majeurs des matériaux nitrures est l'absence de substrat adapté à leur croissance en épitaxie. Les couches planaires III-N hétéro-épitaxie contiennent une forte densité de dislocations, en raison de la contrainte induite par l'incompatibilité thermique et du désaccord de réseau avec un substrat étranger, ce qui pourrait limiter l'amélioration des performances des dispositifs à base de III-N. Les nanofils (NWs) III-N, en revanche, offrent une solution alternative à ce problème. Grâce à leur unidimensionnalité, les NWs peuvent relaxer facilement les contraintes sur leur périphérie et se développer sans dislocation sur des substrats ayant des paramètres de maille très différents.

Les premiers NWs de GaN auto-assemblés ont été annoncés par deux groupes de recherche dirigés par Kishino au Japon [START_REF] Yoshizawa | Growth of selforganized GaN nanostructures on Al2O3 ( 0001 ) by RF-radical source molecular beam epitaxy[END_REF] et Calleja en Espagne [START_REF] Sanchez-Garcia | The effect of the III/V ratio and substrate temperature on the morphology and properties of GaN-and AlN-layers grown by molecular beam epitaxy on Si(1 1 1)[END_REF] à la fin des années 1990. Depuis lors, les NWs III-N ont trouvé application dans des dispositifs variés, dont les LEDs, les LDs, les photodétecteurs, les sources de photons individuelles, les l'exception des températures des cellules Si.

L'incorporation de Si induit une variation morphologique des NWs à une température de cellule Si supérieure à 938 °C. Un élargissement du NW a été observé et les facettes supérieures du NW sont passées d'une symétrie d'ordre 6 à une symétrie d'ordre 12 lorsque la température de la cellule Si a atteint 950 °C. Un élargissement des largeurs à mi-hauteur (FWHM) du bord de bande et une augmentation de l'émission de paire donneur-accepteur (DAP) dans les spectres de PL ont été reconnus lors du dopage Si.

Plusieurs modes de défauts liés au Si ont été observés sur les spectres Raman, et une tension de traction liée à la variation de fréquence du mode E 2h augmente avec la température de la cellule Si jusqu'à 950 °C, où la relaxation se produit. La cartographie du contenu en Si à l'échelle nanométrique par spectroscopie d'EDX permet de comprendre ces observations. Les NWs crûs avec une température de cellule Si de 950 °C présentaient un coeur avec une concentration moyenne en Si de 2,5 × 10 20 at / cm 3 , et une coquille avec une concentration en Si de 6,5 × 10 20 at / cm 3 , alors que les NWs avec la température de la cellule Si de 938 °C contiennent une distribution en Si homogène à 1 × 10 20 at / cm 3 . Plus de Si peut être incorporé dans un NW de GaN, comparativement aux couches planaires.

Un processus de contact NW basé sur la lithographie par faisceau d'électrons a été développé pour effectuer des mesures électriques sur des NWs uniques. Les mesures de transport direct sur les NWs uniques dopés par le Si ont montré un dopage contrôlé avec une résistivité de 10 2 à 10 -3 Ω.cm et une densité de porteurs de 10 17 à 10 20 cm -3 . Les mesures FET combinées à la simulation des éléments finis ont montré une mobilité élevée dans ces NWs, comparable à la valeur de mobilité de couches planaires de GaN dans l'état de l'art.

Jonction p-n axiale NWs de GaN

Dans la deuxième partie du manuscrit, les conditions de croissance par EMJ des NWs de GaN dopés au Mg ont été étudiées, afin d'obtenir une incorporation en Mg importante. Les propriétés électriques de la jonction p-n axiale NWs de GaN ont été étudiées en utilisant la technique EBIC.

En particulier, nous avons constaté que la température des cellules Mg et la température du substrat de croissance jouaient un rôle important dans l'incorporation du Mg dans le système de EMJ. Une recette de croissance en deux étapes a été proposée pour améliorer l'incorporation du Mg, et elle a été utilisée pour la croissance des jonctions pn axiales.

L'analyse EBIC a permis de visualiser la présence de la jonction p-n dans deux NWs uniques et a clairement démontré son fonctionnement sous polarisation inverse et vers l'avant. Le niveau de dopage accepteur obtenu est d'environ 2-3 × 10 17 cm -3 , en prenant le niveau de dopage du donneur à 2-3 × 10 18 cm -3 estimé à partir des résultats des NWs dopés au Si. La longueur de diffusion des trous dans le n-GaN a été mesurée à 75 nm pour le NW # 1 et à 43 nm pour le NW # 2. En polarisation positive, l'EBIC révèle la nature résistive élevée du p-GaN, ce qui est compatible avec l'extension de la largeur de l'appauvrissement de la jonction p-n réduite sous une polarisation négative. Le contraste de tension des électrons secondaires s'est révélé limitée dans notre cas en raison des contaminations par faisceau électronique. Enfin, et non des moindres, nous avons montré que le contact ITO forme un contact ohmique ou quasi-ohmique sur les NWs de GaN dopés type n et p.

INTRODUCTION General context

The emerging interests in GaN nanowires (NWs) derive from the rapid development in III-nitride semiconductors. Thanks to their direct band gap and the wide wavelength range, spanning from the near infrared through the visible spectrum into the deep ultra violet, III-nitride semiconductors are the ideal materials for fabricating optoelectronic devices, such as light-emitting diodes (LEDs), laser diodes (LDs) and light detectors. In the view of these device applications, decades of research activities have been devoted to improve the crystal quality, optical, structural, and electrical properties of III-nitride materials through different growth methods and characterization techniques. In the history of nitrides, two important discoveries are worth mentioning: (1) the proposal of the use of an AlN buffer layer to greatly improve the crystal quality of GaN epitaxial layer by Amano et al. in 1986 [START_REF] Amano | Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer[END_REF]; (2) the revelation of Mg acceptor doping activation in GaN achieved by either annealing in a hydrogen free ambient [START_REF] Nakamura | Thermal annealing effects on p-type Mg-doped GaN films[END_REF] or low-energy electron-beam irradiation [START_REF] Amano | p-type conduction in Mgdoped GaN treated with low-energy electron beam irradiation (LEEBI)[END_REF] at the beginning of the 90s. These two discoveries have paved the way for the fabrication of the first blue LEDs [START_REF] Nakamura | Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes[END_REF] and later on the first LDs [START_REF] Nakamura | InGaN-based multi-quantum-well-structure laser diodes[END_REF], which are the core technology components in Blue-ray Disc. These advances have transport properties of this series of Si-doped GaN NWs are investigated. A contacting procedure based on electron beam lithography was developed In order to perform electrical measurements on single NW. Important physical parameters of these NWs, such as resistivity, doping level, and mobility have been further evaluated using measurements of four-probe and field effect transistor configurations.

In Chapter 3, I will switch to Mg-doped and GaN p-n junction NWs. In a first session, the suitable growth conditions for the Mg-doped GaN NWs are investigated, and then axial GaN p-n junction NWs are grown with Mg-doped part on top of the Si-doped part.

Photoluminescence characterization will demonstrate the signatures of the both dopants.

In the second session, the axial GaN p-n junction NWs are characterized by electron beam induced current technique, with a special exploration on p-type ohmic contacts.

Collaborations

One of the attracting feathers of this PhD work is that it has been carried out in two laboratories ("Nanophysics and Semiconductors" group, INAC, CEA and "Wide bandgap semiconductor" group, Institut Néel) in Grenoble, with the aim of combining their expertise in the field of growth and electrical characterization, respectively. In addition, in order to deepen our understanding of the physics of doping in GaN NWs, several successful collaborations have been realized with external collaborators. To "conclude this introduction", I would like to name those who have contributed to the results hereafter presented in this manuscript.

Growth by PAMBE was carried out under the guidance of my PhD supervisor Dr. Bruno Daudin ("Nanophysics and Semiconductors" group, INAC, CEA, Grenoble) and in collaboration with previous / current PhD students from the group.

Electrical characterization was carried out under the guidance of my PhD co-supervisor Prof. Julien Pernot ("Wide bandgap semiconductor" group, Institut Néel, Grenoble) and in collaboration with Fabrice Donatini (Institut Néel, Grenoble).

All the devices process have been realised in Nanofab Institut Néel, Grenoble.

High resolution energy-dispersive X-ray spectroscopy (EDX) was performed by Dr.

Eric Robin (Minatec Campus, INAC, CEA, Grenoble).

Raman spectroscopy was performed in collaboration with Dr. Ana Cros from University of Valencia, Spain.

THE BASICS

The objective of this chapter is to give a brief description of some basic properties of the main subject of this work: nitride materials, including nitride nanowires (NWs), as well as the main growth method (molecular beam epitaxy).

1.1 Nitride properties

Structural properties

The III-N semiconductor family (InN, GaN, AlN as well as their ternary and quaternary alloys) mainly exists in the form of two different crystalline structures: wurtzite (WZ) and zinc-blende (ZB). The former contains a hexagonal unit cell with two lattice constants a and c whereas the latter is made of cubic unit cells. The WZ structure is composed of two interpenetrating hexagonal close-packed sublattices formed by metallic and nitrogen atoms respectively, ideally shifted by (3/8)c along the [0001] direction. The ZB structure contains two interpenetrating face-centered cubic sublattices, shifted by one quarter of the distance along the cube diagonal.

Thermodynamically, the WZ structure is more stable than the ZB phase under ambient conditions. Thus, the WZ structure is generally the main interest of epitaxial growth;

however, ZB could be present in the form of stacking faults [START_REF] Morkoç | Handbook of Nitride Semiconductors and Devices, Materials Properties[END_REF]. As illustrated in Figure 1.1, the WZ crystal structure of GaN is presented with a ball-stick schematic, in which the Ga and N atoms are portrayed by the blue and pink balls, respectively. The basic parameter is lattice constant a, and c is the length of the hexagonal primitive cell. The atoms are stacked in form of the ABABA along the [0001] axis in the WZ hexagonal unit cell. Figure 1.1 also shows the most common planes in the WZ structure, including polar c-plane, non-polar a-and m-planes as well as semi-polar [START_REF] Zhu | Unintentional doping in GaN[END_REF][START_REF] Keller | Recent progress in metal-organic chemical vapor deposition of (000-1) N-polar group-III nitrides[END_REF][START_REF] Kaun | Growth optimization of metal-polar III-nitride high-electronmobility transistor structures by molecular beam epitaxy[END_REF][START_REF] Suzuki | First-principles calculations of effective-mass parameters of AlN and GaN[END_REF][START_REF] Bernardini | Spontaneous polarization and piezoelectric constants of III-V nitrides[END_REF][START_REF] Dwiliński | Excellent crystallinity of truly bulk ammonothermal GaN[END_REF][START_REF] Mori | Growth of bulk GaN crystal by Na flux method under various conditions[END_REF][START_REF] Grzegory | High pressure growth of bulk GaN from solutions in gallium[END_REF][START_REF] Motoki | Development of gallium nitride substrates[END_REF][START_REF] Liu | Substrates for gallium nitride epitaxy[END_REF][START_REF] Mccray | MBE deserves a place in the history books[END_REF][START_REF] Cho | How molecular beam epitaxy (MBE) began and its projections into the future[END_REF] plane.

Recommended values of lattice parameters a and c of wurtzite InN, GaN, AlN at 300K are given in Table 1.1 [START_REF] Wu | When group-III nitrides go infrared: new properties and perspectives[END_REF].

Table 1.1 Lattice parameters a and c for wurtzite InN, GaN, AlN at 300K [START_REF] Wu | When group-III nitrides go infrared: new properties and perspectives[END_REF] Polarity In the WZ structure, the [0001] and the [000-1] directions are not equivalent, because of a lack of center of symmetry. The vector going from the metallic atom (In, Ga, Al) and pointing towards N is conventionally defined as the positive direction of the c-axis, i.e. [0001]. Therefore, two polarities can be distinguished, metal-polar (Ga-polar in the case of GaN) when its growth direction is along [0001]; N-polar when its growth direction is along [000-1] (see Figure 1.2). Meanwhile, piezoelectric polarization is also present in the III-nitride materials due to strain. Therefore, the total polarization is the sum of spontaneous polarization and piezoelectric polarization. The presence of this polarization can have significant effects on device structures and has inspired new applications for III-nitride materials.

1.2 Epitaxial layers and nanowires (NWs)

1.2.1 2D layer growth -substrate issues
The choice of substrate is one of the first things to do when it comes to the epitaxy of a given material. Unfortunately, for III-nitrides, this choice is not easy. In fact, the main issue for the epitaxy of 2D III-nitride layers is the lack of suitable substrate.

Homoepitaxy Homoepitaxy could be ideal for the epitaxy growers since there would be no worries with mismatch and influence from the foreign substrates. However, for a long time, commercial bulk GaN or AlN wafers were not available. Many efforts have been devoted to optimize the growth conditions for producing large bulk nitride substrates with low dislocation density. Additional to traditional vapor phase methods, such as Hydride Vapor Phase Epitaxy (HVPE) and Metal Organic Chemical Vapor Deposition (MOCVD), novel solution-based methods such as ammonothermal [START_REF] Dwiliński | Excellent crystallinity of truly bulk ammonothermal GaN[END_REF], Naflux [START_REF] Mori | Growth of bulk GaN crystal by Na flux method under various conditions[END_REF], high pressure [START_REF] Grzegory | High pressure growth of bulk GaN from solutions in gallium[END_REF] etc. have been developed to improve the crystal growth.

Even though the defect density can be reduced to 10 2 -10 3 cm -2 , these methods are still limited in terms of the crystal size (around 10 mm×10 mm) and cost. Nowadays only a few companies, such as Unipress (Poland), and Sumitomo Electric (Japan), sell GaN bulk substrate with 2 inch size. † Although these substrates have already been use to fabricate for example, laser diodes [START_REF] Motoki | Development of gallium nitride substrates[END_REF], and power electronic devices, bigger and cheaper good quality bulk nitride substrates could really boost the applications of these materials.

Heteroepitaxy Based on this situation, most researchers have relied on heteroepitaxy, which means to epitaxially grow a single crystal structure on a foreign substrate. Many criteria need to be considered, when it comes to choose this foreign substrate, including lattice mismatch, thermal expansion coefficient (TEC) difference, surface chemistry, temperature stability, thermal conductivity, electrical conductivity, substrate size availability, and last but not the least cost. All these parameters could influence the crystal orientation, polarity, strain, defect concentrations of the epilayer structure, and eventually the device performance.

In Table 1.3, I have listed some of the crucial properties of three common substrates in the case of GaN epilayer growth. Concerning the cost, only the price of a 2 inch wafer is listed as an example. Other factors, such as wafer processing and packaging, should also be considered in device fabrication. Moreover, Si holds the unique advantage of being compatible with the standard COMS technology in microelectronics.

NWs

On the other hand, NWs could provide an interesting solution to this substrate dilemma.

In the particular geometry of NWs, the strain can be relieved at the free sidewalls, the substrate lattice mismatch and thermal expansion compatibility are much less important; therefore fabrication on a wide variety of substrates, including Si, is possible.

Moreover, better crystal quality can be obtained compared to 2D epilayers counterparts because of the absence of dislocations.

Growth methods

Molecular beam epitaxy

Based on the knowledge from solid-state physics, surface physics, and materials science, molecular beam epitaxy (MBE) was firstly developed as a new crystal growth technology for epitaxial GaAs layers by the scientists and engineers from IBM and Bell in the 1960s [START_REF] Mccray | MBE deserves a place in the history books[END_REF], [START_REF] Cho | How molecular beam epitaxy (MBE) began and its projections into the future[END_REF]. With the growing interest in III-nitrides materials in the 1990s, MBE has become an essential tool for fundamental studies in this field. The definition of MBE could be "the deposition of epitaxial films onto single crystal substrates using atomic and molecular beams produced from Knudsen cells under ultra-high vacuum (UHV) conditions", as described in a review paper in 2004 [START_REF] Joyce | Basic studies of molecular beam epitaxy -past, present and some future directions[END_REF].

In the specific case of III-nitride systems, MBE can be distinguished depending on how the nitrogen is introduced. For instance, nitrogen can be provided either by dissociating ammonia molecules (ammonia-MBE, often referred as NH 3 -MBE), or by creating a plasma with the help of a radio-frequency (RF) discharge (plasma-assisted MBE, or PA-MBE) [START_REF] Joyce | Basic studies of molecular beam epitaxy -past, present and some future directions[END_REF].

In this thesis, all the samples have been grown in a plasma-assisted MBE.

The traits of MBE

The choice of growth techniques largely depends on the desired structure and needs.

Some of the characteristics of MBE are listed in the following:

 An UHV -based technique: the control on the vacuum environment and on the quality of the source materials allows a high material purity and crystal quality. Inside the growth chamber, ballistic transport is fullfilled instead of diffusive.

 Insitu monitoring techniques such as reflection high-energy electron diffraction (RHEED) are available to investigate the growth mechanisms.

 In MBE, it is possible to grow atomically sharp interface thanks to lower growth temperature and growth rate.

 However, MBE suffers from a lower yield, due to a lower growth rate and wafer capability, in terms of mass production [START_REF] Biasiol | Molecular beam epitaxy: principles and applications[END_REF].

SILICON DOPED GAN NWS

Ever since the very first epitaxial growth of GaN layer by hydride vapour phase epitaxy [START_REF] Maruska | The preparation and properties of vapordeposited single-crystal-line GaN[END_REF], efforts have been spent to study doping in these layers. However, this study of impurity incorporation was very ambiguous, since the as-grown GaN epitaxial layers at that time had a poor crystal quality and very high non-intentional doping with electron concentrations in the range of 10 19 cm -3 [START_REF] Manasevit | The use of metalorganics in the preparation of semiconductor materials[END_REF]. In 1986, Amano et al. discovered that the use of an AlN buffer layer could greatly improve the crystal quality of GaN epitaxial layer [START_REF] Amano | Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer[END_REF], which paved the way to systematically examine the effect of doping.

In the late 90s, with the development of growth techniques, impurity incorporation in epitaxial GaN layers grown under different conditions has been investigated both theoretically [START_REF] Bogusławski | Doping properties of C, Si, and Ge impurities in GaN and AlN[END_REF], [START_REF] Neugebauer | Native defects and impurities in GaN[END_REF] and experimentally [START_REF] Prystawko | Doping of Homoepitaxial GaN Layers[END_REF], [START_REF] Leroux | Luminescence and reflectivity studies of undoped , nand p-doped GaN on ( 0001 ) sapphire[END_REF].

