Dr Gaelle Kociniewski

Dr Amador Pérez-Tomás

Prof Tamar

Dr Yunlin Zheng

Prof Georges Bremond

Prof Jean-Marie Bluet

Prof Gérard Guillot

Sumit, Nour, Hamid, Mohamed Ismail Clarisse

Keywords: Semiconductor, Oxide, Ultra-wide band gap, Electronic properties, β-Ga2O3, ZnGa2O4

Improving energy efficiency and reducing power consumption is important for accelerating climate saving. To this end, efficient power electronics devices based on new generations of wide and ultra-wide band gap (UWBG) semiconductors are an ultimate solution. Last several years, Gallia (β-Ga2O3) and Zinc gallate (ZnGa2O4) have attracted much attention due to their UWBG (Eg > 4.5 eV) and realizable high n-type electrical conductivity. Though, to fully realize the functionality of these two materials, power devices based on bipolar structure (p-n, or p-i-n) are required. However, p-type doping is a challenge for both materials: β-Ga2O3 and ZnGa2O4.

The objective of this PhD work is to investigate the electronic properties of β-Ga2O3 and ZnGa2O4 materials to disclose their potential for applications in power electronics.

Enfin, une étude préliminaire des contacts métalliques électriques au p-Ga2O3 est discutée, cette problématique est abordée en regardant la perspective d'utilisation du p-Ga2O3 dans les structures de dispositifs de puissance. Pt et Ti/Pt/Au ont été identifiés comme formant : des contacts Schottky et quasi-ohmiques avec p-Ga2O3, respectivement. La méthodologie CTLM pour évaluer la résistance de contact spécifique correspondante a été développée avec des masques photo-lithographiques.

VII

Acknowledgement

At this point, I would like to express my deepest gratitude and appreciation to all those who have supported and guided me throughout my PhD journey.

The first part of the thesis describes the realization of native defect related hole conductivity in undoped β-Ga2O3. According to thermodynamic analysis, the realization of hole conductivity in β-Ga2O3 is possible thanks to the comparatively high enthalpy of compensating donor creation. Indeed, p-type conductivity (p = 2×10 14 cm -3 and mobility μ = 9 cm 2 /(V•s) at 800 K) in MOCVD grown β-Ga2O3 thin film has been experimentally demonstrated. The origin of the conductivity is attributed to native defect gallium vacancies (VGa) with an ionization energy Ei = 1.2 eV. To further increase the hole conductivity, Zn doping was studied. Based on thermodynamic analysis, Zn can take substitutional or interstitial site, and act as an acceptor or a donor dopant in β-Ga2O3. Then, I studied Zn-doped β-Ga2O3//Al2O3 thin films with incorporated Zn concertation in 10 16 -10 19 cm -3 range. Compared to undoped film, ptype conductivity was enhanced when [Zn] = 10 16 cm -3 . The origin is ZnGa defect, its ionization energy was estimated to be Ei = 0.77 eV by Hall effect measurement. With increasing Zn doping level (> 10 18 cm -3 ), the "autocompensation" effect takes place, i.e., acceptor ZnGa and donor Zni defects start to compensate each other, resulting in the decrease of hole concertation by more than one order of magnitude. Though, the "autocompensation" effect has been used as a positive phenomenon for increasing the critical electrical field (ECR) of β-Ga2O3, which was experimentally estimated to be ECR = 13.2 MV/cm.

With the further increasing (> 6.85%) incorporated Zn concentration in β-Ga2O3, cubic spinel ZnGa2O4 starts to form during MOCVD growth. I have studied the electronic properties of ZnGa2O4//Al2O3 thin films. Comparative analysis of structural, chemical, optical, and electrical transport measurements demonstrated that both semi-insulating p-type (by ZnGa) and conducting n-ZnGa2O4 thin films were achieved by tuning the growth conditions, with the native defect conductivity controlled up to 10 orders of magnitude thanks to "selfdoping" effect. It is suggested that the native high electron concentration was achieved due to the hybridization of the Zn-O orbitals resulting in a "selfimpurity" band where the Zni hopping occurs. The important influence of oxygen on electrical properties can be clearly seen and shown. The critical electric field ECR > 5.3 MV/cm was estimated for the first time.

Finally, a preliminary study of electrical metal contacts to p-Ga2O3 is discussed, by looking at the perspective of the use of p-Ga2O3 in power device structures. Pt and Ti/Pt/Au was identified to form Schottky and quasi-Ohmic contacts in the measurement temperature range to p-Ga2O3, respectively. CTLM methodology to evaluate the corresponding specific contact resistance was developed with photolithographic masks. La première partie de la thèse étudie la conductivité de type p liée aux défauts intrinsèques dans β-Ga2O3 non dopé. Selon l'analyse thermodynamique, β-Ga2O3 du type p est réalisable grâce à une enthalpie relativement élevée de création de donneur. En effet, le type p (p = 2×10 14 cm - 3 et mobilité μ = 9 cm 2 /(V•s) à 800 K) dans la couche mince de β-Ga2O3 élaborée par MOCVD a été démontrée expérimentalement. L'origine de la conductivité est attribuée à la lacune de gallium (VGa) avec une énergie d'ionisation Ei = 1,2 eV. Pour augmenter la conductivité du type p, un dopage du Zn a été étudié. Par une analyse thermodynamique, Zn peut prendre un site de substitution ou interstitiel et agir comme un accepteur ou un donneur dans le β-Ga2O3. Ensuite, j'ai étudié des films minces de β-Ga2O3//Al2O3 dopés au Zn avec une concentration de Zn incorporée dans la gamme 10 16 -10 19 cm -3 . Par rapport au film non dopé, la conductivité de type p augmente avec [Zn] = 10 16 cm -3 . L'origine est le défaut ZnGa, son énergie d'ionisation a été estimée à Ei = 0,77 eV par mesure d'effet Hall. Avec l'augmentation du niveau de dopage en Zn (> 10 18 cm -3 ), l'effet "auto-compensation" se produit, les défauts accepteur ZnGa et donneur Zni commencent à se compenser, provoquant la diminution de la concentration en trous de plus d'un ordre de grandeur. Cependant, cet effet a été utilisé comme un phénomène positif qui a permis d'augmenter le champ électrique critique (ECR) de β-Ga2O3, avec une valeur expérimentale estimée à ECR = 13,2 MV/cm. Avec l'augmentation de la concentration de Zn incorporé (> 6,85%) dans le β-Ga2O3, la spinelle cubique ZnGa2O4 commence à cristalliser durant la croissance du MOCVD. J'ai étudié les propriétés électroniques de films minces de ZnGa2O4//Al2O3. L'analyse comparative des mesures structurales, chimiques, optiques et de transport électrique a démontré que les couches minces semi-isolantes de type p (par ZnGa) et conductrices n-ZnGa2O4 ont été réalisées en ajustant les conditions de croissance, la conductivité du défaut intrinsèque étant contrôlée jusqu'à 10 ordres de grandeur grâce à l'effet "auto-dopage". Il est suggéré que la concentration élevée d'électrons intrinsèque a été obtenue par l'hybridation des orbitales Zn-O résultant en une bande « d'auto-impuretés », où le saut entre zincs interstitiels (Zni) se produit. L'influence importante de l'oxygène sur les propriétés électriques est démontrée. Un champ électrique critique ECR > 5,3 MV/cm a été estimé expérimentalement, pour la première fois.

Enfin, une étude préliminaire des contacts métalliques électriques au p-Ga2O3 est discutée, cette problématique est abordée en regardant la perspective d'utilisation du p-Ga2O3 dans les structures de dispositifs de puissance. Pt et Ti/Pt/Au ont été identifiés comme formant des contacts Schottky et quasi-ohmiques avec p-Ga2O3, respectivement. La méthodologie CTLM pour évaluer la résistance de contact spécifique correspondante a été développée avec des masques photo-lithographiques.

Résumé substantiel :

Ce travail de recherche en science des matériaux se situe dans le contexte de réduction de l'utilisation des énergies fossiles et de la lutte contre le dérèglement climatique. En effet, de près d'un siècle, la production d'énergie a été principalement basée sur la consommation de ressources fossiles, qui d'une part ne sont pas inépuisables, et d'autre part produisent une pollution énorme. Ce sont l'amélioration de l'efficacité de conversion énergétique et la réduction de la consommation d'énergie au global, qui apporteront des accélérations dans la préservation du climat. Pour cela, des dispositifs d'électronique de puissance basés sur des semi-conducteurs à ultra-large bande interdite (UWBG) de nouvelle génération sont une solution ultime. Ces dernières années, β-Ga2O3 et ses dérivés, dont le ZnGa2O4, ont attiré beaucoup d'attention grâce à leur bande interdite ultra-large (Eg > 4,5 eV) et de la capacité à les doper très fortement et de manière contrôlée de type n, comme de nombreux semiconducteurs oxydes. Cependant, pour réaliser pleinement les fonctionnalités des deux matériaux β-Ga2O3 et ZnGa2O4, des dispositifs de puissance basés sur une structure bipolaire de type jonction p-n ou p-i-n sont nécessaires. Néanmoins, le dopage de type p est un défi matériau et propriétés pour ces deux oxydes UWBG. L'objectif de ce travail de doctorat est d'étudier expérimentalement les propriétés électroniques des matériaux β-Ga2O3 et ZnGa2O4 en films minces pour qualifier leur potentiel pour des applications en électronique de puissance.

La première partie de la thèse étudie la conductivité de type p liée aux défauts intrinsèques dans β-Ga2O3 non dopé. Selon l'analyse thermodynamique pour les défauts ponctuels, β-Ga2O3 du type p est réalisable grâce à une enthalpie relativement élevée de création des donneurs. En effet, le type p (p = 2×10 14 cm -3 et mobilité μ = 9 cm 2 V -1 s -1 à 800 K) dans la couche mince de β-Ga2O3 élaborée par la technique de dépôt chimique par précurseurs métal-organique (MOCVD), fonctionnant à l'équilibre, a été démontrée expérimentalement. L'origine de la conductivité est attribuée à la lacune de gallium (VGa) avec une énergie d'ionisation Ei ~ 1,2 eV d'après la littérature. La couche présente une bande interdite très large à 4.7 eV, comme espérée. Ces réalisations ouvrent la voie à une nouvelle amélioration de la conductivité des trous par dopage accepteur. L'influence de la température de croissance est brièvement présentée : l'augmentation de la température de croissance de 775 à 825 °C, diminue la concentration du donneur intrinsèque compensatoire, et donc augmente la concentration de l'accepteur intrinsèque majoritaire.

V Afin d'augmenter la conductivité du type p, l'élément Zn du groupe II a été choisi, et l'effet du dopage de Zn a été étudié. Par une analyse thermodynamique pour les défauts ponctuels, Zn pourrait prendre un site de substitution ou interstitiel et agir comme un accepteur (ZnGa) ou/et un donneur (Zni) dans le β-Ga2O3, suivant les conditions de croissance (température, pression dans la chambre de croissance, et surtout concentration en dopant Zn extrinsèque). Ensuite, j'ai étudié des films minces de β-Ga2O3 déposés sur substrats Al2O3(0001), dopés au Zn avec une concentration de Zn incorporée dans la gamme 10 16 -10 19 cm -3 . La symétrie cristalline de phase β est conservée avec le dopage, selon l'analyse de diffraction par rayons X. Par rapport au film non dopé, la conductivité de type p augmente (p = 1 × 10 15 cm -3 à 800 K) avec [Zn] = 10 16 cm -3 . L'origine est identifiée comme le défaut ZnGa, dont l'énergie d'ionisation a été estimée à Ei = 0,77 eV par mesure d'effet Hall. Avec l'augmentation du niveau de dopage en Zn (> 10 18 cm -3 ), « l'auto-compensation » se produit, les défauts accepteur zinc en site de gallium ZnGa et donneur zinc interstitiel Zni commencent à se compenser, provoquant la diminution de la concentration en trous mobiles de plus d'un ordre de grandeur. Cependant, cet effet a été exploité positivement pour augmenter le champ électrique critique (ECR) de β-Ga2O3, avec une valeur expérimentale évaluée à ECR = 13,2 MV/cm. Avec l'augmentation de la concentration de Zn incorporé (> 6,85%) dans le β-Ga2O3, la spinelle cubique ZnGa2O4 commence à cristalliser durant la croissance par MOCVD.

Lorsque l'incorporation du Zn dépasse 13%, la couche devient pure spinelle ZnGa2O4, selon la diffraction des rayons X et des électrons. Ensuite, j'ai étudié les propriétés électroniques de films minces de ZnGa2O4 sur substrats Al2O3 : l'analyse comparative des mesures structurales, chimiques, optiques et de transport électrique a démontré que les couches minces semi-isolantes de type p (via la substitution ZnGa) et conductrices n-ZnGa2O4 ont été réalisées en ajustant les conditions de croissance, la conductivité associée au défaut intrinsèque étant contrôlée jusqu'à 10 ordres de grandeur grâce à l'effet d'« auto-dopage ». Il est suggéré que la concentration intrinsèque élevée d'électrons mobiles a été obtenue par l'hybridation des orbitales Zn-O formant une bande « d'auto-impuretés ». Le mécanisme de conduction est alors de type « sauts » entre zincs interstitiels (Zni). L'influence importante de l'oxygène sur les propriétés électriques est démontrée. Un champ électrique critique ECR > 5,3 MV/cm a été estimé expérimentalement, pour la première fois pour la spinelle ZnGa2O4.

Introduction

At the global level, energy production has mainly been based on the consumption of fossil resources, this not only consumes excess fossil energy, which is limited but also leads to pollution. The Paris Conference (COP 21) led to a new international climate agreement, applicable to all countries, aimed at keeping global warming to 1.5 -2 °C, in accordance with the recommendations of the Intergovernmental Panel of Experts on climate change (IPCC) (Ministère de l'Europe et des Affaires, 2015). The COP 26 summit held in Glasgow brought parties together to accelerate action towards the goals of the Paris Agreement and the UN Framework Convention on Climate Change (COP26 Webpage, 2021). Two separate developments are needed to secure stable energy supplies soon: widespread adoption of revolutionary sustainable generation technologies and efficient energy use. The one very concrete way to reach the target of energy efficiency is to turn to more efficient power electronics, which is the application of solid-state electronics to the control and conversion of electric power, it plays a crucial role in achieving the goal of reduced power consumption.

Power semiconductor electronics is the application of electronics to the control and conversion of electric power. Power electronics based on silicon has already been widely used in industrial, commercial, and transportation systems [START_REF] Bose | Power Electronics in Smart Grid and Renewable Energy Systems[END_REF]. However, it has low operating temperature and low breakdown voltage, which makes its applications limited.

Consequently, a clear transition to more electric energy and efficient systems is still mandatory [START_REF] Steimer | Enabled by high power electronics -Energy efficiency, renewables and smart grids[END_REF]. Indeed, for the time being, different semiconductor materials such as 4H-SiC, GaN,diamond,AlN,etc. are competing to be the next choice for highly efficient power electronics. Among wide and ultra-wide band gap (UWBG) semiconductors, monoclinic β-Ga2O3 has attracted much attention for power electronics applications recently.

β-Ga2O3 has an ultra-wide band gap of up to 5 eV, high critical electrical field compared to wide band gap semiconductors SiC and GaN (Figure 1-1), and the successful growth and availability of 6-inch wafers from bulk single crystals on the market (Novel Crystal Technology, Japan). The targeted power electronic devices are high voltage rectifiers, aiming to reduce energy consumption, achieve compact designs, and expand the voltage and temperature range of applications (Figure 12), For the time being, high electron concentration (up to 10 20 cm -3 ) in β-Ga2O3 can be achieved usually by Sn, Si, and Ge dopants.

Currently, β-Ga2O3 based power electronic devices made are all unipolar (i.e., fabricated with n-type β-Ga2O3): field effect transistors (Higashiwaki et al., 2016a;[START_REF] Lv | Lateral β-Ga2O3 MOSFETs With High Power Figure of Merit of 277 MW/cm2[END_REF], Schottky barrier diode [START_REF] Hu | Beveled Fluoride Plasma Treatment for Vertical β -Ga2O3 Schottky Barrier Diode With High Reverse Blocking Voltage and Low Turn-On Voltage[END_REF][START_REF] Wang | Parametric Electrochemical Deposition of Controllable Morphology of Copper Micro-Columns[END_REF], p-NiO/n-Ga2O3 diode [START_REF] Gong | Field-Plated NiO/Ga2O3 p-n Heterojunction Power Diodes With High-Temperature Thermal Stability and Near Unity Ideality Factors[END_REF][START_REF] Zhang | Ultra-wide bandgap semiconductor Ga2O3 power diodes[END_REF], etc have been demonstrated recently. The breakdown voltage can reach 8.32 kV for a p-NiO/n-Ga2O3 diode [START_REF] Zhang | Ultra-wide bandgap semiconductor Ga2O3 power diodes[END_REF].

However, the vertical bipolar (i.e. p-n or p-i-n structure) power electronic devices are required to sustain ultra-high (> 10 kV) reverse voltage. The p-type conductivity of UWBG oxides is well-known to be very challenging, due to large hole effective mass, and thus low hole mobility, and the compensation by donor defects such as oxygen vacancies VO [START_REF] Zhang | Recent progress on the electronic structure, defect, and doping properties of Ga2O3[END_REF]. The first reported hole concentration of undoped p-type β-Ga2O3 at room temperature is as low as 2×10 13 cm -3 (Chikoidze et al., 2017a), which is far to be enough for the requirement of device operation.

Figure 1-1. Comparison of semiconductor material parameters [START_REF] Speck | Ultrawide Bandgap β-Ga2O3 Semiconductor: Theory and Applications[END_REF].

Similar to β-Ga2O3, cubic spinel oxide zinc gallate (ZnGa2O4) also has an ultra-wide band gap of up to 5 eV. The existing reports related to ZnGa2O4 are mainly focused on its application in photonic and opto-electronic devices. Consequently, the optical properties are largely studied, while the research on the electrical properties is very limited, though ZnGa2O4 based metal oxide semiconductor field effect transistor (MOSFET) (L.-C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF][START_REF] Shen | Characterizations of Metal-Oxide-Semiconductor Field-Effect Transistors of ZnGaO Grown on Sapphire Substrate[END_REF], thin film transistor (TFT) [START_REF] Cheng | Effect of Defects on the Properties of ZnGa2</sub>O4 Thin-Film Transistors[END_REF][START_REF] Jang | Thin film transistors based on ultra-wide bandgap spinel ZnGa2O4[END_REF], deep ultra-violet phototransistors (Y.-C. Shen et al., 2019) have already been demonstrated. However, further deep studies of ZnGa2O4 electrical conductivity and point defects is still clearly required. Ga2O3. Ga2O3 has potential application in both medium and high-voltage range.

Overall, it is clear that the study and the understanding of the electronic properties of ZnGa2O4 and β-Ga2O3 are of great importance for the application of these materials in various electronic devices.

The objective of my work is to study the electronic properties of the metal organic chemical vapor deposition (MOCVD) grown p-type β-Ga2O3 and both n-type and p-type ZnGa2O4 thin films. The manuscript is arranged as follows:

Chapter 1 (State of the Art) provides an overview of the fundamental properties, recent theoretical and experimental reports on the point defects, and electronic properties for β-Ga2O3 and ZnGa2O4.

Chapter 2 (Experimental Techniques and Methods) describes the experimental methods, techniques, and facilities used to carry out presented works, including thin films growth technique, characterization methods and set-ups. Detailed descriptions are given for the electrical transport properties measurements (both set-ups and methods).

In Chapter 3 (β-Ga2O3: Experimental Results and Discussion), the electronic properties of MOCVD grown β-Ga2O3 layers are discussed. The first objective is, to get an undoped highly compensated semi-insulating p-type β-Ga2O3 layer, suitable for further p-type doping trials. As a II group element, Zn is expected to substitute Ga and become an effective dopant in β-Ga2O3. Thus, Zn was selected as a dopant, in order to improve the hole conductivity in β-Ga2O3. My objective was to study the influence of Zn dopant on electrical and optical properties in β-Ga2O3. The investigation of Zn-doped β-Ga2O3 is started with the thermodynamic study of point defects in the β-Ga2O3:Zn system. Then, the experimental results of β-Ga2O3:Zn thin films grown by MOCVD, with different Zn doping levels (10 16 -2×10 19 cm -3 ), are presented. According to both of the experimental facts and thermodynamic calculations, we observed the amphoteric nature of Zn in β-Ga2O3, Zn can take both interstitial and gallium sites, being donor Zni and acceptor ZnGa centres depending on the doping concentration, which is the so-called impurity "auto-compensation" effect. Taking advantage of this effect, by further lowering the hole concentration, we aimed to further increase the critical electric field of β-Ga2O3. Therefore, the critical electric field of undoped and Zn (2×10 19 cm -3 ) doped β-Ga2O3 thin films is experimentally estimated.

In Chapter 4 (ZnGa2O4: Experimental Results and Discussion), the experimental results

for the MOCVD-grown ZnGa2O4 layers are presented. With the further incorporated Zn concentration in β-Ga2O3, the ternary semiconductor ZnGa2O4 started to form on the sapphire substrates. I first showed the transformation from pure monoclinic β-Ga2O3 to pure cubic spinel ZnGa2O4. As a ternary compound, ZnGa2O4 has a higher flexibility of doping than binary semiconductors. A bunch of theoretical works reported the "self-doping" effect [START_REF] De Vos | First-Principles Study of Antisite Defect Configurations in ZnGa 2 O 4 :Cr Persistent Phosphors[END_REF]Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF][START_REF] Stoica | P-type zinc oxide spinels: application to transparent conductors and spintronics[END_REF] in ZnGa2O4, which generally refers to the creation of cross-substitution of the cations on the tetrahedral and octahedral sites, leading to variations in the electrical, optical properties and offering opportunities for tailoring the electronic behavior of spinel oxide compounds. Besides, though the room-temperature conducting (~10 2 S/cm) intrinsic n-type ZnGa2O4 thin films with electron concentration n > 2×10 19 cm -3 have already been achieved (L.-C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF][START_REF] Cheng | Effect of Defects on the Properties of ZnGa2</sub>O4 Thin-Film Transistors[END_REF][START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF], while the origin of conductivity and the conduction mechanism are still open questions. Therefore, I aimed to address these open questions by conducting a comprehensive investigation of the electronic properties and carrier transport mechanisms. Additionally, further experimental evidence of the "selfdoping" effect of ZnGa2O4 is shown by a comparative study of the structural, optical, and electronic properties between intrinsic semi-insulating p-type and conducting n-type ZnGa2O4 layers. Since the study on the electrical properties of ZnGa2O4 is still very limited, we aimed to gain a deeper understanding of the growth parameters influencing the conductivity in the ZnGa2O4 films. Thus, the influence of the oxygen content in MOCVDgrown ZnGa2O4 layers is investigated. At the end of this chapter, the first experimental investigation of the critical electric field of ZnGa2O4 is reported.

Chapter 5 (Electrical Contacts to p-type β-Ga2O3) presents my preliminary study of electrical metal contacts to p-type β-Ga2O3, in perspective of higher current conditions for future power-electronic applications under high voltages. The objective was to first establish a protocol for electrical contact preparation by photolithography, and identify the electrical contact types among the metals selected (Ag, Pt, Ti/Pt/Au) and p-type β-Ga2O3. The related experimental methods, including the photolithography process, metal deposition, and I-V characterization methods, are presented in this chapter.

Chapter 6 (Conclusion and Perspectives) summarizes the results in this manuscript and discusses future works.

β-Ga 2 O 3 and ZnGa 2 O 4 -Overview of Properties

β-Ga2O3

Gallium oxide (Ga2O3) has, at least, six crystalized polymorphs of which only the monoclinic β phase is thermodynamically stable at high temperatures, while the others are metastable and tend to convert to β upon high-temperature treatments including the phases: corundum α, cubic δ, hexagonal ε, defective-spinel γ, and orthorhombic κ polymorph [START_REF] Spaziani | Silicon, GaN and SiC: There's room for all: An application space overview of device considerations[END_REF]. Early crystallographic studies for single crystals [START_REF] Geller | Crystal Structure of β-Ga2O3[END_REF] together with diverse luminescence studies of doped β-Ga2O3 were reported as early as the 1960s [START_REF] Blasse | Some observations on the luminescence of β-Ga2O3[END_REF]. [START_REF] Lorenz | Some electrical properties of the semiconductor β Ga2O3[END_REF] reported in 1966 that ntype Ga2O3 exhibits mobilities in the range of 100 cm 2 /(V•s) and an adequate device doping of 10 18 cm -3 can be achieved just by controlling the native oxygen vacancies' density. Its deep-ultraviolet intrinsic bandgap of around 4.5 -5 eV and excellent photoconductivity are also well-known from early contemporary studies [START_REF] Tippins | Optical Absorption and Photoconductivity in the Band Edge of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF]

Fundamental properties of β-Ga2O3

Structure: The monoclinic structure of β-Ga2O3 belongs to the space group C2/m as shown in properties (e.g., anisotropic effective mass, impact ionization parameters (Ghosh and Singisetti, 2018a, 2018b[START_REF] Bose | Power Electronics in Smart Grid and Renewable Energy Systems[END_REF], optical absorption [START_REF] Ricci | Theoretical and experimental investigation of optical absorption anisotropy in β-Ga2O3[END_REF]), and possible device development opportunities (e.g., different electrical contact performance depending on the β-Ga2O3 single crystal orientation (Lee et al., 2022a)).

Figure 1-1. Unit cell of β-Ga2O3 [START_REF] Mastro | Assessment of the (010) β-Ga2O3 surface and substrate specification[END_REF].

Band structure: The electronic structure of β-Ga2O3 has been studied using the density functional theory (DFT) and photoemission spectroscopy measurements, the general consensus is that, β-Ga2O3 has a direct band gap of ~4.88 eV for the vertical Г-Г transition, although there is a much weaker Г-M transition leads to an indirect band gap of with only a few tens of meV less [START_REF] He | First-principles study of the structural, electronic, and optical properties of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ in its monoclinic and hexagonal phases[END_REF][START_REF] Janowitz | Experimental electronic structure of In2O3 and Ga2O3[END_REF][START_REF] Mock | Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3[END_REF][START_REF] Peelaers | Brillouin zone and band structure of β-Ga2O3[END_REF][START_REF] Varley | Oxygen vacancies and donor impurities in β-Ga2O3[END_REF].

Thermal conductivity: β-Ga2O3 has a poor thermal conductivity of ~10 -27 W/(m•K) at room temperature, which is also anisotropic and dependent on the direction of planes [START_REF] Galazka | On the bulk β-Ga2O3 single crystals grown by the Czochralski method[END_REF][START_REF] Guo | Anisotropic thermal conductivity in single crystal βgallium oxide[END_REF][START_REF] Jiang | Three-dimensional anisotropic thermal conductivity tensor of single crystalline β-Ga2O3[END_REF][START_REF] Santia | Lattice thermal conductivity in β-Ga2O3 from first principles[END_REF], though the highest value was found along the [010] direction up to 27 ± 2 W/(m•K). However, several solutions have been proposed to address the thermal dissipation difficulty for actual device applications. [START_REF] Oda | Schottky barrier diodes of corundum-structured gallium oxide showing on-resistance of 0.1 mΩ•cm2 grown by MIST EPITAXY®[END_REF] lifted off the α-Ga2O3 epilayer from the sapphire substrate to fabricate the Schottky barrier diode. Hetero-growth of β-Ga2O3 on GaN [START_REF] Cao | β-Ga2O3 epitaxial films deposited on epi-GaN/sapphire (0001) substrates by MOCVD[END_REF][START_REF] Lyu | Band alignment at β-Ga2O3/III-N (III = Al, Ga) interfaces through hybrid functional calculations[END_REF][START_REF] Muhammed | High optical and structural quality of GaN epilayers grown on (2¯01) β-Ga2O3[END_REF] or AlN [START_REF] Lyu | Band alignment at β-Ga2O3/III-N (III = Al, Ga) interfaces through hybrid functional calculations[END_REF][START_REF] Sun | Valence and conduction band offsets of β-Ga2O3/AlN heterojunction[END_REF] substrates was also studied, the in-plane mismatch between the (-201)

β-Ga2O3 and (0002) AlN was found to be as low as 2.4% [START_REF] Sun | Valence and conduction band offsets of β-Ga2O3/AlN heterojunction[END_REF]. Additionally, flip-chip technology was employed for the thermal management at the device level [START_REF] Chatterjee | Device-Level Thermal Management of Gallium Oxide Field-Effect Transistors[END_REF].

Other parameters:

The melting point of β-Ga2O3 is ∼1800 °C, which allows the meltgrowth at high temperatures [START_REF] Galazka | Czochralski growth and characterization of β-Ga2O3 single crystals[END_REF]. All the other polymorphs will transform into the beta phase within ∼750 -950 °C. Ghosh and Singisetti [START_REF] Ghosh | Ab initio velocity-field curves in monoclinic β-Ga2O3[END_REF] calculated the drift velocity of electrons of β-Ga2O3 and found that, an average peak velocity at an electric field of 200 kV/cm can reach ~2×10 7 cm/s. The critical electric field was first proposed to be as high as 8 MV/cm [START_REF] Higashiwaki | Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates[END_REF] by extrapolation.

Experimentally, a high critical field of 5.2 MV/cm was demonstrated [START_REF] Yan | High breakdown electric field in β-Ga2O3 /graphene vertical barristor heterostructure[END_REF], and up to 13.2 MV/cm for Zn doped p-type β-Ga2O3 (Chikoidze et al., 2020b). Experimental works demonstrated the electron mobility μn ~ 200 cm 2 /(V•s) of β-Ga2O3 [START_REF] Feng | Probing Charge Transport and Background Doping in Metal-Organic Chemical Vapor Deposition-Grown (010) β-Ga2O3[END_REF][START_REF] Rajapitamahuni | Plasmon-Phonon Coupling in Electrostatically Gated β-Ga2O3 Films with Mobility Exceeding 200 cm2 V-1 s-1[END_REF].

Bulk and thin films growth techniques

To explore the structural, electrical, and optical characteristics of β-Ga2O3 and develop devices, it is crucial to begin with high-quality bulk crystals and thin films. Commonly used growth techniques of bulk β-Ga2O3 crystal are: Verneuil method [START_REF] Chase | Growth of β-Ga2, O3 by the Verneuil Technique[END_REF][START_REF] Harwig | Electrical properties of β-Ga2O3 single crystals[END_REF][START_REF] Lorenz | Some electrical properties of the semiconductor β Ga2O3[END_REF], Czochralski (CZ) method [START_REF] Galazka | \upbeta$-Ga2O3 for wide-bandgap electronics and optoelectronics[END_REF][START_REF] Galazka | Bulk single crystals of β-Ga2O3 and Ga-based spinels as ultra-wide bandgap transparent semiconducting oxides[END_REF]Galazka et al., , 2020bGalazka et al., , 2020a[START_REF] Galazka | Scaling-Up of Bulk β-Ga2O3 Single Crystals by the Czochralski Method[END_REF][START_REF] Irmscher | Electrical properties of β-Ga2O3 single crystals grown by the Czochralski method[END_REF][START_REF] Saleh | Degenerate doping in β-Ga2O3 single crystals through Hf-doping[END_REF], floating-zone (FZ) method [START_REF] Cui | Tuning electrical conductivity of β-Ga2O3 single crystals by Ta doping[END_REF][START_REF] Hossain | Optimization of Gas Ambient for High Quality β-Ga2O3 Single Crystals Grown by the Optical Floating Zone Technique[END_REF][START_REF] Suzuki | Fabrication and characterization of transparent conductive Sn-doped β-Ga2O3 single crystal[END_REF][START_REF] Tomioka | Compensation effects between impurity cations in single crystals of a wide gap semiconductor $\upbeta$-Ga2O3 prepared by the floating zone method[END_REF]Víllora et al., 2004;[START_REF] Zhou | Controlling n-type conductivity of β-Ga2O3 by Nb doping[END_REF], edge-defined film fed (EFG) method (Higashiwaki et al., 2016b;[START_REF] Kuramata | Bulk Crystal Growth of Ga2O3[END_REF][START_REF] Kuramata | High-quality β-Ga2O3 single crystals grown by edge-defined film-fed growth[END_REF][START_REF] Yao | Identification of Burgers vectors of dislocations in monoclinic β-Ga2O3 via synchrotron x-ray topography[END_REF], Bridgman (horizontal or vertical, HB and VB) method (Hoshikawa et al., 2020b(Hoshikawa et al., , 2020a[START_REF] Hoshikawa | Growth of β-Ga2O3 single crystals using vertical Bridgman method in ambient air[END_REF]. Table 1-1 summarizes the basic features of melt growth methods reported so far. It is worth noting that the largest wafer size of 6-inch width was achieved by EFG growth [START_REF] Kuramata | High-quality β-Ga2O3 single crystals grown by edge-defined film-fed growth[END_REF]. For epitaxial thin film growth of β-Ga2O3, various methods have been used, such as Molecular Beam Epitaxy (MBE), metal organic chemical vapor deposition (MOCVD), mist-CVD, pulsed laser deposition (PLD), halide vapor phase epitaxy (HVPE), atomic layer deposition (ALD), and so on. Here, I will focus on recent progress of the properties of the MOCVD-grown layers, since our thin films are grown by this technique.

The MOCVD technique has demonstrated its ability to generate high-quality epitaxial films with a rapid growth rate and consistent, controllable doping. It is highly scalable, thereby suitable for large-scale production. β-Ga2O3 thin films grown by the MOCVD technique uses Ga-based organic material such as Trimethylgallium (TMGa) and Triethylgallium (TEGa) as metal precursors, and N2O or pure O2 gas as the source of oxygen.

TMGa is cheaper than TEGa and provides a higher growth rate of up to 10 µm/hour (Alema et al., 2017b), due to a shorter pyrolysis pathway of 2 steps vs. 3 steps for TEGa [START_REF] Baldini | Semiconducting Sn-doped β-Ga2O3 homoepitaxial layers grown by metal organic vapour-phase epitaxy[END_REF], and high vapor pressure that allows the large concentration introduced during the growth [START_REF] Seryogin | MOCVD growth of high purity Ga2O3 epitaxial films using trimethylgallium precursor[END_REF]. [START_REF] Seryogin | MOCVD growth of high purity Ga2O3 epitaxial films using trimethylgallium precursor[END_REF] demonstrated that the growth rate is almost linearly proportional to the TMGa flow during the MOCVD growth, which can be as high as 5.8 µm/hour, with 580 µmol/min TMGa. The highest growth rate to date is 4 µm/hour using TEGa [START_REF] Tadjer | Characterization of $\upbeta$-Ga2O3 homoepitaxial films and MOSFETs grown by MOCVD at high growth rates[END_REF]. However, TEGa allows a relatively less contamination of carbon and hydrogen than TMGa, while it is process dependent (e.g., high O2/TMGa ratio can reduce carbon contamination [START_REF] Seryogin | MOCVD growth of high purity Ga2O3 epitaxial films using trimethylgallium precursor[END_REF]). The use of N2O as the source of oxygen can lead to a high resistivity of the film, which is attributed to the incorporation of N (substituting O becoming acceptor impurity NO) compensating donors [START_REF] Tadjer | High resistivity halide vapor phase homoepitaxial β-Ga2O3 films co-doped by silicon and nitrogen[END_REF][START_REF] Wong | Acceptor doping of β-Ga2O3 by Mg and N ion implantations[END_REF]. Besides, high quality β-Ga2O3 epilayers can be achieved by this technique, [START_REF] Li | Single crystalline β-Ga2O3 homoepitaxial films grown by MOCVD[END_REF] reported a homoepitaxially grown film with FWMH and surface roughness of 21.6 arcsec, and 0.68 nm, respectively. The highest mobility achieved using MOCVD was 194 cm 2 /(V•s) [START_REF] Feng | Probing Charge Transport and Background Doping in Metal-Organic Chemical Vapor Deposition-Grown (010) β-Ga2O3[END_REF]. This technique is also available for both nand p-type dopability [START_REF] Alema | Low temperature electron mobility exceeding 104 cm2/V s in MOCVD grown β-Ga2O3[END_REF]Chikoidze et al., 2020c).

Point defects studies and doping issues

A number of experiments and calculations-based studies provide the electronic behaviors of intrinsic and extrinsic defects, and interactions between intrinsic and dopants in β-Ga2O3. Here, I will focus on the studies on the intrinsic defects, including oxygen interstitials (Oi), oxygen vacancies (VO), gallium vacancies (VGa), gallium interstitials (Gai), divacancy complex (VO -VGa), and interstitial -divacancy (2 VGa -Gai) complex.

Oxygen vacancies were considered as the source of the n-type conductivity in β-Ga2O3

according to the experimental observations that the electrical conductivity is inversely dependent on the oxygen partial pressure [START_REF] Aubay | Magnetic bistability and Overhauser shift of conduction electrons in gallium oxide[END_REF][START_REF] Hajnal | Role of oxygen vacancy defect states in the n-type conduction of β-Ga2O3[END_REF][START_REF] Ueda | Synthesis and control of conductivity of ultraviolet transmitting β-Ga2O3 single crystals[END_REF][START_REF] Yamaga | Donor structure and electric transport mechanism in β-Ga2O3[END_REF]. Based on the electron paramagnetic resonance (EPR) study, VO was proposed as a shallow donor [START_REF] Aubay | Magnetic bistability and Overhauser shift of conduction electrons in gallium oxide[END_REF][START_REF] Yamaga | Donor structure and electric transport mechanism in β-Ga2O3[END_REF].

However, DFT and ab initio calculations (Deák et al., 2017;Ingebrigtsen et al., 2019a;[START_REF] Usseinov | Calculations of Oxygen Vacancy in GaO Crystals[END_REF][START_REF] Usseinov | Pair vacancy defects in β-Ga2O3 crystal: Ab initio study[END_REF][START_REF] Varley | Oxygen vacancies and donor impurities in β-Ga2O3[END_REF] proposed that VO is too deep (transition energy is more than 1 eV) to be responsible for the n-type conductivity, its formation energy is also very high in oxygen-rich condition (Deák et al., 2017;Ingebrigtsen et al., 2019a;[START_REF] Matsubara | Migration mechanisms and diffusion barriers of vacancies in ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF][START_REF] Usseinov | Pair vacancy defects in β-Ga2O3 crystal: Ab initio study[END_REF][START_REF] Varley | Oxygen vacancies and donor impurities in β-Ga2O3[END_REF][START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga2O3[END_REF].

Experimentally, the VO was also correlated with blue luminescence by the comparison of the intensity between pure and doped β-Ga2O3 [START_REF] Onuma | Correlation between blue luminescence intensity and resistivity in β-Ga2O3 single crystals[END_REF]Q. Shi et al., 2019;[START_REF] Shimamura | Excitation and photoluminescence of pure and Si-doped β-Ga2O3 single crystals[END_REF]. Besides, only neutral state VO and double charged state 𝑉 𝑂 2+ are predicted to be stable in β-Ga2O3 [START_REF] Akiyama | Role of charged oxygen vacancies and substrate lattice constraint on structural stability of Ga2O3 polymorphs[END_REF][START_REF] Varley | Oxygen vacancies and donor impurities in β-Ga2O3[END_REF], and was speculated by EPR results [START_REF] Bhandari | Charge trapping at Fe due to midgap levels in Ga2O3[END_REF]. Instead of causing n-type conductivity, they may compensate acceptors [START_REF] Dong | Effects of oxygen vacancies on the structural and optical properties of β-Ga2O3[END_REF][START_REF] Mccluskey | Point defects in Ga2O3[END_REF]. The observed n-type conductivity in unintentionally doped β-Ga2O3 single crystals were explained by the unintentionally incorporated shallow impurities such as H, Sn, etc. [START_REF] Varley | Oxygen vacancies and donor impurities in β-Ga2O3[END_REF].

Gallium vacancies are generally recognized as common deep acceptors in β-Ga2O3, it has low formation energy in oxygen-rich condition, and high (-2/-3) transition energy of 0.7 -2.5 eV depending on the sites, calculation methods (Deák et al., 2017;Ingebrigtsen et al., 2019a;[START_REF] Peelaers | Deep acceptors and their diffusion in Ga2O3[END_REF][START_REF] Varley | Hydrogenated cation vacancies in semiconducting oxides[END_REF]. It is suggested that it may act as selftrapped holes (STHs) and contribute to the so-called polaron behavior of hole conductivity.

Tetrahedrally coordinated VGa (I) has a lower formation energy than octahedrally coordinated VGa (II) [START_REF] Varley | Hydrogenated cation vacancies in semiconducting oxides[END_REF]. Based on infra-red (IR) absorption spectra, the concentration of VGa (II) in a Czochralski-grown sample was estimated to be 2 -3 orders of magnitude lower than that of VGa (I) [START_REF] Portoff | Hydrogen centers as a probe of VGa(2) defects in β-Ga2O3[END_REF]. Gallium vacancies was also studied by several experimental methods such as EPR and positron annihilation. In an n-type conducting β-Ga2O3 sample, the gallium vacancy is expected to be diamagnetic in the fully occupied state with a charge q = -3 acting as compensating acceptor [START_REF] He | The effect of vacancy defects on the electronic properties of β-Ga2O3[END_REF]. In this case, there is no EPR signal as the electrons are paired. However, irradiation can create vacancy and lower the Fermi energy below the (-2/-3) transition level, leading to 𝑉 𝐺𝑎 2-with one unpaired spin. Then the monovacancy VGa was observed [START_REF] Bhandari | Charge trapping at Fe due to midgap levels in Ga2O3[END_REF][START_REF] Kananen | Gallium vacancies in β-Ga2O3 crystals[END_REF][START_REF] Von Bardeleben | Proton irradiation induced defects in β-Ga2O3: A combined EPR and theory study[END_REF]. Positron annihilation experiments have confirmed that VGa can form efficiently and act as compensating acceptor in Si-doped n-type β-Ga2O3 [START_REF] Korhonen | Electrical compensation by Ga vacancies in Ga2O3 thin films[END_REF]. Besides, the ionization energy Ei = ~1.2 eV (Chikoidze et al., 2017a;[START_REF] Chikoidze | Enhancing the intrinsic p-type conductivity of the ultra-wide bandgap Ga2O3 semiconductor[END_REF] was determined for the free holes in the intrinsic p-type β-Ga2O3, which was attributed to gallium vacancies. In deep level transient spectroscopy (DLTS) measurements, a hole trap peak at Ev+ ~1.2 eV (H2) has also been observed [START_REF] Polyakov | Point defect induced degradation of electrical properties of Ga 2 O 3 by 10 MeV proton damage[END_REF].

There are limited studies on the interstitial defects in β-Ga2O3.

Oxygen interstitials exhibit different site preferences and electronic behavior depending on the Fermi level (Ingebrigtsen et al., 2019a). It can act as either a deep donor (split-interstitial Osi configurations on the O (I) site) or a deep acceptor (other interstitial configurations in n-type) depending on the Fermi levels (Deák et al., 2017;Ingebrigtsen et al., 2019a). It is proposed that the Oi is electrically inactive and acts as a hole trap (Deák et al., 2017) in n-type β-Ga2O3. Also, both Oi and Osi configurations have low formation energy in oxygen-rich condition (Deák et al., 2017;Ingebrigtsen et al., 2019a;[START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga2O3[END_REF].

Ho et al. [START_REF] Ho | Origin of photoluminescence in $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_ {3}[END_REF] assigned the green luminescence to Oi defect centre.

Gallium interstitial was indirectly presumed to be responsible for the n-type conductivity in a β-Ga2O3 single crystal [START_REF] Irmscher | Electrical properties of β-Ga2O3 single crystals grown by the Czochralski method[END_REF] and predicted as an alternative source with respect to VO for the electron conductivity. However, it is suggested that Gai is highly mobile and has a high formation energy at extreme oxygen-poor growth conditions (Deák et al., 2017;[START_REF] Ma | First-principles calculations of electronic and optical properties of aluminum-doped β-Ga2O3 with intrinsic defects[END_REF][START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga2O3[END_REF], making it less likely to be present.

Additional to the single defects, complex defects can also be created due to the interactions between intrinsic or/and extrinsic defects [START_REF] Binet | Relation between Electron Band Structure and Magnetic Bistability of Conduction Electrons in β-Ga2O3[END_REF]Ingebrigtsen et al., 2019a;[START_REF] Varley | Hydrogenated cation vacancies in semiconducting oxides[END_REF], and also play crucial roles in β-Ga2O3. I will focus on the intrinsic complex defects here.

Divacancy pair (VGa -VO) in β-Ga2O3 has a long history. According to Vasiltsiv et al. [START_REF] Vasiltsiv | On the nature of blue and green luminescence bands of beta-GA2O3[END_REF], the vacancies pair VGa-VO are charge-active centers that, together with single Ga vacancies, can act as acceptors, and might be responsible for the blue luminescence. [START_REF] Binet | ORIGIN OF THE BLUE LUMINESCENCE OF β-Ga2O3[END_REF] studied the temperature dependent blue luminescence, and proposed that, a trapped exciton is formed by the capture of an electron in a donor cluster (VO) via tunnel transfer by acceptor level (pair of charged VO + VGa), resulting in the formation of a donor band, this radiative recombination emits a blue photon. The ionization energy of this acceptor level was speculated to be EV + ~ 0.42 eV. Similar propositions have also been made by later photoluminescence experiments [START_REF] Nie | Modulating the blue and green luminescence in the β-Ga2O3 films[END_REF][START_REF] Onuma | Modeling and interpretation of UV and blue luminescence intensity in β-Ga2O3 by silicon and nitrogen doping[END_REF][START_REF] Onuma | Correlation between blue luminescence intensity and resistivity in β-Ga2O3 single crystals[END_REF][START_REF] Shimamura | Excitation and photoluminescence of pure and Si-doped β-Ga2O3 single crystals[END_REF][START_REF] Zhu | Defect energy levels in monoclinic β-Ga2O3[END_REF]. Very recently, Zhu et al. [START_REF] Zhu | Defect energy levels in monoclinic β-Ga2O3[END_REF] proposed that the native VGa-VO divacancy defects level can be at 4.42 eV from the conduction band (EV + 0.27 eV in their undoped β-Ga2O3 single crystal) by photoluminescence. Furthermore, abundant gallium and oxygen vacancy complexes were identified by positron-electron annihilation signals irrespective of the conductivity of β-Ga2O3 single crystals [START_REF] Karjalainen | Split Ga vacancies in n-type and semi-insulating β-Ga2O3 single crystals[END_REF]. Theoretically, in oxygenrich condition, this defect complex was predicted to have comparable or even lower formation energy than single vacancies in oxygen-rich conditions based on ab initio and DFT calculations [START_REF] Frodason | Multistability of isolated and hydrogenated Ga--O divacancies in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF][START_REF] Usseinov | Pair vacancy defects in β-Ga2O3 crystal: Ab initio study[END_REF]. The role and the charge state transition of this defect depend on the Fermi level position [START_REF] Frodason | Multistability of isolated and hydrogenated Ga--O divacancies in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF]Ingebrigtsen et al., 2019a). As calculated in the ref. [START_REF] Frodason | Multistability of isolated and hydrogenated Ga--O divacancies in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF], the (+2/+1) transition of (VGa (II) -VO (II)) is about EV + 0.4 eV (to clarify, the notations of Ga and O sites are the same as Section 1.1.1), while other configurations such as (VGa (I) -VO (II)) or (VGa (II)

-VO (I)) in n-type condition might be correlated with the 𝐸 2 * trap at EC -0.75 eV observed by DLTS (McGlone et al., 2019;[START_REF] Wang | Identification and Suppression of Majority Surface States in the Dry-Etched β-Ga2O3[END_REF].

Divacancy -interstitial complex (VGa (I) -Gai -VGa (I)) was first discovered by [START_REF] Varley | Hydrogenated cation vacancies in semiconducting oxides[END_REF], it is suggested that the VGa (I) is metastable, and its presence induces a nearby Ga atom to leave its tetrahedral site, leading to the creation of a second vacancy and the movement of the Ga atom (a migration barrier of 0.53 eV) towards an interstitial site located between the two vacancies. As a result, a divacancy -interstitial complex (VGa (I) -Gai -VGa (I)) complex is formed, which is lower in energy than the isolated vacancy and acts as a deep acceptor. It was then confirmed by scanning transmission electron microscopy (STEM) [START_REF] Johnson | Unusual Formation of Point-Defect Complexes in the Ultrawide-Band-Gap Semiconductor $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF]. Besides, [START_REF] Von Bardeleben | Proton irradiation induced defects in β-Ga2O3: A combined EPR and theory study[END_REF] also proposed that the model of such a complex defect is the most plausible for the one of the EPR center observed in their proton irradiated β-Ga2O3 single crystals.

β-Ga2O3 has very good n-type dopability up to the degenerate state, n-type doped β-Ga2O3 with carrier concentration from 10 16 to 10 20 cm -3 [START_REF] Chikoidze | Electrical, optical, and magnetic properties of Sn doped α-Ga2O3 thin films[END_REF][START_REF] Guo | Review of Ga2O3-based optoelectronic devices[END_REF] has been achieved by Sn and Ge doping by MBE, Si and Sn doping by MOVPE, and Sn doping by MOCVD [START_REF] Leedy | Highly conductive homoepitaxial Si-doped Ga 2 O 3 films on (010) β-Ga 2 O 3 by pulsed laser deposition[END_REF]. A high electron mobility at room temperature of 145 -194 cm 2 /(V•s) [START_REF] Feng | Probing Charge Transport and Background Doping in Metal-Organic Chemical Vapor Deposition-Grown (010) β-Ga2O3[END_REF][START_REF] Feng | MOCVD homoepitaxy of Si-doped (010) β-Ga2O3 thin films with superior transport properties[END_REF][START_REF] Goto | Halide vapor phase epitaxy of Si doped β-Ga2O3 and its electrical properties[END_REF][START_REF] Zhang | MOCVD grown epitaxial β-Ga2O3 thin film with an electron mobility of 176 cm2/V s at room temperature[END_REF] has been reached by Si doping, and even till 10 4 cm 2 /(V•s) at 46 K [START_REF] Alema | Low temperature electron mobility exceeding 104 cm2/V s in MOCVD grown β-Ga2O3[END_REF].

On the contrary, there is a lack of high hole conductivity in β-Ga2O3. And consequently, it is probably the main limitation of emerging gallium oxide technology for power and UV diode electronics.

Native p-type conductivity: Interestingly, based on thermodynamic calculations for point defects, gallium oxide has been shown that for a growth at 500° C, P ≈ 1.33 × 10 -2 atm, a hole concentration around p ≈ 10 15 cm -3 can be achieved (Chikoidze et al., 2017a).

Experimentally, the native hole conductivity was reported in undoped β-Ga2O3 thin film grown on c-sapphire substrates by pulsed laser deposition (PLD) elaborated by Nanovation (SME, France), with ρ = 1.8 × 10 2 Ω•cm resistivity, and p = 2 ×10 13 cm -3 and 4.2 cm 2 /(V•s), hole concentration and hole mobility respectively (Chikoidze et al., 2017a). The determination of conductivity mechanism showed that Ga vacancies act as deep level acceptors with the activation energy of 0.56 eV in the low compensated sample, having ionization energy of 1.2 eV. Later it was shown the improvement of native p-type conductivity by post-annealing in an oxygen atmosphere for β-Ga2O3 thin film grown on csapphire substrates by MOCVD (Ekaterine Chikoidze et al., 2019). After oxygen annealing, the hole concentration increased from 5.6 × 10 14 cm -3 to 5.6 × 10 17 cm -3 at 850 K. The authors claimed that the annealing effect is related to the formation of VGa --VO ++ complexes as a shallow acceptor center with 𝐸 𝑎 = 0.17 eV activation energy.

For device application, higher room temperature hole concentration is required, which could be probably achieved by external acceptor impurity incorporation.

There are already extensive theoretical studies [START_REF] Goyal | Computational Fermi level engineering and doping-type conversion of Ga2O3 via three-step synthesis process[END_REF][START_REF] Kyrtsos | On the feasibility of p-type Ga2O3[END_REF][START_REF] Lyons | A survey of acceptor dopants for β -Ga 2 O 3[END_REF]Sun et al., 2019;[START_REF] Varley | Role of self-trapping in luminescence and p -type conductivity of wide-band-gap oxides[END_REF] (standard density functional theory such as DFT and DFT with GGA+U) of acceptor impurity doping of β-Ga2O3 in order to identify efficient p-type dopant. Zn, Mg, N can introduce acceptor level but relatively deep (more than 1 eV). Besides, co-doping (doping by two elements) has been predicted by DFT, which showed a promising method to get p-type β-Ga2O3, as it can break the solubility limit of mono-doping and improves the photoelectric properties of semiconductor materials.

Consequently, conductivity can be increased (L. [START_REF] Li | Single crystalline β-Ga2O3 homoepitaxial films grown by MOCVD[END_REF][START_REF] Ma | Achieving high conductivity p-type Ga2O3 through Al-N and In-N co-doping[END_REF][START_REF] Sabino | Bismuth-doped Ga2O3 as candidate for p-type transparent conducting material[END_REF]Zhang et al., 2012a). The impurity level can be as shallow as 0.149 eV above the VBM (Zhang et al., 2012a). More details of theoretical and co-doping can be found in ref. [START_REF] Chi | Ga2O3 and Related Ultra-Wide Bandgap Power Semiconductor Oxides: New Energy Electronics Solutions for CO2 Emission Mitigation[END_REF].

Zn has been predicted to be an effective dopant in β-Ga2O3 and was widely studied, the related state-of-the-art will be presented in Section 3.2 (Zn doping in β-Ga2O3) together with my experimental results of Zn doping effect in β-Ga2O3.

Besides, there are limited experimental works reported regarding p-type doping of gallium oxide. Mg-doped β-Ga2O3 has been studied by [START_REF] Qian | Mg-doped p-type β-Ga2O3 thin film for solar-blind ultraviolet photodetector[END_REF] for the photo-blind detector, and the β-Ga2O3 containing 4.92 at. % Mg has shown an acceptor level by XPS. A variation of band gap has also been reported [START_REF] Tao | Investigation of growth characteristics, compositions, and properties of atomic layer deposited amorphous Zn-doped Ga2O3 films[END_REF][START_REF] Yue | Structural and optical properties of Zn-doped β-Ga 2 O 3 films[END_REF].

Islam et al. [START_REF] Islam | Chemical manipulation of hydrogen induced high p-type and n-type conductivity in Ga2O3[END_REF] reported that hydrogen annealing could vastly reduce the resistivity and reach a remarkable hole density of ~ 10 15 cm -3 at room temperature. The ionization energy of acceptor is as low as 42 meV by incorporation of hydrogen in the lattice.

This improvement is related to hydrogen decorated gallium vacancies VGa-H.

Nitrogen-doped p-Ga2O3 has been experimentally achieved by non-conventional growth technique. [START_REF] Wu | Energy-driven multi-step structural phase transition mechanism to achieve high-quality p-type nitrogen-doped β-Ga2O3 films[END_REF]) demonstrated a multi-step structural phase transition growth (oxidation of GaN substrate to GaNxO3(1-x)/2, total transformation to β-Ga2O3, finally to N-doped β-Ga2O3), with the acceptor ionization energy of 0.165 eV. The resistivity, hole concentration and hole mobility are 17.0 Ω•cm, 1.56 ×10 16 cm -3 , and 23.6 cm 2 /(V•s), respectively, by employing the Hall effect measurements. This method was also used for the fabrication of metal-semiconductor-metal solar-blind photodetectors [START_REF] Jiang | P-type β-Ga2O3 metal-semiconductor-metal solar-blind photodetectors with extremely high responsivity and gain-bandwidth product[END_REF]. The sizable mobility was attributed to the increase of the elastic constant, enhancement of Valence Band dispersion (the decrease of the hole effective mass) using the DFT calculation [START_REF] Ma | Exploring the feasibility and conduction mechanisms of P-type nitrogen-doped β-Ga2O3 with high hole mobility[END_REF]. Luan et al. [START_REF] Luan | The further investigation of N-doped β-Ga2O3 thin films with native defects for Schottky-barrier diode[END_REF] fabricated N doped β-Ga2O3

by N implantation, the decrease in carrier concentration (1 -2 orders of magnitude) further proved that the N can introduce acceptor impurity in β-Ga2O3.

Additionally, dilute alloying was proposed theoretically using Bi [START_REF] Cai | Approach to achieving a $p$-type transparent conducting oxide: Doping of bismuth-alloyed ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ with a strongly correlated band edge state[END_REF], and experimentally using NiO [START_REF] Ezeh | Wide gap p-type NiO-Ga2O3 alloy via electronic band engineering[END_REF], Ir (α-Ga2O3) [START_REF] Kaneko | Ultrawide bandgap corundum-structured p-type α-(Ir,Ga)2O3 alloys for α-Ga2O3 electronics[END_REF] and Se [START_REF] Bai | Dilute-selenium alloying: A possible perspective for achieving p-type conductivity of β-gallium oxide[END_REF]. It provides an alternative way to get p-type conductivity. A significant decrease in band gap of ~1 eV or even more is envisaged.

Overall, achieving high room temperature p-type conductivity remains a priority challenge, further experimental studies for identification/creation of shallow acceptor defects are required. This is part of my motivation for this PhD work.

ZnGa2O4

Spinel structure materials were first discovered in 1915 by Bragg [START_REF] Bragg | XXX. The structure of the spinel group of crystals[END_REF], with the formulation of AB2X4, where A and B are either II-valent and III-valent or IV-valent and II-valent metal cations, respectively, and X being the O, S, Se, or Te [START_REF] Hill | Systematics of the spinel structure type[END_REF]. There are about 1000 known spinels including ~130 oxides. Among these oxides, zinc gallate ZnGa2O4, which is almost the stochiometric mixture of binary semiconductor oxides Ga2O3

and ZnO, has an ultra-wide band gap. The research on optical and Raman spectra of ZnGa2O4 (Cr doped) was started from 1970s, for the interest to magnetic insulators, that were used as the substrate of magnetic spinel ferrites [START_REF] Kahan | Optical and Microwave Spectra of Cr3+ in the Spinel ZnGa2O4[END_REF][START_REF] Van Der Straten | Flux growth of ZnGa2O4 single crystals[END_REF][START_REF] Van Gorkom | Infrared and Raman spectra of the spinel ZnGa2O4[END_REF]. We need to wait until 1994 for Omata et al. [START_REF] Omata | New ultraviolet-transport electroconductive oxide, ZnGa 2 O 4 spinel[END_REF] proposition that spinel ZnGa2O4 is a new ultraviolet-transparent electroconductive oxide. Only very recently, ZnGa2O4 has shown potential in power electronics applications as the high electron concentration (n > 10 19 m -3 ) and mobility (μ = 107 cm 2 /(V•s)) have been achieved in ZnGa2O4 single crystal [START_REF] Boy | Charge carrier density, mobility, and Seebeck coefficient of melt-grown bulk ZnGa2O4 single crystals[END_REF][START_REF] Cheng | Effect of Defects on the Properties of ZnGa2</sub>O4 Thin-Film Transistors[END_REF][START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF][START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF]. For example, the ZnGa2O4 based power thin-film-transistors (PTFTs)

have been demonstrated (L. C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF][START_REF] Shen | Characterizations of Metal-Oxide-Semiconductor Field-Effect Transistors of ZnGaO Grown on Sapphire Substrate[END_REF]. However, its main battlefield is optoelectronics applications for the time being. It has been recently investigated for photonics (phosphors [START_REF] Luchechko | Afterglow, TL and OSL properties of Mn 2+ -doped ZnGa 2 O 4 phosphor[END_REF][START_REF] Maldiney | The in vivo activation of persistent nanophosphors for optical imaging of vascularization, tumours and grafted cells[END_REF]), deep-ultraviolet photodetectors (Tsai et al., 2019), phototransistors [START_REF] Huang | Energy-Saving ZnGa 2 O 4 Phototransistor Improved by Thermal Annealing[END_REF]Y. C. Shen et al., 2019;Y.-C. Shen et al., 2020)). Besides, a few works studied ZnGa2O4 based gas sensors for Liquid-petroleum-gas (LPG), NO2, and NO (C. Chen et al., 2015;[START_REF] Satyanarayana | Liquid-petroleumgas sensor based on a spinel semiconductor[END_REF][START_REF] Tung | Adsorption of NO2 and H2S on ZnGa2O4(111) Thin Films: A First-Principles Density Functional Theory Study[END_REF].

Fundamental properties

Structure: Spinel oxides generally refer to the compound with the formulation of AB2O4. Arranging a close-packed face-centred cubic crystal structure (Fd-3m), in an orderednormal phase, the oxygen ions in such AB2O4 materials form tetrahedral (Td) sites where 1/8 occupied by all A cations, whereas the entire B cations reside in one-half of octahedral (Oh) sites. Figure 1-2 shows the cubic spinel structure of ZnGa2O4, displaying the tetrahedrally coordinated Zn atoms and octahedrally coordinated Ga atoms (W.-K. Wang et al., 2019b). eV [START_REF] Brik | First-principles calculations of electronic, optical and elastic properties of ZnAl2S4 and ZnGa2O4[END_REF][START_REF] Dixit | Electronic structure and band gap of zinc spinel oxides beyond LDA: ZnAl 2 O 4 , ZnGa 2 O 4 and ZnIn 2 O 4[END_REF][START_REF] Karazhanov | Ab Initio Study Of Double Oxides ZnX2O4 (X=Al, Ga, In) Having Spinel Structure: ZnX2O4 (X=Al, Ga, In) Spinals[END_REF][START_REF] López-Moreno | Lattice dynamics of ZnAl2O4 and ZnGa2O4 under high pressure[END_REF][START_REF] Pisani | Effects of Fe substitution on the electronic, transport, and magnetic properties of $\mathrm{Zn}{\mathrm{Ga}}_{2}{\mathrm{O}}_{4}$: A systematic ab initio study[END_REF][START_REF] Zerarga | Structural, electronic and optical properties of spinel oxides ZnAl2O4, ZnGa2O4 and ZnIn2O4[END_REF][START_REF] Zhang | First-principles study of the structural, mechanical and electronic properties of ZnX2O4 (X=Al, Cr and Ga)[END_REF]. While experimentally, the indirect band gap has not yet been evidenced to the best of my knowledge. Galazka et al. [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF] estimated the band gaps 4.59 eV (direct), or 4.33 eV (indirect) by different plot methods (absorption coefficient α in power 2 for direct, while in power 1/2 for indirect) for the bulk crystal. General experimental band gap values estimated are in the range of 4.0 -5.0 eV depending on the growth methods and conditions [START_REF] Bairagi | Zinc gallate (ZnGa2O4) epitaxial thin films: determination of optical properties and bandgap estimation using spectroscopic ellipsometry[END_REF][START_REF] Boy | Charge carrier density, mobility, and Seebeck coefficient of melt-grown bulk ZnGa2O4 single crystals[END_REF][START_REF] Brik | First-principles calculations of electronic, optical and elastic properties of ZnAl2S4 and ZnGa2O4[END_REF][START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF][START_REF] Krishna | ELECTRICAL AND OPTICAL PROPERTIES OF ZnGa2O4 THIN FILMS DEPOSITED BY PULSED LASER DEPOSITION[END_REF].

Other parameters: The high melting point at 1900 ± 20 °C and poor thermal conductivity of 22.1 W/(m•K) of ZnGa2O4 single crystal have been reported by [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF], one of the pioneers in the field of this material.

Bulk and thin film growth techniques

At the early stage, ZnGa2O4 was grown by flux growth technique, while the important contamination of Pb from PbO-PbF2-B2O3 flux results in poor quality of the bulk crystal [START_REF] Van Der Straten | Flux growth of ZnGa2O4 single crystals[END_REF][START_REF] Yan | Flux growth of single crystals of spinel ZnGa2O4 and CdGa2O4[END_REF]. Some other methods such as solid state [START_REF] Can | Synthesis and characterization of ZnGa2O4 particles prepared by solid state reaction[END_REF], and laser heat pedestal growth (LHPG) [START_REF] Gazit | Laser-heated pedestal growth of high Tc Bi-Sr-Ca-Cu-O superconducting fibers[END_REF] have been used as well. Recently, Galazka et al. [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF] synthesized the ZnGa2O4 single crystal by CZ and VGF methods (Figure 1-3). Colors (light blue, blue, dark blue) depend on the growth conditions, and can be attributed to the free carrier absorption. As-grown crystals can be annealed in an oxidizing atmosphere (air or O2) at T > 700 °C to become colorless and electrically insulating, while annealing in the presence of hydrogen can turn them into a semiconducting state with lower electron mobility. Large single crystals can be easily fabricated into wafers with high structural quality and cubic shape. (b) (100)-oriented wafers prepared from the as-grown and annealed bulk crystals [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF].

Similar to β-Ga2O3, spinel ZnGa2O4 thin films can also be easily and directly grown epitaxially on cheap sapphire substrates, using several techniques such as PLD, radio frequency (RF) magnetron sputtering, and CVD. Here, I will briefly introduce the outcomes of the MOCVD-grown layers, since ZnGa2O4 thin films presented in this manuscript were all grown using MOCVD technique.

Metal organic precursors TEGa, TMGa are usually used for the source of Ga as in Section 1.1.2, while diethylzinc (DEZn) is used as the source of Zn. Though investigation on the growth itself is still limited, it is evident that this ternary spinel oxide has a much higher doping flexibility than binary semiconductors by tuning the growth conditions. The electron concentration in undoped ZnGa2O4 thin films can be tuned from 1.9×10 14 to 2×10 20 cm -3 , and electron mobility μn = 2 -20 cm 2 /(V•s) at room temperature using different DEZn precursors flow rate, growth time, growth temperature, etc [START_REF] Cheng | Effect of Defects on the Properties of ZnGa2</sub>O4 Thin-Film Transistors[END_REF][START_REF] Horng | Epitaxial Growth of ZnGa 2 O 4 : A New, Deep Ultraviolet Semiconductor Candidate[END_REF][START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF]. The semi-insulating p-type thin film has also been demonstrated (Chikoidze et al., 2020a). Though oxygen vacancies are well-known deep donors (Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF], the impact of oxygen on the electronic properties has been evidenced (L.-C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF][START_REF] Horng | Reliability study on deep-ultraviolet photodetectors based on ZnGa2O4 epilayers grown by MOCVD[END_REF]H. Shen et al., 2020).

Point defects and self-doping effect

Though works have been carried out on the optical properties in (Cr, Mn, Eu doped)

ZnGa2O4 for the interest of (persistent) luminescence and phosphor related applications, the study on the intrinsic defects in ZnGa2O4 is limited.

In an ordered-normal system of spinel AB2O4, i.e., atoms A and B take their own sites (Td and Oh sites, respectively), a stable octet, so-called closed-shell, is made up of the system, it then leads to an electrical insulator behavior (Paudel et al., 2011b). However, the distribution of cations in Td and Oh sites is dependent on several factors, such as impurities [START_REF] Dazai | Cation-Deficiency-Induced Crystal-Site Engineering for ZnGa2O4:Mn2+ Thin Film[END_REF][START_REF] Lu | Cation distributions and microwave dielectric properties of Cu-substituted ZnGa2O4 spinel ceramics[END_REF] and preparation methods [START_REF] Li | Cation distribution dependence of magnetic properties of sol-gel prepared MnFe2O4 spinel ferrite nanoparticles[END_REF][START_REF] Reddy | Effect of type of fuel used and calcination temperature on the disorder-order transformation of zinc aluminate spinel during combustion synthesis[END_REF].