Silicon, oxygen, germanium are common donor impurities typically used for GaN ntype doping. In fact, impurity incorporation is more complicated in GaN than in other semiconductors, such as Si, or GaAs, due to the large mismatch in the atomic radii of Ga and N. The property of the substitutional impurity depends on its location: for silicon or germanium, when substituting for Ga, it is a donor in GaN; while replacing N, it is an acceptor; whereas, for oxygen, the situation is the opposite. Both Si and Ge prefer to substitute Ga atoms energetically, which make them donors in GaN. This can be intuitively explained by the fact that Si and Ge have atomic radii very close to gallium. For the very same reason, O prefers to replace N atom, thus serves as a donor in GaN [START_REF] Bogusławski | Doping properties of C, Si, and Ge impurities in GaN and AlN[END_REF], [START_REF] Neugebauer | Native defects and impurities in GaN[END_REF].

GaN epitaxial layers grown by various techniques doped with either silicon, or oxygen, or germanium, have already been investigated experimentally, showing that these three dopant impurities are effective shallow donors [START_REF] Prystawko | Doping of Homoepitaxial GaN Layers[END_REF]- [START_REF] Niebuhr | Electrical and optical properties of oxygen doped GaN grown by MOCVD using N 2 O[END_REF]. In an MBE growth system, Si and Ge are often employed since they can be provided by an effusion cell like for Ga.

Comparing to Ge, Si is a more widely used, more abundant, and cheaper material, thus it becomes the first choice for doping in GaN.

However, it has been evidenced by several groups that Si doping is associated with defects formation and increasing strains in GaN epilayers [START_REF] Lee | Stress relaxation in Si-doped GaN studied by Raman spectroscopy[END_REF]- [START_REF] Chine | Stress and density of defects in Si-doped GaN[END_REF].

As discussed in the previous chapters, GaN NWs provide an interesting alternative for new nanoelectronic devices due to remarkable crystal quality and quasi-1D structure [START_REF] Zhao | Aluminum nitride nanowire light emitting diodes: breaking the fundamental bottleneck of deep ultraviolet light sources[END_REF]- [START_REF] Bavencove | GaN-based nanowires: from nanometric-scale characterization to light emitting diodes[END_REF]. For realizing these various devices, a precise control and quantitative assessment of the doping is essential. [START_REF] Stoica | Doping of III-nitride nanowires grown by molecular beam epitaxy[END_REF]- [START_REF] Calarco | Size-dependent photoconductivity in MBE-grown GaN -Nanowires[END_REF] and Sanford et al. [START_REF] Mansfield | GaN nanowire carrier concentration calculated from light and dark resistance measurements[END_REF]- [START_REF] Parkinson | Noncontact measurement of charge carrier lifetime and mobility in GaN nanowires[END_REF] have carried out extended studies to extract the carrier concentration and mobility of GaN NWs via various photoconductivity measurements.

Interesting phenomena such as the effect of surface Fermi-level pinning and surface recombination have been witnessed. Notwithstanding, direct transport measurements on single MBE-grown GaN NW are in great need for the further understanding of the electrical properties of these NWs.

This chapter intends to present our study of the structural and electrical properties of Sidoped GaN NWs. In the first section, we will briefly introduce PAMBE and the growth method employed in this thesis. In the second section, we will discuss the structural properties of Si-doped GaN NWs with the help of Raman spectroscopy and high resolution energy disperse X-ray spectroscopy. Lastly, we will address the electrical properties of single NWs via direct transport measurements (four-probe resistivity and its temperature dependence, field effect transistor measurements, etc.).

One of the merits of MBE system is the possibilities of in situ characterizations. In our MBE, RHEED is the only tool available for in situ and real time characterization. It presents a live picture of the reciprocal space lattice of the sample surface; therefore, it can be employed to monitor the surface morphology during the growth. As illustrated in Figure 2.2, an electron beam of 32 keV is sent towards the substrate with a grazing angle (<3°). The diffracted beam patterns are projected on a phosphorescent screen. These patterns are processed by image treatment software called "AnaRheed", which is developed by Y. Cure from INAC, CEA. In addition, RHEED is very useful for the calibration of MBE atomic fluxes through RHEED oscillations, which will be addressed in 2.1.2.3. The substrate temperature is a very important parameter for the growth of nanostructures in MBE. However, the precise measurement of the substrate temperature in vacuum is not easy. In our case, three methods have been applied in order to estimate this temperature reasonably:

 The electrical power applied on the heater filament is recorded for each sample, (unit is watts). However, it depends on the thermal inertia of the molybloc, and the gradual diminution of the filament diameter along with its use.

 The temperature measured by a thermocouple at the backside of the substrate, (unit is Celsius degree). Yet, this measurement depends on the exact environment geometry and the exact contact position of the thermocouple.

 A characteristic time of Ga adatoms desorption on clean Si [START_REF] Donatini | Comparison of three e-beam techniques for electric field imaging and carrier diffusion length measurement on the same nanowires[END_REF] surface in situ followed by RHEED, (unit is second). A typical example for such desorption data is shown in Figure 2.3. This Ga desorption method [START_REF] Mata | Nucleation of GaN nanowires grown by plasma-assisted molecular beam epitaxy: The effect of temperature[END_REF][52] can keep a good reproducibility from sample to sample.

Additionally, the temperature is not homogenous on the wafer substrate, due to heating inhomogeneity and the mechanical design of the substrate holder. The temperature difference from the center to the edge of the wafer, estimated to be around 40 °C, is important for the NW morphology, as we will see later, therefore, the Ga desorption calibration has been done systematically at the center of the wafer for each growth in order to be reproducible.

The impact of the nitrogen plasma cell

One of the limitations of PAMBE for mass production is the low growth rate (typically 200-400 nm/h). The production of active nitrogen species is very crucial for improving the growth rate. However, the high N 2 molecule bond energy of 9.5 eV [START_REF] Yang | GaN grown by molecular beam epitaxy at high growth rates using ammonia as the nitrogen source[END_REF] makes it difficult to break the molecules into atoms, and further to be incorporated in III-V nitrides. Efforts in developing high-density nitrogen radical plasma source have been reported to reach more than 2 m/h growth rate in the case of GaN 2D layer [START_REF] Cordier | GaN films and GaN/AlGaN quantum wells grown by plasma assisted molecular beam epitaxy using a high density radical source[END_REF]- [START_REF] Mcskimming | Plasma assisted molecular beam epitaxy of GaN with growth rates > 2.6µm/h[END_REF].

In our MBE, a standard Riber nitrogen plasma cell is used. The N 2 molecules are resonantly excited by a RF electromagnetic wave at 13.56 MHz, and N 2 flow is adjusted by a mass-flow regulation. In principle, the N 2 can be varied between 0.2 and 10 standard cubic centimeters per minute (sccm); the input power can be varied up to 600W. In fact, a RF power of 300W and a N 2 flow of 0.6 sccm are routinely employed as growth conditions, in order to obtain a stable plasma in the MBE machine. And these conditions lead to a typical N-limited growth rate of 0.23 ML/s (see Figure 2.9 (a)).

As part of this thesis, a new plasma cell Riber RFN-50/63 has been installed for producing higher N flux. Through working at a higher RF power (400-500 W) and a higher N 2 flow (1.1-1.4 sccm), more active nitrogen species are indeed produced (see (around 3 nm thick) is deposited to ensure a more homogeneous nucleation and decrease the mosaicity of the NWs [START_REF] Rigutti | Investigation of the electronic transport in GaN nanowires containing GaN/AlN quantum discs[END_REF]. The nominal Ga/N flux is 1/3 and the same for all the samples in this series. The growth time was 20 hours unless otherwise mentioned. Sample N2059 is non-intentionally doped (NID) GaN NWs and serves as a reference. In addition, sample N2129 has been grown at the exact same growth conditions as N2059, as the second reference. For the other samples, n-type doping is achieved by exposing GaN NWs to the Si flux, starting 20 minutes after completion of their nucleation till the end of the growth. In a nutshell, this series of samples have been grown in the same conditions except the doping level via varying the Si cell temperature from 850 °C to 950 °C. Doping produces energy levels within the band gap of the semiconductor, and these levels can serve as recombination centers, manifesting in the PL spectra. Therefore, we can employ PL characterization to learn more about the doping of the material.

In the particular case of GaN, doping has a significant impact on emissions from the near band edge, DAP, as well as YL. The strongest peak of the near band edge emission (D 0 X line) is situated as 3.472 eV (357 nm) at low temperature (5-10 K) for relaxed NID GaN material. [START_REF] Kornitzer | Photoluminescence and reflectance spectroscopy of excitonic transitions in high-quality homoepitaxial GaN films[END_REF] The doping in GaN 2D layer can vary both the position and the full width at half maximum (FWHM) of the near band edge peak through different physics effects, such as strain, band gap renormalization (BGR) and band filling effects.

Si doping can induce strain in GaN, it has been reported in [START_REF] Leroux | Luminescence and reflectivity studies of undoped , nand p-doped GaN on ( 0001 ) sapphire[END_REF] that there is a linear relationship between the biaxial strain and the free exciton energies. When increasing the doping, band gap renormalization (BGR) is becoming more evident due to electronelectron and electron-ion interaction. This effect can lead to the energy downshift of the low-energy edge of the PL line, and dominates until a carrier concentration of around 9×10 18 cm -3 [START_REF] Yoshikawa | Band-gap renormalization and band filling in Sidoped GaN films studied by photoluminescence spectroscopy[END_REF], [START_REF] Feneberg | Band gap renormalization and Burstein-Moss effect in silicon-and germaniumdoped wurtzite GaN up to 10 20 cm -3[END_REF]. Under heavy doping, especially above the metal-insulator transition (MIT) (critical doping level N d = 1.6×10 18 cm -3 [START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF]), band filling effects occur, shifting the PL peak to higher energy. Additional broadening of the PL linewidth can come from potential fluctuations induced by the random distribution of the dopant atoms [START_REF] Schubert | Optical properties of Si-doped GaN[END_REF], [START_REF] Iliopoulos | Broadening of near-band-gap photoluminescence in n-GaN films[END_REF].

Moreover, both the DAP and the YL emission intensities can reflect the amount of impurities and defects in the crystal, acting as an intuitive optical signature of the doping level. When adding Si (N2061, N2076 & N2067), the near-band edge emission peak becomes broader, and more asymmetric towards lower energies due to Si incorporation as shallow donors, meanwhile, the intensity of the DAP emission arises, even higher than that of the near-band edge emission in sample N2061, indicating a significant increase of impurities in the doped samples. Similar features have been observed in the literature as well [START_REF] Furtmayr | Optical properties of Siand Mg-doped gallium nitride nanowires grown by plasma-assisted molecular beam epitaxy[END_REF]. At higher Si cell temperature (N2074, N2088 & N2060), we can see a more obvious broadening of the PL peak as well as a shift to higher energy due to band filling effects.

Various efforts have been made to determine the carrier concentration n quantitatively through PL spectra. However, the combining effect of BGR and band filling effect makes it very challenging to resolve this issue. [START_REF] Feneberg | Band gap renormalization and Burstein-Moss effect in silicon-and germaniumdoped wurtzite GaN up to 10 20 cm -3[END_REF] Near-band edge peak position shift As stated before, the combining effect of BGR and band filling effect makes the position of the near-band edge peak almost constant at moderate doping; it is only when the band filling effect is much more prominent at higher doping, that we can observe a blue shift of the peak position [START_REF] Prystawko | Doping of Homoepitaxial GaN Layers[END_REF].

As we can see in Figure 2.14 (a), compared to the NID sample, the band edge peaks of highly doped samples (N2088 & N2060) exhibit a noticeable blue shift and significant broadening. Indeed, for N2088, the PL peak position is located at 3.49 eV with a linewidth of 71 meV, whereas, for N2060, the maximum of band-edge emission is situated at 3.52 eV with a FWHM of 129 meV. In the light of PL measurements on homoepitaxial GaN layers, we can estimate a carrier concentration of 4×10 19 cm -3 and 7×10 19 cm -3 for sample N2088 and N2060, respectively. These values are relatively consistent with the EDX data, which will be discussed later in this chapter. NW could be responsible, furthermore, it has been reported that there is a significant discrepancy between the PL spectra from as-grown sample to single NW, as well as from NW to NW [START_REF] Sam-Giao | Optical study of GaN nanowires and GaN / AlN microcavities[END_REF]. Therefore, we need to be more careful when using the optical signals to estimate the carrier concentrations in NWs. It was one of the main goals of this thesis to perform direct transport measurements in order to have a more reliable estimation of the carrier concentrations.

Figure 2.15 FWHM of low temperature PL peak as a function of electron concentration n at room temperature for Si doped GaN epilayer [START_REF] Leroux | Luminescence and reflectivity studies of undoped , nand p-doped GaN on ( 0001 ) sapphire[END_REF], [START_REF] Yoshikawa | Band-gap renormalization and band filling in Sidoped GaN films studied by photoluminescence spectroscopy[END_REF], [START_REF] Tang | Growth of high mobility GaN by ammonia-molecular beam epitaxy[END_REF], as well as NWs in this PhD. Both the x and y axes are in logarithmic scale. The short dashed line shows the critical electron concentration for the MIT at1.6×10 18 cm -3 [START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF], the dash-dot line is a fitting of the data from [START_REF] Leroux | Luminescence and reflectivity studies of undoped , nand p-doped GaN on ( 0001 ) sapphire[END_REF], exposing that the FWHM follows a n 2/3 power law.

Structural properties

Defect modes evidenced by Raman spectroscopy

Ever since the discovery by C. V. Raman in 1928 [START_REF] Raman | A Change of Wave-length in Light Scattering[END_REF], Raman spectroscopy has become a versatile and interesting material investigation tool. By probing the inelastic light scattering, Raman spectroscopy can reveal detailed information on crystal structure, electronic states, chemical composition, and strain and so on. Moreover, it does not require sophisticated sample preparations, and is often referred as a fast and non-destructive technique.

Concerning the Raman spectra of GaN, two modes have been intensively studied in the literatures. The E 2h mode is sensitive to the strain and the phonon shift can be directly related with the stress. The coupled LO-phonon plasmon modes (LPP modes) result from the interaction between the macroscopic electric field of the longitudinal-optical phonons and the field of the collective excitation of the free carriers, therefore, its frequency strongly depends on the free carrier concentration. Both the low (LPP -) and high (LPP + ) energy branches have been employed to estimate the concentration and mobility of the carriers (electrons) in GaN epilayers, through the modelingof the peak position and the width of these modes. [START_REF] Haboeck | Lattice dynamics in GaN and AlN probed with first-and second-order Raman spectroscopy[END_REF]- [START_REF] Kozawa | Raman scattering from LO phonon-plasmon coupled modes in gallium nitride[END_REF] Regarding GaN wires, surface optical phonon modes (SO) due to the high surface / volume ratio has been reported previously. [START_REF] Mata | Surface optical phonon modes in GaN nanowire arrays: dependence on nanowire density and diameter[END_REF] The attempts to approximate the carrier concentrations of NID and Si doped wires have been addressed in a few publications [START_REF] Stoica | Doping of III-nitride nanowires grown by molecular beam epitaxy[END_REF], [START_REF] Jeganathan | Raman scattering of phonon-plasmon coupled modes in selfassembled GaN nanowires[END_REF]- [START_REF] Tchoulfian | Thermoelectric and micro-Raman measurements of carrier density and mobility in heavily Si-doped GaN wires[END_REF]. Therefore, it was very interesting to perform Raman measurements on this series of Si doped GaN NWs.

As stated in Chapter 1, micro-Raman measurements are conducted in collaboration with Prof. Ana Cros from University of Valencia, Spain. A 532 nm doubled YAG laser has been employed to excite the samples while a HORIBA Jobin Yvon iHR320 spectrometer was used to detect the spectra. The spectrometer is equipped with a Peltier-cooled CCD detector. Spectra were obtained in backscattering geometry at room temperature from as-grown NWs. A ×50 microscope objective was used to focus the excitation laser on the sample and collect the scattered light to the spectrometer.

Figure 2.16 shows the spectra obtained from this series of Si doped samples. The spectrum of the Si substrate has been included at the bottom as a reference. The peak corresponding to the E 2h mode is observed in all samples. For NID sample, its center is at 565.6 cm -1 , somewhat lower than the value expected for relaxed bulk GaN (567 cm -1 ) [START_REF] Perlin | Raman scattering and x-ray absorption spectroscopy in GaN under high pressure[END_REF]. A small but progressive decrease of the phonon frequency is observed as the silicon content of the samples increases (Figure 2.16(b)). This trend is broken in the last sample, where the mode shifts back to higher frequencies. This behavior points to an increase of the tensile strain with silicon content up to a value of 0.15%, beyond which the relaxation of the lattice takes place. A similar behavior has been previously reported by Sánchez-Páramo et al. for silicon doped GaN layers [START_REF] Sánchez-Páramo | Optical investigation of strain in Si-doped GaN films[END_REF], where the lattice relaxation was observed for silicon concentrations above 5×10 18 cm -3 . As the amount of silicon in the lattice increases, the E 2h peak becomes somewhat wider, changing from 7 cm -1 to 10 cm -1 . This is a consequence of the lattice disorder induced by the impurities.

The LPP + peak is observed in NID GaN NWs at 739.0 cm -1 , right above the SO peak, which is often observed in thin NWs [START_REF] Mata | Surface optical phonon modes in GaN nanowire arrays: dependence on nanowire density and diameter[END_REF]. The frequency of this mode corresponds to a free carrier density around 2×10 17 cm -3 . This estimation is consistent with the red-shift of the E 2h mode. Unfortunately, for higher Si concentrations the plasmon is overdamped and the LPP + peak cannot be observed. For the sample with moderate Si cell temperature (900 °C), a broad band centered at 658 cm -1 starts to arise. The intensity of this band increases strongly with higher silicon content. This peak is ascribed to a disorder activated mode and has been reported for Mg, Ge and Si doped samples [START_REF] Cuscó | Local vibrational modes of H complexes in Mg-doped GaN grown by molecular beam epitaxy[END_REF], [START_REF] Fritze | High Si and Ge n-type doping of GaN doping -Limits and impact on stress[END_REF]. At the same time, four new modes arise at 319, 390, 414 and 763 cm -1 . They are La1 line at 1.10 keV. However, the spatial resolution is not only limited by the electron NW interaction distribution, but also electron scattering along the NW, moreover, no Si distribution information can be extracted in this case since the NW is laying on the substrate.