Therefore, the disorder distribution of cations could result in additional routes for selfdoping effects. According to a number of theoretical works, spinel oxides are well-known to have the inverted distribution of cations caused by antisite defects (e.g., in the case of ZnGa2O4 as illustrated in Figure 1-4) [START_REF] De Vos | First-Principles Study of Antisite Defect Configurations in ZnGa 2 O 4 :Cr Persistent Phosphors[END_REF]Paudel et al., 2011a;[START_REF] Seko | Classification of spinel structures based on firstprinciples cluster expansion analysis[END_REF][START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF][START_REF] Stoica | P-type zinc oxide spinels: application to transparent conductors and spintronics[END_REF], which is an usual self-doping defect and could improve materials' conductivity (Paudel et al., 2011b;[START_REF] Perkins | Inverse design approach to hole doping in ternary oxides: Enhancing p -type conductivity in cobalt oxide spinels[END_REF][START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF][START_REF] Zakutayev | Cation off-stoichiometry leads to high p -type conductivity and enhanced transparency in Co 2 ZnO 4 and Co 2 NiO 4 thin films[END_REF][START_REF] Zhang | Self-doping of cadmium stannate in the inverse spinel structure[END_REF]. For example, when the cation Ga remains at its high valent moving from its home-base octahedral site in normal ZnGa2O4, then such cross-substitution to the tetrahedral site would lead to a donor level, capable of releasing electrons.

Figure 1-4. Illustration of cations inversion in spinel ZnGa2O4.

As mentioned above, both room-temperature conducting n-type (up to conductivity σ = 1.78×10 2 S/cm) and semi-insulating p-type ZnGa2O4 thin films without any intentional doping have been reported. This self-doping effect may release us from the doping difficulty which is often very challenging in binary wide-bandgap oxides. According to theoretical works (Paudel et al., 2011b;[START_REF] Sabino | Hole conductivity through a defect band in ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}[END_REF][START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF], a n-type conductivity can be expected when the Ga content is more than the stoichiometric scenario (Zn/Ga < 1/2 in ZnGa2O4), or vice versa.

Due to the higher formation energy of other intrinsic defects (vacancies (VO, VZn, and VGa), antisites (GaO, ZnO, OZn, and OGa), and interstitials (Zni, Gai and Oi)) than ZnGa and GaZn, the study on these defects in ZnGa2O4 is very limited to date. Photoluminescence measurements suggested that the blue luminescence may be assigned to the oxygen vacancies [START_REF] Jeong | Two self-activated optical centers of blue emission in zinc gallate[END_REF][START_REF] Sambandam | Oxygen vacancies and intense luminescence in manganese loaded Zno microflowers for visible light water splitting[END_REF][START_REF] Satya Kamal | Blue luminescence from ZnGa2O4: Effect of lattice distortion and particle size[END_REF]. DFT-based calculations suggested that, in oxygen-rich condition, VZn, VGa and ZnGa are stable and act as acceptors in the n-type case (Fermi level in the upper band gap), which makes the effective n-type conductivity difficult to be realized due to the compensation. On the other hand, acceptor defects have much higher formation energy than donors GaZn, Gai, Zni and VO in the region near the valence band in oxygen-poor condition, which makes p-type conductivity difficult to be achieved [START_REF] Sabino | Hole conductivity through a defect band in ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}[END_REF]Y.-P. Wang et al., 2019).

Different from the antisite defect ZnGa induced p-type conductivity predicted previously (Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF], [START_REF] Sabino | Hole conductivity through a defect band in ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}[END_REF] recently proposed that the excess of Zn may lead to a creation of polaronic band resulting in small polaron hopping conduction. In any case, outstanding prospects due to the high degree of freedom for doping in this ternary oxide has been demonstrated.

Summary

Overall, both β-Ga2O3 and ZnGa2O4, show promise, while β-Ga2O3 is more developed than ZnGa2O4, having commercially available 6-inch wafer from bulk crystals, while ZnGa2O4 single crystal elaboration from melt growth was just started in an academic laboratory level. However, ZnGa2O4 has been long time targeted for applications in optoelectronics and photonics in particular. Its cubic structure is easier for thin film growth, and point defects creation than β-Ga2O3, and as a spinel, it has higher doping flexibility, though both compounds have poor thermal conductivity (for comparison, that of 4H-SiC is 490 Max. electron concentration, n [cm -3 ] ~10 19-20 cm -3 d,e (Si, Sn, Ge doped) ~10 19-20 cm -3 d,e (undoped) Max. hole mobility, µp

W/(m•K)).
[cm 2 /(V•s)] ~10 d (800 K) ~10 d (800 K) Max. hole concentration, p [cm -3 ]
~10 16 cm -3 d (300 K, N doped) ~10 15 cm -3 d (800 K, undoped)

Experimental Techniques and Methods

In this chapter, I will describe the experimental facilities and methods used during my work.

Metal organic chemical vapor deposition (MOCVD)

The β-Ga2O3 and ZnGa2O4 layers investigated in this manuscript were all grown on csapphire substrates by the metal organic chemical vapor deposition (MOCVD) technique. In GEMaC laboratory, we use a radio frequency (RF) heated horizontal MOCVD reactor (MR Semicon, 1992) with separate inlets of precursors with their own mass flow controllers (Figure 2-1). The pressure can be tuned from 30 Torr to ambient, the temperature range is 20 -1000 °C, the maximum substrate size is 2 inches.

The sources of gallium and oxygen were trimethylgallium (TMGa) and pure O2 gas, respectively. The diethylzinc (DEZn) was used as the precursor for Zn for the growth of Zndoped β-Ga2O3 and ZnGa2O4 layers. Pure Ar gas was used as vector gas. In GEMaC, the growth of β-Ga2O3 and ZnGa2O4 is carried out by Dr. Corinne Sartel.

Studied n-type ZnGa2O4 layers (that will be shown in Chapter 4) were grown by colleagues Dr. Fu-Gow Tarntair, and Prof. Ray-Hua Horng in National Yang Ming Chiao

Tung University (NYCU). The used metal organic precursors, the oxygen source as well as the vector gas were DEZn, TEGa, pure O2, and pure Ar.

Structural, morphological, and chemical characterizations 2.2.1 X-ray diffraction (XRD)

X-ray diffraction (XRD) measurements were used to identify the crystalline structure and crystallinity of the deposited thin films.

The dominant effect that occurs when an incident beam of X-rays interacts with a target material is the scattering of those X-rays from atoms within the target material [START_REF] Cullity | Elements of X-ray Diffraction[END_REF].

In materials with regular structure (i.e. crystalline), the interaction of the incident beam with the refracted beam produces constructive interference (and a diffracted ray) when conditions satisfy Bragg's Law:

𝑛𝜆 = 2𝑑sin𝜃 (2 -1)
Where n, λ, d, θ are the order of reflection, the wavelength of the incident beam, interplanar spacing of the crystal, and angle between incidence beam and reticular plane, respectively. I performed θ-2θ scans for samples in GEMaC using a Bruker-Siemens XRD diffractometer D5000 (Figure 2-2). The XRD diffractometer D5000 consists of a conventional copper X-ray source with a nickel filter, giving a working wavelength (λ) Cu-Kα of 1.54 Å, and a detector (scintillation photomultiplier). X-rays are generated from a copper tube with a voltage of 30 kV and a current of 20 mA. While the rocking curves (ω scan) and in-plane measurements for β-Ga2O3 were carried out using the diffractometer

Scanning electron microscopy (SEM):

Scanning electron microscopy (SEM) measurements were used to characterize the surface morphology of samples, and to determine the sample layers' thicknesses by the crosssection.

SEM works by scanning a focused beam of electrons lighting a sample surface thickness, which then generates secondary and backscattered electrons that are collected by detectors to form an image. The high resolution of SEM images is due to the small wavelength of electrons, allowing for the imaging of sub-micron features. Additionally, SEM can be used to analyze the elemental composition of a sample using energy-dispersive X-ray spectroscopy (EDS), which detects X-rays emitted by the sample when it is bombarded by the electron beam. This allows for the identification and mapping of Mendeleyev table elements composition on a surface.

The SEM measurements were performed systematically for all samples by Dr. Corinne Sartel, using the commercial scanning electron microscope JSM 7001F (JEOL).

Transmission electron microscopy (TEM):

Transmission electron microscopy (TEM) measurements were mainly used to characterize the crystal structure of samples and interfaces. In TEM measurement, a highenergy electron beam is transmitted through a thin sample, and the electrons that pass through are collected and focused onto a detector to produce an image. This technique can provide detailed information about the microstructure, crystal structure, and defects in a material. Additionally, selected area electron diffraction (SAED) can be performed using TEM to obtain information about the crystallinity and crystallographic orientations of a material. Thereby, by controlling the size of the electron beam and the position of the sample, the diffraction pattern can be obtained from a specific area of the sample, providing insight into the crystal structure and orientation. SAED can be particularly useful in the characterization of polycrystalline materials, where the orientation of individual grains can vary.

The TEM measurements were performed by collaborators either in National Yang Ming Chiao Tung University (NYCU) for the ZnGa2O4 samples elaborated in their lab., or Dr.

Amador Pérez-Tomas and coworkers in Catalan Institute of Nanoscience and Nanotechnology (ICN2) for the ZnGa2O4 samples elaborated in GEMaC. In NYCU, the ZnGa2O4 films were investigated by high-resolution transmission electron microscopy (HR TEM, JEOL-2100 F CS STEM) equipped a 200-kV field emission electron gun (FEG) and combined with selected area electron diffraction (SAED) (for details see (NYCU Instrumentation Webpage, 2023)). In ICN2, the layers were characterized by a FEI Tecnai G2 F20 with a 200kV field emission gun (FEG) high resolution and analytical TEM.

Secondary ion mass spectrometry (SIMS):

Secondary ion mass spectrometry was used in GEMaC by Dr. Francois Jomard to analyze the chemical composition and elements profile for undoped and doped β-Ga2O3, using the ions analyzer IMS 7f, CAMECA.

SIMS method involves bombarding a solid sample placed in a vacuum by primary ion beam which has an energy greater than the energy of atoms extraction from the surface of the material. The interaction between the ions beam and the surface of the sample gives rise to different secondary emissions, photons, electrons, or molecules. Secondary ions are the source of the information in this method, they are sorted according to their mass and energy.

Raman spectroscopy

Raman spectroscopy measurements were performed by Dr. Corinne Sartel using Horiba Jobin Yvon Labram HR 8500 in GEMaC. It was used to investigate the vibrational and rotational modes of Ga2O3 and ZnGa2O4 layers, thus, identifying the phase of Ga2O3 and the presence of the cubic spinel ZnGa2O4.

Raman spectroscopy provides information about molecular structure, chemical composition, and crystallography. The technique is based on the inelastic scattering of light, known as the Raman effect, which occurs when photons interact with the vibrational modes of a sample. In a Raman measurement, a laser beam is directed onto the sample, and the scattered light is collected and analyzed. The Raman spectrum is a plot of the intensity of the Raman scattering as a function of the frequency shift from the incident laser beam. The spectrum reveals peaks at specific frequencies, known as Raman bands, which correspond to the vibrational modes of the sample. Each Raman band provides information about the molecular bonds and functional groups present in the sample, allowing for the identification and characterization of the material.

X-ray photoelectron spectroscopy (XPS)

X-ray photoemission spectroscopy (XPS) measurements were used to characterize the local bonding environment as well as the chemical state of the elements, and the chemical compositional analysis. Additionally, the valence band tails can be used to determine the Fermi level positions in the samples (B. J. Carey et al., 2017).

The XPS measurement is based on the study of the kinetic energy distribution of photoelectrons ejected from a sample under the impact of the photon (UV/ X-ray) of known energy hν. The variation of photoelectron binding energy as a function of the chemical environment atoms from which they come is the main interest of this technique [START_REF] Seah | The quantitative analysis of surfaces by XPS: A review[END_REF].

The XPS spectrometry provides elemental and chemical information on various types of materials with a lateral resolution ranging from 10 to a few hundred μm. The depth probed is generally less than 10 nm, depending on the incident photon energy. XPS spectra are obtained by irradiating a material with a beam of X-rays while simultaneously measuring the kinetic energy and number of electrons that escape from the top 0 to 10 nm of the material being analyzed. A typical XPS spectrum is a graph of the number of electrons detected per second (Y-axis, ordinate) versus the binding energy of the electrons detected (X-axis, abscissa). Each element produces a characteristic set of photo-peaks at characteristic binding energy values, then each element that exists in or on the surface of the material can be analyzed. The chemical shift is due to a change in the potential of the electronic level of an atom when it chemically bonds to other atoms.

XPS measurements were performed in Institut Lavoisier Versailles (ILV), UFR des Sciences at Versailles by Dr. Mathieu Frégnaux with the participation of master 2 student Hamid Néggaz, using the Thermofisher Scientific Escalab 250 xi equipped with a mono-chromated Al-Kα anode (1486.6 eV) and a dual flood gun (low energy electron and ion). The photoelectron detection was performed using a constant analyzer energy (CAE) mode ( 20eV pass energy). To avoid the surface charge effect, we used carbon tape for drain electrons and Flood Gun (low energy electron beam) for charge compensation and improvement of charge distribution on samples that are not conducting enough. To access the bulk chemical composition, alternate sequences of ion bombardment (Ar) and XPS measurements were used. It allowed us to reconstruct the chemical depth profile of the material. Argon ions were accelerated under 4000 V and projected to the sample surface with an angle of 30°, the XPS measurements were performed subsequently.

Optical characterization

Transmittance and reflectance spectroscopy

The optical transmittance and reflectance measurements were used to determine the optical band gaps and check the transparency of thin films in the 200 -2500 nm wavelength range.

Optical spectrophotometry is a method to measure how much a sample absorbs light by measuring the intensity of light as a beam of light passes through this sample. When light strikes an object, it can be either reflected, transmitted, or absorbed. The measurement setup is fairly straightforward in transmission measurements. To calculate transmittance, a measurement of the source (incident flux, 𝛷 𝑖 ) is acquired by placing it in line with the detector without the sample in place, the result of this measurement is the so-called baseline, and allows to subtract the effect of the environment. The sample then is placed between the source and detector, and the transmitted light, 𝛷 𝑡 is measured. The ratio of these two measurements is the transmission of the sample (which is calculated automatically):

𝑇(𝜆) = 𝛷 𝑡 (𝜆) 𝛷 𝑖 (𝜆)
. The reflectance R was measured with the same methodology for extracting the "base line" reference.

The band absorption edge can be then determined by Tauc's relation:

(𝛼ℎ𝜐) 𝑛 ∝ (ℎ𝜐 -𝐸 𝑔 ) (2 -2)
Where α is the absorption coefficient, hυ is the incident photon energy, and the power factor n takes 0.5 or 2 for indirect or direct transition, respectively. The α and hυ can be calculated by:

𝛼 = 𝑙𝑛10 × 𝐴 𝑡 (2 -3) 𝐸 = ℎ𝜐 = ℎ𝑐 𝜆 (2 -4)
Where A is the absorbance that can be determined by the transmittance and reflectance, c is the speed of light, λ is the incident wavelength. Plotting the (𝛼ℎ𝜐) 2 versus incident photon energy hυ, the band absorption edge can be determined.

GEMaC has a Perkin Elmer LAMBDA 950 2 ways spectrophotometer. So, the baseline is measured at the same time as the one with the sample, by a splitting of source light in two equi-intensity beams. This allows a get rid of the source intensity fluctuations. It is equipped with modules for transmission, reflection, and with an integration sphere for diffusive samples, for the measurements of the transmittance and the reflectance in the 200 -3300 nm wavelength range and 10 -770 K temperature interval. I carried out the optical transmittance and reflectance measurements at room temperature in 200 -2500 nm wavelength range for β-Ga2O3 and ZnGa2O4 thin films.

Photoluminescence spectroscopy

Photoluminescence (PL) spectroscopy was used to study the point defects (emission and corresponding defects)

This technique involves the absorption of incident photons by a material and the subsequent emission of photons as the excited electrons return to their ground state. By analyzing the intensity, peak position, and linewidth of the PL spectra, it can provide valuable information about the electronic structure as well as defects and impurities within the material The PL measurements were carried out by Mr. Guillaume Bouchez in GEMaC, using a home-built photoluminescence spectroscopy set-up, with 266 nm excitation wavelength (YAG laser, FQCW266-10-C, CryLaS), at room temperature. The collected signals were

analysed by the spectrometer (IsoPlane 320, Princeton Instrument).

Electrical transport characterization

Electrical contact preparation

Samples to be measured in a Van der Pauw configuration were cut by the diamond wire saw (Well 3241, Well Diamond Wire Saws) in a square shape of 10 mm × 10 mm. Several methods were used to prepare the metals contacts:

(i) Four-point silver paste contacts were made manually at the four corners of the sample (Figure 2-3), they are connected by silver wires to the electrodes (Au) in the cell (Linkam, UK) for the electrical measurements. Ag paste contacts were dried and then followed an in-situ annealing during the heating process.

(ii) Radio radio-frequency (RF) sputtering using the shadow mask made for 10 mm × 10 mm sample (

Current-voltage characteristics and photocurrent test

To

Hall effect measurements

GEMaC has a home-built "high impedance high temperature" Hall Effect set up in Van Der Pauw configuration, which is specially adapted to measure very resistive (R > 10 10 Ohm) materials. It operates in 80 -850 K temperature interval under various gas atmosphere and Van Der Pauw (VDP) method is a technique for the evaluation of electrical properties in semiconductor materials, such as resistivity; and carrier density, carrier mobility, via Hall effect. It involves applying a current and measuring voltage using four small contacts on the circumference of a flat, arbitrarily shaped sample of the uniform thin thickness (≪ sample dimension, inter-contact distances). This method is particularly useful for measuring very small samples because the geometric spacing of the contacts is unimportant. Effects due to a sample's size, which is the approximate probe spacing, can be neglected until contact's size is more than ten times smaller than the sample size [START_REF] Van Der Pauw | A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape[END_REF].

Using this method, the resistivity can be derived from a total of eight measurements that are made around the periphery of the sample with the configurations shown in Figure 2-6 (a). Once all the voltage measurements are taken, two values of resistivity, 𝜌 𝐴 and 𝜌 𝐵 , are derived as follows:

𝜌 𝐴 = 𝜋 𝑙𝑛2 𝑓 𝐴 𝑡 𝑠 (𝑉 1 -𝑉 2 + 𝑉 3 -𝑉 4 ) 4𝐼 (2 -5) 𝜌 𝐵 = 𝜋 𝑙𝑛2 𝑓 𝐵 𝑡 𝑠 (𝑉 5 -𝑉 6 + 𝑉 7 -𝑉 8 ) 4𝐼 (2 -6)
Where 𝜌 𝐴 and 𝜌 𝐵 are volume resistivities in Ω•cm; 𝑡 𝑠 is the sample thickness in cm;

{𝑉 𝑖 } represents the DC voltages in volts (V) measured by the voltmeter; 𝐼 is the DC current through the sample in amperes (A); 𝑓 𝐴 and 𝑓 𝐵 are geometrical factors based on sample symmetry, in our case they are equal to 1, because of the square shape of the sample associated to a small size of metal contacts. Once 𝜌 𝐴 and 𝜌 𝐵 are known, the average resistivity (𝜌 𝐴𝑉𝐺 ) can be determined as follows:

𝜌 𝐴𝑉𝐺 = 𝜌 𝐴 + 𝜌 𝐵 2
(2 -7)

Hall effect, experimental set-up, and measurement details

The Hall Effect is a fundamental measurement to determine carrier type and carrier density; to deduce the free carrier mobility with the known electrical resistivity of a material.

It can be observed when a potential difference is observed between the edges of a conducting strip carrying a longitudinal current when placed in a magnetic field perpendicular to the plane of the strip. The basic physical principle underlying the Hall Effect is the Lorentz force, which is a combination of two separate forces: the electric force and the magnetic force.

When an electron moves along the electric field direction perpendicular to an applied magnetic field, it experiences a magnetic force -𝑞𝜗 × 𝐵 acting normally to both directions. The resulting Lorentz force F is therefore equal to -𝑞(𝐸 + 𝜗 × 𝐵) where q is the elementary charge, E is the electric field, 𝜗 is the particle velocity, and B is the magnetic field (Figure 234567). where 𝐼 is the current, B is the magnetic field, d is the sample thickness, n is the electron concentration (Otherwise, p if the majority free charge carriers are holes) and q is the elementary charge. For the majority of free charge carriers, the type (electron 𝑛 or hole 𝑝), the carrier concentration, mobility 𝜇 can be then determined by following formulas:

𝑛 = - 1 𝑒 × 𝑅 𝐻 , or 𝑝 = 1 𝑒 × 𝑅 𝐻 (2 -8) 𝜇 = |𝑅 𝐻 | 𝜌 (2 -9)
Where the 𝑅 𝐻 is the Hall coefficient, it is negative when the majority of the free carriers are electrons, whereas it is positive when the majority of the free carriers are holes.

During the Hall effect measurement, there are several possible errors that can be summarized as follow [START_REF] Lindberg | Hall Effect[END_REF]:

(i) Voltmeter offset (Voff): When a voltmeter is not properly zeroed, it introduces an offset voltage (Voff) to every measurement. This offset remains constant and does not change with the direction of the current or magnetic field.

(ii) Current meter offset (Ioff): Similarly, an improperly zeroed current meter adds an offset current (Ioff) to every measurement. This offset remains consistent and is independent of the current or magnetic field direction.

(iii) Thermoelectric effect (voltage VSeebeck): It is also known as the Seebeck effect that will also be presented later in Section 2.4.5. This results in thermoelectric voltages (VTE) due to the Seebeck effect. Thermoelectric voltages can also be generated in the wiring connected to the sample in response to temperature gradients. These thermoelectric voltages are not affected by the current or magnetic field.

(iv) Ettingshausen effect (voltage, VEttingshausen): Even in the absence of an external temperature gradient, the sample itself can create its own temperature gradient. This leads to the Ettingshausen effect, where slow and fast electrons are displaced to different sides of the sample under the influence of the Lorenz force. This internally generated Seebeck effect results in the Ettingshausen effect voltage (VEttingshausen). Unlike other effects, VEttingshausen is proportional to both the current and magnetic field, and it cannot be eliminated by reversing the current or magnetic field.

(v) Nernst effect (voltage, VNernst): If there is a longitudinal temperature gradient along the sample, electrons tend to diffuse from the hot end to the cold end, creating a diffusion current affected by a magnetic field. This produces the Nernst effect or Nernst-Ettingshausen effect, which results in the Nernst effect voltage (VNernst). VNernst is proportional to the magnetic field but not to the external current.

(vi) Righi-Leduc voltage (VRL): Electrons experiencing the Nernst (diffusion) effect also exhibit an Ettingshausen-type effect due to their spread of velocities, creating hot and cold sides. This establishes a transverse Seebeck voltage known as the Righi-Leduc voltage (VRL).

Similar to the Nernst effect, VRL is proportional to the magnetic field but not to the external current.

(vii) Misalignment voltage (VM): Geometrical variations and imperfect alignments of contacts lead to a misalignment voltage (VM), which often contributes the most significant spurious component to the measured Hall voltage, as it gives a contribution proportionally to the sample resistivity.

By varying the DC applied current direction, applied magnetic field, and amperemeter and voltmeter configurations (Figure 2345678), the majority of errors can be eliminated. We note that the V1 -V4 are measured in a positively applied magnetic field, while V5 -V8 are measured in a negatively applied magnetic field. And we note that the current direction I1 (I3, I5, and I7) is negative. Then, we have:

𝑉 1 = -𝑉 𝐻 + 𝑉 𝑜𝑓𝑓 -𝑉 𝐸𝑡𝑡𝑖𝑛𝑔𝑠ℎ𝑎𝑢𝑠𝑒𝑛 + 𝑉 𝑁𝑒𝑟𝑛𝑠𝑡 + 𝑉 𝑅𝐿 -𝑉 𝑀 + 𝑉 𝑆𝑒𝑒𝑏𝑒𝑐𝑘 (2 -10) 𝑉 2 = +𝑉 𝐻 + 𝑉 𝑜𝑓𝑓 + 𝑉 𝐸𝑡𝑡𝑖𝑛𝑔𝑠ℎ𝑎𝑢𝑠𝑒𝑛 + 𝑉 𝑁𝑒𝑟𝑛𝑠𝑡 + 𝑉 𝑅𝐿 + 𝑉 𝑀 + 𝑉 𝑆𝑒𝑒𝑏𝑒𝑐𝑘 (2 -11) 𝑉 5 = +𝑉 𝐻 + 𝑉 𝑜𝑓𝑓 + 𝑉 𝐸𝑡𝑡𝑖𝑛𝑔𝑠ℎ𝑎𝑢𝑠𝑒𝑛 -𝑉 𝑁𝑒𝑟𝑛𝑠𝑡 -𝑉 𝑅𝐿 -𝑉 𝑀 + 𝑉 𝑆𝑒𝑒𝑏𝑒𝑐𝑘 (2 -12) 𝑉 6 = -𝑉 𝐻 + 𝑉 𝑜𝑓𝑓 -𝑉 𝐸𝑡𝑡𝑖𝑛𝑔𝑠ℎ𝑎𝑢𝑠𝑒𝑛 -𝑉 𝑁𝑒𝑟𝑛𝑠𝑡 -𝑉 𝑅𝐿 + 𝑉 𝑀 + 𝑉 𝑆𝑒𝑒𝑏𝑒𝑐𝑘 (2 -13) (𝑉 2 -𝑉 1 + 𝑉 5 -𝑉 6 ) 4 = 𝑉 𝐻 + 𝑉 𝐸𝑡𝑡𝑖𝑛𝑔𝑠ℎ𝑎𝑢𝑠𝑒𝑛 ≈ 𝑉 𝐻 (2 -14)
Then the corresponding Hall coefficient RHC can be calculated by:

𝑅 𝐻𝐶 = 𝑑 𝐵𝐼 × 𝑉 2 -𝑉 1 + 𝑉 5 -𝑉 6 4 (2 -15)
Similar measurements are performed using another configuration, and the corresponding Hall coefficient RHD is:

𝑅 𝐻𝐷 = (𝑉 4 -𝑉 3 + 𝑉 7 -𝑉 8 ) 4 × 𝑑 𝐵𝐼 (2 -16)
Where d is the thickness of the thin film. Finally, the Hall coefficient is:

𝑅 𝐻 = 𝑅 𝐻𝐶 + 𝑅 𝐻𝐷 2 (2 -17)
A verification of Ohmic contact was always carried out before the measurements of resistivity and Hall effect. (iii) Conduction mechanism: in hopping conduction, carriers hop between spatially localized states through thermally activated hopping processes, rather than flowing freely delocalized states as in conventional band conduction. Many works reported the anomalies observed in Hall effect measurements when the hopping conduction becomes dominant in the samples [START_REF] Emin | The sign of the Hall effect in hopping conduction[END_REF]Gal'perin and German, n.d.;[START_REF] Holstein | Sign of the hall coefficient in hopping-type charge-transport[END_REF][START_REF] Holstein | Hall Effect in Impurity Conduction[END_REF][START_REF] Klein | Investigation of the Hall effect in impurity-hopping conduction[END_REF][START_REF] Movaghar | The Hall mobility in hopping conduction[END_REF]. However, it can be overcome by performing Seebeck effect measurements.

Therefore, in such difficult experimental conditions, after applying the set-up and errors elimination methods presented above, we apply a systematic measurement procedures and data validation before extracting relevant electrical transport properties behaviours and values. After analyzing and measuring about 30 -40 resistive p-type β-Ga2O3 samples, one illustrative example is given as follow (Figure 23456789).

Before performing the electrical measurements, the first step is always to check the Ohmic contact behavior. Ag-paste after drying and then in-situ annealing starts to form Ohmic contact to p-type β-Ga2O3 thin films above around 550 K (depending on different samples).

Physical property measurement system (PPMS)

The PPMS, Quantum Design Inc. (QD) is an automated low-temperature (2 -400 K) and high magnet field [-9 T; 9 T] measurement system for electrical transport and magnetic properties of the material (Quantum Design, 2008).

In GEMaC, with PPMS-9T of QD (Figure 2

Seebeck effect measurements

The Seebeck effect is a phenomenon in which a temperature gradient across a semiconductor generates an electric voltage. When a temperature gradient is applied to a semiconductor, the free charge carriers within the material tend to diffuse from the hotter region to the cooler region. As a result, an imbalance in charge distribution is created, leading to the development of an electric field. This electric field causes the charge carriers to migrate. At equilibrium, a compensating electromotive force caused by the temperature gradient is developed across the semiconductor [START_REF] Geballe | Seebeck Effect in Silicon[END_REF]. The ratio between the voltage difference induced and the temperature difference is called the Seebeck coefficient, and is defined as:

𝑆 = ∆𝑉 ∆𝑇 [ 𝑉 𝐾 ] (2 -18)
By this convention, the direction of the thermoelectromotive force of the n-type semiconductor is from the low-temperature end to the high-temperature end (the Seebeck coefficient is negative), on the contrary, the direction of the thermoelectromotive force of the p-type semiconductor is from the high-temperature end to the low-temperature end (the Seebeck coefficient is positive).

β-Ga 2 O 3 : Experimental Results and Discussion

In this chapter, I will focus on the characterizations of the undoped and Zn-doped p- measurements for the estimation of this critical electric field will be discussed.

Undoped β-Ga2O3 thin films

Prior to studying the acceptor doping effect in β-Ga2O3, it is necessary to obtain high crystalline quality layers with lower possible donor defects concentration, as they act as "hole-killers", preventing hole conductivity realization. Most non-intentionally doped wide bandgap oxide semiconductors are predominately n-type due to the low formation energy of oxygen vacancies, which are donors compensating the intentional acceptors (e.g., in ZnO).

The majority of oxides have such fundamental thermodynamic constraints, making p-type doping difficult. However, there is still a small family of oxide compounds which have naturally p-type conductivity: Cu2O [START_REF] Napari | Role of ALD Al2O3 Surface Passivation on the Performance of p-Type Cu2O Thin Film Transistors[END_REF], CuInO2 [START_REF] Yanagi | Bipolarity in electrical conduction of transparent oxide semiconductor CuInO2 with delafossite structure[END_REF],

CuCrO2 [START_REF] Banerjee | Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films[END_REF], SnO [START_REF] Yang | Preparation and characterization of p-type transparent conducting SnO thin films[END_REF], NiO [START_REF] Sato | Transparent conducting p-type NiO thin films prepared by magnetron sputtering[END_REF], etc.

According to the pioneering work on p-type β-Ga2O3 reported by my colleagues (Chikoidze et al., 2017b), based on the thermodynamics analysis, β-Ga2O3 is a favorite case,

as it has comparatively high formation energy of native donors -"hole killers", and consequently the electrical compensation by intrinsic donors is diminished (Chikoidze et al., 2017b). The native hole conductivity is thus possible, and β-Ga2O3 was also distinguished from other wide band gap oxides (e.g., ZnO, SnO2, or In2O3) that have low donor formation energies. Then, all of the further works were progressed based on these findings.

Structural characterizations

The undoped doped β-Ga2O3 samples were grown in a radio-frequency (RF) heated horizontal metal organic chemical vapor deposition (MOCVD) reactor on insulating c-plane sapphire Al2O3(0001) substrates. (details see Table 3-4) During the growth, the flow rate of the gallium precursors and oxygen were kept at 6 µmol/min and 600 sccm respectively. The growth temperature and pressure were set at T = 775 °C and total pressure in reactor 30 Torr, respectively.

It is well established that β-Ga2O3 can be epitaxially grown on c-sapphire with six equivalent orientations following the relationship [START_REF] Garten | Structure property relationships in gallium oxide thin films grown by pulsed laser deposition[END_REF][START_REF] Oshima | Ga2O3 Thin Film Growth on c-Plane Sapphire Substrates by Molecular Beam Epitaxy for Deep-Ultraviolet Photodetectors[END_REF]: The rocking curve of β-Ga2O3 (020) plane (Inset in Figure 3-1 (b)) and that of (201) plane display a FWHM of 6°, i.e. the IP misorientation is twice larger than that of OP. The fact that the film lattice expands out-of-plane and contracts in-plane implies an increase in the lattice parameters a and c by 0.14% and 0.12% respectively with respect to the bulk, as well as an increase in the β angle of 0.31% (Table 3-1). In parallel, the parameter b is in the contraction of -0.49%.

β-Ga2O3(-
a (Å) b (Å) c (Å) β (°)
β-Ga2O3 this work 12.247 3.025 5.807 104.02 Bulk ref. [START_REF] Geller | Crystal Structure of β-Ga2O3[END_REF] the Γ-point, these belong to the irreducible representation [START_REF] Dohy | Raman spectra and valence force field of single-crystalline β Ga2O3[END_REF].

𝛤 𝑜𝑝𝑡 = 10𝐴 𝑔 + 5𝐵 𝑔 + 4𝐴 𝑢 + 8𝐵 𝑢 (3 -1)
The modes with Ag and Bg symmetry are Raman active, while those with odd parity

Electrical transport properties

In this sub-section, a detailed electrical transport properties study for the undoped β-Ga2O3 layers is presented.

To perform the electrical measurements correctly, the first step is to check the Ohmicity of contacts for the undoped β-Ga2O3 sample. The contacts were prepared by painting the silver paste at 4 corners of a square-shaped sample (in a Van der Pauw configuration).