Another sample preparation procedure is more complicated, and it is similar to traditional transmission electron microscope (TEM) sample preparation. Firstly, a few drops of epoxy resin were dipped onto the as-grown sample, then the sample was stored in an oven for 24 hours. Once the resin was solidified, subsequent polishing steps were followed by using different polisher machines and solutions without colloidal Si. The purpose of the polishing is to remove the excess resin on top of the NW and to create a flat top surface for EDX observations. With this procedure, the resin that fills the space screens the electron scattering in between the NWs, and the influence of the Si substrate can be neglected due to the micrometer length of the NWs. In the end, carbon coating is deposited on the sample to avoid charging effect during the EDX observation.

All the samples in this Si-doped NWs series have been prepared using the procedure above, unfortunately, quantitative results are only obtained for two samples with higher Si cell temperatures (938 °C and 950 °C), for the rest of the samples in the series, the Si level is below the detection limit (around 10 19 at cm -3 as mentioned before).

Two NWs grown with the highest Si cell temperature (950 °C) have been analyzed by EDX in a TEM and SEM, respectively. ( Si from 6×10 20 up to 10 21 at/cm 3 . The overall thickness of this Si-rich shell ranges between 10 nm up to 40 nm.

On the other hand, similar measurements on the sample grown with Si cell temperature of 938 °C have shown significantly different outcome (Figure 2.19 (a&b)). TEM-EDX presents a relatively constant Si concentration throughout the NW with an average value of 10 20 at/cm 3 , and it is consistent with concentrations measured by SEM-EDX ((0.5-with crack formation in the 2D layer [START_REF] Sánchez-Páramo | Optical investigation of strain in Si-doped GaN films[END_REF]. The present results suggest that the large amount of free surfaces, which are specific to NWs, are favorable for the relaxation of tensile strain induced by the presence of Si, making its incorporation easier, while leading to an elastic strain relaxation without the formation of cracks. Surface segregation of Si in the periphery of the GaN NWs when above the solubility limit is consistent with the increasing intensity of the broad Raman band around 658 cm -1 for increasing Si content and is assigned to an increase of Si-related defects in the periphery of the NWs for the Si cell temperature above 900 °C. This feature is consistent with the theoretical prediction of Si segregation to the surface under N-rich and Si-rich growth conditions [START_REF] Rosa | Adsorption and incorporation of silicon at GaN(0001) surfaces[END_REF], [START_REF] Neugebauer | Surfactants and antisurfactants on group-III-nitride surfaces[END_REF]. In fact, a similar phenomenon has been recently reported on highly doped GaN NWs grown on diamond where the presence of a shell with Si content above the solubility limit has been observed [START_REF] Schuster | Doped GaN nanowires on diamond: Structural properties and charge carrier distribution[END_REF].

In the case of the highest Si content related with the formation of Si-enriched GaN outer shell, the symmetry of the top facets of the NWs is changed from 6 to 12. It has been demonstrated for long that MBE-grown NID GaN NWs exhibit a 6-fold symmetry top facet, with vertical walls made of m-planes [START_REF] Mata | Nucleation of GaN nanowires grown by plasma-assisted molecular beam epitaxy: The effect of temperature[END_REF], [START_REF] Largeau | Facet and in-plane crystallographic orientations of GaN nanowires grown on Si(111)[END_REF]. Such a morphology is consistent with theoretical calculations which have shown that m-plane surface energy (118 meV/Å 2 ) is indeed smaller than a-plane surface energy (123 meV/Å 2 ) [START_REF] Northrup | Theory of GaN(10-10) and (11-20) surfaces[END_REF]. The symmetry change of the most heavily doped sample is a clue that a Si enriched shell exists and the associated defects have a tendency to equalize the surface energy of mplanes and a-planes in this case. Moreover, the trend of symmetry change is already observable for some NWs for the sample with Si cell temperature of 938 °C and the appearance of a broad Raman band around 658 cm -1 further confirms the association of the symmetry change and the progressively increased defect concentration in the shell of the NWs. Furthermore, this lattice deformation and change in surface energy is expected to discourage nucleation on the NW sidewalls and promote either Ga adatom desorption or diffusion along them, consistent with the previous hypothesis that the increase of Ga adatom diffusion length along the sidewalls might be responsible for the progressive NW widening.

Electrical transport properties

Understanding the growth mechanism of Si doped GaN NWs through PL, Raman as well as EDX can provide insightful guidelines for the fabrication of the NWs, whereas, the study of electrical transport properties is very crucial for device applications.

Direct electrical transport measurements on single NW devices can provide significant information on doping level, resistivity, and mobility, which paves the way to eventually investigate the NW devices on an ensemble or device level [START_REF] Bugallo | Visible-blind photodetector based on p-i-n junction GaN nanowire ensembles[END_REF]. In 2D layer structures, the transport properties are often assessed by mainly two methods, Hall-effect measurement (carrier concentration) and capacitance-voltage measurement (doping level). There are a few pioneering papers showing similar measurements on NWs [START_REF] Storm | Spatially resolved Hall effect measurement in a single semiconductor nanowire[END_REF]- [START_REF] Blömers | Hall effect measurements on InAs nanowires[END_REF], however, it demands very high precision on the lithography process, and is still challenging concerning the dimensions of GaN NWs.

In this thesis, four-probe resistivity and its temperature dependence measurement have been performed on single GaN NW devices. With this, we are able to systematically study the impact of Si doping on the NW resistivity and investigate different conduction regimes. Moreover, by combining field effect transistor (FET) measurements and finite element simulation, we are able to determine the carrier concentration and furthermore the mobility of NID NWs. Controlled doping in a wide range of concentrations can advance the process of device development. It is noteworthy that the specific geometry (the conical shape and the length of around 1.5 m) and inhomogeneous dopant distribution (Si enriched shell witnessed by EDX measurements) of the most doped sample make it difficult to perform reliable electrical characterization on these NWs, therefore the following explorations concern only the other Si-doped samples from this series.

All the measurements have been performed in the FEI Inspect F50 FESEM-setup equipped with a nano-probing SmarAct system. A Gatan liquid helium stage has been used in the case of temperature dependence measurements.

Single NW contacting

One of the obligatory and challenging tasks to achieve direct electrical measurements in this thesis was to develop a high yield, reproducible, facile NW contacting procedure.

In the literature, several interesting techniques have been proposed [START_REF] Langford | Comparison of different methods to contact to nanowires[END_REF]. Scanning tunneling microscopy (STM) tips have been reported to directly contact ZnO NWs and perform four-probe resistivity measurements [START_REF] Lord | Factors that determine and limit the resistivity of high-quality individual ZnO nanowires[END_REF]. Metal electrodes on NWs can be deposited via ion or electron beam induced deposition technique [START_REF] Hernández-Ramírez | Characterization of metal-oxide nanosensors fabricated with focused ion beam (FIB)[END_REF], or more frequently, by electron beam lithography (EBL) [START_REF] Richter | Doping concentration of GaN nanowires determined by opto-electrical measurements[END_REF]. More particularly, an innovative EBL technique based on cathodoluminescence (CL) imaging has been developed in Institut Néel [START_REF] Donatini | A single-step electron beam lithography of buried nanostructures using cathodoluminescence imaging and low temperature[END_REF], and this technique has been successfully implemented to study GaN microwires [START_REF] Tchoulfian | High conductivity in Si-doped GaN wires[END_REF] as well as ZnO NWs [110][111].

Table 2.2 lists some practical characteristics of a few techniques used in my thesis. And single NWs, an area with the smallest density (mostly the center of the Si substrate) is chosen for dispersion.

With the aim of transferring NWs onto foreign substrates, two methods are generally used nowadays, through either solution or mechanical scratch.

In the first method, a small piece of as-grown sample (around a few mm 2 ) was cleaved, then put into a small plastic container with volatile solvents such as IPA, or ethanol. Afterwards an ultrasonic bath was employed to harvest the NWs from the as-grown substrate. The NWs were transfer onto foreign substrates by casting a few drops of the NWs suspension, and evaporation of the solvents. This method has the advantage of being reproducible; meaning the density of the NW dispersion can be controlled by the concentration of the solution, and the number of the drops casted.

In practice, the evaporation of the solvents is not always complete, leaving some residues, which could be a potential source of contamination for the NWs. Therefore, I have chosen to use a simple mechanical scratch method. In this case, a cleanroom paper has been used to transfer the as-grown sample onto foreign substrates, by scratching it gently on the growth substrate. The density of the dispersion was first monitored under optical microscopy, and afterwards observed by SEM.

Meanwhile, the single NWs with good dimensions were identified under SEM and their positions were noted using the corresponding coordinates with respect to the markers, such as in Figure 2.23 (c).

Then this sample was transferred inside the FEI Inspect F50 FESEM, and field calibration alignments have been done in two fields: 700×700 m for making big contacts to be connected with metal tips, 70×70 m for the delicate contacts on single NW, respectively. The e-beam working distance is 10 mm, with an energy of 30 keV. The e-beam current is 1 nA for the bigger field, and 20 pA for the smaller one. Then a high-resolution image is taken in the field of 70×70 m for each intended single NW with respect to the "crosses" (Figure 2.25 (a)), in order to locate and draw lithography mask later on.

Spin coating of the resist EBL is a technique based on the chemical modification of polymer resist films induced by electron irradiation. Poly-methyl methacrylate (PMMA), one of the first positive † † electron beam resists developed in 1968, is still widely used today, due to its simplicity, high resolution, and excellent adhesion to most surfaces. The exposure of the electron beams can break the long polymer chain of PMMA into smaller, more soluble fragments (Figure 2.24). Similarly, copolymer (PMMA/MMA), is also a high sensitive resist. In addition, it is often used in bi-layer resists with PMMA, with the aim of producing undercut profiles beneficial in the lift-off process later on.

In the case of NWs, the thickness of the resist needs to be at least two times the diameter of the NWs, in order to facilitate the lift-off process. Therefore, the choice of the resist depends on the diameter of the NW. In terms of Si-doped GaN NWs series, one PMMA layer of thickness around 310 nm is used to contact NWs with diameter less than 80 nm, whereas, for NWs with a diameter up to 150 nm, a bi-layer consisting of PMMA/MMA and PMMA is employed. Table 2.3 lists the spin coating conditions of these resists.

Table 2.3 Spin coating conditions of the resists used in this thesis

Electron beam exposure and development After coating the sample with the resist, it is replaced inside the SEM, at the same position as before. The lithography software allows to draw a mask of the patterns which will be realized on the NWs. The exact same calibration alignments were done, so that the overlap between the real NWs and the mask is optimized. The SEM setting is the same as before, and the e-beam The resistivity of a semiconductor ρ is related with both the density of available free carriers n and their mobility through the following equation:

= (2.1)
Where q is the electric charge. It is crucial to obtain information of these three basic parameters for the understanding of the electrical properties of the semiconductor.

Carrier concentration n Carrier concentration n and doping level (N d or N a ) are inextricably connected in semiconductors. When dopants (donors or acceptors) are incorporated into a semiconductor, they create energy levels within the band gap. Taking donors as an example, the doping atoms produce an impurity level E d within the band gap, close to the conduction band. As shown in Figure 2.26 (a), the extra electrons of these donor atoms need a small thermal energy to jump to the conduction band, and this energy is called the ionization energy. From the energy diagram, we can see that the ionization energy equals the energy distance between E d and the bottom of the conduction band E c , in the case of low Si doping (N d < 10 17 cm -3 ) in GaN, this energy is about 30 meV [START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF].

With increasing doping level, E d will split into a band of energies, widening and approaching to the conduction band; eventually overlap with the bottom of the conduction band E c . Above this point, the Fermi level lies inside the conduction band, the ionization energy becomes 0 meV, and all the donors are ionized (n = N d ). In this case, the semiconductor has a metallic behavior, with the carrier concentration constant with varying temperature. This semiconductor is degenerate, and the critical Si doping concentration in GaN to reach metal-insulator transition (MIT) is experimentally determined to be around 1.6×10 18 cm -3 [START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF].

Mobility The carrier mobility in a semiconductor is determined by scattering processes, such as phonon scattering, impurity scattering, or defects scattering. If more than one scattering process occurs, the mobility  can be approximated by a so-called

Matthiessens' rule: = ∑ (2.4)
The scattering processes present in n type GaN are generally polar optical phonon scattering, piezoelectric phonon scattering, acoustic phonon scattering and ionized impurity scatterings.

= × + (2.5)
where R C is the contact resistance, considering that the two electrodes are identical; and R GaN is the resistance of the wire between the two electrodes. This estimation is only valid when the contact resistance is much smaller than the wire resistance.

However, in the real world of GaN NWs, this requisite of low-resistance ohmic contacts is difficult to meet. The contact resistance generally depends on the relative semiconductor / metal work functions, interface states, which induce Fermi level pinning, as well as the active contact area. It is challenging to find the ideal metal to match with the work function (Fermi level) of GaN, which is a function of doping. In addition, the non-negligible interface states and small contact area in the case of NWs can hinder the formation of low-resistance ohmic contacts. Consequently, the contact resistance (even if it is ohmic) is non-negligible or even significant compared to the resistance of the wire itself, as shown in Figure 2.28.

Therefore, four-probe configuration is adopted to measure the resistivity of GaN NWs.

As shown in the inset of Figure 2.28 (b), a current I is injected through the two outer contacts on the NW while the voltage drop V between the two inner contacts is measured. Using this method, the resistivity of the NW can be inferred independently to the contact resistance. Assuming a homogeneous conduction through the whole section of the NW, the resistivity of the NW between the two inner contacts can be calculated using equation (2.9).

= × √ / (2.6)
where L is the length of the NW between the two inner contacts, r is the radius of the circumscribed circle of the hexagonal cross section of the NW, and √ represents the surface area of the hexagonal cross section of the NW.

Room temperature resistivity measurements

Numerous NWs were connected in four-probe configuration by traditional EBL, and room temperature resistivity measurements have been performed on 20 single NWs from various samples of Si doped GaN NWs as well as the NID ones, (see Table 2.1 for the detailed growth conditions), except for the most heavily doped sample N2060. Current density is limited to 900 A.cm -2 to avoid heating issues during the measurement, and reverse polarity measurements have been done to exclude the effect of the potential offset.

Figure 2.29 presents the four-probe resistivity value as a function of NW radius for five samples with different doping levels. The resistivity value spreads from 10 2 Ω.cm to 10 -3 Ω.cm, corresponding to the range from NID NWs to the one with Si cell temperature of 938 °C.

For NID NWs, the resistivity spreads from 10 2 to 3×10 -2 Ω.cm for 6 NWs, suggesting a different residual doping among these NWs or the influence of different surface states in NWs. The possible origins of this residual doping will be discussed in the section 2.4.4.

For the doped NWs, the resistivity of NWs having different radii and coming from the same sample is quite constant. This is a signature of negligible surface conduction or reduced conduction due to near-surface depletion at room temperature, and hence validating the assumption of a homogeneous conduction through the whole section of the NW. However, caution must be taken for the sample grown with Si cell temperature of 875 °C since the two wires radii are close (27 nm and 31 nm). The resistivity of NWs from the different samples gradually decreases from 2×10 -2 Ω.cm to 10 -3 Ω.cm, while increasing the doping level. These two features have revealed the ability to achieve homogeneous doping level from one wire to another and furthermore to control the doping level through variation of the Si cell temperature in the MBE system.

Specific contact resistance We can easily deduce the contact resistance R c (Ω) by combining two-probe and four-probe measurements. However, R c is area-dependent, thus, another important parameterspecific contact resistance (also referred as contact resistivity) ρ c is generally used to study the metal / semiconductor contacts. We have

 c = R c A (Ω.cm 2 )
, where A is the active area of the contact. A is difficult to determine since the current transport can occur in only part of the physical contact depending on the geometry of the contact. A model has been described by Mohney et al. on the adaptation of the traditional transmission line model (TLM) to the specific case of semiconductor NWs. [START_REF] Mohney | Measuring the specific contact resistance of contacts to semiconductor nanowires[END_REF] In this model, l is the length of the physical contact, L T is called the transfer length, which represents the part of the contact participating in the current transport. In the case of hexagonal NWs, we have:

= ( ) , = √ √ (2.7)
where ρ stands for NW resistivity, and = √ represents the surface area of the resistivity of the wire.

In other cases, an upwards band bending as well as a depletion of electrons are present at the wire surface. Therefore, an effective conduction radius r 0 , instead of real wire radius r (r 0 < r) should be used for resistivity measurement analysis. Furthermore, when r 0 = 0, the wire is fully depleted, and it behaves like an insulator, as shown in last column in Figure 2.31 [START_REF] Pernot | Doping and Transport[END_REF].

The origins of this Fermi-level pinning is normally the surface states induced by the interaction between the wire and species in atmosphere [START_REF] Gurwitz | Method for electrical characterization of nanowires[END_REF]. Regarding GaN wires, the pinning of the Fermi level at the surface has been observed to create a depletion layer (no accumulation layer reported so far) [START_REF] Sanford | Studies of photoconductivity and field effect transistor behavior in examining drift mobility, surface depletion, and transient effects in Si-doped GaN nanowires in vacuum and air[END_REF], [START_REF] Richter | Doping concentration of GaN nanowires determined by opto-electrical measurements[END_REF], [START_REF] Gurwitz | Method for electrical characterization of nanowires[END_REF]. The thickness of this depleted region highly depends on the characteristics (such as density, energy) of the surface states and on the doping level of the sample. A model has been proposed to describe the surface depletion in GaN NWs [START_REF] Calarco | Size-dependent photoconductivity in MBE-grown GaN -Nanowires[END_REF], [START_REF] Richter | Doping concentration of GaN nanowires determined by opto-electrical measurements[END_REF], and the critical diameter d crit below which the wire is completed depleted is presented by: In this equation, N c stands for the effective density of states in the conduction band, which equals 1.2×10 18 cm -3 for GaN at 300K *** . kT is 26 meV at room temperature. ɛ is the dielectric constant of GaN, and q is the elementary charge. Φ signifies the distance between the level where the Fermi-level is pinned and the condition band, which is between 0.1 and 1 eV depending on different samples [START_REF] Chevtchenko | Surface band bending of a-plane GaN studied by scanning Kelvin probe microscopy[END_REF], and expected to be 0.55 eV below the conduction band according to previous photoemission spectroscopy studies on GaN surfaces [START_REF] Kocan | Surface potential at as-grown GaN (0001) MBE layers[END_REF]. From this equation, we can see that d crit is inversely proportional to the doping level N D , meaning that for low doping wires, the surface depletion is more significant than for highly doped samples. Regarding for wires with different radii, we can conclude that the surface depleted layer has more influence for wires with smaller radius.