Current-voltage (I-V) dependence was measured at 850 K (Figure 3 In a non-magnetic material, when the majority of free carriers is p-type (holes), the Hall voltage (VH) should be positively proportional to the applied magnetic field (H), and the values should be positive when the applied magnetic field is positive (vice versa for negative magnetic field). To further validate the sign of majority carriers in the film, the Hall voltage dependence on the applied magnetic field was measured at 850 K with increasing magnetic fields from -1.6 to 1.6 T. As shown in Figure 3-4 (a), the VH has the same sign as the applied magnetic field, and increases linearly with a perpendicularly applied increasing magnetic field, indicating that the layer is p-type. Moreover, the experimental off-set voltage at zero magnetic field is very small. (3 -3)

Thus:

𝑝 = 𝑁 𝐴 -𝑁 𝐷 𝑁 𝐷 𝑁 𝑉 2 𝑒 - ∆𝐸 𝑎 𝑘 𝐵 𝑇 (3 -4)
With NV  T 3/2 . ΔEa in this case equals the ionization energy Ei of the acceptor level, is obtained from a linear regression on a ln(p×T -3/2 ) vs. (1/T) plot (Figure 34). Following this, the Ei was determined to be 1.11 ± 0.02 eV, which gives the activation energy in this case. The origin of the conductivity can be attributed to the deep acceptor gallium vacancy (VGa) (Jesenovec et al., 2021b;[START_REF] Lany | Defect phase diagram for doping of Ga2O3[END_REF][START_REF] Polyakov | Point defect induced degradation of electrical properties of Ga 2 O 3 by 10 MeV proton damage[END_REF].

Optical band gap and photoluminescence

Reflectance and transmittance measurements were conducted on both β-Ga2O3 thin film at room temperature, from 200 to 2000 nm wavelength range. The layer exhibits a high transparency (> 80%) in the vis-NIR range and a sharp cut-off without any other absorption (Figure 345). The absorption coefficient (α) was then calculated, and the optical band gap (Eg) was estimated to be 4.66 ± 0.05 eV using a Tauc plot for direct band gap materials (inset in Figure 345). Indeed, there are several broad bands typically assigned to intrinsic defects or impurities.

For example, peaks at ~ 3.3 -3.6 eV (UV emission) were correlated with self-trapped holes (STHs) at the intrinsic defects [START_REF] Ho | Origin of photoluminescence in $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_ {3}[END_REF][START_REF] Onuma | Correlation between blue luminescence intensity and resistivity in β-Ga2O3 single crystals[END_REF]) (e.g.several charged gallium vacancy states 𝑉 𝐺𝑎 𝑞 , with q = -1, -2, -3 [START_REF] Nie | Modulating the blue and green luminescence in the β-Ga2O3 films[END_REF]), ~ 2.7 -3.0 eV (blue emission) were assigned to (VGa-VO) di-vacancy complex defect [START_REF] Binet | ORIGIN OF THE BLUE LUMINESCENCE OF β-Ga2O3[END_REF][START_REF] Nie | Modulating the blue and green luminescence in the β-Ga2O3 films[END_REF], ~2.3 -2.5 eV (green emission) originate from Oi [START_REF] Ho | Origin of photoluminescence in $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_ {3}[END_REF], and ~1.8 -2.0 eV (red emission) originate from NO (when N doping), VO [START_REF] Onuma | Correlation between blue luminescence intensity and resistivity in β-Ga2O3 single crystals[END_REF] T. Zhang et al., 2013) and Cr 3+ impurity [START_REF] Sun | On the origin of red luminescence from iron-doped β -Ga 2 O 3 bulk crystals[END_REF]. Very recently, Zhu et al. (Zhu et al., 2022) proposed that the (𝑉 𝐺𝑎 -𝑉 𝑂 ) 𝑥-level lies ~ 4.42 -4.48 eV below the conduction band minimum (CBM) for all their undoped, Si-doped, and Mg-doped β-Ga2O3 single crystals. There is a secondary ultraviolet (UV) emission peak at ~ 3.74 eV, which can be ascribed to the electron transition from the gallium vacancy level, located at about ~ 1 eV from the valence band, as it is quite similar to the ionization energy determined by electrical measurements. Discussion on the luminescence in β-Ga2O3 about the emission origin is still ongoing.

XPS valence band tail states

X-ray photoelectron spectroscopy (XPS) is a powerful tool for investigating the valence band characteristics of a material, and it can provide evidence of the presence of states within the bandgap as well (B. J. Carey et al., 2017;[START_REF] Wertheim | X-Ray Photoemission Band Structure of Some Transition-Metal Oxides[END_REF][START_REF] Xu | Effect of Surface Defect States on Valence Band and Charge Separation and Transfer Efficiency[END_REF].

When used in high resolution in the valence band vicinity (i.e., for the lowest binding energies), it is possible to directly detect whether there are states in the lower part of the bandgap (those responsible for p-type character) [START_REF] Michling | Resonant Photoemission at the O1s threshold to characterize β-Ga2O3 single crystals[END_REF]. As shown in Figure 3-7, there was found to be a clear correlation between the amount of states in the lower half of the bandgap and the p-type character in the sequence: n-type (Si-doped) commercial sample as a reference and our p-type layer. The n-type control sample is a commercial (Novel Crystal Technology, Inc.) nominally n-type Si-doped β-Ga2O3 (ND -NA = 1.3×10 18 cm -3 ) epitaxy (500 nm) grown on a single crystal β-Ga2O3 (labelled ''n-type (Sidoped)''). For β-Ga2O3 layer, the valence band edge is shifted towards more p-type using the Ga3d peak as the calibration peak (lower Fermi level implies more p-type character), see

Influence of the growth temperature on electrical properties

The influence of growth temperature (775 -825 °C) on electrical properties for undoped β-Ga2O3 has been investigated. The MOCVD growth parameters and the film thicknesses (determined by SEM cross-section) are summarized in

Zn doping in β-Ga2O3

Achieving p-type conductivity in β-Ga2O3 has been proven to be a great challenge.

Researchers have focused on identifying an efficient acceptor dopant, we have selected a II group element, zinc.

State of the art for Zn doping in β-Ga2O3

Theoretical works based on first principle calculations suggested that Zn doping (~ 2%)

does not change the basic electronic structure of β-Ga2O3, but only generates an empty energy level above the maximum of the valence band, which is shallow enough to make the Zn-doped β-Ga2O3 a typical p-type semiconductor [START_REF] Li | Electronic structures and optical properties of Zn-doped β-Ga 2O3 with different doping sites[END_REF]. However, for C. Zhang and co-authors, an atomic Zn concentration of ~ 2.5% has been estimated to introduce shallow levels above the valence band at around 0.33 eV [START_REF] Zhang | Electronic transport properties in metal doped beta-Ga2O3: A first principles study[END_REF]. However, several works proposed that Zn introduces a deep acceptor level at > 1.2 eV above the valence band maximum (ΔEVBM +1.2 eV) with a low activation rate [START_REF] Tang | Electronic structure and optical property of metal-doped Ga2O3: A first principles study[END_REF], which is difficult to contribute to the p-type conductivity [START_REF] Kyrtsos | On the feasibility of p-type Ga2O3[END_REF][START_REF] Lyons | A survey of acceptor dopants for β -Ga 2 O 3[END_REF]. It is worth noting that the difference may come from the computational methods but also the doping level (i.e., the superlattice size and the number of zinc atoms used). A high n-type conductivity was explained by a shallow donor complex Zni -ZnGa for Zn-doped β-Ga2O3 [START_REF] Hommedal | Trap-limited diffusion of Zn in β -Ga 2 O 3[END_REF]. Co-doping Zn-N has been predicted to offer shallow acceptor levels (0.01 -0.48 eV) above the VBM [START_REF] Yan | Reducing the acceptor levels of p-type β-Ga2O3 by (metal, N) co-doping approach[END_REF]Zhang et al., 2012b).

There are some experimental works dedicated to high amount (> 1%) Zn incorporation into β-Ga2O3 for different purposes such as improvement of oxygen gas sensing properties [START_REF] Li | Investigation of the oxygen gas sensing performance of Ga2O3 thin films with different dopants[END_REF], band gap engineering [START_REF] Guo | Decrease of oxygen vacancy by Zn-doped for improving solar-blind photoelectric performance in β-Ga2O3 thin films[END_REF][START_REF] Tao | Investigation of growth characteristics, compositions, and properties of atomic layer deposited amorphous Zn-doped Ga2O3 films[END_REF], enhancement of the photocatalytic activity [START_REF] Yamakata | Core-Shell Double Doping of Zn and Ca on β-Ga 2 O 3 Photocatalysts for Remarkable Water Splitting[END_REF].

For electrical properties induced by Zn doping, Feng et al. [START_REF] Feng | Catalytic growth and characterization of single crystalline Zn doped p-type β-Ga2O3 nanowires[END_REF] demonstrated the p-type conductivity using a p-n junction. Agnitron Technology Incorporated (USA) reported β-Ga2O3 Zn-doped thin films on c-sapphire by MOCVD the incorporation of 10.9 %. Zn XRD patterns yielded a mono-phase polycrystalline structure with an increase of lattice parameters with doping, though room temperature Hall measurements were not successful due to the very high resistivity of the samples (Alema et al., 2017a). Interestingly, [START_REF] Wang | Electrical properties and emission mechanisms of Zn-doped β-Ga 2O3 films[END_REF] studied the electrical characterization by Hall effect at room temperature for undoped and Zn doped β-Ga2O3 thin films, showed an electron concentration of 1.4×10 14 for undoped β-Ga2O3 layer, it was decreased to 7.2×10 11 cm -3 after 3 at. % Zn incorporation, and increased to 6.3×10 12 cm -3 with further increasing the nominal Zn content at 7 at. %. However, the authors could not validate the carrier type after Zn incorporation, which was attributed to the co-existence of comparable hole and electron concentrations. From cathodoluminescence measurements, the acceptor level of ZnGa is estimated to be 0.26 eV above the valence band maximum. Su et al. [START_REF] Su | Deep level acceptors of Zn-Mg divalent ions dopants in b-Ga2O3 for the difficulty to p-type conductivity[END_REF] deposited Mg-Zn (4.68 at. % (Mg)/ 11.1 at. % (Zn)) co-doped β-Ga2O3

on sapphire (0001), anti-site defect ZnGa was determined as deep acceptors at 0.79 eV by absorption spectra. Zn doping (10 at. %) in β-Ga2O3 has also been observed to stabilize the optical band gap and reduce the dielectric constant for atomic layer deposition (ALD) grown films [START_REF] Baji | Atomic layer deposition and characterization of Zn-doped Ga2O3 films[END_REF].

Experimental works reported about low doping cases (< 1 at. %) are relatively limited.

Shrestha et al. [START_REF] Shrestha | Self-organization and zinc doping of Ga2O3 nanoporous architecture: A potential nano-photogenerator for hydrogen[END_REF] studied the properties of 0.59% Zn-doped β-Ga2O3 nano-porous layers for photo-induced hydrogen generation. It has been concluded that the presence of a small amount of zinc doping in β-Ga2O3 can reduce trapping sites at the donor level under the conduction band, and thereby increase the mobility of electrons. On the other hand, zinc doping also creates additional trapping sites as acceptor levels over the valence band, which hampers the activation of holes. An improvement of photocatalytic activity by Zn doping (up to 1 atomic % of zinc) on H2O splitting is found and associated with the increase in the mobility and concentration of holes due to the formation of an acceptor level [START_REF] Sakata | Effect of metal ion addition in a Ni supported Ga2O3 photocatalyst on the photocatalytic overall splitting of H2O[END_REF]. Several recent works showed that Zn acts as an acceptor in β-Ga2O3

for 1.8 wt. % Zn doped thin film grown by Halide Vapor-Phase Epitaxy (HVPE), 0.25 at. % Zn doped bulk crystals by Czochralski (CZ) and vertical gradient freeze (VGF) techniques [START_REF] Gustafson | Zn acceptors in β-Ga2O3 crystals[END_REF]Jesenovec et al., 2021a;[START_REF] Pansegrau | Zinc-hydrogen and zinc-iridium pairs in β-Ga2O3[END_REF]. The authors [START_REF] Gustafson | Zn acceptors in β-Ga2O3 crystals[END_REF]Jesenovec et al., 2021a) proposed that Zn is a deep acceptor with an ionization energy of more than ~ 0.7 eV, and it takes preferentially Ga octahedral site. Such a discrepancy with the theoretical work [START_REF] Lyons | A survey of acceptor dopants for β -Ga 2 O 3[END_REF] that calculated that Ga tetrahedral site is favored for Zn substitution, was explained by the calculations on Ga3d states treatment.

Previously reported works on Zn doping in β-Ga2O3 showing acceptor characteristics are summarized in Table 3-3. To summarize, significant efforts have been dedicated to Zn doping in β-Ga2O3.

However, as expected and experimentally observed, Zn impurities role in β-Ga2O3 depends on various factors for both experimental and theoretical works. While deep levels related to Zn impurity have been identified, there was still a lack of direct evidence of the p-type behavior. Zn-induced donor Zni has been proposed theoretically and the increase in electron concentration has been observed experimentally, a comprehensive investigation is still required. The effect of Zn doping strongly depends on growth conditions and doping levels, thus, the aim of my work was to carry out a deep study related to Zn doping effect on electrical and optical properties of β-Ga2O3 thin films.

Thermodynamic analysis of point defects for Zn:Ga2O3 system

Zn, as a II group element, is expected to be an acceptor in β-Ga2O3. However, due to its similar atomic radii to Ga, as well as the similar ionic radii of Zn 2+ and Ga 3+ , it can also occupy an interstitial position acting as a donor. This amphoteric nature of Zn may be responsible for the so-called "impurity auto-compensation" effect. Similar auto- semiconductors such as Mg [START_REF] Miceli | Self-compensation due to point defects in Mg-doped GaN[END_REF][START_REF] Wahl | Lattice Location Studies of the Amphoteric Nature of Implanted Mg in GaN[END_REF] and Be [START_REF] Wahl | Direct evidence of Be as an amphoteric dopant in GaN[END_REF] in GaN and Zn in GaAs [START_REF] Longini | Rapid zinc diffusion in gallium arsenide[END_REF], I group elements doping in II-VI semiconductor ZnSe [START_REF] Neumark | Are impurities the cause of ''self''-compensation in large-band-gap semiconductors?[END_REF]. H.Peelaers et al. [START_REF] Peelaers | Deep acceptors and their diffusion in Ga2O3[END_REF] investigated several II elements (Be, Mg, Ca, Sr, Zn, Cd) doped in β-Ga2O3, the first-principle calculations based results revealed that all of them can be amphoteric. Later, after our experimental work (Chikoidze et al., 2020b), Zn and Ca doping in β-Ga2O3 have been studied taking both interstitial (Zni) and substitution (ZnGa) sites into account [START_REF] Hommedal | Trap-limited diffusion of Zn in β -Ga 2 O 3[END_REF][START_REF] Yamakata | Core-Shell Double Doping of Zn and Ca on β-Ga 2 O 3 Photocatalysts for Remarkable Water Splitting[END_REF]. A high n-type conductivity was explained by a shallow donor complex Zni -ZnGa based on the first-principle calculations [START_REF] Hommedal | Trap-limited diffusion of Zn in β -Ga 2 O 3[END_REF].

Therefore, prior to the investigation of Zn doping influence in β-Ga2O3, it is important to conduct the thermodynamic analysis of point defects for β-Zn:Ga2O3 system, to define the dependences of point defects concentration, charge carriers on growth temperature and oxygen partial pressure in the surrounding atmosphere.

The study of native point defects has been reviewed in Section 1.1.3 (Point defects studies and doping issues). Besides, as stated above, Zn can take both interstitial site (Zni)

and substitute Ga (ZnGa), together with the main acceptor defects in β-Ga2O3, gallium vacancy (VGa) have been considered here. The analysis was conducted using the Kroger method of quasi-chemical equations. In this approach, the creation of dominant defects and charge carriers are written as chemical reactions. The corresponding mass action laws, together with the electro-neutrality condition and impurity mass balance equation, give a system of equations for the concentrations of the main charged species (acceptor and donor defects, free electrons and holes) existing in the crystal as follow:

The lattice thermal ionization:

ø ⇆ 𝑒 + ℎ, 𝐾 𝑖 = 𝑛𝑝 (3 -5)
Where 𝑒 and ℎ are electrons and holes, respectively; n and p are their concentrations, respectively. Substitutional Zn transfer to interstitial position:

𝑍𝑛 𝐺𝑎 ⇆ 𝑍𝑛 𝑖 + 𝑉 𝐺𝑎 , 𝐾 𝑍𝑛 = [𝑍𝑛 𝑖 ][𝑉 𝐺𝑎 ] [𝑍𝑛 𝐺𝑎 ] (3 -6)
Where 𝑍𝑛 𝐺𝑎 , 𝑍𝑛 𝑖 , 𝑉 𝐺𝑎 denote zinc substituting gallium, zinc interstitial, and gallium vacancy, respectively. Ionizations of acceptor and donor impurities, and the native acceptor gallium vacancy:

𝑍𝑛 𝐺𝑎 ⇆ 𝑍𝑛 𝐺𝑎 ′ + ℎ, 𝐾 𝑎 = [𝑍𝑛 𝐺𝑎 ′ ]𝑝 [𝑍𝑛 𝐺𝑎 ] (3 -7) 𝑍𝑛 𝑖 ⇆ 𝑍𝑛 𝑖 • + 𝑒, 𝐾 𝑑 = [𝑍𝑛 𝑖 • ]𝑛 [𝑍𝑛 𝑖 ] (3 -8) 𝑉 𝐺𝑎 ⇆ 𝑉 𝐺𝑎 ′ + ℎ, 𝐾 𝐴 = [𝑉 𝐺𝑎 ′ ]𝑝 [𝑉 𝐺𝑎 ] (3 -9)
Where 𝑍𝑛 𝐺𝑎 ′ and 𝑉 𝐺𝑎 ′ denote positively single-charged zinc substituting gallium and gallium vacancies, respectively; [𝑍𝑛 𝐺𝑎 ′ ] and [𝑉 𝐺𝑎 ′ ] are their concentrations, respectively.

𝑍𝑛 𝑖

• is the negatively single-charged zinc interstitial with [𝑍𝑛 𝑖 • ] being the concentration.

Then, considering the interaction with environment, gas phase:

3 2 𝑂 2 ⇆ 3𝑂 𝑂 + 2𝑉 𝐺𝑎 , 𝐾 𝑉 𝐺𝑎 = [𝑉 𝐺𝑎 ] 2 𝑃 𝑂 2 3/2 (3 -10)
To find the concentration of defects and free carriers by the system of equations above, the charge-neutrality condition and mass balance equation are then added:

𝑛 + [𝑉 𝐺𝑎 ′ ] + [𝑍𝑛 𝐺𝑎 ′ ] = 𝑝 + [𝑍𝑛 𝑖 • ] (3 -11) [𝑍𝑛 𝑖 ] + [𝑍𝑛 𝑖 • ] + [𝑍𝑛 𝐺𝑎 ] + [𝑍𝑛 𝐺𝑎 ′ ] = [𝑍𝑛 𝑡𝑜𝑡 ] (3 -12)
Establish the equilibrium concentrations of electrons and holes, as well as impurities and defects in different charge states. Electro-neutrality and mass balance depend on the total Zn concentration ([𝑍𝑛 𝑡𝑜𝑡 ]), temperature (T) and pressure (𝑃 𝑂 2 ) in surrounding atmosphere.

The equilibrium was calculated using the total pressure of 30 Torr in the MOCVD chamber, which is the parameter we used in the experiments. Three regions depending on the impurity concentration were considered as a function of growth temperature as shown in Based on the thermodynamic analysis, it is possible to achieve p-type β-Zn:Ga2O3 thin films in all the three regimes by adjusting Zn concentration and growth temperatures. For example, at 800 °C, the acceptor defect ZnGa becomes dominant when Zn doping concentration exceeds ~10 14 cm -3 , and the impurity p-type conductivity occurs. As the Zn doping concentration further increases to ~10 18 cm -3 , Zn starts to occupy interstitial sites.

Both donor Zni and acceptor ZnGa defects compensate for each other, leading to the autocompensation regime.

Zn doped β-Ga2O3 thin films: experimental results

The objective was to elaborate Zn-doped β-Ga2O3 thin films, and study experimentally the effect of Zn doping on electronic and optical properties of the samples grown on c-plane Al2O3(0001) and on conducting Si(111) substrates simultaneously in the MOCVD reactor.

The conducting Si substrate was used to fabricate vertical parallel plane capacitors, and characterized them vertically in terms of breakdown voltage capability. While the thin films grown on c-sapphire substrates were used for the investigation of the electrical transport properties (resistivity, carrier, mobility). Firstly, results for β-Zn:Ga2O3//c-Al2O3 will be discussed. During the growth, the flow rate of the gallium precursor and oxygen were kept at 6 µmol/min and 600 sccm respectively. The growth temperature and pressure were set at 775 °C and 30 Torr, respectively. The DEZn flow was varied in the following conditions:

1.6, 2.8, 3.9 µmol/min. the growth conditions together with the thicknesses of the layers are summarized in the Zn:Ga2O3#3 3.8 90 (from low to high) were then determined to be 1.0×10 16 cm -3 , 1.4×10 18 cm -3 , and 2.0×10 19 cm -3 , respectively. The 1.0×10 16 cm -3 is close to the detection limit of SIMS equipment. The Zn distribution in the sample at a doping level of 2.0×10 19 cm -3 is homogeneous in depth.

Structural and morphological characterizations

For the convenience of writing and reading, these doping concentrations will be referred to 10 16 cm -3 , 10 18 cm -3 , and 10 19 cm -3 , respectively. To note that the Zn signal intensity corresponding to the doping concentration at 10 16 cm -3 is the detection limit.

Optical properties

Reflectance and transmittance measurements were conducted on both undoped and Zn- In general, optical properties can be modified in doped materials. After impurities are introduced into the crystal lattice of a semiconductor material, additional energy states can be created within the bandgap. A number of reports have investigated the optical properties of β-Zn:Ga2O3 films and single crystals, the optical band gap can be either slightly increased [START_REF] Baji | Atomic layer deposition and characterization of Zn-doped Ga2O3 films[END_REF], or slightly decreased [START_REF] Feng | Catalytic growth and characterization of single crystalline Zn doped p-type β-Ga2O3 nanowires[END_REF][START_REF] Guo | Decrease of oxygen vacancy by Zn-doped for improving solar-blind photoelectric performance in β-Ga2O3 thin films[END_REF][START_REF] Yue | Structural and optical properties of Zn-doped β-Ga 2 O 3 films[END_REF], or remained comparable of undoped one (Jesenovec et al., 2021a;[START_REF] Pozina | Doping of β-Ga2O3 Layers by Zn Using Halide Vapor-Phase Epitaxy Process[END_REF]; X.H. Wang et al., 2014). When incorporated Zn concentration becomes more significant (> 10%), the influence on the optical band gap will be even more apparent, either increased [START_REF] Tao | Investigation of growth characteristics, compositions, and properties of atomic layer deposited amorphous Zn-doped Ga2O3 films[END_REF] (due to Burnstein-Moss effect) or decreased [START_REF] Zhao | Improvement for the performance of solar-blind photodetector based on β-Ga 2 O 3 thin films by doping Zn[END_REF], while keeping the Ga2O3 structure. To note that the difference between the values of optical Eg here and that we reported [START_REF] Chikoidze | Electrical properties of p-type Zn:Ga2O3 thin films[END_REF], comes from two different estimation methods. The optical band gaps were firstly estimated using the Beer-Lambert law [START_REF] Chen | The Use of UV-visible Spectroscopy to Measure the Band Gap of a Semiconductor[END_REF], which allows us to calculate the absorption from the transmittance as the films were transparent and only weakly reflected to the eye, at normal incidence. The reflectance of the films was remeasured later with a longer acquisition time, the optical Eg was then recalculated based on both reflectance and transmittance measurements.

Electrical transport properties

The first step as always was to prepare electrical contacts and test their Ohmicity. The contacts were prepared by painting the silver paste at 4 corners of square-shaped samples in a Van der Pauw configuration as described in the methodology chapter, and in the previous section.

The This result is coherent with Figure 3-9, suggesting that for the doping concentration at 10 16 cm -3 , the impurity hole conduction might be prevalent. Similar to the previous section, the ionization energy of the acceptor centers can be obtained from a linear regression on a ln(pT - It is interesting to compare our results with a recently published report regarding electrical properties of [Zn] = 1.5 ×10 18 cm -3 doped Ga2O3 bulk crystals: Jesenovec et al. (Jesenovec et al., 2021a) stated that Zn introduced deep acceptor with trapping levels at ∼1.3 and ∼0.9 eV above the valence band for one and two holes, respectively, and crystals were insulating. It is supposed that such extremely high resistivity is most probably related to the number of high level unintentional compensating donor impurities presented in the crystal. Contrary to low level doped β-Ga2O3 layers, when the incorporated Zn concentration exceeded 10 18 cm -3 , the resistivity was slightly increased as depicted in Figure 3-16 (a), all films showed normal behavior of semi-insulating material, indicating that Zn is not an effective acceptor dopant at these doping levels. For the [Zn] = 10 18 cm -3 doped β-Ga2O3 sample, at 800 K, the resistivity and hole concentration was determined to be ρ = 9.1×10 3 Ω•cm, p = 6.7×10 13 cm -3 , respectively (vs. ρ = 4.0×10 3 Ω•cm, p = 2.2×10 14 cm -3 for the undoped β-Ga2O3 layer). The activation energy of conductivity was determined to be 0.99 ± 0.01 eV.

Now, I will focus on the sample with [Zn] = 10 19 cm -3 . At 840 K, Hall effect measurements showed a slight decrease of hole concentrations p = 2.1×10 14 cm -3 compared to 5.5×10 14 cm -3 for the undoped sample (Figure 3-16 (c)). Indeed, if the auto-compensation mechanism takes place, Zn dopant cannot increase p-type conductivity, even more, as we see in the experiment, the "amphoteric" nature of Zn can lead to a decrease in charge carriers.

This result corresponds well to the thermodynamic analysis discussed in Section 3.

Critical electric field

The critical electric field (ECR) is a crucial parameter in the characterization of a material's electrical properties, especially for high voltages operating. It is defined as the maximum electric field that a material can withstand before undergoing an avalanche breakdown. Representative values of the critical electric field for the most common power electronics semiconductors, such as silicon (0.3 MV/cm), 4H-SiC (3.5 MV/cm) [START_REF] Trew | Deep-ultraviolet Schottky photodetectors with high deep-ultraviolet/visible rejection based on a ZnGa2O4 thin film[END_REF], GaN (3.9 MV/cm) [START_REF] Fischer | High voltage and high current density vertical GaN power diodes[END_REF], or AlGaN (5.9 MV/cm [START_REF] Allerman | Al0.3Ga0.7N PN diode with breakdown voltage >1600[END_REF]) are well known. For other UWBG such as AlN, the 𝐸 𝐶𝑅 values have also been reported ( 12MV/cm [START_REF] Chu | The Preparation and Properties of Aluminum Nitride Films[END_REF]) while a generally agreed theoretical value for diamond is 10 MV/cm [START_REF] B ; Wort | Diamond as an electronic material[END_REF]. For β-Ga2O3, a common estimation, associated to the band gap value, given in the literature is ~ 8 MV/cm [START_REF] Higashiwaki | Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates[END_REF]. Later, Ghosh and

Singisetti (Ghosh and Singisetti, 2018a[START_REF] Bose | Power Electronics in Smart Grid and Renewable Energy Systems[END_REF][START_REF] Haynes | CRC Handbook of Chemistry and Physics[END_REF] diodes with different thicknesses (7.5 and 13 µm) of β-Ga2O3 layer. The breakdown voltages were 5.1 and 8.32 kV, respectively, and the corresponding breakdown fields are 6.45 and 6.2

MV/cm, respectively.

Impact ionization

This dielectric breakdown capability depends on the free charges (related to native defects or dopants) but also on the semiconductor's fundamental properties (such as bandgap energy Eg) and the impact ionization parameters. Impact ionization occurs when an electron or a hole acquires sufficient energy from an external electric field and collides with a semiconductor's crystal lattice, producing an electron-hole pair (i.e., two electrons and a hole in place of the initial electron, or two holes and an electron in place of the initial hole) (as illustrated in Figure 3-17). At low electric fields, the electron energy distribution stabilizes as the energy gained from the external electric field is offset by energy loss from collisions [START_REF] Sun | The intrinsic electrical breakdown strength of insulators from first principles[END_REF]. However, as the electric field strength surpasses a certain threshold (i.e., the critical electric field ECR), this process can result in an avalanche effect, where the newly generated carriers gain enough energy to produce further electron-hole pairs, leading to the subsequent multiplication of carriers. In turn, the avalanche breakdown occurs. There are two main types of impact ionization: band-to-band impact ionization and trap-to-band impact ionization. Band-to-band impact ionization (Ghosh and Singisetti, 2018a) occurs when an electron in the conduction band gains enough energy from the electric field to overcome the band gap and enter the valence band. This process generates an electron-hole pair and releases energy. The newly created electron can then gain energy and produce additional electron-hole pairs, leading to a cascade effect. On the other hand, trap-to-band impact ionization [START_REF] Yakimov | Role of hole trapping by deep acceptors in electron-beam-induced current measurements in β-Ga 2 O 3 vertical rectifiers[END_REF] involves the excitation of an electron from a deep trap level to the conduction band. The domination between these two processes depends on several factors such as the density of trap states, band gap energy, and the external electric field strength. For example, at medium or high field strengths the band-to-band contribution may be expected to dominate. While the trap-to-band can occur at lower electric fields than band-to-band impact ionization and can be important in materials with a high density of states within the gap (Robbins, 1980a(Robbins, , 1980b)).

Figure 3-17. Schematic illustration of the impact ionization process (in the case of electron).

In a strong electric field, the probability of impact ionization for electrons is mainly determined by the likelihood that the electron will gain an amount of energy equal to the ionization threshold energy from the field. The electron's energy increase depends on how much it is accelerated by the external field and how much energy is lost through collisions.

According to theoreticians [START_REF] Keldysh | Kinetic Theory of Impact Ionization in Semiconductors[END_REF], there are two possibilities for an electron to acquire this energy, either by receiving it from the field without experiencing any collision or gradually through many collisions with less energy lost than gained in each collision.

Therefore, the mean free path that determines the average distance that a carrier must travel to obtain sufficient energy for ionization, plays a crucial role [START_REF] Keldysh | Kinetic Theory of Impact Ionization in Semiconductors[END_REF][START_REF] Wolff | Theory of Electron Multiplication in Silicon and Germanium[END_REF].

This parameter together with the effective mass can be influenced by the energy band structure of the material. Consequently, the impact ionization coefficients of electrons and holes can be different, and depend on the crystallographic directions of a semiconductor (e.g., Si, Ge, GaAs, InP [START_REF] Anderson | Threshold Energies for Electron-Hole Pair Production by Impact Ionization in Semiconductors[END_REF][START_REF] Bude | Thresholds of impact ionization in semiconductors[END_REF]). Monoclinic β-Ga2O3 has a low symmetry, the effective mass of holes can be quite anisotropic as reported [START_REF] Mock | Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3[END_REF], it also explains the crystallographic direction dependence of the critical electric field (Ghosh and Singisetti, 2018a) as mentioned above. For example, the hole effective mass is fairly anisotropic in 𝑎 ⃗, 𝑏 ⃗⃗ , and 𝑐 ⃗ directions in the first and topmost valence band: 𝑚 ℎ,𝑎 * = 1.77𝑚 0 , 𝑚 ℎ,𝑏 * > 10𝑚 0 , and 𝑚 ℎ,𝑐 * = 0.41𝑚 0 for the first and topmost valence band [START_REF] Mock | Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3[END_REF].

To summarize, a higher critical electrical field (EBR) for a material can be expected with a lower impact ionization coefficient. Additionally, the critical electrical field strength is also dependent on doping density, in an inverse proportion. Therefore, for the same materials, we can expect a higher critical electrical field (EBR) at lower density and a shorter mean free path of free carriers.

Experiment results and discussion

To estimate experimentally the critical electric field, undoped and Zn-doped β-Ga2O3 layers on conductive B-doped Si(111) substrate were simultaneously carried out with the growth on the insulating c-plane sapphire substrate. Recall, the objective of the growth on conducting Si substrate (ρ < 0.01 Ω•cm) is to fabricate a parallel plane capacitor, to carry out the breakdown voltage measurements, and estimate the critical electric field in this simple vertical structure. While the β-Zn:Ga2O3//c-Al2O3 was used for the electrical measurements which were presented in the previous sub-sections.

Summary

The results in Section 3.3 can be summarized as follow:

Zn can be successfully incorporated in β-Ga2O3 thin films with the doping levels of 10 16

-10 19 cm -3 without the appearance of transition peaks or secondary phase by MOCVD, while maintaining a high transparency (~80%) in vis-NIR wavelength range and an ultra-wide band gap (with a cut-off wavelength of 260 -266 nm). When [Zn] > 10 21 cm -3 , the β-Zn:Ga2O3 thin film was amorphous. (i) When Zn = 10 16 cm -3 , the p-type conductivity can be enhanced in β-Ga2O3. The origin is attributed to the substitution defect ZnGa with an ionization energy of Ei = 0.77 eV.

It is direct evidence that the Zn is an acceptor dopant in β-Ga2O3.

(ii) With the increasing doping level when [Zn] > 10 18 cm -3 , Zn is not an effective acceptor dopant, the "auto compensation" effect takes place, resulting in a decrease in hole concentration.

(iii) On the base of impact ionization theory, we hypothesized that the critical electric field can be increased by reducing the impact ionization probability (shortening the mean free path of free carriers, decreasing the carrier concentration). Taking advantage of the "auto compensation" effect of Zn doping, breakdown voltage measurements were carried out for parallel capacitors based on β-Ga2O3//Si and β-Ga2O3:Zn//Si structures. The corresponding critical electric fields were deduced to be ECR = 5.7 and 13.2 MV/cm, respectively.