= √ - • ⁄ (2.8)
In Figure 2.32, we have plotted the ratio between the four-probe resistance of the wire R and the length of the wire between the two inner contacts L as a function of the wire radius r. The dotted lines present simulations of bulk-like conduction, in which the ratio = ⁄ ⁄ follows a / relationship. Note that in Figure 2.32, both the x axis and the y axis are in logarithmic scale, therefore, the bulk-like conduction manifests itself as a straight line. We can find that indeed, for highly Si doped GaN samples, either microwires [START_REF] Watanabe | The quantitative analysis of thin specimens: A review of progress from the Cliff-Lorimer to the new ζ-factor methods[END_REF], or NWs N2088 (GaN-Si-938°C), the surface effects are negligible, evidenced by the fit with the simulated lines. For smaller and less doped NWs, the d crit is on the same order of magnitude compared to the wire radius, the surface depletion (even full depletion) is witnessed by the deviations of the R/L values from the dotted line with ρ = 8.9 mΩ.cm in [START_REF] Gurwitz | Method for electrical characterization of nanowires[END_REF].

For my samples, it is clear that for N2088 (GaN-Si-938°C), the wire follows a bulk-like conduction regime, in fact, the critical diameter d crit calculated using equation (2.8) for this sample is 7.5 nm, which is negligible compared to the average diameter of the wires from this sample (117 nm). For the other less doped GaN NWs, the current data seems to show that the surface depletion plays a rather minor role in the resistivity measurements; further investigation is limited due to the number of the measured NWs and the NW radius dispersions from each sample. In terms of NID NWs, it is difficult to draw a reliable conclusion, since either an inhomogeneous residual doping (evidenced by FET measurements later) or surface depletion could be responsible for the high resistivity of some NWs.

*** Data from website: http://www.ioffe.ru/SVA/NSM/Semicond/GaN/bandstr.html epilayers containing a carrier concentration of 0.1 to 0.6×10 18 cm -3 . However, the resistivity temperature dependence of these two NWs differs from that of epilayers at low temperature (T < 50 K). Whereas nearest neighbor hopping happened in epilayers [START_REF] Songmuang | Identification of III-N nanowire growth kinetics via a marker technique[END_REF], a metallic conduction is found to control the resistivity in NWs. This degenerated conduction could be assigned to two different mechanisms in the specific case of NWs:

i) near surface carrier depletion due to upward band bending induced by surface states or adsorbed species [START_REF] Gurwitz | Method for electrical characterization of nanowires[END_REF], leading to metallic conduction in a core at low temperature, surrounded by a semiconducting shell, which dominates the conduction at high temperature; ii) inhomogeneous radial doping with a NW shell doping above the n MIT .

For more doped NWs, the resistivity does not vary with respect to temperature, until down to 5 K, showing a metallic behavior. This finding is consistent with EDX observation (an average Si concentration of 10 20 at / cm 3 ) for sample grown with Si cell temperature of 938°C. In addition, this outcome is also compatible with the high doping level achieved on microwires previously reported (the gray dashed line) [START_REF] Tchoulfian | High conductivity in Si-doped GaN wires[END_REF].

experimentally found to be -8 V. We have the total charge in the NW = ℎ , where C is the gate-NW capacitance. C can be represented by equation (2.9):

≅ , (2.9)
where is the relative dielectric constant of the oxide, h is the thickness of the gate oxide, and L, r are the length and the radius of the NW channel between source and drain, respectively. Therefore, the doping density (donor density in this case) N d can be calculated with the following equation:

= (2.10)
Meanwhile, the mobility of the carriers can be estimated through the transconductance of the device in the linear regime. We have equation (2.11):

⁄ = ⁄ (2.11)
However, this model lacks of accuracy due to difficulties to estimate the gate-NW capacitance C and the interface charges between NW and the oxides. Indeed, this model assumes that an electrostatically metallic cylinder wire is surrounded entirely by the dielectric oxide, and there is no movable charges at the interface, which are not true in reality. In fact, it has been already reported that this model overestimates the capacitance with a factor of 2 to 3 compared with the value obtained by numerical simulation [START_REF] Wunnicke | Gate capacitance of back-gated nanowire field-effect transistors[END_REF], [START_REF] Khanal | Gate coupling and charge distribution in nanowire field effect transistors[END_REF].

Thus, we have performed 2D finite element simulations by NextNano 3 † † † to model the † † † www.nextnano.de/ (accessed Jan 1, 2015)

Finite element simulations

In our simulation, the device is modelled as a cross section cut in the (y, z) plane direction, and GaN NW was represented by a hexagon. The oxide, BG and LG were modeled as rectangles with the corresponding physical dimensions (see in Figure 2.36).

The device is simulated at V sd = 0 V to electrostatically model the charge depletion at a certain gate voltage. Firstly we presume a doping level of the NW as an input parameter, and then by applying a small voltage sweep of either BG or LG, the NW is gradually depleted as shown in Figure 6 (h, j, l) and (i, k, m), respectively. Thanks to NextNano 3 , the 2D electron density in the NW at each voltage sweep step can be visualized by considering all the device geometry and different materials properties, as well as solving the Poisson equation. As shown in Figure 2.36, the electron density in the NW cross section at zero gate voltage is 1×10 18 at / cm 3 , which is the input doping level. The NW is gradually depleted of carriers when applying a negative gate bias with the BG or the LG. Noticeably, the depleted region starts from the bottom of the NW, and gradually increases when applying a BG; whereas, the NW is depleted starting from the right side when using a LG. When applying a small gate voltage, we have the gate-NW capacitance:

= (2.12)
where dQ/dV can be extracted as the slope of 2D electron density in the NW versus the gate voltage curve, from Nextnano 3 simulation result at an assumed doping level N d .

Assuming that C does not vary while changing the gate voltage, we have

= = √ (2.13)
where V th is the threshold voltage determined experimentally when the I sd is below the measure limit, Q is the total charge in the NW. Numerically solving these two equations, we can determine N d.

Numerous NID NW FET devices have been evaluated using this method. The doping level of these NWs ranges from 4×10 17 at/cm -3 to 6×10 18 at/cm -3 , showing an inhomogeneous residual doping among these NWs, which is consistent with resistivity measurements. The gate-NW capacitance value is around a factor of 2 or 3 lower than that calculated by the analytical equation (2.9), which agrees with the literature and confirms the necessity of numerical simulation in the NW FET system [START_REF] Wunnicke | Gate capacitance of back-gated nanowire field-effect transistors[END_REF], [START_REF] Khanal | Gate coupling and charge distribution in nanowire field effect transistors[END_REF].

In addition, we have found that the doping level determined by BG is twice larger than that evaluated by LG for the same NW measured in both geometries. One reason for this discrepancy could be that in the case of LG, only the part of the NW facing the LG was depleted, whereas the whole NW channel was involved in depletion in the case of BG. Moreover, the method of BG is less accurate due to the difficulties to estimate the

Mobility

Since the doping level obtained for NID NW is around the metal-insulator transition, we consider that full ionization is achieved in the NWs. Combining the four-probe resistivity and the doping level, we can deduce the mobility by using equation (2.1). For N2088, we can assume n = N d , with N d determined by FET and EDX, respectively. Mobility dependence on the carrier concentration of these NID NWs is shown in Figure 2.38. Most of the NID GaN NWs have a state-of-art mobility and a similar behavior compared to GaN films [START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF], [START_REF] Khan | Growth of high optical and electrical quality GaN layers using low-pressure metalorganic chemical vapor deposition[END_REF]- [START_REF] Halidou | Heavily silicondoped GaN by MOVPE[END_REF] limited by impurity scattering. The two NWs with low mobility values are affected by surface scattering due to their extreme small radius around 20 nm [START_REF] Motayed | Experimental investigation of electron transport properties of gallium nitride nanowires[END_REF]. Even with doped NWs, such as N2088, the mobility value is quite similar compared to the state-of-art value on the Si doped MOVPE GaN microwires, it implies that we can achieve high doping level in GaN NWs without reducing the mobility. (a) (b)

Conclusions of the chapter

To summarize, we fabricated GaN NWs with different Si doping levels by PAMBE, and systematically investigated their optical, structural, and electrical properties.

In particular, we found that the Si content in GaN NWs is higher than in the 2D layer counterparts, up to 2-4×10 20 at/cm 3 accompanied by a Si-enriched shell for the most doped sample. Direct transport measurements on single NWs have shown a controlled doping with resistivity from 10 2 to 10 -3 Ω.cm, and a carrier concentration from 10 17 to 10 20 cm -3 . FET measurements combined with 2D finite element simulation have shown a high mobility in these NWs, comparable to the state of the art mobility value of GaN epilayer. black and red correspond to NID GaN NWs and GaN wires grown with Si cell temperature of 938 °C, respectively. For NID NWs, the radii of the two NWs with lower mobility (less than 10 cm 2 .V -1 .s -1 ) are 24 nm and 20 nm, and those of the other ones are in the range of 30-40 nm.

GAN P-N JUNCTIONS

In the previous chapter, I have demonstrated a detailed investigation on n-type GaN NWs from different perspectives. I have studied the influence of the doping growth condition (namely Si cell temperature) on optical, structural, and electrical properties of the NWs, and further facilitated the understanding of the growth mechanism, the doping process and the peculiar properties of the doped NWs. In this chapter, I would like to extend the study to one of the most important basic building blocks of semiconductors devicesp-n junctions. In particular, I will focus on the growth optimization of the GaN p-n junction NWs in PA-MBE system, with a special attention on p-type GaN NWs, and furthermore, the electrical properties of the axial GaN p-n junction NWs through electron beam based techniques, including some investigations on p-type contact.

Compared to GaN epilayer p-n junctions, GaN wires p-n junctions manifest many advantages.

 First of all, as mentioned in Chapter 1 & 2, GaN wire structures can be readily grown on lattice mismatched substrates, such as Si, without creating a high density of dislocations. It permits a reasonable flexibility for device fabrications, and facilitates integration with other technologies, such as Si based technology in microelectronic industry.

 Secondly, it is possible to incorporate more dopants, and likely to achieve high carrier concentrations in the wires. As concluded in Chapter 2, Si dopants up to 10 20 at/cm 3 can be incorporated in GaN NWs without element segregation and defect formation, which is above the theoretical solubility prediction ( around 5×10 19 at/cm 3 ) [START_REF] Neugebauer | Surfactants and antisurfactants on group-III-nitride surfaces[END_REF]. In terms of Mg dopants, a significant Mg content in both AlN and InN NWs have been reported by Mi's group associated with a reduced

Mg formation energy at the NW surface [START_REF] Zhao | Aluminum nitride nanowire light emitting diodes: breaking the fundamental bottleneck of deep ultraviolet light sources[END_REF], [START_REF] Zhao | p-type InN nanowires[END_REF], [START_REF] Connie | Optical and electrical properties of Mg-doped AlN nanowires grown by molecular beam epitaxy[END_REF]. Therefore, GaN wires could be a promising solution to obtain high Mg (p-type) doping, which will greatly ameliorate the performance of most GaN based devices.

 Moreover, the wires could provide more degrees of freedom in heterojunction growth, such as facet-selective growth aiming at achieving multicomponent and multifunction nanodevices [START_REF] Kempa | Facet-selective growth on nanowires yields multi-component nanostructures and photonic devices[END_REF]. Device design on different facets (polar, nonpolar) can be used to integrate radial, axial, or core-shell heterojunctions, which offers new possibilities compared to epilayers [START_REF] Ra | Single nanowire lightemitting diodes using uniaxial and coaxial InGaN/GaN multiple quantum wells synthesized by metalorganic chemical vapor deposition[END_REF]. For example, GaN coreshell p-n junction wires can benefit from the increased active surfaces due to their particular geometries, candidating for more efficient LEDs [START_REF] Tchoulfian | Direct imaging of p-n junction in core-shell GaN wires[END_REF], [START_REF] Tchernycheva | Core-shell InGaN/GaN nanowire light emitting diodes analyzed by electron beam induced current microscopy and cathodoluminescence mapping[END_REF].

However, new opportunities always come with new challenges. There are only a few publications on the growth of p-type or p-n junction GaN NWs [START_REF] Furtmayr | Optical properties of Siand Mg-doped gallium nitride nanowires grown by plasma-assisted molecular beam epitaxy[END_REF], [START_REF] Limbach | Morphology and optical properties of Mg doped GaN nanowires in dependence of growth temperature[END_REF], [START_REF] Park | Electron trap level in a GaN nanorod p-n junction grown by molecular-beam epitaxy[END_REF]. Mg doping in GaN is influenced by many parameters at the same time, such as Mg cell temperature, surface stoichiometry and substrate temperature. It is necessary to study systematically the Mg doping behavior in the MBE system.

Moreover, in the case of NW hetrostructures, one of the biggest challenges is the lack of metrology. New measurements and models are crucial to understand the underlying physics of these structures and further facilitate their use in various devices. Last but not the least, achieving ohmic contact on p-type GaN epilayer is difficult despite the tremendous efforts devoted to it. Many parameters, such as surface treatments and annealing conditions, play important roles in determining the specific contact resistance. Furthermore, ohmic contacts on NW structures are even more challenging due to the reduced contact areas, which make the contact resistance very sensitive to the technological processes and the annealing conditions. This absence of knowledge to fabricate ohmic contact especially on p-type GaN NWs, not only limits the understanding of the characteristics of the NW structures, but also restricts the further device developments based on these structures.

In terms of axial GaN p-n junction NWs, only a few novel characterization techniques have been reported (Figure 3.1). Non-contact, atomic-force-microscope-based (AFMbased) techniques such as scanning microwave microscope and kelvin probe force microscopy (KPFM) have shown to be able to distinguish n-type region from p-type part, and further map the space charge region in the p-n junction [START_REF] Imtiaz | Imaging the p-n junction in a gallium nitride nanowire with a scanning microwave microscope[END_REF], [START_REF] Minj | Direct assessment of pn junctions in single GaN nanowires by Kelvin probe force microscopy[END_REF]. However, quantitative understanding of doping levels at each side of the junction needs extensive modeling and more complete input parameters. Techniques, which require the fabrication of electrical contacts, such as electroluminescence (EL) and secondary electron voltage contrast (VC) have also been applied to characterize axial GaN p-n junction NWs [START_REF] Brubaker | Toward discrete axial p-n junction nanowire light-emitting diodes grown by plasma-assisted molecular beam epitaxy[END_REF], [START_REF] Lu | Dynamic visualization of axial p-n junctions in single GaN nanorods under electrical bias[END_REF]. EL signal has indicated the presence of the p-n junction, however, non-ideal p-doping and asymetric Schottky-like p-contact are shown to significantly suppress the EL signal, suggesting that this work is far from complete  What are the diffusion lengths of minority carriers or exciton concentrations near the junction? What is the influence of the surface states?

Growth optimizations

Before investigating the properties of p-n junction NWs, it is necessary to master their growth. As shown in chapter 2, well-controlled n-type GaN NWs can be achieved by varying the Si cell temperature in the MBE system. Now we will focus on the more complicated part: p-type.

p-type doping has always been a big challenge and a subject of study in the nitride field.

Neugebauer and Van de Walle have made a comparison of possible acceptor impurity candidates (Li, Na, K, Be, Zn, Mg, Ca) in GaN using first-principles total-energy calculations. They have found that Mg substitute on the Ga site is superior compared to the other candidates considering solubility and stability against compensation by interstitials [START_REF] Neugebauer | Chemical trends for acceptor impurities in GaN[END_REF].

In this section, I will first briefly review the state of art literature in the growth of Mg doped GaN epilayers as well as NWs. Then I will present our investigations on the PA-MBE growth of Mg doped GaN NWs through adjusting different parameters (Mg cell temperature, substrate temperature, surface stoichiometry). At last, I will extend the study to the growth of axial GaN p-n junction NWs.

State of art literature

Mg doped GaN 2D layer One of the most important breakthroughs in the field is the discovery of Mg acceptor doping activation by post-growth process in the case of hydrogen involved growth techniques at the beginning of the 90s. This post-growth process can be either low-energy electron-beam irradiation [START_REF] Amano | p-type conduction in Mgdoped GaN treated with low-energy electron beam irradiation (LEEBI)[END_REF] or annealing in a hydrogen free ambient [START_REF] Nakamura | Thermal annealing effects on p-type Mg-doped GaN films[END_REF]. This discovery has enabled p-type conductivity for the development of the first blue LEDs [START_REF] Nakamura | Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes[END_REF] and later on the first LDs [START_REF] Nakamura | InGaN-based multi-quantum-well-structure laser diodes[END_REF]. Since then, tremendous efforts have been made to improve hole concentrations in order to reduce series resistance and achieve better ohmic contacts on p-type.