ZnGa 2 O 4 : Experimental Results and Discussion

In this chapter, I will focus on the characterizations of the spinel zinc gallate (ZnGa2O4) thin films grown by metal-organic chemical vapor deposition (MOCVD) on c-plane sapphire substrates. With the increasing Zn incorporation in β-Ga2O3 (Zn at. % > 6.85%), the spinel ZnGa2O4 starts to form. In the first section (Section 4.1), I will discuss the transformation of pure β-Ga2O3 to a mixed phase of β-Ga2O3 and ZnGa2O4, later to pure ZnGa2O4 spinel. The bipolar dopability (n-type and p-type) was theoretically predicted for ZnGa2O4 (Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF]. Experimentally, the first p-type (at high temperature) ZnGa2O4 thin films have been reported by colleagues in GEMaC (Chikoidze et al., 2020a). The conductivity was attributed to ZnGa anti-site defect with an ionization energy of carriers Ei = 0.93 eV. Besides, native n-type conductivity (n = 10 20 cm -3 ) in ZnGa2O4 thin films has been shown [START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF], but the origin of conductivity and the conduction mechanism are still open questions. In Section 4.2, I show a comparative analysis of structural, optical, chemical, and electrical measurements for native semi-insulating p-type and highly conducting n-type ZnGa2O4 thin films grown by the MOCVD technique. In Section 4.3, the influence of oxygen content during the growth on the electrical properties of ZnGa2O4 thin films will be discussed. In the last section of this chapter (Section 4.4), the breakdown voltage measurements for the assessment of the critical electric field will be shown.

From β-Ga2O3 to ZnGa2O4: structural characterizations

The objective was to study the structural transformation of β-Ga2O3 thin films from monoclinic structure to cubic spinel ZnGa2O4, with increasing Zn incorporation. A series of samples with different Zn precursor flows were grown on both c-sapphire and conducting Si(111) substrates using the MOCVD technique. Same as in Chapter 3, the electrical transport measurements were carried out on the films grown on insulating sapphire substrates, while Ga2O3:Zn//Si was elaborated to fabricate parallel plane capacitors, to conduct the breakdown voltage measurements.

During the film deposition, the O2 flow was set at 1200 sccm, the oxygen partial pressure was estimated to be 12 Torr. The Zn precursor flow was ranging (3.88 -8.9

µmol/min). The growth parameters, Zn content in the films determined by EDX, and the thicknesses are summarized in Table 4-1. Ga2O3 (Alema et al., 2017a;[START_REF] Horng | Epitaxial Growth of ZnGa 2 O 4 : A New, Deep Ultraviolet Semiconductor Candidate[END_REF]. Although the observed XRD families of the Bragg reflections of monoclinic and spinel cubic are compatible, their distinct lattice symmetries result in different vibrational modes of Raman scattering. ZnGa2O4 exhibits mainly A1g (709.7 cm -1 ) and T2g (603.1 cm -1 ) vibration modes (Figure 4-2), in good agreement with previously reported work [START_REF] López-Moreno | Lattice dynamics of ZnAl2O4 and ZnGa2O4 under high pressure[END_REF][START_REF] Relvas | Trends in Cr3+ red emissions from ZnGa2O4 nanostructures produced by pulsed laser ablation in a liquid medium[END_REF]. Besides, it is interesting to note that the vibration mode Eg at 397.2 cm -1 for cubic spinel ZnGa2O4 observed in the mixed phase disappeared in the pure spinel, it needs further investigation.

Bipolar self-doping in ultra-wide band gap spinel ZnGa2O4

As mentioned in Section 1.2 (state of the art for ZnGa2O4), the doping centers in spinel oxide are specific because of crystalline symmetry (interstitials and anti-sites). According to theoretical calculation, both n-type and p-type can be achieved for spinel ZnGa2O4 (Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF] by the intrinsic antisite defects (GaZn or ZnGa, respectively) through the cations inversion, while tuning the cations quantity. Such disordered distribution of cations belongs to the so-called "self-doping" effects [START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF][START_REF] Zhang | Self-doping of cadmium stannate in the inverse spinel structure[END_REF].

As natural for an ultra-wide bandgap oxide Fermi level lying near the mid-gap, poor conductivity (if any) has been found for undoped as-grown ZnGa2O4 thin films [START_REF] Horng | Epitaxial Growth of ZnGa 2 O 4 : A New, Deep Ultraviolet Semiconductor Candidate[END_REF][START_REF] Krishna | ELECTRICAL AND OPTICAL PROPERTIES OF ZnGa2O4 THIN FILMS DEPOSITED BY PULSED LASER DEPOSITION[END_REF][START_REF] Yan | Electrical Conductivity in Transparent ZnGa2O4: Reduction and Surface-Layer Structure Transformation[END_REF]. However, high electron conductivity was already reported in the past for hydrogen annealed ZnGa2O4 thin films [START_REF] Krishna | ELECTRICAL AND OPTICAL PROPERTIES OF ZnGa2O4 THIN FILMS DEPOSITED BY PULSED LASER DEPOSITION[END_REF][START_REF] Omata | New ultraviolet-transport electroconductive oxide, ZnGa 2 O 4 spinel[END_REF]. Besides, intrinsic donor electron conductivity has also been reported for some bulk blue colored crystals [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF] thin films grown by pulsed laser deposition (PLD) [START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF], and metal-organic chemical vapor deposition (MOCVD) (L. C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF]. In these conducting ultra-wide transparent conducting oxides (TCOs), different electron concentrations ranging from 5.9×10 16 cm -3 [START_REF] Horng | Epitaxial Growth of ZnGa 2 O 4 : A New, Deep Ultraviolet Semiconductor Candidate[END_REF][START_REF] Shen | Characterizations of Metal-Oxide-Semiconductor Field-Effect Transistors of ZnGaO Grown on Sapphire Substrate[END_REF]W.-K. Wang et al., 2019a) to 6.16×10 19 cm -3 [START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF] have been reported. The n-type conductivity was usually explained by the presence of oxygen vacancies (Kim et al., 2004;[START_REF] Krishna | ELECTRICAL AND OPTICAL PROPERTIES OF ZnGa2O4 THIN FILMS DEPOSITED BY PULSED LASER DEPOSITION[END_REF][START_REF] Omata | New ultraviolet-transport electroconductive oxide, ZnGa 2 O 4 spinel[END_REF][START_REF] Yan | Electrical Conductivity in Transparent ZnGa2O4: Reduction and Surface-Layer Structure Transformation[END_REF], but they are well-known to arguably be deep centers in ZnGa2O4 [START_REF] Pandey | Atomistic Simulation Study of Spinel Oxides: Zinc Aluminate and Zinc Gallate[END_REF]Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF]. Although these observations and that a bunch of theoretical works deals with the issue [START_REF] De Vos | First-Principles Study of Antisite Defect Configurations in ZnGa 2 O 4 :Cr Persistent Phosphors[END_REF][START_REF] Stoica | P-type zinc oxide spinels: application to transparent conductors and spintronics[END_REF][START_REF] Xia | Theoretical and Experimental Investigations on Effects of Native Point Defects and Nitrogen Doping on the Optical Band Structure of Spinel ZnGa 2 O 4[END_REF], the actual phenomenological origin and mechanisms of the ZnGa2O4 spinel self-doping remain elusive.

It should be underlined that experimentally, study related to p-type ZnGa2O4 is very limited so far. It has been demonstrated the first time by GEMaC colleagues, a native hightemperature p-type conductivity for ZnGa2O4 thin films elaborated by MOCVD (Chikoidze et al., 2020a). The conductivity was attributed to antisite defects ZnGa with an ionization energy of carriers around Ei = 0.93 eV (Chikoidze et al., 2020a).

The objective of my study in the framework of collaborative (several labs) work was to determine the origin of the n-type conductivity in ZnGa2O4 layer mechanism of conduction and later to make a comparative analysis of native p-type and n-type ZnGa2O4 thin films by a range of spectroscopic and transport measurement techniques.

All ZnGa2O4//c-sapphire thin films were grown by MOCVD in GEMaC and in National Chiao Tung University. The growth condition as well as the thicknesses of the layers are summarized in

Structural studies of n-type and p-type ZnGa2O4 thin films

Electronic properties of n-type and p-type ZnGa2O4 thin films

X-ray photoelectron spectroscopy (XPS) measurements were carried out by Dr.

Mathieu Frégnaux at Institute Lavoisier de Versailles (ILV), UFR des Sciences at Versailles.

It was used firstly to identify the potential impurities contamination. grown by MOCVD always contain a certain amount of carbon contamination from organometallic precursors used during the growth (Y. Chen et al., 2015;Kim and Kim, 2004;[START_REF] Takiguchi | Effect of post-deposition annealing on low temperature metalorganic chemical vapor deposited gallium oxide related materials[END_REF], it can be largely reduced by post-annealing treatment.

Besides, Na measured is merely trace elements in the sample. The conclusion is that there are no external impurities with important quantities except carbon on the surface. was used as calibration for all the spectra in the absence of a better procedure [START_REF] Greczynski | X-ray photoelectron spectroscopy: Towards reliable binding energy referencing[END_REF]. One first observation is that, regardless of whether is nor p-ZnGa2O4, the Ga and Zn core level binding energies (BEs) are larger for spinel ZnGa2O4 (the complex oxide from binary Ga2O3:ZnO) than for either, reference monoclinic β-Ga2O3 (p-type) and wurtzite ZnO (n-type), which is a result consistent with previous literature. It is customary to attribute the cation's shift towards higher binding energies to larger oxidation states although, in theory, the Zn 2+ and Ga 3+ are in the same oxidation state in ZnGa2O4, Ga2O3, and ZnO. For example, the Ga2p3/2 peak in reference monoclinic Ga2O3 appears at a smaller binding energy of 1117.6 eV which perhaps may be understood because of the reduced coordination of half of the metal ions. There are two kinds of coordination for Ga 3+ ions in β-Ga2O3 structure, namely tetrahedral Td and octahedral Oh whose average inter-ionic distances are the following [START_REF] Geller | Crystal Structure of β-Ga2O3[END_REF] eV for n-ZnGa2O4, respectively. Therefore, it can be concluded that the effect of self-doping in the ZnGa2O4 cation's shift on Zn2p (BE ~0.2 eV) and Ga2p (BE ~0.1 eV) is rather small (when compared with the ZnGa2O4 vs Ga2O3 or ZnO energy shifts BE ~0.7 eV). In contrast to simple binary oxides, where dominant defects are vacancies and interstitials, dominant defects in spinels are suggested to be antisites [START_REF] Perkins | Inverse design approach to hole doping in ternary oxides: Enhancing p -type conductivity in cobalt oxide spinels[END_REF][START_REF] Zakutayev | Cation off-stoichiometry leads to high p -type conductivity and enhanced transparency in Co 2 ZnO 4 and Co 2 NiO 4 thin films[END_REF]. These antisites are donor (GaZn) [donor-like Ga 3+ (Oh)-on-Td antisite defects] and acceptor (ZnGa) [acceptor-like Zn 2+ (Td)-on-Oh antisite defects]. The degree of inversion in zinc gallate has been estimated by the deconvolution of the Ga2p and Zn2p XPS peaks in two components at different binding energies (BEs) [START_REF] Li | Cation distribution dependence of magnetic properties of sol-gel prepared MnFe2O4 spinel ferrite nanoparticles[END_REF]. For p-ZnGa2O4, Ga2p3/2 and peak appears at 1118.2 eV. By deconvolution, a normal Ga 3+ (Oh) and an inversion Ga 3+ (Td) appear at 1118.3 eV and 1116.8 eV, respectively. Whereas a Zn2p3/2 normal Zn 2+ (Td) and an inversion Zn 2+ (Oh) are at ~1022 eV and ~1023 eV, respectively. The inversion sites ZnGa and GaZn could be estimated to ~5.3% and ~2.8% of the total area of Zn2p3/2 and Ga2p3/2, respectively (Chikoidze et al., 2020a). Nevertheless, the binding energy curve of Zn2p and Ga2p of n-ZnGa2O4 is well symmetric, indicating a unique chemical contribution on each atomic binding energy implying that the antisite defects are either, too few to be detected or inexistent. This already suggests a different origin for the self-doping in the case of donors and acceptors. and Ga2O3 appears at the same energy (~531 eV). There is also a clear difference in the O1s shoulder features between n-ZnGa2O4 and p-ZnGa2O4 which is clearly visible for n-ZnGa2O4

(as for n-ZnO) and much smaller for p-ZnGa2O4 (as for p-Ga2O3). Interestingly, the most notable difference between n-type and p-type ZnGa2O4 precisely is found in the shape of the O1s. A double feature at higher binding energy can be seen clearly in the n-ZnGa2O4 peak.

In zinc oxide thin films (but also in many other metal-oxide semiconductors), this oxygen shoulder (OII) has been related to hydroxide [START_REF] Marrani | Electrochemically deposited ZnO films: an XPS study on the evolution of their surface hydroxide and defect composition upon thermal annealing[END_REF], hydrate [START_REF] Majumder | Investigations on solution derived aluminium doped zinc oxide thin films[END_REF] or oxygen deficiency [START_REF] Kumar | Origin of the red emission in zinc oxide nanophosphors[END_REF]. The absence of shoulder features in p-

ZnGa2O4 and p-Ga2O3

O1s may be correlated with a lower donor compensation (e.g. very low concentration of oxygen vacancies). In n-type ZnGa2O4, the O1s lattice peak appears at 530.9 eV, and the shoulder maxima was found at 532.1 eV (Figure 4-6 (e)). Again, according to the interpretation proposed by [START_REF] Dupin | Systematic XPS studies of metal oxides , hydroxides and peroxides[END_REF][START_REF] Wu | Method for estimating ionicities of oxides using O1s photoelectron spectra[END_REF], the lower BE peak is assigned to O 2-ions, the middle BE peak to O 1-ions, and the higher BE peak to OChem, chemically adsorbed oxygen on the surface. In any case, based on the observables, the degenerated n-type ZnGa2O4 doping has a minimum impact on core Ga2p, a moderate impact on core Zn2p, and, a clear impact on the core O1s shoulder features. A simple coherent explanation of these facts implies Ga vacancies and modified Zn-O hybridization.

XPS atomic quantification suggests an oxygen-deficient scenario with oxygen/metal ratio of ~1, and, perhaps more trustable, Ga/Zn was determined to be ~1.9, revealing the Zinc-rich condition of n-ZnGa2O4. However, recall again that no signature of ZnO has been found structurally either by XRD or by TEM analysis and that n-ZnGa2O4 is considered a pure spinel in nature. ZnGa2O4. However, considering an electronic bandgap of ~5 eV for n-ZnGa2O4, the Fermi level is still around ~1.9 eV from the conduction band edge (Ec). Thus, this would not explain the high concentration of free carriers at room temperature for n-ZnGa2O4. A plausible explanation for the room temperature conductivity of n-ZnGa2O4 is the formation of an impurity conductive band [START_REF] Kabilova | Observation of impurity band conduction and variable range hopping in heavily doped (010) β -Ga 2 O 3[END_REF] as revealed by optical spectroscopy. . Such an absorption band has been already reported in conducting thin films [START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF] without clear identification of the origin. Interestingly, other groups have observed PL emissions peaking at 340 nm in zinc gallate and this emission has been associated with Ga 3+ ions substitution into the Zn 2+ ions site (W.-K. Wang et al., 2019bWang et al., , 2019a)). Our results suggest however that, rather than GaZn antisites, this absorption at 360 nm (~3.4 eV) might be associated with Zn atoms having strong bond with oxygen, leading to Zn-O hybridization. The position of this band agrees with the findings from XPS analysis (location of Fermi level). At high doping levels, the neighboring impurities have overlapping wave functions causing the single donor level to split and turn into a band, known as an impurity band. The states in the impurity band are localized, resulting in electron transport that is dominated by tunneling and hopping [START_REF] Kabilova | Observation of impurity band conduction and variable range hopping in heavily doped (010) β -Ga 2 O 3[END_REF] as we will demonstrate in the following section. As the layer's resistance below 500 K exceeded the measurement limit of our set-up (~ 5×10 10 Ω), the measurement was performed only at high temperatures (500 -850 K). The pure p-ZnGa2O4 thin film is highly resistive: ρ = 1.3×10 3 Ω•cm with a hole concentration of p = 1.6×10 15 cm -3 at 850K. This p-type conductivity was explained by the fact of self dopability, ie. presence of acceptor antisite (ZnGa) defects (Chikoidze et al., 2020a). Though, conductivity is quite low, indicating that those samples are of low inversion degree of cations, still not very far from stoichiometric composition. The measured mobilities were between 7 -10 cm 2 /(V•s), high values for this temperature range. Further work is required to find growth condition with enhancing possibility of acceptor ZnGa defects formation, leading to higher hole conductivity.

Valence Band and Optical

Electrical Transport properties of n-and p-ZnGa2O4 layers

Very differently, for n-type ZnGa2O4 190 nm film at room temperature, Van Der Pauw configuration resistivity was found to be exceptionally low: ρ = 3.2 × 10 -2 Ω•cm. Hall effect measurement at 300 K with magnetic field of 1.6 T reveals an electron concentration of n = 3.7 × 10 19 cm -3 , and a mobility of μ = 5.3 cm 2 V -1 s -1 . Additionally, the Seebeck Effect has confirmed n-type conductivity of the thin layer, with a Seebeck coefficient of S300K = -30.2 μV/K. Oxygen vacancies are traditionally considered the source of electrons in semiconductor oxides and for ZnGa2O4 spinel the same origin has already been proposed in several works (Kim et al., 2004;[START_REF] Krishna | ELECTRICAL AND OPTICAL PROPERTIES OF ZnGa2O4 THIN FILMS DEPOSITED BY PULSED LASER DEPOSITION[END_REF][START_REF] Omata | New ultraviolet-transport electroconductive oxide, ZnGa 2 O 4 spinel[END_REF][START_REF] Yan | Electrical Conductivity in Transparent ZnGa2O4: Reduction and Surface-Layer Structure Transformation[END_REF].

However, oxygen vacancy as a native Frenkel type defect is supposed to be a deep level defects in ultra-wide bandgap ZnGa2O4 [START_REF] Pandey | Atomistic Simulation Study of Spinel Oxides: Zinc Aluminate and Zinc Gallate[END_REF]Paudel et al., 2011b;[START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF], thus it cannot be the origin of high electron concentrations at room temperature.

To elucidate the mechanism of conductivity, the temperature dependence electrical transport measurements of the n-type ZnGa2O4 has been carried out in four-point aligned configuration by physical property measurement system (PPMS-9T), Figure 4-9 (a). The resistivity values are 2.7 -6.9 × 10 -2 Ω•cm for 2 -300 K. The resistivity is almost invariant in the 100 -300 K temperature range, while exhibiting a tendency to increase when T < 100 K. To the best of our knowledge, such highly conducting thin films have only been reported by D. Look et al. [START_REF] Look | Electrical and optical properties of degenerate and semi-insulating ZnGa2O4 : Electron/phonon scattering elucidated by quantum magnetoconductivity[END_REF], ρ = 4.2 × 10 -2 Ω•cm for a PLD deposited sample, and ρ = 5.6×10 -3 Ω•cm for a MOCVD grown sample (L. C. [START_REF] Cheng | Thickness effect on operational modes of ZnGa2O4 MOSFETs[END_REF][START_REF] Shen | Characterizations of Metal-Oxide-Semiconductor Field-Effect Transistors of ZnGaO Grown on Sapphire Substrate[END_REF].

Observing such a high electrical conductivity in ultra-wide bandgap material, one can think about surface conduction caused by the charge accumulation [START_REF] Vasheghani Farahani | Valence-band density of states and surface electron accumulation in epitaxial ${\mathrm{SnO}}_{2}$ films[END_REF]K. H. L. Zhang et al., 2013). Though we are discarding this hypothesis since it is not observed any signature of surface 2D conductivity (decrease resistivity with temperature and hockey-stick shape of ρ(T) (E. Chikoidze et al., 2019;[START_REF] Gu | Two-Dimensional Mott Insulators in SrVO3 Ultrathin Films[END_REF][START_REF] Halim | Transparent Conductive Two-Dimensional Titanium Carbide Epitaxial Thin Films[END_REF][START_REF] Nistor | Metalsemiconductor transition in epitaxial ZnO thin films[END_REF][START_REF] Noun | Correlation between electrical and ellipsometric properties on high-quality epitaxial thin films of the conductive oxide LaNiO3 on STO (001)[END_REF]. Thus, the only probable explanation for such high electrical conduction can be the so-called self-doping effect. The last features have a great similarity with ZnO, while the material is structurally ZnGa2O4. Indeed, the defect-defect interaction has already been considered of natively ntype conductivity ZnO. This interaction is driven by the quantum mechanical hybridization between two donor-like defects, the deep donor oxygen vacancy VO and the shallow donor zinc interstitial Zni [START_REF] Asghar | Investigation of VO-Zni native donor complex in MBE grown bulk ZnO[END_REF][START_REF] Kim | Rich Variety of Defects in ZnO via an Attractive Interaction between O Vacancies and Zn Interstitials: Origin of n -Type Doping[END_REF]. This interaction happens in our Zn-rich and O-deficient zinc gallate, and significantly reduces the total energy of the system, leading to a high electron concentration of Zni [START_REF] Kim | Rich Variety of Defects in ZnO via an Attractive Interaction between O Vacancies and Zn Interstitials: Origin of n -Type Doping[END_REF]. Even Zni though they are not as energetically favorable as antisite defects ZnGa and GaZn in stoichiometric ZnGa2O4 (Paudel et al., 2011b;[START_REF] Zhang | Diagrammatic Separation of Different Crystal Structures of A2BX4 Compounds Without Energy Minimization: A Pseudopotential Orbital Radii Approach[END_REF]). An energy level is introduced by these defects within the gap, mainly 3.4 eV from the valence band (determined from XPS valence band tails and optical spectrum). Evidently, this donor level is relatively deep (bandgap Eg = 4.9 eV) and cannot be activated at room temperature, thus being the source of free carriers. Consequently, we suppose that observed room temperature electrical conductivity might be rather due to localized carriers within the defect band, as it happens for impurity conduction for highly doped semiconductors.

We have analyzed the electrical transport properties considering this hypothesis.

Localization of free carriers leads to different hopping mechanism depending on temperature regions. Indeed, two slopes could be distinguished by log(σ) versus 1/T plot (σ = 1/ρ). As

shown by Figure 4-10 (a), the first "high temperature" interval corresponds to nearestneighbor hopping (NNH) conduction. The conductivity in the nearest-neighbor hopping regime can be simply described by the expression σ(T)= σ0T -1 exp(-ε/KBT) [START_REF] Shklovskii | Electronic Properties of Doped Semiconductors[END_REF], where σ0 being a function of the impurity concentration is independent of the temperature T, kB is the Boltzmann constant, ε is an activation energy for hops from one site to the nearest one in the impurity band, it is temperature independent and was estimated as Ea = 20.9 meV (Figure 4-10 (a)). With lower temperatures (< 100 K), electrons do not have enough energy to hop at the nearest-neighbor sites. Thus, the variable range hopping (VRH)

takes place and as it is shown in Figure 4-10 (b), the conductivity in this temperature interval can be well fitted with T -1/4 dependence, corresponding to Mott's VRH mechanism.

As has been demonstrated, in undoped non-stoichiometric n-type ZnGa2O4 the selfdoping effect is due to hybridization between zinc and oxygen orbitals. Such a rich number of point defects usually lead a system disorder where the periodic potential in the crystal structure is destroyed. Other hand, such a disorder could lead to carrier localization which is the so-called Anderson's localization, and the high level of the disorder can induce a metal to insulator transition (MIT) [START_REF] Anderson | Absence of Diffusion in Certain Random Lattices[END_REF][START_REF] Siegrist | Disorder-induced localization in crystalline phase-change materials[END_REF][START_REF] Ying | Anderson localization of electrons in single crystals: Li x Fe 7 Se 8[END_REF]. To further understand the conduction mechanism, the magnetoresistance (MR, in %)

was measured with a magnetic field applied perpendicular to the film plane (i.e. the current).

The resistances as a function of the magnetic field for n-type ZnGa2O4 thin film at different temperature are shown by Figure 4-10 (c). The MR decreases with the increasing field (absolute value), and is negative from 2 K up to 100 K, then vanishes at T > 100 K. Such negative magnetoresistance is usually observed for nonmagnetic semiconductors when heavily doped [START_REF] Chikoidze | Electrical, optical, and magnetic properties of Sn doped α-Ga2O3 thin films[END_REF][START_REF] Sasaki | Electrical properties of impurity conducting n-type germanium[END_REF][START_REF] Toyozawa | Theory of localised spin and Negative MR in metallic impurity conduction[END_REF].

In the present case, in the undoped n-ZnGa2O4 high concentration of carriers is related to native defects. We could think that there is a conducting channel similar to the "impurity band" in external impurity doped semiconductors. Such a "self-impurity" band we attribute to the Zn related donor defect.

Summary

High

Influence of the oxygen content on the electrical properties

In this section, I will present an ongoing work that has the objective to study the influence of oxygen content on the electrical transport properties of ZnGa2O4 thin films.

Samples were deposited on c-sapphire substrates by metal organic vapor deposition (MOCVD) in National Chiao Tung University. Diethylzinc (DEZn), triethylgallium (TEGa), and oxygen were used as the precursors, the growth time was 30 minutes. After the growth, one sample was cooled with an O2 flow of 1000 sccm, while the precursors were all cut for the other one. The growth parameters and the thickness of two samples are summarized in the Table 4-3. ZnGa2O4-#1 DEZn = 100 sccm TEGa = 100 sccm T = 720 °C 500 30 -105

ZnGa2O4-#2 700 1000 120

Structural characterization

Figure 4-12 shows the X-ray diffraction (XRD) patterns of θ-2θ scan for both as-grown ZnGa2O4 film and that cooled in O2, in which 2θ was increased from 15° to 65°. Both thin films possess three XRD peaks located at 2θ positions of 18.50°,37.46°, and 57.56°, corresponding to (111), ( 222), and (333) ZnGa2O4 planes, respectively. Compared to our previously reported work [START_REF] Chi | Bipolar selfdoping in ultra-wide bandgap spinel ZnGa2O4[END_REF], the slight shift of the 2θ positions can result from different Zn content, as demonstrated by Horng et al. [START_REF] Horng | Epitaxial Growth of ZnGa 2 O 4 : A New, Deep Ultraviolet Semiconductor Candidate[END_REF]. Low values of full width at half maximum (FWHM) of 0.172° for the ZnGa2O4-#1 sample indicates the high crystalline quality of the layer. The crystallinity was slightly improved to 0.171° for ZnGa2O4-#2 that was cooled in O2.

Electrical transport properties

To study the actual influence of the O2 content on the electrical properties of the spinel ZnGa2O4 layers, we conducted the electrical resistivity and Hall effect measurements at various temperatures in a Van der Pauw configuration for both thin films. Four electrical contacts by silver paste were painted on the corners of both square-shaped (1 × 1 cm 2 ) samples.

Optical transmittance

Electronic properties

To study the chemical environment of elements, XPS measurements of both samples were carried out by Dr. Mathieu Frégnaux at Institute Lavoisier de Versailles (ILV), UFR des Sciences at Versailles. The O1s, Zn2p3/2, Ga2p3/2, and C1s core levels have been analyzed.

The adventitious carbon contamination related peak C1s was calibrated at 284.8 eV for both spectra (Figure 4 Therefore, considering the inexistence of double absorption in optical transmittance, the conducting ZnGa2O4-#1 sample may have a different origin of conductivity from the ntype ZnGa2O4 thin film discussed in Section 4.2.

Besides, Zn2p3/2 and O1s peaks for both samples have non-symmetrical shapes, suggesting different contributions to atomic binding energies. For Zn2p3/2 peak in sample ZnGa2O4-#2 that was cooled in O2, it evidences the existence of both tetrahedral and octahedral (ZnGa) sites (Chikoidze et al., 2020a;[START_REF] Li | Effects of preparation method and temperature on the cation distribution of ZnGa 2 O 4 spinel studied by X-ray photoelectron spectroscopy[END_REF], the inversion degree can be determined by deconvoluting the peaks which is under progress. Considering the experimental facts, we hypothesized that the electron conductivity may originate from the surface conduction. Surface conduction can be induced by several factors such as the surface-state [START_REF] Zhang | Band Bending in Semiconductors: Chemical and Physical Consequences at Surfaces and Interfaces[END_REF], and adsorption of metal adatoms [START_REF] Wang | Adsorption and Diffusion of Aluminum on β-Ga2O3(010) Surfaces[END_REF], hydrogen [START_REF] Kim | Will surface effects dominate in quasi-two-dimensional gallium oxide for electronic and photonic devices?[END_REF], etc. The hydrogen (or hydroxyl -OH group) related surface conduction can be modified by the presence of oxygen [START_REF] Qin | Editors' Choice-Hydrogen Centers in β-Ga2O3: Infrared Spectroscopy and Density Functional Theory[END_REF]. To confirm the hypothesis, XPS core levels of O1s and valence band tails should be properly treated.

For example, the contribution of surface adsorption can be analyzed by the deconvolution of O1s peaks [START_REF] Horng | Reliability study on deep-ultraviolet photodetectors based on ZnGa2O4 epilayers grown by MOCVD[END_REF]. The surface electron accumulation induced band bending can be determined based on the valence band tails (Navarro-Quezada et al., 2015a;[START_REF] Swallow | Transition from electron accumulation to depletion at β-Ga2O3 surfaces: The role of hydrogen and the charge neutrality level[END_REF], the analysis on these samples is ongoing.

Photo-sensibility test

As presented in the state of the art, ZnGa2O4 shows great potentiality in the applications of deep ultraviolet (DUV) photodetectors. Here, my objective was to demonstrate the photosensibility of our ZnGa2O4-#2 thin film that was cooled in O2 and has a p-type semiinsulating nature. It is a preliminary investigation of the photo-sensibility of the ZnGa2O4 layer without any specific metallization. The test probes are tungsten covered by silver paste.

The test was carried out at room temperature, and an UV lamp of 190 -400 nm was used for the illumination.

At room temperature, the ZnGa2O4-#2 thin film exhibits a tiny dark current. For example, at 10 V, the current under darkness was Idark = 12.6 pA, while it was increased to illumination with a bias of 5 V. Though the photo-sensibility is quite satisfactory for the thin film without any metallization, the response time was not quick enough. For example, the rise time (τon) was determined to be ~10 s. However, a faster response speed can be expected after depositing metal contacts (e.g., Ti/Pt/Au) to fabricate a metal-semiconductor-metal (MSM) photodetector, and following an annealing process [START_REF] Horng | Reliability study on deep-ultraviolet photodetectors based on ZnGa2O4 epilayers grown by MOCVD[END_REF][START_REF] Sood | Performance enhancement of ZnGa2O4 Schottky type deep-ultraviolet photodetectors by oxygen supercritical fluid treatment[END_REF]Tsai et al., 2019).

Estimation of the critical electric field for ZnGa2O4

The objective of this section is to estimate experimentally the critical electric field for the p-type ZnGa2O4. To the best of our knowledge, the critical electric field (ECR) of the ultra-wide band gap semiconductor ZnGa2O4 has yet been reported. While it is a crucial parameter for one semiconductor material to evaluate its breakdown capability. Thus, analogously to p-type β-Ga2O3 in the previous chapter, the breakdown voltage measurements were carried out, for the estimation of the critical electric field for the p-type ZnGa2O4.

Recall again, the ZnGa2O4 layers were simultaneously grown on insulating sapphire and conducting Si substrates. Electrical transport properties were studied for ZnGa2O4 grown on insulating sapphire substrate, as the sapphire substrate is insulating up to high temperatures thus preventing parasitic leakage through the substrate. While a parallel capacitor was fabricated based on ZnGa2O4//Si, for the vertical breakdown voltage characterization.

Structural characterization for ZnGa2O4/Si

Figure 4-18 shows the Cu-Kα X-ray diffraction (XRD) spectra of ZnGa2O4 thin films grown on Si(111) and Al2O3(0001). According to the PDF 28-1240 file, it is pure ZnGa2O4 spinel without a secondary phase. Film on Si(111) is polycrystalline without any preferential texturation, similar to XRD pattern reported by Galazka et al. [START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF] for their melt-grown bulk ZnGa2O4 spinel, milled in a randomly oriented powder. For films on Al2O3(0001) substrates, XRD peaks appearing at 18.6°, 37.6°, 57.6°, 79.7°, and 106.6° correspond to the (111), ( 222), ( 333), (444), and (555) planes of the cubic spinel ZnGa2O4, respectively, as reported by previous literature ( Chikoidze et al., 2020;[START_REF] Yu | Electroluminescence from Er-doped ZnGa2O4 spinel nanofilms fabricated by atomic layer deposition on silicon[END_REF].

ZnGa2O4 thin films can be grown on sapphire substrates by MOCVD, PLD as mentioned above, with a preferential orientation along [111] of cubic spinel and equivalent direction for Al2O3(0001). Analogously, ZnGa2O4 thin films have also been grown on Si substrates by atomic layer deposition (ALD) [START_REF] Yu | Electroluminescence from Er-doped ZnGa2O4 spinel nanofilms fabricated by atomic layer deposition on silicon[END_REF], PLD [START_REF] Yi | Luminescence characteristics of pulsed laser deposited ZnGa2O4 thin film phosphors grown on various substrates[END_REF], and RF magnetron sputtering (W.-K. Wang et al., 2019b). A larger lattice mismatch between ZnGa2O4 and Si(100) (which may also contain a native ultra-thin SiO2 interlayer) results in a relatively weaker orientation of crystallite in the ZnGa2O4 grown on Si substrate than that on sapphire (0001) (W.-K. Wang et al., 2019b). The full width at half maximum (FWHM) values were measured as 0.29° and 0.49° for ZnGa2O4 (111) on sapphire and Si(100)

substrates, respectively, indicating also a smaller size of crystallites in the case of Si( 111)

substrates with respect to Al2O3(0001) ones.

Electrical transport properties of ZnGa2O4//c-Al2O3

According to the kinetic ionization impact theory as discussed previously, to achieve large critical electric fields, it is mandatory to obtain a sample with low remote carrier concentration to reduce the onset of the impact ionization process. Here, we conducted the electrical transport measurements to show the semi-insulating nature of the later. The Ohmic contacts were prepared with silver paint at the four corners of the sample. The resistivity and Hall effect measurements were performed, in a Van der Pauw configuration with perpendicularly to current applied magnetic fields varying from 0 to 1.6 T, in 550 to 850 K temperature range. cm -3 at 550 -850 K. Although the hopping behavior starts to pronounce below 600 K, extrapolating the band-activated regime of the hole concentration versus temperature at the higher temperatures, the hole density is below 10 11 cm -3 at 300 K, confirming the low level of p-type doping with the applied growth conditions. The mobility of the p-type ZnGa2O4 thin film varies between 9 and 15 cm 2 /(V•s).