The state of art MOVPE grown Mg-doped GaN epilayers exhibit a hole concentration of 3×10 18 cm -3 , a hole mobility of 9 cm 2 .V -1 .s -1 , and a resistivity of 0.2 Ω.cm, after postgrowth dopant activation [START_REF] Nakamura | Highly p-typed Mg-doped GaN films grown with GaN buffer layers[END_REF]. Compared to MOVPE, MBE is an interesting alternative growth technique. Due to the UHV (free of hydrogen) growth environment, the Mg dopants are electrically active in as-grown MBE samples, meaning that no postgrown activation is required. Moreover, the MBE samples are grown at a lower substrate temperature, the "Mg memory" effect is less severe in MBE growth, leading to sharp doping profiles [START_REF] Smorchkova | Mg doping of GaN layers grown by plasma-assisted molecular-beam epitaxy[END_REF]. It was reported that the compensation effects are lower in MBE material, since the presence of hydrogen could mediate the formation energy of nitrogen vacancy (V N ) in MOVPE material [START_REF] Alves | Compensation mechanism in MOCVD and MBE grown GaN: Mg[END_REF] and there is less Si diffusion from the substrate in the MBE system. cm -3 , and a mobility of 7.5 cm 2 .V -1 .s -1 under slightly nitrogenrich growth condition [START_REF] Smorchkova | Mg doping of GaN layers grown by plasma-assisted molecular-beam epitaxy[END_REF]. Epilayers with similar electrical characteristics have also been reported using NH 3 -MBE growth technique [START_REF] Dussaigne | High doping level in Mg-doped GaN layers grown at low temperature[END_REF][148] [START_REF] Malinverni | Low temperature p-type doping of (Al)GaN layers using ammonia molecular beam epitaxy for InGaN laser diodes[END_REF]. Novel variants of PA-MBE, such as metal modulated epitaxy (the metal sources are periodically modulated, when the nitrogen flux remains constant), and phase shift epitaxy (desynchronization of host material growth process from dopant incorporation), have been demonstrated to produce GaN epilayers with Mg doping up to 1.45×10 20 cm -3 , and a hole concentration on the order of 10 18 cm -3 [START_REF] Burnham | Reproducible increased Mg incorporation and large hole concentration in GaN using metal modulated epitaxy[END_REF]- [START_REF] Zhong | p-type GaN grown by phase shift epitaxy[END_REF]. gate FET measurements [START_REF] Zhong | Synthesis of p-type gallium nitride nanowires for electronic and photonic nanodevices[END_REF]. Three years later, the Mg-doped GaN NWs grown by PA-MBE were presented [START_REF] Park | The recombination mechanism of Mg-doped GaN nanorods grown by plasma-assisted molecular-beam epitaxy[END_REF], however, no growth investigation or electrical properties were mentioned. Later on, Limbach et al. have studied the influence of substrate temperature (665-785 °C) on the morphological and optical properties of lowly Mg-doped GaN NWs grown by PA-MBE [START_REF] Limbach | Morphology and optical properties of Mg doped GaN nanowires in dependence of growth temperature[END_REF]. The range of 725-785 °C has been identified as a suitable temperature window for producing cylindrical NWs. In addition, the NW nucleation occurs faster, and the coalescence tendency increases under the supply of Mg [START_REF] Stoica | Doping of III-nitride nanowires grown by molecular beam epitaxy[END_REF], [START_REF] Limbach | Morphology and optical properties of Mg doped GaN nanowires in dependence of growth temperature[END_REF], [START_REF] Limbach | The influence of Mg doping on the nucleation of self-induced GaN nanowires[END_REF].

Recently, Mi's group has reported Raman scattering measurements on Mg-doped GaN NWs grown at a substrate temperature of 780 °C in the PA-MBE system. Local vibrational modes at 655 cm -1 and a few modes around 2200 cm -1 have been observed at high Mg doping in the NWs [START_REF] Wang | p-type dopant incorporation and surface charge properties of catalyst-free GaN nanowires revealed by micro-Raman scattering and X-ray photoelectron spectroscopy[END_REF]. These NWs have shown interesting potential applications in overall water splitting [START_REF] Kibria | Tuning the surface Fermi level on p-type gallium nitride nanowires for efficient overall water splitting[END_REF], [START_REF] Kibria | Defect-engineered GaN: Mg nanowire arrays for overall water splitting under violet light[END_REF]. Moreover, Mg doped GaN NWs grown on diamond substrate by PA-MBE have been reported, and Mg content up to 1×10 20 cm -3 has been demonstrated by SIMS measurements [START_REF] Schuster | Doped GaN nanowires on diamond: Structural properties and charge carrier distribution[END_REF]. However, it is difficult to compare between different publications due to difference in the growth method, uncertainty of temperature determination in PA-MBE, and differences in the way Mg content is specified. We can conclude that Mg doping in GaN is complicated by many factors, including surfactant effect, polarity sensitivity, high vapor pressure of Mg, compensation centers, dependence on surface stoichiometry and substrate temperature, etc. As a result, the growth window for producing electrically active p-type GaN is quite narrow. Here, I will present the exploration of the growth of Mg doped GaN NWs in PA-MBE system through the variation of two main parameters:

Mg cell temperature and substrate temperature. Based on the growth knowledge of ntype and p-type GaN NWs, the growth and optical properties of axial GaN p-n junction

NWs is also investigated.

Growth of p-type GaN NWs

Mg cell temperature Although the influence of Mg flux on GaN NWs grown by PA-MBE has already been reported [START_REF] Furtmayr | Nucleation and growth of GaN nanorods on Si (111) surfaces by plasma-assisted molecular beam epitaxy -The influence of Si-and Mg-doping[END_REF], [START_REF] Furtmayr | Optical properties of Siand Mg-doped gallium nitride nanowires grown by plasma-assisted molecular beam epitaxy[END_REF], it is important and necessary to conduct similar experiments in our system in order to get on the right track for the investigation of Mg doping incorporation in GaN NWs.

A series of samples has been grown at the same growth conditions except the variation of the Mg cell temperature from 190 °C to 270 °C (see Table 3.2). The substrate temperature has been calibrated as 5 s for Ga desorption (thermocouple-displayed temperature at 885 °C, and effective temperature around 835 °C) and kept the same during the growth. The nucleation occurs directly on Si substrate without any buffer layer, in order to obtain low density NWs. The nominal Ga/N flux is 1/3 and the same for all the samples in this series. The growth time was 6 hours for all the samples. Sample N2437 is NID GaN NWs and serves as a reference. For the other samples, Mg doping is achieved by exposing GaN NWs to the Mg flux, starting from the nucleation till the end of the growth. steady-state growth conditions [START_REF] Fernandez-Garrido | Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy[END_REF]. Therefore, a slight reduced Ga flux is used during the Mg incorporation, so that the growth surface remains nitrogen-rich.

Growth of axial GaN p-n junction NWs

Following the aforementioned two-step growth method, three GaN p-n junction NW samples have been grown. Table 3.3 lists the detailed growth conditions for each sample. Both the thermocouple displayed temperature and the Ga desorption time have been noted for the substrate temperature during the growth of Si-doped GaN base (see substrate temperature calibration in 2.1.2.2 for more details). Sample N1913 was grown by a previous colleague, and the presence of p-n junction in this sample has been observed by KPFM recently [START_REF] Minj | Direct assessment of pn junctions in single GaN nanowires by Kelvin probe force microscopy[END_REF]. Sample N2490 and N2495 were grown during my thesis in consecutive days. Although the thermocouple displayed temperature of Sidoped GaN base for N1913 is different from those for N2490 and N2495, the real growth temperature should be similar according to the Ga desorption time. All the three samples were grown under nominal nitrogen-rich conditions (Ga/N flux ratio ~ 1/3).

The Ga flux was kept the same for N1913, whereas the Ga cell temperature was decreased by 5 °C starting from Mg-doped part for the other two samples.

Electrical transport properties

As discussed at the beginning of this chapter, the electrical transport properties of Mgdoped or p-n junction GaN NWs are scarcely investigated in the literature. In this thesis, I probed the electrical transport properties of these nanostructures with the help of electron beam based methods, such as EBIC and VC on secondary electron images. Both methods require the fabrication of electrical contacts on the nanostructures, which brings us to the challenging situation on p-type GaN NW contact.

Ohmic contacts on p-type GaN NWs

Ohmic contacts on the n-type GaN and p-type GaN hold significant importance for GaN based devices, such as LEDs, lasers, and photodetectors. After decades of research efforts, ohmic contacts on n-type GaN using Ti / Al based metallization schemes can achieve contact resistivities as low as 10 -6 Ω.cm 2 , whereas the start of art p-type contact using Ni / Au can generally achieve a contact resistivity in the range of 10 -1 -10 -3 Ω.cm 2 [START_REF] Pearton | GaN: Processing, defects, and devices[END_REF].

The main difficulties for the formation of ohmic contacts on p-type GaN epilayer are:

 The unavailability of metals with large enough work function. Since GaN is a wide bandgap semiconductor with E g ≈ 3.4 eV, and the electron affinity in GaN is 4.1 eV, a metal with work function of 7.5 eV is needed for a good ohmic contact on p-type. However, most of the metal work functions are below 5.5 eV.

 The low doping concentrations achievable in p-type GaN. As seen from Table 3.1, the state of art hole concentration of the p-type GaN epilayer induced by Mg doping is limited to a value less than mid 10 18 cm -3 .

Despite these challenges, ohmic contact on p-type GaN NW is even more complicated due to the nanoscale dimensions and wire geometry. Furthermore, in our case, it is even trickier since the hole concentrations in NWs are unknown. Therefore, it is a difficult and time-consuming task to fully investigate the contact mechanism for p-type NW ohmic contacts.

In this session, I will first briefly review the theoretical background of metalsemiconductor contact formation and the state of art literatures on ohmic contact on ptype GaN epilayer. Then, I will present our results on attempting to achieve ohmic contact on Mg doped GaN NWs, as well as GaN p-n junction NWs.

Theoretical background

Figure 3.11 illustrates the formation of a Schottky barrier when a metal and a p-type semiconductor are brought into contact. The metal work function is less than that of the p-type semiconductor, which is generally the case for p-type GaN. In (a), the metal and the origin of this pinning. These surface states commonly have a narrow distribution of energies within the bandgap of the semiconductor surface, and they are characterized by a "neutral level"  0 . In this case, the Schottky barrier between a metal and a p-type semiconductor can be expressed by equation (3.2), where  is a function of the density of the surface states [START_REF] Rhoderick | The physics of schottky barriers?[END_REF].

 , = (  + - ) + - (3.2)
When there are no surface states,  = 1, equation (3.2) becomes the ideal Schottky contact situation in equation (3.1). On the other hand, when the density of the surface states are very high,  is close to 0, the surface states become the main determinant of the Schottky barrier, instead of the metal work function.

Ohmic contact is generally feathered by a linear I-V relationship through the contact with low contact resistance (about 10 -6 Ω.cm 2 ). In the particular case of p-type GaN, studies have shown that the Fermi level at GaN surfaces may not be fully pinned [START_REF] Mori | Schottky barriers and contact resistances on p-type GaN[END_REF], [START_REF] Ishikawa | Effects of surface treatments and metal work functions on electrical properties at p-GaN/metal interfaces[END_REF], thus the Schottky barrier height is weakly dependent on the metal work function. Metals with a large work function (such as Ni, Au, Pd and Pt) are preferred for creating low barrier contacts on p-GaN. Moreover, different approaches can be applied to improve current injection through the Schottky barrier, creating ohmic contacts in the broad sense. These approaches include annealing the junction in order to damage the semiconductor near the contact region, which could create gap states for conduction, or increasing the doping level near the semiconductor surface as high as possible so that the depletion layer is sufficiently narrow, allowing an enhancement of tunneling assisted transport.

State of art literature

In the past two decades, many efforts have been made in achieving p-type ohmic contact with specific contact resistance less than 10 -4 Ω.cm 2 . Different metal schemes, surface preparation methods as well as annealing conditions have been employed to reduce the specific contact resistance of the p-type contact [START_REF] Chen | Ohmic contacts on p-GaN[END_REF]. The characteristics of some of the state of the art p-type ohmic contacts are listed in Table 3.4. The hole concentration of the epilayer (p) is at the level of 10 17 cm -3 in these references.

The Ni/Au metallization is one of the most thoroughly studied p-type contacts. It is generally proposed that the formation of NiO when annealing Ni/Au contact in air or oxygen, is crucial for reducing the contact resistance. Ho et al. reported that contact resistance as low as 10 -6 Ω.cm 2 can be achieved by annealing Ni (5 nm)/Au (5 nm)

contact in air at 500 °C [START_REF] Ho | Low-resistance ohmic contacts to p-type GaN[END_REF]. Upon annealing, Ni can diffuse out through the Au layer and reacts with oxygen in the atmosphere. Thus, the Ni/Au films become a mixture of crystalline NiO, Au particles, and amorphous Ni-Ga-O phases (see Figure 3.12). NiO is a p-type semiconductor, and its direct contact with p-type GaN is probably responsible for the ohmic behavior. Another group has found that ohmic Ni/Au contact can be achieved by first the preoxidation of the GaN surface, inducing more Ga vacancies, and then the removal of the oxides using (NH4) 2 S x solution [START_REF] Sen Lee | Investigation of oxidation mechanism for ohmic formation in Ni/Au contacts to p-type GaN layers[END_REF].

Other types of metal combinations have been explored to create ohmic contact on ptype GaN. Both Pd/Ni and Pd/Ni/Au contacts have been reported to form Pd gallides, Ga 2 Pd 5 and Ga 5 Pd phases upon annealing. This reaction can generate more Ga vacancies below the contact, which help to reduce the contact resistance [START_REF] Jang | Low-resistance and thermally stable ohmic contact on p-type GaN using Pd/Ni metallization[END_REF], [START_REF] Cho | Characterization of Pd/Ni/Au ohmic contacts on p-GaN[END_REF].

Another high work function metal Pt (5.12-5.93 eV) has also been used to obtain ohmic contact. A two-step surface treatment has been reported to achieve ohmic Pt contact with specific contact resistance of 2×10 -5 Ω.cm 2 [START_REF] Jang | Formation of low resistance Pt ohmic contacts to p-type GaN using two-step surface treatment[END_REF].

Moreover, due to the strain-induced piezoelectric field and the large valence band discontinuity between GaN and InGaN, InGaN/GaN superlattices could achieve hole concentration as high as 1×10 19 cm -3 [START_REF] Ingan | Efficient hole generation above 10 19 cm -3 in Mg-doped InGaN / GaN superlattices at room temperature[END_REF]. Therefore, a highly Mg-doped InGaN layer can be used as a contact layer for creating ohmic contact on p-type GaN. A 2 nm thick In 0.19 Ga 0.81 N layer between Pt/Au contact and p-type GaN has been reported to obtain a specific contact resistance of 10 -6 Ω.cm 2 [START_REF] Kumakura | Low resistance non-alloy ohmic contact to p-type GaN using Mg-doped InGaN contact layer[END_REF]. Although these results are promising, the reaction at the p-GaN / contact interface seems to be crucial to reduce the contact resistance; however, the mechanism of the ohmic contact formation is far from being understood. In reality, this ohmic contact formation strongly depends on many factors, such as the doping level and the surface properties of the p-type GaN [START_REF] Chen | Ohmic contacts on p-GaN[END_REF], the contact scheme [START_REF] Ho | Low-resistance ohmic contacts to p-type GaN achieved by the oxidation of Ni/Au films[END_REF], and the annealing conditions (temperature, ambient, etc.) [START_REF] Chen | Thermal annealing effects on Ni/Au contacts to p type GaN in different ambient[END_REF]. Therefore, it is difficult to establish a reproducible ptype ohmic contact recipe.

Besides these metals, indium tin oxide (ITO) is an interesting alternative contact material. In fact, ITO is one of the most widely used transparent contact materials in devices, such as solar cell, liquid crystal displays and photodetectors. A direct contact of ITO on p-type GaN is non-ohmic [START_REF] Lin | InGaN / GaN light emitting diodes with Ni / Au , Ni / ITO and ITO p-type contacts[END_REF], nevertheless, the combinations of ITO with other materials, such as Ni [START_REF] Horng | Low-resistance and hightransparency Ni / ITO ohmic contacts to p-type GaN[END_REF], Zn-Ni [START_REF] Chae | Highly transparent and low-resistant ZnNi /ITO Ohmic contact on p-type GaN[END_REF], and p-InGaN [START_REF] Jang | Low-resistance and thermally stable indium tin oxide ohmic contacts on strained p-In 0[END_REF], have shown ohmic contact behaviors. In fact, the as-deposited ITO films behave as an insulator, and become conducting upon annealing with a wide direct optical band gap of 3.6 eV [START_REF] Antony | Influence of target to substrate spacing on the properties of ITO thin films[END_REF].

The electrical and optical properties of the ITO film are a strong function of many parameters, including deposition conditions and annealing conditions [START_REF] Gulen | Role of annealing temperature on microstructural and electro-optical properties of ITO films produced by sputtering[END_REF]. In addition,

Musolino et al. have reported an improved p-type GaN top contact in GaN NW based

LEDs with 120 nm-thick ITO compared to the common Ni (5 nm)/Au (5 nm) contact scheme [START_REF] Musolino | Understanding peculiarities in the optoelectronic characteristics of light emitting diodes based on (In,Ga)N / GaN nanowires[END_REF].

Contacts on Mg doped GaN NWs

Ni/Au metallization As one of the most commonly used p-type ohmic contacts, Ni/Au metallization scheme was firstly explored on Mg doped GaN NWs.

Ideally, GaN NWs with the highest doping level should be used to investigate the ohmic Sample N2092 has shown a Mg concentration of (3.350.37)×10 19 cm -3 , while the Mg level in the other samples is below the detection limit of the SEM-EDX, which is around 10 19 cm -3 . The hole concentration in N2092 is therefore estimated to be 1×10 18 cm -3 , assuming similar acceptor ionization energy (245 meV) compared to Mg doped GaN epilayers grown by MBE [START_REF] Brochen | Dependence of the Mg-related acceptor ionization energy with the acceptor concentration in p-type GaN layers grown by molecular beam epitaxy[END_REF].

The growth conditions of N2092 are briefly described in the following for further reference. Sample N2092 has been grown at a substrate temperature around 830 °C (Ga desorption of 5.6 s), with a 3 nm thick AlN buffer. The growth was started by GaN NW nucleation for 20 minutes and followed by Mg doped part for 20 hours. The nominal Ga/N flux was 1/3 and the same for both the nucleation and the Mg doped part. The Mg cell temperature was kept at 210 °C during the growth.

Numerous NWs taken from N2092 have been dispersed on Si substrates covered with 500 nm thick insulating thermal oxide and eventually contacted by conventional EBL or laser lithography for testing different surface treatments and contacting schemes. As stated before, the metal deposition is realized by an electron beam evaporator (Plassys company). For contact deposition on Mg doped NWs, the base pressure in the chamber is lower than 3×10 -6 Torr, in order to eliminate contamination as much as possible. The total thickness of the metal contact is on the same level as the diameter of the Mg doped NW (around 80 nm for sample N2092), with the purpose of getting a continuous metal film covering the NW.

As listed in Table 3.5, for N2092_01, Ni/Au contact (30 nm and 50 nm, respectively) was deposited without any surface treatments. The devices were annealed up to 500 °C in air, and no electrical activities were observed from -1 V to +1 V using a Keithley sourcemeter (detection limit down to 1 nA), suggesting the presence of a very high resistance (more than 1 GΩ). These Ni/Au contacts seem to be quite rough and do not have a smooth interface with the NW from SEM observation, such as Figure 3.13 (a).

Surface condition plays an important role in p-type contact formation. A thin layer of surface oxides is possibly creating an insulating layer at the metal/NW interface, preventing the current flow. The same contact process was repeated with an extra dip in HCl solution (37%) for 30 s (N2092_02) and 1 min (N2092_03) before the metal deposition, aiming at removing possible oxides at the NW surface. Both N2092_02 and N2092_03 have shown improved I-V characteristics upon annealing until 500 °C in air.