Critical electric field of ZnGa2O4

To determine the vertical critical electric field experimentally, vertical parallel plane

Summary

Spinel ZnGa2O4 has emerged recently, the study on the electrical properties and conduction mechanism of this ultra-wide band gap semiconductor is still very limited.

However, a few general rules for getting n-type or p-type can still be summarized. Based on the first principles calculations, Sabino et al. [START_REF] Sabino | Hole conductivity through a defect band in ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}[END_REF] suggested that the n-type conductivity is very difficult to be achieved under oxygen-rich condition, which agrees well with our findings in Section 4.3. While a semi-insulating p-type nature can be expected with a near stoichiometric growth (Chikoidze et al., 2020a). Theoretically, to get p-type conductivity, a Zn-rich condition should be attained (Paudel et al., 2011b;[START_REF] Sabino | Hole conductivity through a defect band in ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}[END_REF][START_REF] Shi | Self-Doping and Electrical Conductivity in Spinel Oxides: Experimental Validation of Doping Rules[END_REF]. Besides, the important influence of oxygen has been proposed (Horng et al., 2017;[START_REF] Lee | Enhanced ultraviolet photoconductivity in semiconducting ZnGa2O4 thin films[END_REF][START_REF] Omata | New ultraviolet-transport electroconductive oxide, ZnGa 2 O 4 spinel[END_REF][START_REF] Yan | Electrical Conductivity in Transparent ZnGa2O4: Reduction and Surface-Layer Structure Transformation[END_REF], while a detailed investigation of the mechanism is still required. The results in this chapter can be summarized as follow:

(i) A higher O2 flow (tuning from 600 to 1200 sccm) can enhance the Zn incorporation in β-Ga2O3 during MOCVD growth. With the [Zn] > 6.85 at. %, the spinel ZnGa2O4 can form on c-sapphire substrates. When [Zn] reaches 14 at. %, monoclinic β-Ga2O3 transform to cubic spinel ZnGa2O4 completely.

(ii) The native bipolar conductivity of spinel ZnGa2O4 has been shown. The high electron conductivity was attributed to the hopping conduction mechanism of Zni in a "selfimpurity" band created by Zni-VO located at the mid-gap.

(iii) The influence of O2 content on electrical properties was demonstrated, the ZnGa2O4 thin film can be transformed from conducting n-type to semi-insulating p-type (at least on the surface) with a higher O2 flow during the growth and cooled in O2. While the conduction mechanism and the origin of the conductivity are still under discovery.

(iv) The breakdown voltage measurements were carried out for parallel plane capacitors based on the p-ZnGa2O4//Si structure. The critical electric field was estimated at 5.3 MV/cm.

Electrical Contacts to p-type β-Ga 2 O 3

This chapter is dedicated to the preliminary results of the metal electrical contact study for p-type β-Ga2O3. My objective was to establish a protocol for electrical contact preparation by photolithography, followed by I-V characterization tests. As metals for investigation, Ti/Pt/Au, Pt, and Ag were selected. I will present the state of the art related to Ohmic contacts mainly for n-type β-Ga2O3 in Section 5.1. Section 5.2 focuses on the experimental methods I have used and the experimental results/discussion are presented in Section 5.3.

State of the art

Many promising β-Ga2O3 based electronic and opto-electronic devices have been reported last several years, including Schottky barrier diode (SBD) [START_REF] Hu | The role of surface pretreatment by low temperature O2 gas annealing for β-Ga2O3 Schottky barrier diodes[END_REF][START_REF] Li | ON-Resistance of Ga2O3 Trench-MOS Schottky Barrier Diodes: Role of Sidewall Interface Trapping[END_REF], field effect transistors (FET) [START_REF] Higashiwaki | Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates[END_REF][START_REF] Lv | Lateral β-Ga2O3 MOSFETs With High Power Figure of Merit of 277 MW/cm2[END_REF][START_REF] Zheng | A trapping tolerant drain current based temperature measurement of β-Ga2O3 MOSFETs[END_REF], photodetectors [START_REF] Oshima | Ga2O3 Thin Film Growth on c-Plane Sapphire Substrates by Molecular Beam Epitaxy for Deep-Ultraviolet Photodetectors[END_REF][START_REF] Wu | A general strategy to ultrasensitive Ga2O3 based self-powered solar-blind photodetectors[END_REF]. The performance of SBD is characterized by breakdown voltage (𝑉 𝐵𝑅 ) and on-resistance (𝑅 𝑜𝑛 ) that are dependent on the Schottky contacts, while a good Ohmic contact is necessary requirement for metal oxide semiconductor field effect transistor (MOSFET). An Ohmic contact to n-type semiconductors can be achieved when the Schottky barrier height (𝛷 𝐵 ) is negative, 𝛷 𝐵 can be described by the Schottky-Mott rule [START_REF] Mott | Note on the contact between a metal and an insulator or semi-conductor[END_REF]:

𝛷 𝐵 = 𝛷 𝑀 -ꭓ 𝑆
Where 𝛷 𝑀 and ꭓ 𝑆 being metal work function and semiconductor electron affinity, respectively. The electron affinity of bulk Ga2O3 single crystal with electron concentration of 2 -6 ×10 17 cm -3 grown by Czochralski method [START_REF] Galazka | Czochralski growth and characterization of β-Ga2O3 single crystals[END_REF] was estimated as 4.00 ± 0.05 eV [START_REF] Mohamed | Schottky barrier height of Au on the transparent semiconducting oxide β -Ga 2 O 3[END_REF]. Therefore, in the ideal case, an Ohmic contact to β-Ga2O3 can be formed by choosing the metals with work function of lower than ~4 eV.

However, 𝛷 𝐵 established at the metal-Ga2O3 interface can be influenced by the Fermi level pinning originating from (i) metal-induced gap states (MIGS) [START_REF] Bhattacharyya | Schottky Barrier Height Engineering in β-Ga2O3 Using SiO2 Interlayer Dielectric[END_REF][START_REF] Monch | On the physics of metal-semiconductor interfaces[END_REF], (ii) the presence of surface states [START_REF] Lingaparthi | Surface states on (001) oriented β-Ga2O3 epilayers, their origin, and their effect on the electrical properties of Schottky barrier diodes[END_REF], (iii) adsorbates during the preparation process, or other factors. For example, Lovejoy et al. [START_REF] Lovejoy | Band bending and surface defects in β-Ga2O3[END_REF] demonstrated the negatively charged surface defects of as-grown n-type Ga2O3 make the band bend upwards by X-ray photoemission spectroscopy (XPS), which complicates the formation of Ohmic contact [START_REF] Müller | Comparison of Schottky contacts on β-gallium oxide thin films and bulk crystals[END_REF][START_REF] Pearton | A review of Ga2O3 materials, processing, and devices[END_REF]. However, as Swallow et al. [START_REF] Swallow | Transition from electron accumulation to depletion at β-Ga2O3 surfaces: The role of hydrogen and the charge neutrality level[END_REF] reported, suggested by XPS measurements, the hydrogen terminated surface of bulk (-201) β-Ga2O3 leads to electron accumulation and downward band bending. According to the authors, this difference is attributed either to the use of the wrong bandgap energy and/or to the underestimation of the surface valence band maximum (VBM) with respect to the Fermi level. A post-annealing up to 800 °C can remove the hydrogen from the surface, resulting in surface electron depletion and upward band bending (Navarro-Quezada et al., 2015b;[START_REF] Swallow | Transition from electron accumulation to depletion at β-Ga2O3 surfaces: The role of hydrogen and the charge neutrality level[END_REF].

As a result, it is often found that 𝛷 𝐵 is either independent or weakly dependent on 𝛷 𝑀 [START_REF] Huan | Recent Advances in β-Ga2O3-Metal Contacts[END_REF][START_REF] Xue | An Overview of the Ultrawide Bandgap Ga2O3 Semiconductor-Based Schottky Barrier Diode for Power Electronics Application[END_REF]. Indeed, Yao et al. [START_REF] Yao | Investigation of Different Metals as Ohmic Contacts to β-Ga2O3: Comparison and Analysis of Electrical Behavior, Morphology, and Other Physical Properties[END_REF] investigated nine contact metals with low-to-moderate work function (Ti, In, Ag, Sn, W, Mo, Sc, Zn, and Zr) to Sn doped β-Ga2O3 (dopant level at 5 ×10 18 cm 3 ), only Ti contact with Au capping layer and In contact after annealing at 600 °C are Ohmic, though the latter one has poor morphology. The current-voltage characterization of all other metal contacts to β-Ga2O3 did not display good linearity even after annealing at temperatures up to 600 -800 °C.

Though the difficulties mentioned above, there are several approaches to achieving the Ohmic contact to β-Ga2O3. (i) the Schottky-Mott relation can be used as a guide for preliminary selection of metals with sufficiently low work functions. (ii) Heavily doping can facilitate the tunneling effect to reduce contact resistance, the commonly used approach is Si-implantation [START_REF] Higashiwaki | Depletion-mode Ga2O3 metal-oxidesemiconductor field-effect transistors on β-Ga2O3 (010) substrates and temperature dependence of their device characteristics[END_REF][START_REF] Sasaki | MBE grown Ga2O3 and its power device applications[END_REF][START_REF] Wong | Electron channel mobility in silicon-doped Ga2O3 MOSFETs with a resistive buffer layer[END_REF]. (iii) surface treatment such as reactive-ion-etching (RIE) [START_REF] Higashiwaki | Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates[END_REF], Ar plasma bombardment (H. Zhou et al., 2017) have been performed to reduce the contact resistance, and the introduction of surface defects such as oxygen vacancies has been considered as the mechanism. (iv) post-metallization annealing has been demonstrated to improve the Ohmic contact effectively.

For n-type β-Ga2O3, Ti/Au is a good candidate of Ohmic contact, which has also been widely used for the time being [START_REF] Higashiwaki | Depletion-mode Ga2O3 metal-oxidesemiconductor field-effect transistors on β-Ga2O3 (010) substrates and temperature dependence of their device characteristics[END_REF]Lee and Peterson, 2019a;Liu et al., 2019;[START_REF] Lyle | Electrical and chemical analysis of Ti/Au contacts to β-Ga2O3[END_REF][START_REF] Sasaki | MBE grown Ga2O3 and its power device applications[END_REF][START_REF] Wong | Electron channel mobility in silicon-doped Ga2O3 MOSFETs with a resistive buffer layer[END_REF]. The choice of Ti is based on its low work functions, while Au is a capping layer to protect Ti from oxidation. For Siimplanted β-Ga2O3 with a dopant concentration of ~5×10 19 cm -3 , the specific contact resistance (𝜌 𝑐 ) of the Ohmic contact formed by Ti/Au can be as low as ~10 -6 Ω•cm 2 after a rapid-thermal-annealing at 450 °C or 470 °C under N2 [START_REF] Higashiwaki | Depletion-mode Ga2O3 metal-oxidesemiconductor field-effect transistors on β-Ga2O3 (010) substrates and temperature dependence of their device characteristics[END_REF]Sasaki et al., 2013). Recently, Lee et al. (Lee et al., 2022b(Lee et al., , 2022a;;[START_REF] Lee | Accelerated Aging Stability of β-Ga2O3-Titanium/Gold Ohmic Interfaces[END_REF], 2019a, 2019b) investigated intensively Ti/Au contact to β-Ga2O3. It was shown that Ti can attract oxygen from β-Ga2O3 forming a n-type Ti-TiOx layer to reduce the barrier height during a rapid thermal annealing (RTA) process (1 min at 470 °C) (Lee and Peterson, 2019a), while the contact can be degraded following a higher annealing temperature (e.g., 520 °C (Lee et al., 2022b)) or a longer annealing period (e.g., 10 or 15 mins (Lee and Peterson, 2019b)), due to the in-diffusion of Au into the Ti-TiOx layer and out-diffusion of Ga from β-Ga2O3.

Additionally, the effect of anisotropy on Ti/Au contact was demonstrated (Lee et al., 2022a), Ti/Au metallization on ( 100) and ( 010) oriented β-Ga2O3 followed a RTA at 470 °C for 1 min showed specific contact resistivity of 5.1×10 -5 Ω•cm 2 and 3.3 × 10 -3 Ω•cm 2 , respectively. Besides, a few groups has demonstrated β-Ga2O3 based photodetector [START_REF] Feng | Synthesis of two-dimensional β-Ga2O3 nanosheets for high-performance solar blind photodetectors[END_REF] and field effect transistor (FET) [START_REF] Ma | Low Subthreshold Swing Double-Gate β -Ga2O3 Field-Effect Transistors With Polycrystalline Hafnium Oxide Dielectrics[END_REF]) by using Cr/Au to form Ohmic contact. Mg/Au metal contact has also been demonstrated to form Ohmic contact to slightly Sn doped β-Ga2O3 (n = 4 ×10 17 cm -3 ), after a post-annealing at 500 °C for 2 minutes under Ar gas, the 𝜌 𝑐 was estimated as 2.1 ×10 -5 Ω•cm 2 (J. Shi et al., 2019). Intermediate semiconductor layers such as Al-doped ZnO (AZO) (P. H. Carey et al., 2017a), Indium Tin Oxide (ITO) (P. H. Carey et al., 2017b;[START_REF] Oshima | Formation of indium-tin oxide ohmic contacts for β-Ga 2 O 3[END_REF] have been inserted between Ga2O3 and metal. As shown in Figure 5-1, the purpose is to facilitate electron transport by reducing the barrier height, the conduction band offsets between AZO, ITO and Ga2O3 are 0.79 eV, and 0.32 eV, respectively. The 𝜌 𝑐 were determined as 2.82×10 -5 , and 6.3×10 -5 Ω•cm 2

for AZO/Ti/Au and ITO/Ti/Au stacks to β-Ga2O3, respectively. [START_REF] Bai | Dilute-selenium alloying: A possible perspective for achieving p-type conductivity of β-gallium oxide[END_REF] and In [START_REF] Liu | Compositions and properties of high-conductivity nitrogen-doped p-type β-Ga2O3 films prepared by the thermal oxidation of GaN in N2O ambient[END_REF] were used to form Ohmic contact to p-type β-Ga2O3. It is clear that further investigation is required.

Experimental methods

Circular transmission line model (CTLM) method

High-quality Ohmic contacts between metal and semiconductors with a low contact resistance (RC) play a crucial role in reducing the operating voltage of high-power semiconductor devices. For usual thin film resistance measurement, the total resistance measured is composed of the electrical contact resistance (RC1, RC2), metal resistance (RM1, RM2) and the sheet resistance (RS): 𝑅 𝑡𝑜𝑡 = 𝑅 𝑀1 + 𝑅 𝐶1 + 𝑅 𝑆 + 𝑅 𝐶2 + 𝑅 𝑀2 (Figure 5-2),

where the metal resistances RM1 and RM2 can be neglected with respect to other terms for semiconductors.

Figure 5-2. Schematic cross-sectional illustration of equivalent circuit during the currentvoltage characterization.

For a given interface between two materials, the intrinsic quantity is the specific contact resistance ρC, defined as ρC = RC × S, where S is the contact area. In the case of equal dimensions between metal contact patterns, 𝑅 𝑡𝑜𝑡 = 2𝑅 𝐶 + 𝑅 𝑆 . When S1 ≫ S2, for a same ρC of the metal-semiconductor contact, the contribution of RC1 can be neglected compared to RC2. Consequently, a way to reduce practically the contact resistance in technological device, is to increase the contact area. Therefore, it is important to determine a proper method to examine the electrical contact resistance, which allows to further improve the electrical contact performance. The contact resistance RC is usually evaluated by ρC / S [START_REF] Chang | Specific contact resistance of metalsemiconductor barriers[END_REF], where S is the contact area, and ρC being the specific contact resistance cannot be measured directly and must be inferred from a measurement on the same Ohmic contact structure as the device, but with a specially prepared test pattern. For testing the I-V characteristic of the metal-semiconductor Ohmic contact, several transmission line measurement (TLM) models have been developed. The original rectangular TLM layout first proposed by [START_REF] Shockley | Research and investigation of inverse epitaxial UHF power transistors[END_REF][START_REF] Shockley | Research and investigation of inverse epitaxial UHF power transistors[END_REF] provided a possibility to determine the ρC for ohmic contacts. This method defines an array of rectangle patterns of metal contacts with the same dimension (Z × w) but different inter-distance (di) (Figure 5-3 (a)).

The total resistance can then be expressed as:

𝑅 𝑡𝑜𝑡 = 𝑅 𝑆 𝑍 𝑑 𝑖 + 2𝑅 𝐶 (5 -1)
Therefore, the sheet resistance of the sample is deduced from the slope However, this TLM method requires a mesa etch step, which is not only technically difficult but also affects measurement precision [START_REF] Parsons | Low specific resistance (<6×10-6 Ω cm2) TiC ohmic contacts to n-type β-SiC[END_REF][START_REF] Reeves | Obtaining the specific contact resistance from transmission line model measurements[END_REF]. A concentric TLM model proposed by Reeves [START_REF] Reeves | Specific contact resistance using a circular transmission line model[END_REF] could efficiently avoid the requirement of mesa etching and improves precision. However, the complex calculation procedure and imprecise measurement of contact end resistance will result in a large inaccuracy in the extraction of the specific contact resistance [START_REF] Xu | Reeves's circular transmission line model and its scope of application to extract specific contact resistance[END_REF]. At the time being, the circular transmission line measurement (CTLM) model is commonly used, it consists of an inner metal contact and an outer metal contact that are separated by a metalfree ring [START_REF] Goyal | Multilayer Pt/Al based ohmic contacts for AlGaN/GaN heterostructures stable up to 600°C ambient air[END_REF]Lee et al., 2022b;[START_REF] Marlow | The effects of contact size and non-zero metal resistance on the determination of specific contact resistance[END_REF][START_REF] Sheoran | A Comprehensive Review on Recent Developments in Ohmic and Schottky Contacts on Ga2O3 for Device Applications[END_REF] (Figure 5-4). Employing this sophisticated model, the value of ρC by deriving the sheet resistivity (RS) and transfer length (LT) can be computed from the correlation between the total resistance and the pattern size.

Photolithography and metal deposition process

Photolithography is a process used to transfer desired patterns onto the sample using UV light. Different photoresists and different materials have different properties that can affect the effectiveness of the photolithography process. Therefore, the spin-coating and photolithography parameters, such as maximum spin coating speed and time, exposure time, and developing time need to be optimized to ensure the desired pattern is accurately transferred onto the material surface. For example, a thicker photoresist layer can be expected with a higher maximum spin coating speed, then, the exposure and development time should be increased to efficiently remove the exposed photoresist.

Since it is the first time to deposit metal contacts on β-Ga2O3 through the photolithography process in GEMaC, I started with the adjustment of lithography parameters.

The patterns were designed in the software Klayout. The photolithography process steps are as follow:

(i) Cleaning: The substrate surface is cleaned to remove any contaminants or particles that could interfere with the subsequent steps. The samples were cleaned by sonication in acetone and then 2-propanol for 10 min each, followed by 1 min rinsing in deionized (DI)

water and blowing dry with ultra-high purity N2 gas.

(ii) Spin coating: A thin layer of photoresist is applied to the substrate by spinning it at a high speed. AZ1512HS and AR-P 5350 were used as photoresists deposited by the spin coater POLOS SPIN150i (Figure 5-5 (a)).

(iii) Soft baking: Bakery at 100 °C for 1 min for sample deposited photoresist AZ1512HS, and 2 mins for sample deposited photoresist AR-P 5350, to remove the moisture and harden the photoresist.

(iv) Alignment: The substrate is aligned with a mask containing the desired pattern, which is positioned between the substrate and a light source using Smart Print (Figure 5 (vii) Post-baking: The remaining photoresist can be hardened by post-baking at a high temperature, making it resistant to subsequent etching or deposition processes. However, this step is not required for the used photoresists.

(vii) Metal deposition: The patterned substrate is deposited onto the patterned regions by RF-sputtering machine Leybold Z400, carried out by Dr. Bruno Bérini. Three kinds of metal contacts were selected:

(vii-1) Ag (200 nm). It was selected systematically given that the Ag paste was used to make Ohmic contact to p-type β-Ga2O3 thin films for electrical measurements, for the determination of the specific contact resistance.

(vii-2) Multilayer of Ti (50 nm)/Pt (50 nm)/Au (200 nm), it was selected systematically since it forms Ohmic contact to n-type β-Ga2O3, p-type GaN [START_REF] Zhou | Low resistance Ti/Pt/Au ohmic contacts to p-type GaN[END_REF], and borondoped p-type diamond [START_REF] Chen | Investigation of specific contact resistance of ohmic contacts to B-doped homoepitaxial diamond using transmission line model[END_REF][START_REF] Hoff | Ohmic contacts to semiconducting diamond using a Ti/Pt/Au trilayer metallization scheme[END_REF]. The additional layer of Pt was used to prevent the interdiffusion of Ti and Au, and finally of Au in Ga2O3 film, at elevated temperatures (up to 500 °C), [START_REF] Hoff | Ohmic contacts to semiconducting diamond using a Ti/Pt/Au trilayer metallization scheme[END_REF] which are usually our resistance measurement conditions. (viii) Lift-off: lift-off process was carried out by immersing the metal coated sample into acetone solution.

(ix) Post-annealing: The metal contacts were then annealed in nitrogen for 30 min at 5-2. For figure (g), due to the limit of magnification, the whole group of patterns could not be captured together, each concentric circle was captured separately with the same magnification and then merged.

Calculation and measurement methods

The measurement accuracy of the specific contact resistance RC is generally susceptible to three factors:

(i) Electrical measurement technique. More specifically, the four-probe technique can effectively reduce the series resistance resulting from the probes, the contact between the probes and the metal pad in the two-probe measurement. I used the two-probe measurement for the manipulation convenience (tiny patterns without micro-probe station equipment), and the series resistance resulting from the probes is considered negligible for the highly resistive p-type β-Ga2O3. The resistance of an Ohmic contact is typically determined by the I-V measurement. If an I-V characteristic demonstrates a unique linear relationship, then the total resistance can be calculated using the slope of the straight line. In this work, the voltage was swept through n steps, the real voltage Uk applied and the corresponding current Ik were then measured. The statistical total resistance Rtot and its uncertainty can be expressed as:

𝑅 𝑡𝑜𝑡 = 𝑅 0 + 𝛥𝑅 = ∑ 𝑈 𝑘 𝐼 𝑘 𝑛 𝑘 𝑛 + √ ∑ ( 𝑈 𝑘 𝐼 𝑘 ) 2 𝑛 𝑘

𝑛

(5 -3)

Here, the contact resistances were measured at different temperatures using a KEITHLEY 4200-SCS (Semiconductor Characterization System) with a measurement cell (Linkam, UK) with tungsten contact probes.

(ii) Contact area correction. The contact areas are typically expected to be equivalent to the size of the pattern designed by the photolithography mask. In this work, one group of designed CTLM pattern consists of 6 rings with a constant inner circle radius (r) of 250 µm and varying outer circle radii (rout) ranging from 40 µm to 140 µm. In reality, the contact areas are impacted by the diffraction of ultraviolet light during the exposure, the actual radius will thus be influenced during the lift-off or metal deposition process. Thus, the contact areas should be calculated by measuring their actual radii. the inner circle radius (r), outer circle radii (rout), and their uncertainties were determined by microscope (Nikon L-UEPI) equipped with a measurement system "NIS Elements". The average of the six values obtained by six measurements with ~60° between each measurement was calculated to estimate the di of the contact patterns:

𝑑 𝑖 = 1 6 ∑ 𝑑 𝑘 6 𝑘 = ∑(𝑟 𝑜𝑢𝑡 𝑘 -𝑟 𝑘 ) 6 𝑘
(5 -4)

Therefore, the specific contact resistance ρC and the sheet resistance RC can be estimated by plotting the total resistance Rtot versus gap spacing d.

The designed and measured dimensions of the CTLM patterns for Ti/Pt/Au and Pt contacts are summarized in ) is generally less than 3%. The error [%] becomes smaller with the increasing ring size, which may be due to the precision limit of the lithography equipment (the pixel size for ×1 objective is 7.12 µm, and the smallest achievable structure is < 23 µm). A similar trend can be found in Pt contact as well, though it has a larger error than for Ti/Pt/Au contact. (5 -5)

where I0 (I1) and K0 (K1) are the zero-order (first-order) modified Bessel functions, of first and second kind, respectively. The equation is generally expressed as:

𝑅 𝑡𝑜𝑡 = 𝑅 𝑆 2𝜋 [ln ( 𝑟 𝑜𝑢𝑡 𝑟 ) + 𝐿 𝑇 ( 1 𝑟 𝑜𝑢𝑡 + 1 𝑟 )]
(5 -6)

The simplification for I0/I1 = 1 and K0/K1 = 1 relies on the assumption that the rout and r are at least four times greater than LT [START_REF] Liu | Study on the measurement accuracy of circular transmission line model for low-resistance Ohmic contacts on III-V wide band-gap semiconductors[END_REF]. However, this condition was not satisfied in our case after plotting 𝑅 𝑡𝑜𝑡 vs. ln ( 𝑟 𝑜𝑢𝑡 𝑟 ). For example, Figure 5-7 shows the Rtot plotted versus ln(rout/r) at 700 K, the extracted transfer length LT is even comparable with the inner radius r. One explanation is that the plot is, in fact, not linear, the slope might be underestimated, thus leading to an underestimation of sheet resistance and a large intercept at y axis. As a result, the transfer length is overestimated. To make a correct fitting, it is necessary to make a Taylor expansion of the Bessel functions (6 -5), and calculate the LT with corresponding rout/r. However, these obtained results may be influenced by other factors that will be discussed below, the method might not be applicable here. The sheet resistance (RS), specific contact resistance (ρC) were determined by the 𝑅 𝑡𝑜𝑡 vs. di plot: 𝑅 𝑆 = 2𝜋𝑟 𝑜𝑢𝑡 × 𝑠𝑙𝑜𝑝𝑒, 𝜌 𝐶 = (𝐿 𝑇 ) 2 × 𝑅 𝑆 [START_REF] Jacobs | Optimisation of the Ti/Al/Ni/Au ohmic contact on AlGaN/GaN FET structures[END_REF][START_REF] Klootwijk | Merits and limitations of circular TLM structures for contact resistance determination for novel III-V HBTs[END_REF].

Figure 567. Rtot plotted versus ln(rout/r) at 700 K.

Experimental results and discussion

The Zn-doped β-Ga2O3 samples were grown in a by metal organic chemical vapor deposition (MOCVD) reactor on insulating r-plane sapphire substrates at 775 °C. The doping concentration is [Zn] = 2×10 19 cm -3 determined by SIMS.

Please note that the study on sputtered Ag contact resistance is still in process. Here, A tiny change in the slope can be found at T = 550 K, and at T < 500 K, it started to rectify.

The total resistance Rtot as a function of measured gap spacing di (Table 5- The usually dominant transport mechanisms of Schottky type M-S contact, including thermionic emission and thermionic field emission, are strongly influenced by the temperature [START_REF] Fontserè | Temperature dependence of Al/Ti-based Ohmic contact to GaN devices: HEMT and MOSFET[END_REF]. The corresponding total current density equation can be given by [START_REF] Rideout | A review of the theory and technology for ohmic contacts to group III-V compound semiconductors[END_REF][START_REF] Rideout | Effects of image force and tunneling on current transport in metal-semiconductor (Schottky barrier) contacts[END_REF]:

𝐽 𝑡𝑜𝑡𝑎𝑙 = 𝐽 𝑟 [exp ( 𝑞𝑉 𝑛𝑘 𝐵 𝑇 ) -exp (( 1 𝑛 -1) 𝑞𝑉 𝑘 𝐵 𝑇 ) ]
(5 -7)

Where 𝐽 𝑟 = 𝐴 * 𝑇 2 exp (-

𝑞𝛷 𝑏 𝑘 𝐵 𝑇
), 𝐴 * is the Richardson constant for the semiconductor, kB is the Boltzmann's constant, 𝛷 𝑏 is the barrier height, T is the temperature, V is the applied forward bias, n is the diode ideality factor.

When the impurity concentration is further increased, the barrier thickness becomes thin enough for a significant number of carriers to tunnel through. This mechanism of current transport is known as field emission tunneling, which is not dependent on temperature, and is the dominant mode of current transport in metal-semiconductor Ohmic contacts. The specific contact resistance follows the relation in the case of n-type doping, with the donor concentration ND [START_REF] Greco | Ohmic contacts to Gallium Nitride materials[END_REF]:

𝜌 𝐶 ∝ exp ( 𝛷 𝑏 √𝑁 𝐷 ) (5 -8)
Therefore, observing the temperature dependent specific contact resistance, it is suggested that a barrier exists between the Ti/Pt/Au contact and p-type β-Ga2O3, which was reduced during measurements with increasing temperatures. Therefore, the linear behavior of I-V curves, the Ti/Pt/Au contact forms "quasi-Ohmic" contact to p-type β-Ga2O3 around zero for current density in the measurement temperature range. increased ~10 times after several measurements at elevated temperatures, which might be due to the degradation of the contact. Such contact deterioration that might be induced by the interdiffusion of metals/cation can be further confirmed by energy-dispersive X-ray spectroscopy (EDX) carried out for the sample cross-section, which is programmed to be done, as it is important to know the high temperature stability of the electrical contact.

Besides, the areas of the outer metal contacts are different for each concentric cycle group, leading to the varying ratio Souter/Sinner ~ 1.5 -4 depending on the gap spacing. Subsequently, it is also a factor that influences the analysis of measured resistance. The CTLM method for the determination of specific contact resistance was applied for Ti/Pt/Au contact, while the results are difficult to analyze. To go further in this metallic contact study, I propose the following next steps:

Summary and next steps

(i) High measurement temperatures are susceptible to degrading the contacts (by interdiffusion). Therefore, lower measurement temperatures (T < 300 °C) should be used.

(ii) The non-linear plots of total resistance Rtot versus gap spacing di may also be attributed to the inhomogeneity of the sample surfaces and different outer areas. Thus, an entire outer metal pattern (Figure 5-13) of an area much larger than the inner metal contact should be used during the lithography process, with the same inter area. Thus, we can neglect the outer contact contribution to R total with respect to the inner contact contribution. [START_REF] Freitas | Ga2O3 Schottky barrier and heterojunction diodes for power electronics applications[END_REF][START_REF] Zhang | Ultra-wide bandgap semiconductor Ga2O3 power diodes[END_REF] or oxidation from a seed layer of metal Ni [START_REF] Qiao | A study of the Au/Ni ohmic contact on p-GaN[END_REF]. Cu2O can also be directly deposited on n-Ga2O3 to make p-n junction diode [START_REF] Watahiki | Heterojunction p-Cu2O/n-Ga2O3 diode with high breakdown voltage[END_REF].

All developments are long, but are important for the integration of p-type Ga2O3 materials on real devices.

Conclusion and Perspectives Conclusion

In this PhD thesis work, the electronic properties of two ultra-wide band gap semiconductors, β-Ga2O3 and ZnGa2O4, having potentiality for high power electronic devices and UV photodetectors, were studied. The results in this manuscript can be summarized in three main parts as below:

(i) Hole conductivity realization: p-type doping in ultra-wide band gap is well-known to be challenging, the prerequisite for further p-type doping is to get a highly compensated semi-insulating β-Ga2O3 thin film. Therefore, firstly, high crystalline quality undoped β- Zn, as a II group element, was selected as an acceptor dopant. Thermodynamic analysis suggested that Zn can take interstitial site or substitute Ga, forming Zni donor defect or ZnGa acceptor defect depending on the growth conditions (pressure, temperature) and the doping level. For example, at the total pressure P = 30 Torr in the growth chamber, if growth temperature T = 800 °C, the impurity p-type conductivity can take place when Zn concentration > 10 14 cm -3 . while when [Zn] ~10 18 cm -3 , Zn atoms start to occupy interstitial sites and consequently, Zni donor and ZnGa acceptor defects compensate each other, resulting in the so-called impurity "auto-compensation" effect. Following the conclusions from the thermodynamic analysis, the experimental study has been carried out. Pt/β-Ga2O3 contact showed quasi-linear behavior at T = 600 and 550 K, while started to rectify clearly at T ≤ 500 K. I-V curves of Ti/Pt/Au contact to p-type β-Ga2O3 suggested that the contact is Ohmic at T > 550 K. However, the specific contact resistance extracted using the circular transmission line model (CTLM) approach is temperature dependent (at T = 450 -700 K), suggesting that this metal contact pad may form quasi-Ohmic contact in the measurement temperature range. Additionally, the measured resistance of Ti/Pt/Au/β-Ga2O3

did not increase linearly with the increasing gap spacing between the inner and outer metal contacts, which made the analysis and the extraction of parameters of the CTLM based measurements not accurate.

However, the existing difficulties I met have been analyzed, the degradation of metal contacts might be due to the interdiffusion of metal/cation (Au, Ga) after measurements at high temperatures (up to 700 K); another factor that could influence the extraction of sheet resistance and the specific contact resistance, is the varying outer metal contact area. In light of these issues, the next steps can be proposed to improve the I-V characterizations, as presented bellow as a perspective.

Perspectives

Both β-Ga2O3 and ZnGa2O4 exhibit tremendous potential for next-generation power electronic applications, while β-Ga2O3 has witnessed more significant advancements in this area compared to ZnGa2O4. To unlock the full potential of these materials, the deeper study of point defects, and in turn, the control of electrical conductivity is very important.