A non-linear, asymmetric I-V relation with around 10 nA under 1V has been observed for a few devices in both samples. However, it was not possible to use FET measurement on these devices in order to evaluate the doping level due to the large This phenomenon has also been observed by other researchers [START_REF] Herrero | Microstructure evolution and development of annealed Ni/Au contacts to GaN nanowires[END_REF]. As cited in Figure 3.14, the Ni/Au contacting film is rather smooth and conformal before annealing, and it becomes rough and contains micro-cracks after annealing. A possible explanation is illustrated in Figure 3.14 (c). Upon annealing, Ni atoms diffuse through the Au layer to the surface, and react with O 2 , forming NiO. The contact layer thus contains a Au-rich underlying layer with large voided areas and a NiO layer on top. These void areas (the dark feathers in the SEM images) are present at both the metal/SiO 2 and the metal/NW interfaces. They can cause severe cracking or delamination of the Ni/Au film from the SiO 2 substrate, as observed in the SEM images. Moreover, the size of the void regions is on the same order of magnitude to that of the NWs. The reduced contact areas due to these void regions are much more significant in the case of NWs compared to microwires or epilayers. Therefore, a very high contact resistance, with a non-ohmic behavior, has been observed on annealed Ni/Au contact to Mg-doped GaN NWs.

(c)

Other metallization schemes: ITO As stated before, ITO is an interesting alternative contact material. There are many techniques to deposit ITO films, and the sputtering method is known for producing high quality and conformal ITO films. In this thesis, ITO films were deposited by striking the ITO target using argon plasma at room temperature, in a sputtering machine (DP850 "Alliance concept "company).

GaN p-n junction NWs from sample N1913 have been employed to experiment the ITO contact, since the presence of p-n junction in this sample has been witnessed by KPFM previously [START_REF] Minj | Direct assessment of pn junctions in single GaN nanowires by Kelvin probe force microscopy[END_REF]. For the growth details of sample N1913, please refer to Table 3.3. The diameter of the NWs is around 70 nm at the bottom, and it increases gradually reaching up to 120 nm on the top because of Mg incorporation. Therefore, the thickness of the ITO films has been chosen to be 100 nm.

GaN p-n junction NWs have been dispersed on Si substrates covered with 500 nm thick insulating thermal oxide and patterned with two-probe contact by conventional EBL. O 2 plasma RIE process has been carried out for 5 s and a dip in HCl solution (37%) has been realized for 1 min precedent of the ITO sputtering.

The as-patterned devices did not show any electrical activities since the as-deposited ITO film is an insulator. Annealing was proceeded by putting the sample at different temperatures (250 °C, 300 °C, 350 °C, 400 °C, 450 °C, 500 °C, 550 °C gradually) in air for 10 min, and electrical measurements (I-V and EBIC) were conducted after annealing at each temperature. As expected, the ITO becomes more conductive with increasing annealing temperature, and interesting EBIC results have been obtained on two axial pn junction NWs after annealing the devices at 550 °C. The details and comprehension of the EBIC characterization results will be discussed in the following sections.

Before switching to EBIC measurements, I would like to mention a side study on ITO electrical and morphological evolution under different annealing temperatures. ITO films were sputtered on Si+SiO 2 substrates. SEM observations and I-V measurements were carried out after annealing the films under different temperatures in air for 10 min. The as-deposited ITO films are smooth, and the morphology of the film does not vary much with increasing annealing temperature until 600 °C. As shown in Figure 3.15 (b), some micro-cracks start to appear after annealing the films at 600 °C. On the other hand, the resistivity of the ITO film gradually decreases when increasing annealing temperature until 600 °C. At 600 °C, the film seems to be more resistive and electrically unstable. Therefore, 550 °C is a favorable temperature for annealing ITO films.

The localization of p-n junction on the axial GaN NWs

The principle of EBIC

In EBIC measurements, the charge carriers generated by the electron beam of the microscope are collected by an electric field within the material and sensed as a current in an external circuit. This technique reveals inhomogeneities in the electrical properties of the material, and was originally developed for mapping electrically active defects in Si based integrated circuit technology. Along with the improvements in SEM instrumentation, EBIC technique has a high spatial resolution due to the small beam size (around a few nanometers), and it has been employed to determine important physical parameters nowadays, such as carrier lifetime, diffusion length, defect energy levels, and surface recombination velocities [START_REF] Leamy | Charge collection scanning electron microscopy[END_REF].

As illustrated in Figure 2.17 in Chapter 2, the interaction between the incident electrons and the sample can give rise to phonons, plasmons, Auger electrons, X-rays, photons, secondary electrons, and charge carriers (electron-hole pairs). Some of them, such as Auger electrons, X-rays, photons, secondary electrons, tend to leave the sample, whereas the others, such as heat, electrons, and charge carriers, will stay in the sample. In the absence of an internal electric field, these charge carriers will either recombine or diffuse to recombination sites, thus no current is produced. If there is an electric field localized within the sample such as at a p-n junction or near a Schottky contact, the electrons and holes drift in opposite directions, creating a low current. With the help of an amplifier, this current can be measured in an external circuit and used as the video the n-side, and a net negative charge on the p-side. Consequently, an electrical field is formed between the n-side and the p-side. This electrical field can induce a drift current, which moves electrons back to the n-side, and holes back to the p-side. At equilibrium, the diffusion current is completely balanced by the drift current, and the Fermi levels are aligned between n-side and p-side, accompanied with a band bending at the junction.

As shown in Figure 3.17, the n-type semiconductor is neutral from x = - to x = X L , and it is charged with the ionized donors in the region ≤ ≤ , whereas for the ptype semiconductor, it is neutral from x = X R to x = + and it is charged with the uncompensated acceptor ions in the region < ≤ . Assuming there are no free carriers in the depletion region (from x = X L to x = X R ), we have the charge neutrality equation:

| | = | | (3.3)
where Parameter ɛ GaN is the permittivity of GaN, given by = 9.7 × at 300 K, where ɛ 0 is the vacuum permittivity (8.854 x 10 -12 F.m -1 ). And ρ is the volume charge density.

From equation (3.4), we can eventually deduce that the total depletion width W:

= √ ( - ) ⁄ (3.5)
In this equation, = + is the effective doping level, V pn is the applied voltage on p-region of the p-n junction and V bi is called the "built-in voltage", which is the electrostatic potential drop at the junction without external bias. We have = ( 2) , where k is the Boltzmann constant, T is the temperature in Kelvin, and n i is the intrinsic carrier concentration in GaN (n i = 1.9 x 10 -10 cm -3 at room temperature).

The thermal voltage = is 0.026 V at 300 K, if N D is on the level of 10 18 cm -3 , V bi ranges between 3.3 V and 3.2 V for N A varying from 10 17 to 10 15 cm -3 , respectively.

When increasing forward bias (V pn > 0), the depletion width reduces, and an increasing current will flow through the p-n junction; on the other hand, under reverse bias (V pn < 0), the depletion region expends, the p-n junction acts like an insulator with only a very small leakage current. The I-V characteristic of a p-n junction can be described by Shockley diode equation:

= - (3.6)
Where I pn is the current passing through the p-n junction, I s is the saturation current, and n is the ideality factor. Under positive bias, I pn increases exponentially as a function of V pn . Under negative bias, I pn rapidly reaches a small saturation value (J s ). n is generally ranging between 1 and 2. at each end and the length between two contacts were measured using high resolution SEM images and summarized in Table 3.6. We can see the diameters of the two NWs are quite similar, with a difference of 5% or less. The I-V curves of NW #1 and NW #2 are presented in Figure 3.19 (a). Although these two NWs are taken from the same sample, different electrical behaviors have been observed. For NW #1, a nonlinear, nonexponential I-V behavior can be discerned when applying voltage from -3 V to +3 V. The current passing in the device is 40 nA under +3 V and 10 nA under -3V, corresponding to a high current density of 600 A/cm 2 and 150 A/cm 2 , respectively, when taking the average diameter of 100 nm. On the other hand, for NW #2, the current is below detection limit (1 nA) when changing the voltage from -3 V to +3 V.

From the I-V curve in log-log scale of NW #1, two transport regimes are exhibited with different α values in ~ . An ohmic behavior (~ with a very high resistance of For NW #1, no voltage contrast can be observed on the SEM images due to the contaminations, while the EBIC profile consists of the contributions of the depletion region and the carrier diffusions from each neutral side. Notice that the EBIC signal is asymmetrical, indicating different physical behaviors of the neutral n and p parts. On the other hand, for NW #2, the position of the EBIC signal coincides with the location of the contrast change in SEM profile, and furthermore it corresponds to the enlargement of the NW diameter, confirming the presence of the axial p-n junction. In addition, the SEM profile is influenced by a few factors, such as topography of the sample and the existence of the p-n junction. The small peak on p-GaN in the SEM profile is correlated to the "dust" of unknown origin seen on the p-side of NW #2 (see A comparison of the EBIC signal between NW #1 and NW #2 is shown in Figure 3.23.

The EBIC signal is normalized and aligned with respect to the maximum value, presented in linear scale. The EBIC signal from the depletion region is similar for the two NWs, whereas a discrepancy can be observed from the diffusion part. Both NWs side, whereas a small deviation is noticed on the p-side. It is difficult to say whether this deviation is a signature of the p-n junction depletion width extension under negative bias, therefore modeling is needed for more quantitative studies. For NW #2, the situation is more complicated. The presence of "dust" on p-side of NW has led to an inflection point on the EBIC signal. Moreover, the EBIC behaviors of p-GaN on the two sides of the "dust" are different. On the right, the EBIC current does not vary with different voltages, whereas on the left, it gradually increases with the rise of the voltage, suggesting the existence of an electric field on this part of the NW. Therefore, it is necessary to perform modeling of the EBIC signal to disclose the underlying physics of these two NW devices.

The EBIC signal simulations of the p-n junction

The EBIC signal of a p-n junction in core-shell GaN microwires has been modelled by a previous colleague [START_REF] Tchoulfian | Direct imaging of p-n junction in core-shell GaN wires[END_REF], and the same method has been employed in this thesis. Only a brief description of the modelingprocess is presented here, for more information please refer to the thesis of P. Tchoulfian [START_REF] Tchoulfian | Propriétés électriques, optiques et électro-optiques de microfils GaN pour la réalisation de LEDs[END_REF].

Injection conditions The EBIC signal is closely related with the excess carriers created by the interaction between incident electron beam and the sample. When the amount of excess carriers is smaller than that of the majority carriers in the sample, only the diffusion current of the minority carriers is measured in EBIC. In this case, the device is under low injection conditions and the analysis of the EBIC signal provides us the diffusion length of the minority carriers. On the contrary, if the concentration of excess carriers is higher than the majority carriers concentration, the diffusions of both minority and majority carriers contribute to the EBIC current, giving rise to a more complicated system [START_REF] Cavalcoli | Evaluation of diffusion length at different excess carrier concentrations[END_REF]. Therefore, the concentration of excess carriers ∆n, p has been firstly estimated by equation (3.7), assuming the average electron-hole pair energy is 3E g :

∆ , = -× × × (3.7)
where E 0 is the e-beam energy, a = 0.176 is the backscattering coefficient, V is the electron sample interaction volume, E g = 3.4 V is the GaN bandgap energy, i B is the beam current, is the excess carrier lifetime, and e is the elementary charge.

The interaction volume can be then approximated by a sphere with diameter D K-O [START_REF] Kanaya | Penetration and energy-loss theory of electrons in solid targets[END_REF] given by:

-= . × × . . × (3.8)
where = 42 g/mol is the average atomic mass of GaN, = 19 is the average atomic number of GaN, d = 6.15 g/cm 2 is the density of GaN.

Based on these two equations, ∆n, p is plotted as a function of i B under different e-beam energy assuming = ps in Figure 3.30 [START_REF] Tchoulfian | Propriétés électriques, optiques et électro-optiques de microfils GaN pour la réalisation de LEDs[END_REF]. As mentioned before, i B equals 4.6 pA, while the electron beam energy is kept at 5 keV and 4 keV, for NW #1 and #2 respectively. As indicated by the red arrows, the densities of the excited excess carriers are around 4×10 14 cm -3 for NW #1 and 1×10 15 cm -3 for NW #2. These values have been compared with the majority carrier concentrations extracted from EBIC analysis in both n and p type NWs later, in order to determine whether the low injection conditions are fulfilled.

A more accurate evaluation of the interaction volume can be achieved by using a Monte Carlo simulation program named CASINO. This software is able to simulate the electron trajectory in solid upon the interaction with low energy e-beam (0.1 to 30 keV). Figure 3.31 illustrates the simulation results of absorbed energy distribution in GaN when struck by an e-beam with 4 keV energy (the e-beam condition for NW #2) [START_REF] Tchoulfian | Propriétés électriques, optiques et électro-optiques de microfils GaN pour la réalisation de LEDs[END_REF].

The value of each line in (a) and (b) corresponds to the percentage of the energy outside of each equivalent region. 95% of the incident electron energy is concentrated within 60 nm from the impact point at vertical (depth) and lateral distance. Therefore, for a NW with a diameter of 70 nm on the n-side, and 120 nm on the p-side, most of the incident e-beam energy is focused within the NW. Moreover, the cumulated absorbed energy can be plotted as a function of interaction depth (c) and lateral position (d) for e-beam with different energies [START_REF] Tchoulfian | Propriétés électriques, optiques et électro-optiques de microfils GaN pour la réalisation de LEDs[END_REF]. We can conclude that both the interaction depth and lateral position are less than 100 nm for e-beam energies of 4 keV and 5 keV. Accordingly, the interaction volume V simulated by CASINO remains completely inside the NW, and thus has been employed to model the EBIC signal. The modeling of EBIC current in the vicinity of a p-n junction Once created, the excess minority carriers will diffuse in the materials, and the nonequilibrium minority carrier density ∆p (x,y,z), taking the n-side as an example, fulfills the continuity equation (3.9):

∆ , , - ∆ , , + , , = (3.9)
Here, D represents the diffusivity and is related with the diffusion length L and carrier lifetime by = ⁄ . Function g(x,y,z) describes the generation of minority carriers.

Hence, the first part of this equation signifies the diffusion of created carriers, the second part indicates the radiative and non-radiative recombination of these carriers, and the last part stands for the generation of the carriers upon e-beam bombardment.

With the EBIC measurements configuration shown in Figure 3.32, equation (3.9) can be solved using a method developed by Bonard and Ganière [START_REF] Bonard | Quantitative analysis of electron-beam-induced current profiles across p-n junctions in GaAs/Al 0.4 Ga 0.6 As heterostructures[END_REF]. The p-n junction is located between -dj and 0 along the x-axis with a depletion width of W, and the e-beam scans parallel to the p-n junction (the same to the case in this thesis). If the system is translational invariant along the y-axis, the generation function g(x,y,z) can be summed across y to yield h(x,z). For e-beam bombardment on the surface at x = 0, the generation of electron-hole pairs in the small volume dxdz is estimated by equation (3.10): where A and B are constants. After the linearization of the functions k(x) and j(z), the values of and are related to the slopes of the corresponding curves as shown in Figure 3.33 [START_REF] Tchoulfian | Propriétés électriques, optiques et électro-optiques de microfils GaN pour la réalisation de LEDs[END_REF]. By plotting the Monte Carlo data k(x) and j(z) is the linearized fashion, we can have access to the values of and under specific e-beam conditions. Following this process, the values of and in our case are estimated to be 38 nm and 11 nm for NW #2 (4 keV), and 55 nm and 17 nm for NW #1 (5 keV).

The analytical solution of the equation (3.9) can be obtained by the use of Green functions and Fourier transforms. Alternatively, Bonard and Ganière [START_REF] Bonard | Quantitative analysis of electron-beam-induced current profiles across p-n junctions in GaAs/Al 0.4 Ga 0.6 As heterostructures[END_REF] has come out with an expression to numerically simulate the EBIC current by adapting the collection efficiency proposed by Donolato [START_REF] Donolato | Reciprocity theorem for charge collection by a surface with finite collection velocity: application to grain boundaries[END_REF].

The EBIC current along x-axis can be expressed by the minority collection efficiency of the junction at a distance:

= ∫ ̃∫ ̃-, ̃ ̃, ∞ +∞ -∞ ̃ ̃ (3.12)
where h(x, z) is defined by (3.10), and , is the carrier collection efficiency.

Different boundary conditions in different regions can lead to the expression of , in each part of the p-n junction. If there is no carrier recombination in the depletion region, then , = , -≤ ≤ . Whereas for the minority carriers created on the neutral n and p side, , is a function of the minority carrier diffusion length, diffusivity, and surface recombination velocity if surface recombination effect is not neglected. The detailed expressions of , can be found in reference [START_REF] Bonard | Quantitative analysis of electron-beam-induced current profiles across p-n junctions in GaAs/Al 0.4 Ga 0.6 As heterostructures[END_REF], therefore will not be listed here.

It is worth mentioning that the EBIC current in the neutral region far from the contact fulfils the exponential decay relationship with the diffusion length when we neglect the surface recombination.

-⁄ , = √ (3.13)

Quantitative analysis of the depletion width and carrier diffusion length in the axial GaN p-n junction NWs

With no external bias As we discussed in the previous section, the EBIC signal is closely related with the depletion width, carrier diffusion length and surface recombination velocity. In order to quantitatively evaluate these values in the axial GaN p-n junction NW, the Bonard and Ganière model [START_REF] Bonard | Quantitative analysis of electron-beam-induced current profiles across p-n junctions in GaAs/Al 0.4 Ga 0.6 As heterostructures[END_REF] has been used. This method has been successfully applied on the EBIC signal of p-n junction in core-shell GaN microwires [START_REF] Tchoulfian | Direct imaging of p-n junction in core-shell GaN wires[END_REF]. The spatial distribution of the excited excess carriers is taken into account by using equation (3.10), in which the values of and are calculated from the previous section. Therefore, all the excess carriers generated in the depletion region, and the neutral n-and p-regions are considered.

The reported surface recombination velocity values are in the range of 1.1×10 4 -7×10 4 cm/s for the GaN epilayers [START_REF] Onuma | Comparative study of surface recombination in hexagonal GaN and ZnO surfaces[END_REF], and 9×10 3 cm/s for GaN NWs [START_REF] Schlager | Steady-state and time-resolved photoluminescence from relaxed and strained GaN nanowires grown by catalyst-free molecular-beam epitaxy[END_REF] in the literature.

Another EBIC study of GaN epilayer devices has found that the surface recombination is negligible, probably arising from the surface passivation by the polymerization of the hydrocarbon layer deposited by e-beam. Hence, the surface recombination is considered negligible in the EBIC signal modeling. 2.5×10 17 cm -3 , taking V pn = 0V and W = 116 nm. From the growth condition of sample N1913 (see Table 3.3), the donor N d1 doping level is estimated to be 2-3×10 18 cm -3 , therefore the acceptor N a1 doping level is calculated to be 2.8-2.9×10 17 cm -3 using N eff = N A N D /(N A +N D ). For NW #2, the modeling curve coincides with the experimental data in the region of the p-n junction except near the "dust" on the p-GaN. As discussed before, the "dust" on this NW is possibly acting as a carrier recombination center, influencing the carrier dynamics in the NW. The modeling parameters for this NW are: W = 125 nm, L e,p = 170 nm, L h,n = 40 nm. If we perform the same calculations for NW #2, N eff2 is found to be 2.2×10 17 cm -3 . Assuming N d2 is also about 2-3×10 18 cm -3 , we can estimate N a2 = 2.4-2.5×10 17 cm -3 . The estimated doping levels and carrier diffusion lengths of NW #1 & #2 are summarized and compared with literature values in Table 3.7.

For both NW #1 & #2, the n-GaN part is metallic at a Si donor doping concentration of 2-3×10 18 cm -3 , thus the electron concentration in this part n = N d = 2-3×10 18 cm -3 . And this value is much higher than the densities of the excited excess carriers created by the e-beam (4×10 14 cm -3 for NW #1 and 1×10 15 cm -3 for NW #2). Therefore, the low injection condition is satisfied on the n-GaN part, and L h,n represents the minority carrier (hole) diffusion length. On the other hand, the situation for the p-GaN part is complicated. With acceptor doping level of (2.4-2.9)×10 17 cm -3 , the hole concentration is in the range of 1×10 15 cm -3 , considering an acceptor ionization energy of 245 meV [START_REF] Brochen | Dependence of the Mg-related acceptor ionization energy with the acceptor concentration in p-type GaN layers grown by molecular beam epitaxy[END_REF]. Moreover, as discussed before, the p-GaN part is possibly partially depleted due to surface states, which gives a free hole concentration lower than the densities of the excess carriers during EBIC measurements. Therefore, the low injection condition is probably not fulfilled on the p-GaN part, and the extracted value of L e,p is actually a result of both minority and majority carriers diffusion. The values of L e,p are listed in Table 3.7 as the modeling parameters of the EBIC signal, and thus will not be compared with the other L e,p values in the literature. In addition, the hole concentration level of 1×10 15 cm -3 on p-GaN is consistent with the I-V measurements.

As revealed in 2.4.4, the NID NWs manifests a high inhomogenous non-intentional ntype doping ranging from 4×10 17 to 6×10 18 at/cm -3 from one NW to another. The discrepancy between NW #1 and NW #2 is probably originated from a different level of non-intentional doping. In particular, the non-intentional n-type doping is possibly lower in NW #1 than NW #2, signified by a higher L h,n value in NW #1. Moreover, this non-intentional doping could act as compensating donors in p-GaN part. Thus, although both NW #1 and NW #2 are from the same sample N1913, a higher acceptor doping level N a is observed in NW #1 due to less compensation. In addition, this dissimilarity in non-intentional doping is also in agreement with the different I-V electrical behaviors between the two NWs.

Table 3.7 also lists the doping levels and carrier diffusion lengths on n-GaN and p-GaN in core-shell microwires [START_REF] Tchoulfian | Direct imaging of p-n junction in core-shell GaN wires[END_REF] and bulk device [START_REF] Gonzalez | Minority-carrier diffusion length in a GaN-based light-emitting diode[END_REF]. The values of L h,n in these two NWs are on the order of the 50 nm and comparable to the reported values in GaN microwires and bulk device, suggesting that the surface recombination indeed does not play a role in our case. Bulk [START_REF] Gonzalez | Minority-carrier diffusion length in a GaN-based light-emitting diode[END_REF] N d (cm -3 ) 2-3×10 18 2-3×10 18 3.5×10 value increases maybe a little with the rising negative voltage for NW #1, and it was considered at the same value for NW #2. This disagreement can be explained by the presence of the highly resistive and possibly partial depleted p-GaN part. The p-GaN part and the p-n junction are connected in series, and the most of the applied voltage will drop on the p-GaN part which is more resistive. The voltage at the boundary of the As witnessed in Figure 3.26, the p-GaN part appears to be whiter than the n-GaN, and this contrast enhances with increasing negative bias and reduces with increasing positive bias. For more quantitative analysis, the SEM profiles of NW #2 under different biases are plotted in Figure 3.37. Indeed, a bias dependent SEM contrast is observed in the neighborhood of the p-n junction (the red dashed rectangle). Meanwhile, the "dust" on the p-GaN has appeared as a small peak in the SEM profile. In addition, the morphological shape of the NW could also influence the SEM signal.

The SEM contrast in the vicinity of the p-n junction (around 600 nm length) under negative bias has been fitted according to the parabolic potential equation in ideal abrupt p-n junction in Figure 3.38. Surprisingly, the depletion width of the p-n junction extracted from the fitting reduces with increasing negative voltages. From the previous EBIC analysis, we know that the depletion width does not change much with respect to the applied voltages. One possible reason of this disparity is the e-beam contamination during SEM and EBIC observations. As shown in Figure 3.39, the e-beam contamination is obvious when we compare the SEM image of NW #2 before (a) and after (b) EBIC measurements. The e-beam seems to deposit a hydrocarbon layer around the surface of the NW, which enlarges the NW diameter and reduces the emission of the secondary electrons. Therefore, in our case, SEM VC is very limited for determining the doping levels on each side of the p-n junction.

CONCLUSIONS AND PROSPECTS

The aim of this PhD work was to investigate the n and p-type doping of GaN NWs. To do so, two extensive studies have been dedicated to Si-doped GaN NWs and axial GaN p-n junction NWs. The NWs were grown by plasma-assisted molecular beam epitaxy and a combination of optical, structural, and electrical characterization techniques was employed. In particular, it has to be stressed that there were almost no direct electrical measurements on GaN NWs at the beginning of this PhD. The current work advances the field by demonstrating the experimental evidence of a p-n junction in GaN NW.

Si-doped GaN NWs

Regarding n-type doping, I have presented a systematic investigation on a series of Sidoped GaN NWs grown at the same conditions except Si cell temperatures.

The incorporation of Si induces a morphological variation of the NWs at Si cell temperature above 938 °C. A widening of the NW was observed and the top facets of the NW switched from 6-fold symmetry to 12-fold symmetry when Si cell temperature reached 950 °C. A broadening of the near-band edge emission peak and a rising of the donor-acceptor pair emission in photoluminescence spectra have been recognized upon Si doping. Several Si related defect modes have been observed on Raman spectra, and a tensile strain related with E 2h mode frequency variation, increases with Si cell temperature until 950 °C, where the relaxation occurs. The Si content mapping at the nanoscale by energy-dispersive X-ray spectroscopy helps to elucidate the above observations. NWs grown with Si cell temperature of 950 °C were shown to have a core with an average Si concentration of 2.5×10 20 at/cm 3 and an outer part with Si concentration of 6.5×10 20 at/cm 3 , whereas the NWs with Si cell temperature of 938 °C contains a homogenous Si distribution of 1×10 20 at/cm 3 . More Si can be incorporated in GaN NWs compared to 2D layer counterparts.

A NW contacting process based on electron beam lithography has been developed to perform electrical measurements on single NWs. Direct transport measurements on single Si-doped NWs have shown a controlled doping with resistivity from 10 2 to 10 -3 Ω.cm, and a carrier concentration from 10 17 to 10 20 cm -3 . FET measurements combined with 2D finite element simulation have shown a high mobility in these NWs, comparable to the state of the art mobility value of GaN epilayer.

GaN p-n junction NWs

Regarding the second part of the manuscript, the MBE growth conditions of Mg-doped and axial GaN p-n junction NWs have been explored in order to achieve significant Mg incorporation, and the electrical properties of the axial GaN p-n junction NWs have been investigated using EBIC technique.

In particular, Mg cell temperature and growth substrate temperature have been found to play an important role in Mg incorporation in the PA-MBE system. A two-step growth method has been proposed for improving Mg incorporation and employed for the growth of axial GaN p-n junction NWs.

EBIC technique has visualized the presence of the p-n junction in two single NWs and clearly demonstrated its operation under reverse and forward polarization. The acceptor doping level was determined to be around 2-3×10 17 cm -3 , taking the donor doping level at 2-3×10 18 cm -3 estimated from the results of Si-doped GaN NWs. The hole diffusion length in n-GaN was measured to be 75 nm for NW #1 and 43 nm for NW #2. Under positive bias, EBIC reveals the high resistive nature of the p-GaN, which is consistent with reduced p-n junction depletion width extension under negative bias. In addition, SEM VC technique has been found to be limited in our case due to e-beam contaminations. Last but not the least, ITO contact has been shown to form an ohmic or quasiohmic contact on n and p-type GaN NWs.

Prospects

As estimated by the EBIC measurements in Chapter 3, the Mg doping level achieved on axial GaN p-n junction NWs is around 2-3×10 17 cm -3 , which still has some distance compared to the Mg concentration in the state of art Mg-doped GaN epilayers listed in Table 3.1. Therefore, it would be interesting to improve the Mg content in GaN p-n junction NWs and perform EBIC measurements on them. With a less resistive p-GaN, more voltages will drop on the boundary of the p-n junction, thus typical behaviors such as depletion width extension under increasing negative bias could be observed.

Moreover, ITO was found to achieve quasiohimic contact on p-GaN NWs, and the detailed contact formation mechanism is beyond the scope of the thesis. The investigation on the ITO contact formation would be beneficial for GaN NWs, even IIInitrides NWs based devices.

The following of this work

The work presented in this manuscript not only provides guidelines for the fabrication of the GaN NW based devices, but also demonstrates a good protocol for studying the doping of other III-nitride NWs. Indeed, a new ANR project called EMOUVAN (emission de lumière UV avec des nanofils) has been launched recently. Under the frame of this project, Madalina Siladie has started her thesis on the MBE growth and electrical transport properties of AlGaN NWs since October 2016. I hope that the knowledge and technological process developed in the current work will help to progress the study on these NWs.

CONTENTS

  INTRODUCTION ........................................................................................................... 1 1 THE BASICS ................................................................................................................ 4 1.1 NITRIDE PROPERTIES ................................................................................................ 4

2 67 3. 1 . 1

 6711 SILICON DOPED GAN NWS .................................................................................. 11 2.1 GROWTH BY PAMBE ............................................................................................. 13 2.1.1 Plasma-Assisted Molecular Beam Epitaxy ................................................................. 2.1.2 Sample preparation procedures and calibrations ....................................................... 2.1.3 The growth of GaN NWs ............................................................................................. 2.1.4 The growth of Si doped GaN NWs .............................................................................. 2.2 BASIC CHARACTERIZATIONS .................................................................................. 23 2.2.1 Morphology evolution followed by FESEM ................................................................ 2.2.2 Optical characterizations by photoluminescence ....................................................... 2.3 STRUCTURAL PROPERTIES ...................................................................................... 30 2.3.1 Defect modes evidenced by Raman spectroscopy ....................................................... 2.3.2 Si content mapped by high-resolution Energy-dispersive X-ray spectroscopy (HR-EDX) ..................................................................................................................................... 2.4 ELECTRICAL TRANSPORT PROPERTIES..................................................................... 38 2.4.1 Single NW contacting .................................................................................................. 2.4.2 Electrical transport theoretical background ............................................................... 2.4.3 Resistivity measurements ............................................................................................ 2.4.4 Doping level of NID NWs determined by FET ............................................................ 2.4.5 Mobility ....................................................................................................................... 2.5 CONCLUSIONS OF THE CHAPTER ............................................................................. 62 3 GAN P-N JUNCTIONS ............................................................................................. 63 3.1 GROWTH OPTIMIZATIONS ....................................................................................... State of art literature ................................................................................................... 3.1.2 Growth of p-type GaN NWs ........................................................................................ 3.1.3 Growth of axial GaN p-n junction NWs ......................................................................

3. 2 77 3. 2 . 2 86 3. 2 . 3 95 3. 2 . 4

 2772286239524 ELECTRICAL TRANSPORT PROPERTIES..................................................................... 3.2.1 Ohmic contacts on p-type GaN NWs ........................................................................... The localization of p-n junction on the axial GaN NWs ............................................. The determination of depletion width and diffusion length on the axial p-n junction GaN NWs .............................................................................................................................. Secondary electron voltage contrast (VC) of the p-n junction .................................. 110 3.3 CONCLUSIONS OF THE CHAPTER ........................................................................... CONCLUSIONS AND PROSPECTS ....................................................................... REFERENCES ............................................................................................................ APPENDICES .............................................................................................................

Figure 1 . 1

 11 Figure 1.1 Wurtzite (WZ) crystal structure of GaN [11]. (a) The blue and pink balls represent the Ga and N atoms, respectively. The hexagonal unit cell is highlighted with bold lines. (b) The most common plane in this hexagonal structure, including the polar c-plane, the non polar a-and m-planes as well as semi-polar (11-22) plane.

Figure 2 . 2

 22 Figure 2.2 The principle of RHEED [48].

Figure 2 . 8

 28 Figure 2.8 NW grown on bare Si and with a AlN buffer on Si [59]. SEM images and corresponding RHEED patterns of GaN NWs grown directly on Si (111) (a, b) and with an AlN buffer layer on Si. (c, d).

Figure 2 .

 2 Figure 2.9 (b)).

Figure 2 .

 2 Figure 2.13 displays the low temperature PL spectra of this Si doped GaN NWs series.For NID samples (N2059 & N2129), the PL spectra are dominated by a thin intense near-band edge emission at 3.47 eV with a FWHM of a few meV, suggesting a good crystal quality. DAP emissions at 3.28 eV are present in both samples, and about 10 times less intense than the corresponding near-band edge emissions. As usual, two phonon replicas with around 90 meV separations accompany them.

Figure 2 .

 2 Figure 2.13 PL spectra of as-grown Si doped GaN NWs series. The spectra of NID samples (N2059 & N2129) are shown at the bottom as references, whereas the Si cell temperature is increasing gradually from the bottom to the top. All the spectra have been collected at 5 K. The PL intensity is in logarithmic scale and shifted vertically for clarity.

Figure 2 .

 2 19 (c, d, e)) As discussed previously, the top facet of these NWs possesses 12-fold symmetry. The hexagonal top facet owes to polishing steps, which has cut the NWs at a certain height at radius of 100-130 nm, below the symmetry change of top facet. The measured Si concentrations from the two NWs with two techniques are similar, which confirms the accuracy of SEM-EDX, as well as excludes a potential contamination of the samples. From the TEM-EDX data profile, the NW has a core with an average Si concentration of 2.5×10 20 at/cm 3 and an outer part of around 17 nm with a much higher Si concentration of around 6.5×1020 at/cm 3 . The SEM-EDX data (white points in (d)) from the other NW fall in the same range. More observations show that all NWs grown with the highest Si cell temperature have very similar Si concentrations ranging from 2-4 x 10 20 at/cm 3 in the core with a mean value around (2.8±0.4)×10 20 at/cm 3 (calculated from 10 NWs, see Figure2.20). The outer part of the NWs is strongly enriched in Si compared to the core and contains

Figure 2 .

 2 Figure 2.21 shows an example of the SEM images of GaN NWs contacted by these techniques.

Figure 2 .

 2 Figure 2.24 (a) Chemical structure of PMMA. (b) The scission of the polymer chain after electron beam exposure [112].

Figure 2 . 25 (

 225 b) has shown a mask of four-probe contact patterns in the field of 70×70 m, and bigger patterns have been drawn in the field of 700×700 m.

  [START_REF] Morkoç | Handbook of Nitride Semiconductors and Devices, Materials Properties[END_REF] 2.4.3 Resistivity measurements 2.4.3.1 The necessity of four-probe resistivity measurements Two probe measurements are often used to estimate the resistivity of a wire assuming insignificant contact resistances. In this configuration (shown in the inset of Figure2.28 (a)), a current is introduced into the wire, while the voltage between the two same contacts is measured. The deduced resistance consists of one part from the wire and another part from the contact, as written in equation (2.5):

Figure 2 .

 2 Figure 2.27 (a) Fermi-Dirac distribution function at T > 0. (b) The energy distribution of the electrons and holes for an n-type, intrinsic and p-type semiconductor [9].

Figure 2 .

 2 Figure 2.28 The comparison of two-probe and four-probe measurements. Two-probe (a) and four-probe (b) I-V characteristics of a highly Si-doped GaN microwire [109]. (c) two-probe and four-probe I-V curves for a highly Si-doped GaN NWs (sample N2074).

Figure 2 .

 2 Figure 2.29 Four-probe resistivity as a function of NW radius for samples with different Si doping levels at room temperature, and a SEM image of one contacted NW is shown in the inset.

Figure 2 .

 2 Figure 2.31 Band bending along the wire radius and its effect on the spatial distribution of electrons in n-type wire under different surface Fermi-level pinning [116]. (a) The wire section considered. (b) Radial distribution of electrons in the wire. (c) Band diagrams of the wire in the case of n-type semiconductor.

Figure 2 .

 2 Figure 2.34 BG-FET measurement from Lieber's group [37] (a) Schematic of a BG FET NW device, and (inset) a SEM image of GaN NW FET device. (b) Source and drain I sd -V sd characteristics under different gates measured on a GaN NW of 17.6 nm diameter. The gate voltages for each I sd -V sd curve are indicated. (c) I sd -V g characteristics while varying V sd from 0.1 V to 1 V. The conductance G as a function of gate voltage V g is shown in the inset.

Figure 2 .

 2 Figure 2.37 Evidences of Si diffusions into the NWs. (a) Relative atomic compositions at the GaN NW / Si substrate interface measured by EELS [41]. (b) Conductivity values for nine different single NID NWs at three different segments, each NW is represented by one of type of symbol. The three individual segments marked by A, B, C, are in accordance with the sample structure shown in the inset [123].

Figure 2 .