Therefore, several future works can be envisaged:

(i) The exploration of defects complexes, such as VGa-VO and VGa-Gai-VGa, in β-Ga2O3, is still in its early stages. These defects may exhibit diverse charge states, leading to distinct and significant effects on the properties and behavior of β-Ga2O3 [START_REF] Frodason | Multistability of isolated and hydrogenated Ga--O divacancies in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF]Ingebrigtsen et al., 2019b;[START_REF] Johnson | Unusual Formation of Point-Defect Complexes in the Ultrawide-Band-Gap Semiconductor $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}[END_REF][START_REF] Mcglone | Identification of critical buffer traps in Si δ-doped β-Ga2O3 MESFETs[END_REF][START_REF] Usseinov | Pair vacancy defects in β-Ga2O3 crystal: Ab initio study[END_REF].

Further research in this area is crucial to unraveling the roles of these complex defects.

Positron annihilation [START_REF] Karjalainen | Split Ga vacancies in n-type and semi-insulating β-Ga2O3 single crystals[END_REF][START_REF] Korhonen | Electrical compensation by Ga vacancies in Ga2O3 thin films[END_REF][START_REF] Tuomisto | Ga vacancies and electrical compensation in β-Ga2O3 thin films studied with positron annihilation spectroscopy[END_REF] and scanning transmission electron microscopy measurements are powerful tools to study such defects, combining with GEMaC's home-built Hall effect measurement set up, the roles of complex defects may be expected to put in evidence. The experimental characterizations of these defects by electronic transport studies as well as DLTS spectroscopy, etc., will make it possible to stimulate the ab-initio calculations by experimental parameters.

(ii) The study on the electrical properties as well as the point defects of ZnGa2O4 is only starting, there is much to explore and understand the roles of point defects in both n-type and p-type electrical conductivity. Here, the next step is to continue the work to fully understand the conduction mechanism and its origin (bulk, surface). Surface conduction due to charge accumulation can be studied by XPS analysis on the valence band tails and by electrochemical.

(iii) Regarding the investigation related to electric metal contact to p-type β-Ga2O3, the degradation of (Ti/Pt/Au) contacts at high measurement temperatures up to T = 700 K can be studied by the energy-dispersive X-ray spectroscopy. Otherwise, it was decided to work at lower measurement temperatures (T < 300 °C) that are sufficient for future power device operations. Besides, there should be an entire outer metal pattern, which has a uniform and neglected contact resistance for all the I-V measurements. Additionally, depositing a natural p-type NiO interlayer (~10 -20 nm) between the p-type β-Ga2O3 and the metal (e.g., Pt/Au) contacts. Besides the Ohmic contact, a Schottky contact is also necessary for the DLTS spectroscopy.

B. List of Figures

Titre:

  Propriétés électroniques des semi-conducteurs à ultra-large bande interdite β-Ga2O3 et ZnGa2O4. Mots clés : Semi-conducteur ; Ultra-large bande interdite ; Propriétés électroniques ; β-Ga2O3 ; ZnGa2O4 Résumé : L'amélioration de l'efficacité énergétique et la réduction de la consommation d'énergie sont importantes pour accélérer la préservation du climat. Pour cela, des dispositifs d'électronique de puissance basés sur des semi-conducteurs à ultra-large bande interdite (UWBG) de nouvelle génération sont une solution ultime. Ces dernières années, β-Ga2O3 et ZnGa2O4 ont attiré beaucoup d'attention grâce à leur ultra-large bande interdite (Eg > 4,5 eV) et d'un très fort dopage contrôlé de type n. Cependant, pour réaliser pleinement les fonctionnalités des deux matériaux, des dispositifs de puissance basés sur une structure bipolaire (p-n ou p-i-n) sont nécessaires. Néanmoins, le dopage de type p est un défi pour ces deux oxydes UWBG. expérimentalement les propriétés électroniques des matériaux β-Ga2O3 et ZnGa2O4 en films minces pour évaluer leur potentiel pour des applications en électronique de puissance.

Figure 1 - 2 .

 12 Figure 1-2. Targeted applications of wide bandgap semiconductors (GaN and SiC) andGa2O3. Ga2O3 has potential application in both medium and high-voltage range.

  . It was not until this decade that the research on β-Ga2O3 was rejuvenated due to the limitations of silicon-based electronic devices (low operation temperature and breakdown voltage). β-Ga2O3 itself is also a potential candidate for next-generation power devices because of: (i) its fundamental properties (Section 1.1.1). (ii) the further availability of large-area single crystals by melt growth, and functional epitaxial layers (Section 1.1.2). (iii) easy n-type doping. However, to fully realize the functionality of β-Ga2O3 in electronics, it requires further development on p-type conductivity, thus the control of point defects is a central issue. a state of the art for the current study on defects in β-Ga2O3 and progress in the achievement of p-type is presented in Section 1.1.3.

Figure 1 - 1 (

 11 [START_REF] Mastro | Assessment of the (010) β-Ga2O3 surface and substrate specification[END_REF]. The lattice parameters are a = 12.23 Å, b = 3.04 Å, c = 5.80 Å, and α = γ = 90°, β = 103.83°. Each unit consists of two inequivalent Ga cations and three inequivalent O ions. Ga (I) in the tetrahedral site bonds to four O ions and Ga (II) in the octahedral site bonds to six O ions. O (I) bonds to two Ga (II) ions and one Ga (I) ion, O (II) bonds to one Ga (II) ion and two Ga (I) ions, while O (III) bonds to three Ga (II) ions and one Ga (I) ion. The crystallographically inequivalent sites of different coordination in the unit cell lead to strong orientation dependence and anisotropy of several physical

Figure 1 - 2 .

 12 Figure 1-2. Spinel structure of ZnGa2O4 (W.-K. Wang et al., 2019b).

Figure 1

 1 Figure 1-3. (a) Bulk ZnGa2O4 single crystals synthesized using the VGF/Bridgman method.(b) (100)-oriented wafers prepared from the as-grown and annealed bulk crystals[START_REF] Galazka | Ultra-wide bandgap, conductive, high mobility, and high quality melt-grown bulk ZnGa2O4 single crystals[END_REF].

Figure 2 -

 2 Figure 2-1. MOCVD machine and reactor in GEMaC.

Figure 2 - 2 .

 22 Figure 2-2. Photograph of X-ray diffractometer Bruker-Siemens D5000, in Bragg-Bretano configuration, in GEMaC.

Figure 2 -

 2 3 (b)) in a Van der Pauw configuration (e.g., Ti/Au as shown in

Figure 2

 2 Figure 2-3 (c)).

Figure 2 -

 2 Figure 2-3. (a) Photograph of β-Ga2O3 samples with 4 handmade metallic silver paste contacts, for the resistivity and Hall effect measurements in a Van der Pauw configuration. (b) picture of shadow mask for RF sputtering of metallic contacts. (c) Photograph of β-Ga2O3 samples with sputtered Ti/Au contacts.

  characterize the current-voltage (I-V) measurements of the electrical contacts (Ohmic or Schottky) two-points I-V measurements were performed using Keithley 4200 Semiconductor Characterization System (SCS) (Figure 2-4 (a)) by applying direct voltage, tests are configured and executed from the Keithley Interactive Test Environment (KITE). The measurements at high temperatures were with the help of a Linkam temperature control stage. Besides, to study the photocurrent of ZnGa2O4 thin films, deuterium tungsten high power (DWHP) was used as the UV source with wavelength of 160 -400 nm. The assembly is shown in the Figure 2-4 (b). The tests were performed in a dark environment.

Figure 2 -

 2 Figure 2-4. (a) Keithley Inc. SCS 4200 Semiconductor Characterization System. (b) Photocurrent test platform with fibered lighting.

[- 1

 1 .6 T; 1.6 T] magnetic field ranges (Figure 2-5 (a)). The sample holder (adapted Linkam cell for triaxial connectors to reduce the noise and leakage currents) is shown in Figure 2-5 (b). The number 1 -8 indicates, respectively: 1: exits of water-cooling circuit, 2: sample and heating platform, 3: thermometer connections, 4: air pump, 5: nitrogen inlet, 6: measurement points (example I) with the cables, 7: water inlet, and 8: measurement points (consequently V) with the cables. Triaxial cables and plugs (Keithley) are used to minimize the leakage currents and environment noise.I have studied the electrical properties of the β-Ga2O3 and ZnGa2O4 samples using home-built set up in GEMaC.

Figure 2 -

 2 Figure 2-5. (a) Home-built Hall effect set up in Van Der Pauw configuration. (b) Photo of the measurement cell (adapted Linkam Inc. cell).

Figure 2 - 6 .

 26 Figure 2-6. Van Der Pauw resistivity measurement eight configurations.

Figure 2 -

 2 Figure 2-7. The principle of Hall effect for electrons e-(right) and for hole h (left) inducing in stationary state opposite Hall electric field EH.

Figure 2 - 8 .

 28 Figure 2-8. Van der Pauw Hall effect measurement eight configurations.

Figure 2 -

 2 9 (a) shows a pseudo-linear I-V curve at 570 K with nA current values, which becomes perfectly linear in the measurement range at 850 K (Figure 2-9 (b)) with µA current values, it ensures that the following Hall effect measurements can be carried out. Then, the characteristics majority charge carriers (via the Hall effect measurements) are validated by: (i) The Hall voltage (VH) has the same sign as the applied magnetic field, and increases linearly with the increasing magnetic field if the thin film is p-type, or opposite sign and decreases linearly if the majority of carriers is electron. (ii) The Hall voltages measured in complementary configurations (VHC and VHD) have same sign with similar values (difference < 10%).

Figure 2 - 9 .

 29 Figure 2-9. Results of a representative undoped p-type β-Ga2O3 thin film: (a) -(b) The current-voltage characteristics at 570 K and 850 K, respectively, and (c) -(d)Hall voltage scanned with the perpendicularly applied magnetic field from -1.6 -+1.6 T at 630 K and 850 K, respectively.

  -10), I have studied electrical and magnetotransport properties of n-type ZnGa2O4 samples. in 2 K to 300 K interval, and magnetoresistance 0 -9 T magnetic fields.

Figure 2 -

 2 Figure 2-10. (a) Photo of a sample holder with mounted sample at rotative platform of PPMS-9T (b) 9T PPMS equipment in GEMaC.

  GEMaC laboratory has a Home-made set up, consisting of: two Kelvin probes from Cascade (USA) that we can connect to the Keithley SCS4200 equipment by SubMiniature version A (SMA) connectors and two heaters integrated with the stage with temperature controller (20 -400 °C) (Figure 2-11).

Figure 2 -

 2 Figure 2-11. Home-built Seebeck Effect in GEMaC.

  type β-Ga2O3 thin films grown by the metal organic chemical vapor deposition(MOCVD) technique. The first and essential step before successful acceptor doping is to obtain highquality undoped layers with a low density of donor defects. The first section (3.1) deals with the structural and electronic properties of undoped β-Ga2O3 thin films grown on c-plane sapphire substrate. Owing to the challenges of p-type doping in β-Ga2O3, efforts have been dedicated to finding an effective acceptor dopant at room temperature. Zn is one of the potential candidates among the acceptor dopants. How Zn-doping affects the impurity domination in β-Ga2O3 based on the thermodynamic analysis will be discussed in Section 3.2. Experimental structural, optical, and electrical transport properties of β-Zn:Ga2O3 layers with different doping levels grown on c-plane sapphire substrates by MOCVD will be shown in Section 3.3. Since high-power (voltage) electronic applications are important for β-Ga2O3, the critical electric field ECR is thus a crucial parameter. The breakdown voltage

  201)//Al2O3(0001) and β-Ga2O3 [010]ǁAl2O3[-110]. In the X-ray diffraction (XRD) out-of-plane (OP)  scan, only β-Ga2O3 (-201) reflection and its harmonics were observed as expected (Figure 3-1 (a)). The Bragg angles measured are smaller than those of the bulk, indicating that the lattice is expanded by 0.34% along the normal of the film. The rocking curves of β-Ga2O3 (-201) and its harmonics are of the same shape and angular widths, with a full width at half maximum (FWHM) of ~ 3° (Inset in Figure 3-1 (a)). For in-plane (IP) scan along Al2O3 b*-axis azimuth, β-Ga2O3 (020) and (512) reflections were observed (Figure 3-1 (b)). The Bragg angles are larger than those of the bulk, indicating a lattice contraction of about -0.24%. Along Al2O3 a-axis azimuth, similar lattice contraction was measured with β-Ga2O3 (-201) reflection. It means that the mean strain is in-plane isotropic.

  Figure 3-1. XRD and GIXRD scans in sample β-Ga2O3//c-sapphire. (a) Out-of-plane (OP) scan with in the inset the rocking curve of β-Ga2O3 -201 reflection. (b) In-plane (IP) scan along Al2O3 b*-axis azimuth. The rocking curve of β-Ga2O3 020 reflection is in the inset. Contributions from Cu Kβ radiation and substrate are marked by *.

Figure 3 - 2

 32 Figure 3-2 shows the Raman spectra recorded using 514.5 nm excitation for (-201) textured β-Ga2O3 thin film grown on c-plane sapphire substrates, for a bare c-plane sapphire (0001) Al2O3, and for a (100) β-Ga2O3 single crystal. The primitive unit cell of β-Ga2O3 consists of 10 atoms which results in 30 phonon modes; of which 27 are optical modes. At

(

  index u) are infrared active. According to the authors, the Raman peaks can be categorized into three groups by specific types of different Ga-O bond vibrations. The Raman spectrum for the (-201) textured β-Ga2O3 thin film grown on c-sapphire substrates is a combination of β-Ga2O3 and Al2O3 phonon modes (labelled using ''*''). Notably, no Raman phonon modes belonging to other Ga2O3 polymorphs have been detected, demonstrating that we have a single β-Ga2O3 phase. The β-Ga2O3 thin film Raman phonon modes full width at half maximum (FWHM) is close to that of single crystal β-Ga2O3 and this is indicative of good crystallinity.

Figure 3 - 2 .

 32 Figure 3-2. Raman spectra recorded using 514.5 nm excitation for: red trace: (-201) β-Ga2O3 thin film grown on c-sapphire substrates; grey trace: bare c-sapphire substrate; green trace: (100) β-Ga2O3 single crystal. The phonon modes for β-Ga2O3 are labelled using ''#'' while the phonon modes for a-Al2O3 substrate are labelled using ''*''.

  -3 (a)), which is the highest measurable temperature for our home-built Hall effect set-up, it assures the linear dependence of voltage to current, thus, the electrical contacts are Ohmic. As shown in Figure3-3 (b), the sample was measured in the temperature range of 530 -850 K, at lower temperature measurement was impossible to perform due to very high resistance of the sample. The resistivity ρ = 1.2×10 3 Ω•cm at 840 K, it increases with the temperature decreasing, to 2.6×10 5 Ω•cm at 630 K, showing a typical temperature dependent behavior of a semiconductor. At T < 630 K, the hopping conduction may start to be the dominant conduction mechanism. The activation energy Ea = 1.18 ± 0.02 eV was then determined using the Arrhenius equation for the electrical conductivity σ versus the temperature T (ln(σ) vs. 1000/T plot) (Figure3-3 (c)). Figure3-3 (d) displays the temperature dependent volume resistivities ρA and ρB. As introduced in Chapter 2 (Experimental facilities and methods), ρA and ρB should have similar values (difference < 10%). As shown in Figure 3-3 (d), ρA and ρB have a negligible difference at higher temperatures, indicating that the tested sample as well as the electrical contacts are homogeneous. The difference becomes larger at T < 640 K, which might be attributed to the inhomogeneity of the electrical contacts. Besides, such a high resistance (~ 10 GΩ) to measure nearly attains the limit of our home-built measurement set-up.

Figure 3

 3 Figure 3-3. (a) Typical β-Ga2O3 Ohmic I-V characteristics at 850 K. (b) Resistivity ρ versus temperature. (c) ln(σ) vs. 1000/T plot for the determination of activation energy of conductivity. (d) Temperature dependence of ρA and ρB.

  Figure3-4 (b)shows the mobility in the measurement temperature range, the average mobility μ = 8.7 ± 1.7 cm 2 /(V•s). Such a sizable hole mobility might be due to good crystallinity.

  Figure 3-4 (c) shows the temperature dependent hole concentration at elevated temperatures. The temperature dependence was then analyzed using the general expression for p-type semiconductor based on the Boltzmann statistics (as

Figure 3

 3 Figure 3-4. (a) Hall voltage (VH) versus magnetic field (H) at 800 K and 850 K. (b) Ionization energies of the acceptor center (Ei) determination from ln(pT -3/2 ) vs. (1000/T) plot. (c) Temperature dependence of the Hall free hole concentration in log scale. (d) Hall hole mobility as a function of temperature.

Figure 3

 3 Figure 3-5. Room-temperature optical transmittance for β-Ga2O3 thin film with the estimation of optical band gap by Tauc plot (inset). Oscillations are interferences associated to the film thickness = 450 nm.

Figure 3

 3 Figure 3-6. Photoluminescence spectrum for undoped p-type β-Ga2O3 thin layer excited with 266 nm wavelength at 294 K. Right side: enlarged view of the emission located at around 3.7 eV.

Figure 3 -

 3 Figure 3-7 (a). A zoom of the smallest binding energies further reveals the presence of states within the band gap (Figure 3-7 (b)). The counts per second are normalized to the maximum value in the range of 0-6 eV. The Fermi level is near the conduction band in the case of the commercial Si-doped Ga2O3 reference (~ 4.4 eV). For the Ga2O3 reference, there is no

Figure 3

 3 Figure 3-7. (a) XPS valence band of the β-Ga2O3 valence band for a commercial Si-doped (n-type) reference and our p-type sample. (b) A zoom of the valence band region (VBM) showing the presence of tail states in the lower part of the bandgap for the p-type compounds.

  contacts were prepared: Ohmic contacts were prepared by silver paste painted at 4 corners of square-shaped samples, in order to carry out Hall Effect measurements in a Van der Pauw configuration. The samples are highly resistive requiring measurements at high temperatures (550 -850 K). As is shown in Figure3-8 (a), the higher the deposition temperature, the lower the electrical resistivity (thereby higher the conductivity) of the thin film. For, example, at 850 K,ρ825 K = 3.5×10 2 Ω•cm, ρ790 K = 1.3×10 3 Ω•cm, ρ775 K = 1.4×10 4 Ω•cm.The activation energies of the conductivity were determined to be very similar: Ea = 0.90 ± 0.02 eV, 0.89 ± 0.01 eV, 0.84 ± 0.01 eV, for 775 °C, 790 °C, and 825 °C grown layer, respectively (Figure3-8 (b)). To determine the sign of majority carriers Hall voltage was scanned versus applied magnetic field from 0 to 1.6 T. Figure3-8 (c)The positive slope and the sign of VH confirming that all three samples are of p-type. The measured hole concentrations increase with the increasing growth temperature.

  Figure 3-8 (d) shows hole concentrations versus measurement temperatures. It is clear that Hall hole concentrations aresignificantly different depending on Ga2O3 thin film deposition temperatures. For example, at 850 K, p825 K = 2.1×10 15 cm -3 , p790 K = 6.2×10 14 cm -3 , p775 K = 2.8×10 13 cm -3 .While the activation energies of acceptor obtained by linear fits for ln(pT -3/2 ) vs. 1000/T plots are estimated as Ea ≈ 1.1 eV for all samples. (Figure3-8 (e)) This activation energy corresponds to native VGa acceptor defect, as was shown in Section 3.1.2, having the same activation energies and different carrier concentrations indicates the different compensation level in the samples. In other word, with increasing of growth temperature, the compensating native donor defect concentration decreases.

Figure 3

 3 Figure 3-8. (a) Temperature dependence of resistivity. (b) ln(σ) vs. 1000/T plots and linear fits for the determination of the activation energy of conductivity. (c) Hall voltage (VH) versus applied perpendicular magnetic field (H). (d) Hall hole concentrations versus temperatures. (e) ln(pT -3/2 ) vs. 1000/T plots and linear fits for the determination of the activation energies of acceptor centers.

FigureFigure 3

 3 Figure 3-9:

Figure 3 -

 3 Figure 3-10. (a) XRD patterns for undoped and Zn-doped β-Ga2O3 thin films with different Zn flow (Zn concentration). "*" refers to XRD peaks of c-plane sapphire substrates. (b) Enlarged view of five peaks located at 2θ = 18.94°, 38.38°, 58.98°, 82.14° to show that, there's no transition peak.

Figure 3 -

 3 10 (a) displays the results of the XRD θ-2θ scan for the undoped and Zn-doped β-Ga2O3 thin films with different doping levels, in which 2θ was increased from 10° to 120°. "*" marked at 2θ = 20.62°, 41.74°, and 64.54° refer to the XRD peaks of c-plane sapphire substrates. The XRD patterns of these films are very similar. It can be found that all the undoped and Zn-doped β-Ga2O3 layers possess diffraction peaks located near 2θ positions of 18.94°, 38.38°, 58.98°, and 82.14° which correspond to (-201), (-402), (-603), and (-804) preferential planes of {-201} family of monoclinic β-Ga2O3, respectively, conforming to JCPDS data of β-Ga2O3 (card no. 00-41-1103). We concluded that the studied thin films are a textured (-201) β-Ga2O3 crystalline phase. No secondary phase other than β-Ga2O3 was found. Moreover, focusing on these peaks (Figure 3-10 (b)), all the peaks are at quite similar positions, indicating that the lattice parameters remained comparable although different Zn precursor's flows were used.

Figure 3 -

 3 Figure 3-11 shows the secondary-ion mass spectroscopy (SIMS) depth profiles of Zn dopant content for the three samples at different doping levels. The doping concentrations

Figure 3 -

 3 Figure 3-11. SIMS depth profiles for three Zn doped β-Ga2O3 samples grown at Zn flows at 1.6, 2.8, 3.9 µmol/min, respectively.

Figure 3 -

 3 Figure 3-12 displays the scanning electron microscopy (SEM) top-view images of the films deposited on c-sapphire substrates. It shows smooth granular surface morphology, while there are irregular agglomerations of particulates resembled at the surface of the undoped film. With the increasing amount of incorporated Zn dopants, the surface becomes smoother and finer, the agglomerations become smaller and then invisible on the film with

Figure 3 -

 3 Figure 3-12. Scanning electron microscopy (SEM) top-view images of (a) -(d) undoped, [Zn] = 10 16 cm -3 doped, [Zn] = 10 18 cm -3 doped, and [Zn] = 10 19 cm -3 doped β-Ga2O3 grown on c-plane sapphire substrate, respectively.

  doped β-Ga2O3 thin films at room temperature, covering a broad wavelength range from ultra-violet (UV) to near infra-red (NIR). The transmittance spectra showed that all the thin films exhibit high transparency in the vis-NIR range, with a sharp cut-off in the deep ultraviolet (DUV) region, as depicted in Figure3-13 (a). The little "cusp" at around 860 nm is artificial for all the spectra, due to the detector change in the spectrophotometer. The average transmittance of the films (with the increasing Zn concentration) in the visible (vis) range (380 -700 nm) is 83%, 77%, 80%, and 76%, respectively. The absorption coefficient α of the films was calculated from the transmittance and reflectance measurements, and the optical band gaps Eg were then estimated using Tauc plot for direct band gap materials, which plots (αE)2 vs. E as shown in Figure3-13 (b). The corresponding "cut-off" wavelengths of all the films were found to be below 280 nm, falling in the UV-C range. Considering the error bars, the band gaps remained comparable after Zn incorporation.

Figure 3 -

 3 Figure 3-13. (a) Optical transmittance. (b) Tauc plots (for the determination of the optical band gap). (c) Optical band gaps with error bars versus incorporated Zn concentrations. Different oscillations periods are connected to different film thicknesses.

  Hall Effect measurements were carried out at the temperature range of 500 -850 K. As shown in Figure 3-14, the positive VH increases linearly with a perpendicularly applied increasing magnetic field from 0 to 1.6 T at elevated temperature, indicating that all β-Zn:Ga2O3 samples are p-type. We can note that this figure shows how a continuous variation of magnetic field up to quite a high value (±1.6 T), gives undisputable evidence of the conductivity type (n or p), independently of zero voltages experimental off-set (changing here from zero, positive to negative values).

Figure 3 -

 3 Figure 3-14. Hall voltage (VH) versus magnetic field (H) for Zn-doped β-Ga2O3 with increasing doping levels. Each Hall voltage value and corresponding slope are positive, which is an indication of the p-type conductivity in the samples.

Figure 3 -

 3 Figure 3-15 (a) displays the temperature dependent resistivity of undoped and low ([Zn]= 10 16 cm -3 ) doped β-Ga2O3 thin films in the temperature range of T = 500 to 850 K. It is clearly seen that the resistivity was decreased after Zn incorporation comparing to undoped β-Ga2O3 thin film. For example, at 550 K, the resistivity is ρ = 6.4×10 5 Ω•cm for undoped sample, while ρ = 1.1×10 5 Ω•cm for 10 16 cm -3 [Zn] doped sample. Two conductivity mechanisms can be distinguished corresponding to band activation at around T > 600 K and hopping conduction regime at lower temperatures. Temperature dependent Hall effect measurements revealed a clear increase in free hole concentration after Zn incorporation compare to undoped films. At T = 600 K, hole concentration p = 6.7×10 12 cm -3 for the undoped sample, while for β-Zn:Ga2O3 it increases up to 1.7×10 13 cm -3 Figure 3-15 (b).

3/ 2 )

 2 vs. (1/T) plot (Figure3-15 (c)). The ionization energy Ei =1.1 eV for the undoped sample can be related to VGa acceptor level as reported(Chikoidze et al., 2017b;[START_REF] Chikoidze | Enhancing the intrinsic p-type conductivity of the ultra-wide bandgap Ga2O3 semiconductor[END_REF]. It was decreased to 0.77 eV for 10 16 cm -3 [Zn] doped sample. It is believed that Zn substitutes one gallium atom (ZnGa) thus creating an acceptor level at Ei = 0.77 eV which is completely consistent with the reported thermal activation energy of 0.65 eV and 0.78 eV determined by electron paramagnetic resonance (EPR) spectroscopy for the two ZnGa sites[START_REF] Gustafson | Zn acceptors in β-Ga2O3 crystals[END_REF]. Hall hole mobilities are slightly decreased after Zn incorporation (i.e., μ = 8.7±1.7 cm 2 /(V•s) for undoped, and μ = 7.3 ± 1.1 cm 2 /(V•s) for β-Zn:Ga2O3 in the measurement temperature range) being in both cases weakly depending on T (Figure3

Figure 3 -

 3 Figure 3-15. (a) Temperature dependence of the resistivity. (b) Hole concentration versus temperature. (c) ln(pT -3/2 ) vs. 1000/T plots and linear fits for the determination of the ionization energies. (d) Hall hole mobilities versus temperature. Black squares are for undoped and red disks for Zn-doped Ga2O3 ([Zn] = 10 16 cm -3 ) thin films.

  2.2. As shown in Figure 3-16 (b), both undoped and Zn-doped β-Ga2O3 samples exhibit activation energy of conductivity of Ea = 1.18 ± 0.02 eV. The Hall holes mobility is μ = 2.8 ± 1.5 cm 2 /(V•s) in the measurement temperature range (Figure 3-16 (d)). Such a decrease in hole mobility can be attributed to the high level of doping, resulting in the increase of scattering on Zn impurities.

Figure 3 -

 3 Figure 3-16. (a) Temperature dependence of resistivity. (b) ln(σ) vs. 1000/T plot for the determination of the activation energies. (c) Hall hole concentrations versus temperature. (d) Hall hole mobilities versus temperature. Samples: undoped (black) and Zn-doped Ga2O3 ([Zn] = 10 18 cm -3 (blue), 10 19 cm -3 (green)) thin films.

Figure 3 -

 3 Figure 3-18 displays comparable XRD patterns of undoped and Zn-doped (at 10 19 cm - 3 ) β-Ga2O3 thin films on Si (111) substrates. Both layers are polycrystalline with the most intense peaks of {-201} family of β-Ga2O3, and additional random orientations with tiny XRD peaks. The Zn concentration in β-Zn:Ga2O3 layer estimated by SIMS is 3.2×10 19 cm - 3 , which is comparable with the simultaneous growth carried out on a sapphire substrate. This value agrees very well with the value extracted from the energy-dispersive X-ray spectroscopy (EDX) profile (0.56%) from high-resolution transmission electron microscopy (TEM) measurements. A thin native SiO2 layer (2 -3 nm) at the β-Ga2O3//Si interface was evidenced as shown in Figure 3-19 (a). The selected area electron diffraction (SAED) image

Figure 3 -

 3 Figure 3-18. XRD patterns of undoped (black) and Zn-doped (green, doping level at 10 19 cm -3 ) β-Ga2O3 thin films on conducting Si (111) substrates. "*" refers to the peaks of Si (111) substrates.

Figure 3 -

 3 Figure 3-19. (a) High-resolution TEM cross-section image of β-Ga2O3 grown on Si (111) substrate. SAED patterns of (b) the Si(111) substrate, (c) β-Zn:Ga2O3 layer, and (d) interface between β-Zn:Ga2O3 layer and Si substrate, respectively. (Experiment is done in ICN2, Barcelona Spain)

Figure 3 -

 3 Figure 3-20. (a) Sketch of the vertical heterojunction structures (β-Ga2O3/Si and β-Zn:Ga2O3 //Si) with Ti/Au metal contacts on the top of the Ga2O3 layers. (b) Experimental I-V curves of vertical breakdown voltage measurements through the β-Ga2O3//Si and β-Zn:Ga2O3:Zn//Si structures, indicating a hard breakdown voltage up to 124 V and 540 V at room temperature, respectively.

Figure 3 -

 3 21 summarizes the results related to electrical transport results, as follow:

Figure 3 -

 3 Figure 3-21. Schematic illustration of Zn doping effect.

Figure 4 -

 4 Figure 4-1 (a) displays the XRD patterns for undoped and Zn-doped thin films. The diffraction peaks corresponding to the c-sapphire substrate are labelled "*". For the undoped sample, the five peaks with the increasing 2θ position correspond to the crystalline plans (-201), (-402), (-603), (-804) and (-1005) of the monoclinic β-Ga2O3, respectively. Focusing on Zn incorporated samples, they possess five diffraction peaks located near 2θ positions of 18.5 -19.0°, 37.5 -38.5°, 57.0 -59.0°, 79.5 -82.5°, and 106.0 -110.5°. There are new peaks shifted to lower 2θ values appear and become more intense with the increasing Zn content, while simultaneously the reflections corresponding to β-Ga2O3 start to be less intense and diminish at the end. As shown in Figure 4-1 (b), the enlarged views for these 2θpositions show the same situation for all the peaks. The double peaks presented in the sample with 6.85%[Zn] indicate the coexistence of two crystalline phases. When Zn content increased up to 14.04%, the peaks corresponding to β-Ga2O3 do not exist anymore. These new peaks appear at 2θ values of18.47, 37.40, 57.50, 79.70, and 106.42° are attributed to the cubic spinel ZnGa2O4, and correspond to (111), (222), (333), (444), and (555) plans, respectively. The shift in 2θ peak position of ZnGa2O4 can be ascribed to the inclusion of Zn 2+ in the β-Ga2O3 structure, and the increasing d-spacing (interplanar distance). Similar results are also reported by other groups with high Zn incorporation concentrations in β-

Figure 4

 4 Figure 4-1. (a) XRD patterns for undoped and Zn incorporated β-Ga2O3 thin films with different Zn flow (Zn concentration). "*" refers to the peaks of c-plane sapphire substrates. (b) Enlarged views for 2θ = 17.1 -19.9°, 36.6 -39.1°, 56.0 -60.5°, 78.2 -83.5°, and 103.0 -114.0° to show the double-peak features and the transition of peaks.

Figure 4 - 2 .

 42 Figure 4-2. Raman scattering spectra for pure β-Ga2O3, mixed GaO/ZnGaO, and pure ZnGa2O4.

Figure 4

 4 Figure 4-3. (a) X-ray diffractograms of as-grown n-type and p-type ZnGa2O4 thin films grown c-sapphire, the peak labelled by "*" indicates the XRD reflection corresponding to the sapphire substrate.

  Figure 4-4 (d) shows the fast Fourier transform of the TEM image. Both images indicate that the ZnGa2O4 films have a "single-crystalline" structure.

Figure 4

 4 Figure 4-4. High-resolution transmission electron microscope (HRTEM) images for (a) ntype ZnGa2O4 thin film and (b) p-type ZnGa2O4 thin film. (c) SAED images of n-ZnGa2O4 and (d) The fast Fourier transform of the image p-ZnGa2O4. The experiments were carried out in National Chiao Tung University.

  Figure 4-5 shows the room-temperature XPS spectra of n-ZnGa2O4 sample, the 3 curves correspond to 3 different places of probing on the sample surface. Ga, Na, Zn, O, and C have been detected. Films

Figure 4

 4 Figure 4-5. XPS spectra of 3 probed places on the surface of n-ZnGa2O4 sample.

  : (i) Ga (Td): Ga-O = 1.83 Å and O-O = 3.02 Å. (ii) Ga (Oh): Ga-O = 2.00 Å and O-O = 2.84 Å. The inter-ionic distances for ZnGa2O4 are: Zn(Td)-O = 1.95 Å and Ga(Oh)-O = 2.00 Å, respectively (Errandonea et al., 2009). All the Zn-O bonds are tetrahedral for both, normal ZnGa2O4 and reference wurtzite ZnO where Zn-O bond lengths are usually reported to be Td Zn-O ~2.0 Å (Zn-Zn/O-O ~3.2 Å). Focusing on the ZnGa2O4 samples, the Ga2p3/2 (Figure 4-6 (a)) and Zn2p3/2 (Figure 4-6 (c)) peaks appear at 1118.2 eV and 1022.2 eV for p-ZnGa2O4 and at 1118.1 eV and 1022.0

Figure 4 - 6 .

 46 Figure 4-6. Zoom (intensity normalized) of the main XPS peaks for (a) gallium (Ga2p -Ga2p3/2), (b) oxygen (O1s), (c) zinc (Zn2p -Zn2p3/2), (d) adventitious carbon contamination (C1s, calibration for C-C bonds at 284.8 eV) of n-type ZnGa2O4, pure β-Ga2O3, pure wurtzite ZnO and p-type ZnGa2O4 for comparison. (e) Deconvolution of the main contributions of the O1s oxygen peak for spinel ZnGa2O4.

  Band gap of n-and p-ZnGa2O4 layersI would like to focus on the experimental valence band features extracted from the XPS analysis, as shown in Figure4-7. All the valence band edge has been shifted using the adventitious C-C 284.8 eV following the same procedure as with the core levels (Figure4-6(c)). The experimental valence band width of the ZnGa2O4 thin films is around ~8 eV, having to main contributions; the top of the valence (lower binding energies) is ascribed to O2p states while there is an important contribution at larger binding energies due to Zn3d states peaking at 10.8 eV (n-ZnGa2O4) and 8.2 eV (p-ZnGa2O4). So, the binding energy shifts (BE ~2.6 eV) of the valence band Zn3d peaks (when comparing n-type and p-type ZnGa2O4) is much more pronounced than the one from the core levels. Again, there is a strong reminiscence of the n-ZnO valence band shape and n-ZnGa2O4 in terms of intensity and energy, except for a valley located at 8,6 eV for ZnO (as if the Zn3d and O2p states were more separated for ZnO). Analogously, Ga3d features present in ZnGa2O3 and Ga2O3 in the second valence band peaks at 20.3 eV for n-ZnGa2O4 and Ga2O3 (either n or p) while peaks at 17.7 eV for p-ZnGa2O4 (BE ~2.6 eV). Therefore, in practice, the Fermi level (as determined from the top band slope) is shifted ~2.8 eV from p-ZnGa2O4 (EF ~ 0.5 eV), up to EF ~3.3 eV for n-ZnGa2O4. This result agrees well with the fact that the Fermi energy is in the upper part of the bandgap for n-ZnGa2O4 and in the lower half of the bandgap for p-

  Optical transmittance and optical bandgap determination by Tauc's plot for n-ZnGa2O4 and p-ZnGa2O4 samples are shown in Figure 4-8. The p-type thin layer exhibits high transparency > 80%, and the n-type has even higher transparency ~95% in 360 to 1000 nm wavelength range. The values of optical bandgaps determined from absorption edges in UV region are 4.9 eV and 4.8 eV, respectively (Figure 4-8 (b)). Contrary to the sharp edge of p-ZnGa2O4, for the n-ZnGa2O4 sample, there is another absorption band at around 360 nm (Figure 4-8 (a))

Figure 4

 4 Figure 4-7. (a) Experimental XPS high-resolution valence band for the n-type ZnGa2O4 and p-type ZnGa2O4 as a reference. (b) Experimental XPS high-resolution of the first valence band group for n-type ZnGa2O4, p-type ZnGa2O4, pure ZnO and pure ptype β-Ga2O3 for comparison. (c) Idem, for the first and the second group of valence bands. (d) A zoom of the valence band region (VBM) showing the presence of tail states in the lower part of the bandgap for the p-type compounds (the value of the bandgap is depicted for ZnO, β-Ga2O3 and ZnGa2O4).

Figure 4

 4 Figure 4-8. Room temperature optical transmittance spectra and in inset direct bandgap determination by Tauc's plot for both n-type (a) and p-type ZnGa2O4 (b) thin films.

  Electrical transport measurement of undoped p-type ZnGa2O4 thin film was carried out in a Van der Pauw configuration, Figure 4-9 (c), (d).

Figure 4

 4 Figure 4-9. n-ZnGa2O4 thin film (a) electrical resistivity versus temperature dependence from aligned four-probe measurements; (b) electron concentration from Hall effect measurements in Van der Pauw configuration. Pure p-type ZnGa2O4 layer (c) electrical resistivity and (d) hole concentration versus temperature determined from Hall effect measurement.

  However, for our n-type zinc gallate sample, there is no important change of resistivity, which could indicate the metal-insulator transition (MIT) (Figure4-10 (a)). It emerges that the disorder due to the self-doping effect is not strong enough, indicating the relatively low deviation from stoichiometry.

Figure 4 -

 4 Figure 4-10. n-type ZnGa2O4 (a) log(σT) versus 1/T in the nearest-neighbor hopping regime; (b) ln(σ) versus T -1/4 showing the variable range hopping regime (VRH); (c) Resistance versus magnetic field at different temperatures (2 -100 K) in perpendicular to current magnetic field orientation. Measurements were done in four-probe aligned configuration.

  quality p-type and n-type ZnGa2O4 epilayers can be grown by tuning, oxygen flow and cation ratio during metal-organic chemical vapor (MOCVD) deposition. State-of-the-art analytical techniques provide no evidence of contamination or secondary phases. The intrinsic conductivity can be tuned up to 10 orders of magnitude as summarized in Figure 4-11. These experimental facts raise-up the immediate question: what is the origin of the high n-type conductivity in ultra-wide band gap ZnGa2O4. Here, based on complementary structural, chemical, optical and electrical transport measurements, we conclude that the origin of high room temperature n-type conductivity (~3.2 ×10 -2 Ω cm at room temperature) is related to the "self-impurity" band located at Ev+ ~3.4 eV from the valence band edge. This band is a consequence of Zn-O orbital's hybridization in Zn-rich and O-deficient ZnGa2O4 material. While other hand, hole conductivity ZnGa2O4 occurred thanks to ZnGa antisite defects.

Figure 4 -

 4 Figure 4-11. Schematic summary showing the intrinsic conductivity difference between conducting n-type and semi-insulating p-type ZnGa2O4 thin films, with the corresponding conduction mechanism and origin of the conductivity.

Figure 4 -

 4 Figure 4-12. Cu-Kα XRD θ-2θ patterns of both ZnGa2O4 thin films, the c-plane sapphire substrate is labelled as "*".

Figure 4 -

 4 Figure 4-13. (a) TEM cross-section image of ZnGa2O4-#1 thin film. (b) High resolution TEM image. (c) SAED pattern of the ZnGa2O4-#1 film, selected part is shown in the red circle in figure (b). The results were provided by collaborators from National Chiao Tung University.

Figure 4 -

 4 Figure 4-14 (a) shows a quasi-Ohmic current-voltage (I-V) characteristics of the ZnGa2O4-#1 thin film. The temperature-dependent resistivity (ρ) in the range of 80 -500 K is shown in Figure 4-14 (b), the resistivity decreased very slightly from 4.9×10 -1 Ω•cm at 80 K to 1.6×10 -1 Ω•cm at 500 K. From the temperature dependence of the conductivity σ, in ln(σ) versus 1000/T plot (Figure 4-14 (c)), a single law can be fitted to the entire curve in the measurement temperature range, and a tiny activation of conductivity as Ea = 10 ± 0.4 meV was determined using the Arrhenius equation. Despite multiple attempts over the entire temperature range, the Hall effect measurements could not be validated due to the anomalous sign of the Hall coefficient. Generally, this observation might be due to the hopping conduction (too low mobility) or elevated charged carriers (too low Hall voltage). The ntype nature was later confirmed by the Seebeck effect. Compared to the n-type sample discussed in Section 5.2, the conductivity of this sample is one order of magnitude less, which can be explained by different growth parameters.

Figure 4 -

 4 Figure 4-14. For ZnGa2O4-#1 thin film: (a) Current-voltage (I-V) characteristics at 300 K; (b) Temperature-dependent resistivity (ρ) in the range of 80 -500 K; (c) ln(σ) versus 1000/T for the determination of the activation energy of the conductivity. For the ZnGa2O4-#2 which was cooled in O2: (d) I-V curve at 750 K; (e) Temperature-dependent resistivity in the range of 550 -750 K; (f) ln(σ) versus 1000/T; (g) Hall voltage (VH) versus magnetic field at 750 K, both the values of the Hall voltage and the slope are positive, indicating the p-type conductivity of the ZnGa2O4 sample; (h) Temperature-dependent hole concentration (p) in 550 -750 K.

Figure 4 -

 4 Figure 4-15 displays the room-temperature transmittance spectra for (i) ZnGa2O4-#1, (ii) O2 cooled ZnGa2O4-#2 layers, and (iii) the n-type ZnGa2O4 thin film discussed in Section 4.2 that has an obvious double absorption in optical spectrum (Figure 4-8 (a)), and an one

Figure 4 -

 4 Figure 4-15. Optical transmittance for as grown, O2 cooled ZnGa2O4 samples, n-type ZnGa2O4 thin film discussed in Section 4.2, and only one face polished bare sapphire substrate as reference.

2 (

 2 -16 (d)). Ga2p3/2 binding energy peaks appear at 1117.4 and 1117.8 eV for ZnGa2O4-#1 and ZnGa2O4-#2 samples, respectively (Figure 4-16 (a)). For Zn2p3/2 peaks, sample ZnGa2O4-#1 has a much lower intensity than sample ZnGa2O4-#2 cooled in O2 (Figure 4-16 (b)), indicating an important Zn deficient nature in ZnGa2O4-#1. Regarding O1s peaks, the shoulder feature for the n-type ZnGa2O4 thin film discussed in Section 4.Figure 4-6 (b)) was not observed here (Figure 4-16 (b)).

Figure 4 -

 4 Figure 4-16. XPS peaks for (a) gallium (Ga2p -Ga2p3/2), (b) zinc (Zn2p -Zn2p3/2), (c) oxygen (O1s), (d) adventitious carbon contamination (C1s, calibration for C-C bonds at 284.8 eV) of both ZnGa2O4-#1 and ZnGa2O4-#2 samples.

2. 7

 7 nA under UV illumination (Figure 4-17 (a)). The ratio between photo-current (Iphoto) and dark current (Idark) is ~10 3 , showing a great photo-sensibility.

Figure 4 -

 4 17 (b) shows the time-dependence of the photo-response measured under periodically on/off switched UV

Figure 4 -

 4 Figure 4-17. (a) room-temperature I-V curves under dark and illumination. (b) Dynamic photo-response under UV lamp illumination at a 5 V bias of the ZnGa2O4-#2 thin film.

Figure 4 -

 4 Figure 4-18. Cu-Kα XRD spectra of ZnGa2O4 thin film grown on Si(111) (black), and Al2O3(0001) (red). * and # correspond respectively to Al2O3(0001) and Si(111) Bragg reflections.

Figure 4 -

 4 Figure 4-19 (a) shows a typical Ohmic current-voltage (I-V) behavior at different temperatures. The ohmic contact was made with silver paste painted at four corners of the sample in a square shape. The resistivity versus temperature for the spinel ZnGa2O4 sample is shown in Figure 4-19 (b). At 850 K, the resistivity was measured as 1.9×10 2 Ω•cm, and increased to 5.3×10 4 Ω•cm at 550 K. Hall voltage (𝑉 𝐻 ) versus magnetic field (0 -1.6 T) at 700 -850 K for a ZnGa2O4 sample is shown in Figure 4-19 (c), the positive 𝑉 𝐻 increases with a perpendicularly applied magnetic field in a Van der Pauw configuration, which evidenced that our spinel ZnGa2O4 thin film has p-type conductivity at elevated temperature. The temperature dependence for Hall hole concentration is shown in Figure 4-19 (d) for ptype ZnGa2O4 film, the hole concentration was measured between 8.8×10 11 and 3.7×10 15

Figure 4 -

 4 Figure 4-19. (a) Ohmic I-V characteristics at 700K and 850 K (b) Resistivity versus temperature. (c) Hall voltage (VH) versus magnetic field at different temperatures (700 -850 K). The Hall voltage is positive and increase with the increasing applied magnetic field, indicating the p-type conductivity in ZnGa2O4 layer. (d) Temperature dependence for Hall free hole concentration for ZnGa2O4 thin film.

  capacitors has been fabricated by depositing Ti/Au contacts (with a size of 170 µm × 300 µm) onto p-type ZnGa2O4 grown onto the conducting Si thin films (Figure 4-20 (a)). Figure 4-20 (b) shows the scanning electron microscopy (SEM) cross-section image revealing that the thickness of the ZnGa2O4//Si is 600 nm. Negative bias has been applied on an isolated Ohmic contact with the grounded substrate to access the breakdown voltage. The vertical breakdown voltage VBR was in the range of 270 to 350 V (Figure 4-20 (c)). It can be pointed out that a low leakage current below 1 mA/mm 2 is observed all the way to the breakdown voltage. A thin SiO2 layer (2 nm) at the interface ZnGa2O4//Si can often be seen (W.-K. Wang et al., 2019b) after the growth. To exclude the influence of the SiO2 layer, a bare Si substrate with a native SiO2 (2 -3 nm thick layer) has been characterized as well. The vertical breakdown voltage of around 10 V (Chikoidze et al., 2020c) is considered to produce a negligible contribution to the experimentally measured VBR of p-type ZnGa2O4//Si structure.Taking the experimentally determined 600 nm thickness for the ZnGa2O4 layer and extracting bare Si substrate related 𝑉 𝐵𝑅 into account, the average vertical critical electric field across the film can be as high as 𝐸 𝐶𝑅 = 5.3 MV/cm, which is already significantly larger than the one from SiC and (single crystal) GaN.

Figure 4 -

 4 Figure 4-20. (a) Sketch of the vertical heterojunction structure with Ti/Au metal contacts. (b) SEM cross-section image of ZnGa2O4 polycrystalline film deposited on Si(111). The estimated thickness of the film is 600 nm. (c) Experimental I-V curves of vertical breakdown voltage measurements through the ZnGa2O4//Si structure, indicating a breakdown voltage up to 350 V at room temperature.

Figure 5

 5 Figure 5-1. Schematic of band diagram for (a) Au/Ti/ITO and (b) Au/Ti/AZO on GaO.

  Rtot vs. gap spacing di plot (Figure5-3 (c)). It was demonstrated that the majority of the voltage drop underneath the metal contact takes place within the length of √

Figure 5

 5 Figure 5-3. Schematic illustration of the transfer length method (a) patterns, (b) schema to show the transfer length (Hao Yu et al., 2014), (c) contact resistance and sheet resistance determination by Rtot vs. di plot.

Figure 5

 5 Figure 5-4. (a) Schematic cross-sectional diagram of equivalent circuit in the CTLM measurement technique. The metallization is formed on the inner pad and the areas outside the rings. Where r is the radius of the inner circle (inner metal pad), rout is the outer circle radii, di is the gap spacing between inner and the outer circles. Each group of CTLM pattern includes 6 rings with constant inner circle radius (r) but different outer circle radii (rout). (b) Corresponding schematic top-view of electrodes in a single CTLM pattern.

  This equipment is compatible with the g-line (light sensitivity at ~ 435 nm) photoresists.(v) UV exposure: The substrate is exposed to UV light with the objective of ×1, through the mask designed (e.g., Figure5-5 (c)). The light power density using this objective is fixed at 10.2 mW/cm 2 .(vi) Development: The substrate is immersed in a developer solution that removes the soluble regions of the photoresist, leaving behind the desired pattern. The corresponding developer for AZ1512HS is the AZ developer solution, for AR-P 5350 is a mixed AR 300-35 solution and DI water (1:2). After the development, the samples were immersed in DI water to stop the reactions.

(

  vii-3) Pt (200 nm). Based on Schottky-Mott relation, it is easier to form Ohmic contact to p-type semiconductor using a metal with higher work function. According to the CRC Handbook of Chemistry and Physics (Haynes, 2014), Pt has the highest work function (ΦM = 5.6 -6 eV) among the metals.

Figure 5

 5 Figure 5-5. (a) spin coater "POLOS SPIN150i" in GEMaC. (b) UV-exposure equipment "Smart Print" in GEMaC. (c) An example of designed pattern for lithography process. Right part is circular transmission line model (CTLM) patterns for the contact resistance study, the diameter of inner circular is 0.25 mm, the ring between two circulars are 40, 60, 80, 100, 120, 140 µm, respectively.

Figure 5

 5 Figure 5-6. Microscope image of the CTLM patterns for trail (a) n°1, (b) n°4, (c) n°5 (after development, before metal deposition), (d) n°6 (designed gap di = 120 µm), (e) n°7 (designed gap di = 46 µm) with the enlarged view of the gap, (f) n°9. The lithography parameters for each trail are summarized in the Table5-2. For figure (g), due to the limit of magnification, the whole group of patterns could not be captured together, each concentric circle was captured separately with the same magnification and then merged.

Figure 5 - 8

 58 Figure5-8 shows the linear I-V curves of sputtered Ag contact in a Van der Pauw configuration on p-type β-Ga2O3, at temperatures T decreasing between 700 K and 500 K (in this temporal order), indicating the Ohmic behavior at the tested temperature range.

Figure 5

 5 Figure 5-8. I-V curves for sputtered Ag contact at temperatures ranging between 700 -550 K.

Figure 5

 5 Figure 5-9 (a)-(d) show the I-V characteristics of Ti/Pt/Au contact at temperatures between 700 K and 550 K, all the curves are linear in the measurement temperature range.

2 )

 2 figure 8. At 700 K, the sheet resistance RS = 3.8 ± 2.9 ×10 6 Ω/sq, the specific contact resistance ρC = 4.9 ± 1.2 ×10 2 Ω•cm 2 . While they were increased to RS = 7.6 ± 4.6 ×10 9 Ω/sq, ρC = 3.8 ± 1.1 ×10 5 Ω•cm 2 at 450 K. It is clear that the contact resistance increased significantly with the decreasing temperature, with an "exponential-like" dependence (Figure5-11 (a) in the semi-log plotting for both quantities versus T).

Figure 5

 5 Figure 5-9. I-V curves of Ti/Pt/Au contact at different temperatures (700 -450 K), and different spacing di.

Figure 5 -

 5 Figure 5-10. Total resistance Rtot plotted versus gap spacing di for Ti/Pt/Au contact between T = 700 K and 450 K.

Figure 5 -

 5 Figure 5-11. (a) The calculated sheet resistance (RS) (black) of β-Ga2O3 film and the specific contact resistance (ρC) (red) plotted versus temperature in semi-log shifted scales. (b) The first measurement (black) and the final measurement (dark yellow) after conducting all the I-V tests for the pattern with gap spacing di = 140 µm at 600 K.

Figure 5 -

 5 Figure 5-12. I-V curves of Pt contact at different temperatures (600 -500 K).

  Photolithography parameters has been first adjusted to get the desired dimensions of patterns, Ag, Ti/Pt/Au and Pt contacts were deposited on p-type β-Ga2O3 thin films. I-V curves of Ag/β-Ga2O3 are linear at 550 -700 K temperature range, indicating an Ohmic behavior. Pt/β-Ga2O3 contact starts to rectify at T < 500 K. Ti/Pt/Au forms a quasi-Ohmic contact to p-type β-Ga2O3 in the measurement temperature range.

Figure 5 -

 5 Figure 5-13. Schematic illustration for a new version of CTLM patterns, with large outer metallic electrode.

  Ga2O3 layers were epitaxially grown on c-plane sapphire substrates using the MOCVD technique. For the film grown at T = 775 °C, P = 30 Torr, with the gallium precursor flow fixed at 6 µmol/min, and O2 flow at 600 sccm, it exhibited high transparency (> 80%) in the visible to near-infrared wavelength range with an optical band gap of Eg = 4.66 ± 0.05 eV.The p-type conductivity at high temperatures (T = 550 -850 K) was shown by Hall effect measurements. The native p-type conductivity is attributed to the native gallium vacancy (VGa) acceptor defect with an ionization energy of Ei ~1.2 eV. This achievement encouraged us to study acceptor doping in β-Ga2O3.

  photocurrent for the p-type ZnGa2O4 layer showed an important UV sensibility (IUV/Idark ~10 3 without metallization). The vertical geometry breakdown voltage measurements of the p-ZnGa2O4//Si structure delivered breakdown voltage up to 350 V, resulting in ECR > 5.3 MV/cm. It is also the first experimental determination of the critical electric field for ZnGa2O4.

Figure 1 - 1 .Figure 1 - 2 .Figure 1 - 2 .Figure 2 - 2 .Figure 2 Figure 2 Figure 2 - 7 .Figure 2 - 8 .Figure 2 - 9 .Figure 2 -Figure 2 -Figure 3 - 2 .Figure 4 - 2 .Figure 5 - 2 .

 111212222227282922324252 Figure 1-1. Comparison of semiconductor material parameters (Speck and Esmat, 2023).-2 -Figure 1-2. Targeted applications of wide bandgap semiconductors (GaN and SiC) and Ga2O3. Ga2O3 has potential application in both medium and high-voltage range. ........................................................................................................................ -3 -Figure 1-1. Unit cell of β-Ga2O3 (Mastro et al., 2020). .................................................... -8 -Figure 1-2. Spinel structure of ZnGa2O4 (W.-K. Wang et al., 2019b). ........................... --Figure 1-3. (a) Bulk ZnGa2O4 single crystals synthesized using the VGF/Bridgman method. (b) (100)-oriented wafers prepared from the as-grown and annealed bulk crystals (Galazka et al., 2019). .................................................................................. --Figure 1-4. Illustration of cations inversion in spinel ZnGa2O4. .................................... --Figure 2-1. MOCVD machine and reactor in GEMaC. .................................................. --Figure 2-2. Photograph of X-ray diffractometer Bruker-Siemens D5000, in Bragg-Bretano configuration, in GEMaC. ............................................................................ --Figure 2-3. (a) Photograph of β-Ga2O3 samples with 4 handmade metallic silver paste contacts, for the resistivity and Hall effect measurements in a Van der Pauw configuration. (b) picture of shadow mask for RF sputtering of metallic contacts. (c) Photograph of β-Ga2O3 samples with sputtered Ti/Au contacts. ............ --Figure 2-4. (a) Keithley Inc. SCS 4200 Semiconductor Characterization System. (b) Photocurrent test platform with fibered lighting. ......................................... --Figure 2-5. (a) Home-built Hall effect set up in Van Der Pauw configuration. (b) Photo of the measurement cell (adapted Linkam Inc. cell). ....................................... --Figure 2-6. Van Der Pauw resistivity measurement eight configurations....................... --Figure 2-7. The principle of Hall effect for electrons e-(right) and for hole h (left) inducing in stationary state opposite Hall electric field EH......................................... --Figure 2-8. Van der Pauw Hall effect measurement eight configurations. ..................... --Figure 2-9. Results of a representative undoped p-type β-Ga2O3 thin film: (a) -(b) The current-voltage characteristics at 570 K and 850 K, respectively, and (c) -(d) Hall voltage scanned with the perpendicularly applied magnetic field from -1.6 -+1.6 T at 630 K and 850 K, respectively. ................................................. --Figure 2-10. (a) Photo of a sample holder with mounted sample at rotative platform of PPMS-9T (b) 9T PPMS equipment in GEMaC. .......................................... --Figure 2-11. Home-built Seebeck Effect in GEMaC. ..................................................... --

Table 1

 1

	-1. Outcome of β-Ga2O3 bulk crystal growth methods. Remarks (a) and (b) refer to:
			a) in diameter, b) in width.
	Method	Verneuil	FZ	CZ	EFG	VB
	Bulk size	3/8-inch a 1-inch b	1-inch a	2-inch a	6-inch b 4-inch a	2-inch a
	Growth rate [mm/h]	10	20 -40	2	15	5
	FWMH [arcsec]	-	22	22 -50	17	10 -50
	Dislocation density [cm -2 ]	-	-	~10 3	10 3	10 2 -2×10 3
	Residual impurity [cm -3 ]	2×10 18	~10 17 (Si, Sn)	~10 16 (Si)	~10 17 (Si)
		~10 19 (Mg) ~10 21 (Zr) 900°C	~10 19 (Nb, Ta)	~10 19 (Sn, Si, Hf)	6-7×10 18 (Si, Sn)	3.6×10 18 (Sn)

Table 1

 1

	-2 summarizes some parameters and research outcomes for β-Ga2O3 and
	ZnGa2O4. it should be underlined that the study of point defects and electronic structure in
	both semiconductors is still strongly required.

Table 3 -

 3 1. Lattice parameters of sample β-Ga2O3//c-sapphire inferred with the OP tensile strain of 0.34% and the IP compressive strain of -0.24% measured.

  Where the ND, NA, NV, p, EA, and kB being the donor density, acceptor density, effective density of states at valence band maximum (VBM), free hole concentration, acceptor level energy, and Boltzmann constant, respectively. In the case of deep acceptor (∆𝐸 𝑎 = 𝐸 𝐴 -𝐸 𝑉𝐵𝑀 ≫ 𝑘 𝐵 𝑇, 𝑁 𝐴 > 𝑁 𝐷 ≫ 𝑝):

	𝑁 𝐴 -𝑁 𝐷 -𝑝 𝑝(𝑁 𝐷 + 𝑝)	=	2 𝑁 𝑉	𝑒	𝐸 𝐴 -𝐸 𝑉𝐵𝑀 𝑘 𝐵 𝑇	(3 -2)
	𝑁 𝐴 -𝑁 𝐷 𝑝𝑁 𝐷	=	2 𝑁 𝑉	𝑒	∆𝐸 𝐴 𝑘 𝐵 𝑇

𝐸 𝑉𝐵𝑀 + 3𝑘 𝐵 𝑇 ≪ 𝐸 𝐹 in our case), which is given as follow:

Table 3

 3

-2. Three samples with the only difference being the growth temperature varying from 775 to 825°C, will be discussed. All the layers have a similar growth rate of around 360 nm/hour independent of the growth temperature.

Table 3 -

 3 2. Summary of the growth conditions and β-Ga2O3 film thicknesses layers.

	N°	substrate	Growth conditions	T [°C]

Table 3 -

 3 3. Summary of previously reported Zn-doped β-Ga2O3 from the literature, showing Zn related acceptor characteristics. Remarks (a -e) refer to: a) Overall reduction of conductivity/Zn considered as an acceptor; b) determined by photoluminescence; c= determined by cathodoluminescence; d) nanowire; e) determined by Electron paramagnetic resonance (EPR)

Table 3 -4.

 3

Table 3 -

 3 4. Summary of the growth conditions.

	N°	Structure	Growth conditions	DEZn [µmol]	Deposition time [min]	Thickness [nm]
	Undoped Ga2O3	Ga2O3//c-sapphire Ga2O3//Si(111)	Vector gas: Ar	-	85	450
	Zn:Ga2O3#1		TMGa = 6 µmol	0.99	60	323
	Zn:Ga2O3#2	Zn:Ga2O3//c-sapphire	O2 = 600 sccm P = 30 Torr	2.3	60	323
		Zn:Ga2O3//Si(111)	T = 775 °C

  investigated the impact ionization coefficient for electrons and holes, and in turn, the critical electric field in β-Ga2O3, several 𝐸

𝐶𝑅 values of 4.8 -10.2 MV/cm depending on the crystallographic direction of β-Ga2O3 were estimated. Experimentally, a breakdown field of a β-Ga2O3//Si simple structure parallel plane MOS capacitor was determined to be 7.27 MV/cm

[START_REF] Li | Chemical, optical, and electrical characterization of Ga2O3 thin films grown by plasma-enhanced atomic layer deposition[END_REF]

. Zhang et al.

[START_REF] Zhang | Ultra-wide bandgap semiconductor Ga2O3 power diodes[END_REF]

fabricated and conducted the electric characterizations of two p-NiO/n-Ga2O3

Table 4 -

 4 1. Growth conditions of pure and Zn incorporated β-Ga2O3.

	N°	Structure	Growth conditions	DEZn [µmol/min]	[Zn] (%)	Thickness [nm]
	Undoped	Ga2O3//c-sapphire	Vector gas: Ar	0	-	953
	ZnGaO-#1		TMGa = 11 µmol/min	3.9	6.85	1000
	ZnGaO-#2	Zn:Ga2O3//c-sapphire Zn:Ga2O3//Si	O2 = 1200 sccm T = 775 °C, P = 38 Torr	7.0	14.04	1238
	ZnGaO-#3		Time = 150 min	8.9	15.83	1154

Table 4 -2.

 4

Table 4 -

 4 2. Growth conditions of two ZnGa2O4 thin films.

	P (total) [Torr]	O2	Time [min]	Temperature [°C]	Ga precursor [µmol/min]	DEZn [µmol/min]	Thickness [nm]	Type
	35	1200 sccm	150	775	11 (TMGa)	8.9	1154	p
	25 0.022 mol/min 30	850	27 (TEGa)	49	190	n

Table 4 -

 4 3. Growth parameters and the thickness of samples.

	N°	Growth conditions	O2 flow [sccm]	Time [min]	O2 during cooling [sccm]	Thickness [nm]

Table 5 -

 5 1. Adjustment of parameters for lithography process.

	Photoresist	Trial n°	Max. spin coating speed [tr/min]	Exposure time [s]	Development time [s]
		1	4000	20	10
	AZ 1512 HS	2 3	6000 6000	20 40	10 10
		4	6000	40	30
		5	4000	20	10
		6	4000	20	8
	AR-P 5350	7 8	4000 4500	30 30	10 10
		9	4500	30	8
		10	4500	20	8

Table 5 - 2 .

 52 The designed patterns were successfully transferred to β-Ga2O3 thin film using the adjusted photolithography parameters, for Ti/Pt/Au pad in particular. The relative error (

	|𝑑 𝑖,𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 -𝑑 𝑖,𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 |
	𝑑 𝑖,𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑

Table 5 -

 5 2. Designed and measured r and di with uncertainties for Ti/Pt/Au and Pt contact.

	Metal contact	r (μm)	Ring 1	Ring 2	di (μm), for six rings Ring 3 Ring 4	Ring 5	Ring 6
	Designed	250		40		60	80			100	120	140
	Ti/Pt/Au 251.2±0.5 41.2±0.4 60.7±0.5 81.7±1.0 101.7±0.8 121.8±0.5 141.6±0.7
	Pt	252.3±0.9 47.7±1.0 65.8±1.5 84.7±0.7 104.9±1.1 124.8±0.7 142.5±0.9
		𝑅 𝑡𝑜𝑡 =	𝑅 𝑆 2𝜋	[ln ( 𝑟 𝑜𝑢𝑡 𝑟	) +	𝐿 𝑇 𝑟	•	𝐼 0 (𝑟/𝐿 𝑇 ) 𝐼 1 (𝑟/𝐿 𝑇 )	+	𝐿 𝑇 𝑟 𝑜𝑢𝑡	•	𝐾 0 (𝑟 𝑜𝑢𝑡 /𝐿 𝑇 ) 𝐾 1 (𝑟 𝑜𝑢𝑡 /𝐿 𝑇 )	]

(iii) Simplification or approximation of the CTLM function. Modified Bessel function that can describe the current distribution on a circular contact surface, was used to improve the accuracy of the extraction of the specific contact resistance as suggested by several works

[START_REF] Banerjee | Contact resistance and current crowding in tunneling type circular nano-contacts[END_REF][START_REF] Liu | Study on the measurement accuracy of circular transmission line model for low-resistance Ohmic contacts on III-V wide band-gap semiconductors[END_REF][START_REF] B ; Pan | Analytical and Finite-Element Modeling of a Two-Contact Circular Test Structure for Specific Contact Resistivity[END_REF]

.

of 260 -266 nm. When [Zn] = 10 16 cm -3 , p-type conductivity in β-Ga2O3 is enhanced (e.g., at 800 K, ρ = 5.8×10 2 Ω•cm and p = 1.2×10 15 cm -3 , vs. ρ = 3.1×10 3 Ω•cm and 2.2×10 14 cm - 3 for undoped thin film). This fact proves that Zn is an active acceptor dopant in β-Ga2O3.

The ionization energy was determined to be Ei = 0.77 eV, which corresponds to the ZnGa (octahedral site) defect according to the EPR study in the literature. As the doping level increases [Zn] >10 18 cm -3 , the "auto-compensation" effect occurs, thus hole concentrations are reduced. However, the first "negative" result could be used in a "positive" way. Based on the kinetic impact ionization theory, it is suggested that the critical electric field ECR can be increased by decreasing the impact ionization probability (by shortening the mean free path of free carriers and reducing carrier concentration). Therefore, by leveraging the "autocompensation" effect of Zn doping, we proposed that the critical electric field (ECR) of β-Ga2O3 can be further increased. To prove this concept experimentally, parallel capacitors based on β-Ga2O3//Si and β-Ga2O3:Zn//Si ([Zn] = 10 19 cm -3 ) structures were fabricated to estimate experimentally the ECR values of undoped and Zn doped β-Ga2O3. ECR = 5.7 MV/cm was determined for β-Ga2O3//Si structure, while it was significantly increased up to ECR = 13.2 MV/cm for β-Ga2O3:Zn//Si.

(ii) Spinel ZnGa2O4: The incorporation of Zn in β-Ga2O3 was enhanced increasing the O2 flow rate during MOCVD growth (ranging from 600 to 1200 sccm). Under the same growth conditions (temperature, gallium and zinc precursors' flows, etc) except for a higher O2 flow fixed at 1200 sccm, cubic spinel ZnGa2O4 is formed. The mixed structure (at Zn concentration between 6.85 at. % and 14 at. %) of β-Ga2O3 and ZnGa2O4 was evidenced by both XRD patterns and Raman spectra. At a Zn concentration of 14.04 at. %, the monoclinic β-Ga2O3 completely transforms into cubic spinel ZnGa2O4.

As a ternary semiconductor, spinel oxide is known to have a higher flexibility of doping than binary compounds, due to the three ions with different valences at different sites. Here, intrinsic room-temperature conducting (ρ = 2.7×10 -2 Ω•cm) n-type (n = 10 19 cm -3 ) and semiinsulating p-type (ρ = 10 6 Ω•cm, p = 10 11 cm -3 at 550 K) ZnGa2O4 thin films were studied.

All thin films MOCVD technique are of high crystalline quality with band gaps Eg > 4.8 eV.

An absorption peak at about 3.3 eV was evidenced for the n-type ZnGa2O4 layer, without the identification of any additional phases. According to the investigation of electronic properties, it is suggested that the high electron conductivity (σ = 3.7×10 1 S/cm) in Zn-rich and O-deficient ZnGa2O4 thin films can be attributed to Zni-VO defect related "self-impurity"

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