 2 Figure 2.38 Mobility value versus carrier concentration for GaN. For NID GaN NWs and GaN wires grown with Si cell temperature of 938 °C, we assumed n = N d , determined by FET and EDX, respectively. Experimental mobilities have been reported for NID GaN films (gray open squares)[START_REF] Khan | Growth of high optical and electrical quality GaN layers using low-pressure metalorganic chemical vapor deposition[END_REF],[START_REF] Strite | and InN: a review[END_REF] and Si doped GaN films (black open circles)[START_REF] Wolos | Properties of metal-insulator transition and electron spin relaxation in GaN:Si[END_REF],[START_REF] Fritze | High Si and Ge n-type doping of GaN doping -Limits and impact on stress[END_REF],[START_REF] Strite | and InN: a review[END_REF]-[START_REF] Halidou | Heavily silicondoped GaN by MOVPE[END_REF], and two Si-doped GaN microwires ( blue open triangles)[START_REF] Tchoulfian | Thermoelectric and micro-Raman measurements of carrier density and mobility in heavily Si-doped GaN wires[END_REF],[START_REF] Tchoulfian | High conductivity in Si-doped GaN wires[END_REF]. The mobility values of our NWs are shown as solid stars; black and red correspond to NID GaN NWs and GaN wires grown with Si cell temperature of 938 °C, respectively. For NID NWs, the radii of the two NWs with lower mobility (less than 10 cm 2 .V -1 .s -1 ) are 24 nm and 20 nm, and those of the other ones are in the range of 30-40 nm.

[ 140 ]

 140 . SEM VC imaging has been reported for mapping electrostatic potential along the axial GaN p-n junction NW. The electric field profiles and depletion widths at different biases can provide valuable information about the NW p-n junction, indicating the great potential of electron beam based techniques in the field of NW junction characterization. Indeed, electron beam based techniques are very versatile in the semiconductor characterization field. The interaction of a focused electron beam with a sample / device

Figure 3 . 1

 31 Figure 3.1 Different novel characterization techniques applied on axial GaN p-n junction NWs in recent literatures. (a) Schematics of scanning microwave microscopy measurement on dispersed GaN p-n junction NW, taken from [138]. (b) AFM (left) and KPFM (right) images of one p-n junction NW, clear contrast between n-type and p-type part can be noticed from KPFM image, taken from [139]. (c) SEM and EL images of one n-p NW device, the EL signal is located between the two contacts, signifying the location of the junction, taken from [140]. (d) SEM image and schematics of the secondary electron VC measurements (left), clear potential contrast variation with respect to the applying bias (right), taken from [141].



  techniques such as EBIC and secondary electron VC, including an exploration on p-type contact. So here are the questions I would like to address: What are the main parameters influencing Mg incorporation in GaN NWs grown by MBE? How can we improve Mg content by playing with these parameters? Could we achieve p-n junction NWs? Where is the junction? Is it abrupt? Does its position correspond the growth conditions? What are the donors and acceptors concentrations near the p-n junction? Does the NW structure really show a better dopant incorporation compared to epilayers in the case of Mg doping?

Furtmayr

  et al. have investigated the growth of Mg-doped GaN on Si (111) by PA-MBE at different Mg fluxes, and an increased radial growth rate (see Figure 3.4 (b)) and a decreased nucleation time have been observed upon Mg doping [41]. Further explorations on the samples reveal an Mg incorporation of 4×10 20 cm -3 under the highest Mg cell temperature (see Figure 3.4 (a)), and the presence of stacking faults at Mg cell temperature above 260 °C (corresponding to Mg concentration around 4×10 19 cm -3 ), which cause the inclusions of cubic GaN in the WZ lattice [162].

Figure 3 . 4

 34 Figure 3.4 Mg concentration in GaN NW and NW morphology evolvement versus Mg cell temperature [162]. (a) Mg concentration in GaN NWs (from SIMS measurements) as a function of Mg beam equivalent pressure. The Mg cell temperature is noted near the corresponding data point, and the substrate temperature is 790 °C for the all the samples. (b) Average NW diameter and aspect ratio (height / diameter) as a function of Mg cell temperature.

Figure 3 .

 3 Figure 3.9 shows the top and side view SEM images of these samples. For sample N1913, the NWs have a typical length of around 2 m, with a relative large length dispersion. The top surface of the NWs is flat with a radius around 95-130 nm. The NW widening on the upper part is probably a result of Mg incorporation. For N2490, two types of NWs seem to be present. One type of NWs exhibit a NW widening on the upper part with a length of around 1.6-1.8 m, while the other type is thin along the NW with a length above 2 m. For N2495, the NWs have a length of around 2.1 m with obvious enlargement at the top (NW top radius above 150 nm). A certain degree of NW coalescence is observed from this sample.

Figure 3 .

 3 Figure 3.12 (a) Specific contact resistance of Ni/Au contacts to p-GaN as a function of annealing temperature for different metal thickness. (b) TEM image showing the cross-section microstructure of the Ni / Au contact after annealing at 500 °C in air for 1 min [183].

Figure 3 .

 3 Figure 3.14 Microstructure evolution of Ni/Au contacts on GaN NWs upon annealing [193]. (a) As-deposited Ni/Au contact for a NW device on a SiO 2 substrate. (b) the same NW device after N 2 /O 2 annealing. (c) Illustration of Ni/Au contact structure on a NW dispersed on SiO 2 before and after annealing in N 2 /O 2 ambient.

Figure 3 .

 3 Figure 3.15 The electrical and morphological evolution of ITO films under different annealing temperatures. SEM images of ITO films as-deposited (a) and after annealing at 600 °C (b). (c) The I-V characteristics of ITO films under different annealing temperatures.

  | |,| | are the depletion region on n-side and p-side, respectively. Thus, the total depletion width = | | + | |. Assuming an abrupt transition between neutral material and the space charge region (the Shockley approximation), one can calculate the behavior of the potential  by solving the Poisson equation in the one-dimensional case.

3. 2 . 2 . 3

 223 GaN NWs p-n junction witnessed by EBIC A few axial GaN p-n junction NWs from sample N1913 have been patterned with twoprobe ITO contact. After contact annealing at 550 °C, two NW devices have been successfully characterized by EBIC technique. Figure 3.18 shows the SEM images of these two devices NW #1 (a) and NW #2 (b). Notice that both NW #1 and NW #2 manifest a radial widening from one end (n-type side) to the other end (p-type side), and the ITO contacts are well located at the two ends of the NW. The diameters of the NW

Figure 3 .

 3 Figure 3.18 SEM images of two contacted axial GaN p-n junction NWs

Figure 3 .

 3 Figure 3.21 presents the EBIC images as well as the corresponding SEM images for NW #1 (a) and NW #2 (b) devices under 0V bias. For NW #1, although the SEM image is not very clear due to repetitive high-magnification electron beam scanning contaminations, the EBIC signal (darker area on the EBIC image) can directly localize the position of the p-n junction within the NW. The situation is even more obvious for NW #2. In the SEM image, a voltage contrast can be observed from the left side (bright, p-GaN) to the right side (dark, n-GaN), while the location of the p-n junction is manifested by the respective EBIC signal. No EBIC signal has been observed at both ncontact and p-contact for the two NW devices, a signature of ohmic or quasiohmic contact behavior.

Figure 3 .

 3 Figure 3.21 (b)).

Figure 3 .

 3 Figure 3.21 SEM and EBIC images of the measured NW #1 (a) and NW #2 (b) devices under 0 V bias. The dashed black line delineates the edges of the contacts.

  Now let us focus on the EBIC signal of the axial GaN p-n junction. Normally an extension of the depletion width for the p-n junction is expected when applying negative voltages. Figure 3.29 illustrates the normalized EBIC signals from p-n junction in NW #1 and #2 under different negative biases. For NW #1, at first sight, it seems the EBIC signals at different voltages are very close to each other, and a small deviation is observed near the right end of the EBIC signal. If we compared the SEM image with the EBIC signal, we can see that this variation occurs near the ITO contact on n-type GaN NW. Nevertheless, the EBIC signals at 0 V and -6 V are almost overlapped on the n-

Figure 3 .

 3 Figure 3.28 Schematic band diagram of the NW p-n junction devices under (a) forward and (b) reverse regimes.

Figure 3 .

 3 Figure 3.29 Normalized EBIC signals from p-n junction in NW #1 (a) and #2 (b) under different negative voltages. Corresponding SEM images are placed on top of the plots. The black dashed line in (a) delineates the edge of ITO contact on n-GaN, whereas the red dashed line in (b) locates the position of the "dust" seen on the p-side of NW #2.

Figure 3 . 30

 330 Figure 3.30 The volume density of the excess carriers ∆n, p as a function of the beam current i B with different e-beam energy, taken from [113]. The red arrows indicate the e-beam conditions in this thesis.

Figure 3 .

 3 Figure 3.31 CASINO simulations of the electron beam-sample interaction [113]. (a) Top view and (b) side view absorbed energy distribution in GaN struck by an e-beam with 4 keV energy. The values in the legend represent the percentage of the energy outside of the corresponding lines. The cumulated absorbed energy is plotted as a function of depth (c), lateral position (d) for e-beam with different energies. Depth (nm) Cumulated energy (%)

Figure 3 .

 3 Figure 3.32 The configuration of the EBIC measurement model from Bonard and Ganiere [201].

  where and describe the lateral e-beam extension and its penetration depth, respectively. The values of and depend on the sample as well as the e-beam parameters. Parish et al. has proposed a method to determine the values of and with the help of Monte Carlo simulation[START_REF] Parish | On the use of Monte Carlo modeling in the mathematical analysis of scanning electron microscopy-electron beam induced current data[END_REF]. If we separate the x, z variables, equation (3.10) writes:

Figure 3 .

 3 Figure 3.33 Linearization process on (a) x-axis, (b) z-axis to determine the values of σ x and σ z under e-beam energy of 4 keV, taken from [113].

Figure 3 .

 3 Figure 3.34 has displayed the modeling of EBIC signals under 0 V. For NW #1 (a), the modeling curve fits well the experiment data in the vicinity of the p-n junction, while a discrepancy is observed at the right foot of EBIC signal near the n-contact. The presence of the ITO contact has an influence on the carrier collection, and this feather is not taking into account in the model. This modeling gives a depletion region width W of 116 nm, carrier diffusion length in p-GaN L e,p of 122 nm and carrier diffusion length in n-GaN L h,n of 77 nm. From equation (3.5), we have the effective doping level N eff1 =

Figure 3 .

 3 Figure 3.34 The modeling of the EBIC signal from the p-n junction under 0 V for NW #1 (a) and #2 (b). (a) The modeling parameters for NW #1 are: W = 116 nm, L e,p = 122 nm, L h,n = 77 nm, the black dashed line delineates the edge of the ITO contact on n-GaN. (b) The modeling parameters for NW #2 are: W = 125 nm, L e,p = 170 nm, L h,n = 40 nm, and the red dashed line locates the position of the "dust" on the p-GaN in NW #2. The x-axes are shifted according to the modeling so that the junction is at 0 nm.

2 Parameters

 2 The influence of external voltages The same modeling procedures has been performed on the EBIC negative bias dependence signals for NW #1 in Figure3.35. The same as in Figure3.34, the discrepancy between the modeling and the experimental data at the right foot of EBIC signals is a result of the n-contact. Concerning NW #2, the EBIC negative bias dependence signals are completely overlapped in the vicinity of the p-n junction. Therefore, the three parameters W, L e,p , L h,n are considered the same at different negative biases. Table3.8 lists the modeling parameters for each EBIC signal of NW #1 and #2 at different biases. The error bars represent the range of the parameter values where the modeling curve and the experimental data seems overlapped by naked eyes. As discussed before, both minority and majority carriers diffusion contribute to the EBIC current in the p-GaN part since the low injection condition is not satisfied. The value of L e,p is listed here only for further reference. In terms of L h,n in the n-GaN part, the extracted values from the modeling do not seem to vary much with changing voltages, keeping at 75 nm for NW #1 and 40 nm for NW #2 in average.According to equation (3.5), a linear characteristic is expected between the square of the depletion width (W 2 ) and the applied voltage (V pn ). Thus, W 2 is plotted as a function of the applied voltage V in Figure3.36. Contrary to the dashed theoretical lines, the W

  p-n junction equals to the bias voltage minus the voltage at the boundary of the pregion. In this case, no or limited depletion width extension of the p-n junction is observed under increasing negative biases. Since the acceptor doping level is lower in NW #2 (more resistive), the W 2 does not change for NW #2, while it increases only a little with the rising negative voltage for NW #1.

Figure 3 .

 3 Figure 3.35 The modeling of the EBIC signals from the p-n junction under different negative voltages for NW #1. The EBIC signals under different negative voltages are shifted vertically for clarity, the values of the y-axis have no physical meaning. The black dashed line delineates the edge of the ITO contact on n-GaN. The modeling parameters are listed in Table 3.8.

  1.1.1 Structural properties ..................................................................................................... 1.1.2 Electronic properties ..................................................................................................... 1.2 EPITAXIAL LAYERS AND NANOWIRES (NWS) ............................................................ 8

1.2.1 2D layer growthsubstrate issues .............................................................................. 1.2.2 NWs ............................................................................................................................... 1.3 GROWTH METHODS .................................................................................................. 9 1.3.1 Molecular beam epitaxy ................................................................................................ 1.3.2 The traits of MBE ........................................................................................................

Table 1 .

 1 3 Crucial properties of three most common substrates (sapphire, SiC, Si) for GaN heteroepitaxy growth[START_REF] Liu | Substrates for gallium nitride epitaxy[END_REF]

		Sapphire Al2O3 (0001)	6H-SiC (0001)	Si (111)
	Lateral lattice (a) mismatch (%)	-14%	-3.5%	-17%
	TEC mismatch (1/K)	+1.7×10 -6	-1.1×10 -6	-2×10 -6
	Thermal conductivity (W/cm K)	0.3	4	1.56
	Electrical conductivity	Insulating	From semi-insulating to metallic	From semi-insulating to metallic
	Available size	Up to 6 inch	Up to 6 inch	Up to 8 inch
	Cost / 2 inch wafer	50 €	120-200 €	10 €

Table 2

 2

	.1 The lists of samples studied with different Si cell temperatures

Applications Name Speed (turns/nm) Time (s) Baking conditions Thickness (nm)

	2.4.2 Electrical transport theoretical background
	Monolayer resist	AR-P679.04 (PMMA 4%)	4000	30	180°C, 5min	310
	Bi-layer resist	AR-P619.06 (PMMA/MMA 33%, 6%)	5000	30	200°C, 5min	300
		AR-P679.04 (PMMA 4%)	5000	30	180°C, 5min	200

Table 3 .

 3 1 shows the electrical characteristics for the current state of art Mg-doped GaN epilayers grown by different techniques. One of the best Mg doped GaN epilayers grown by PA-MBE presents a Mg incorporation up to 7.5×10 19 cm -3 , a hole concentration of 1.4×10

  18

Table 3 .

 3

1 Electrical characteristics of the state-of-the-art Mg-doped GaN epilayers grown by different techniques p-type GaN with high hole concentration remains desirable for lower series resistance and ohmic contacts, however, it is challenging due to the complexity of doping GaN

Growth techniques MOVPE NH 3 -MBE PA-MBE Metal modulated epitaxy Phase shift epitaxy

	Substrate temperature (°C)	1030	740	650	500	600
	Mg content (cm -3 )	Not mentioned	3×10 19	7.5×10 19	Not mentioned	1.45×10 20
	Hole concentration (cm -3 )	3×10 18	1×10 18	1.4×10 18	4.5 x 10 18	1×10 18
	Mobility (cm 2 .V -1 .s -1 )	9	9	7.5	1.1	7.8
	Resistivity (Ω.cm)	0.2	0.75	0.6	1.3	0.8

Table 3 .

 3 [START_REF] Nakamura | Thermal annealing effects on p-type Mg-doped GaN films[END_REF] The list of samples studied with different Mg cell temperatures

	Sample Name	N2437	N2442	N2439 N2441 N2446	N2443 N2444
	Mg cell temperature (°C)	95	190	210	230	240	250	270
	Average NW radius (nm)	26.7	28.9	27.6	26.1	31.6	50.6	66.9
	Average NW length (nm)	419	482	521	315	409	239	394

Figure 3.5 shows the top and side view SEM images taken from as-grown samples at the center of the wafer. The NID GaN NWs (sample N2437) have a typical length of 400-550 nm and a radius of 20-30 nm. The NWs are less straight and there is a spread in

Table 3 .

 3

3 Growth conditions of three GaN p-n junction samples

Table 3 .

 3 4 Characteristics of ohmic contacts with different metal schemes on p-type GaN epilayer

	Contact metals and thickness (nm)	p (cm -3 )	Surface treatment	Annealing condition	ρ c (Ω.cm 2 )	Reference
	Ni/Au (5/5)	2×10 17	HCl solution for 1 min	500°C 1 min in air	4×10 -6	[183]
			First preoxidation at
	Ni/Au (20/100)	3.4×10 17	750°C for 30 min in air, then treated with (NH 4 ) 2 S x solution at	500°C 10 min in air	4.5×10 -6	[177]
			60 °C for 30 min
	Pd/Ni (3/7)	3.3×10 17	Dip into boiling aqua regia solution (HCl: HNO 3 = 3:1)	500°C 1 min in air	5.7×10 -5	[178]
	Pd/Ni/Au (10/20/30)	2×10 17	Dip in buffered hydrofluoric acid	500°C 1 min in N 2	2.4×10 -5	[179]
			First boiled BOE for
	Pt (25)	1.8×10 17	10 min and (NH 4 ) 2 S x solution for 10 min,	No	2×10 -5	[180]
			then BOE for 30 s.
	In 0.19 Ga 0.81 N/Pd/Au (2/20/130)	4×10 17	Dip in HCl solution	No	1.1×10 -6	[182]

Table 3 .

 3 6 Summary of NW dimensions in the two devices

Table 3 .

 3 [START_REF] Sanchez-Garcia | The effect of the III/V ratio and substrate temperature on the morphology and properties of GaN-and AlN-layers grown by molecular beam epitaxy on Si(1 1 1)[END_REF] The doping levels and carrier diffusion lengths in NW #1&#2, microwires and bulk GaN extracted from EBIC measurements.

† http://topganlasers.com/nitride-epi-wafers/ http://global-sei.com/sc/products_e/gan/index.html

† † The positive resist means that after development, the exposed structure is deeper than the surrounding due to chopping of polymer chains.

La caractérisation électrique a