Keywords: Energy harvesting, Piezoelectric semiconducting nanowires, Nanogenerators, Surface Fermi level pinning, Atomic force microscopy, Electromechanical measurements VIII

First, I would like to thank my director Mireille Mouis, co-directors Laurent Montès and Gustavo Ardila at IMEP-LaHC, for their guidance and help all the time. By following my research closely, they shared their knowledge, stills and experiences in scientific research to help me overcome difficulties standing in front during the past three years. In addition to advising at least

IV

Résumé

L'alimentation en énergie des réseaux de capteurs miniaturisés pose une question fondamentale, dans la mesure où leur autonomie est un critère de qualité de plus en plus important pour l'utilisateur. C'est même une question cruciale lorsque ces réseaux visent à assurer une surveillance d'infrastructure (avionique, machines, bâtiments…) ou une surveillance médicale ou environnementale. Les matériaux piézoélectriques permettent d'exploiter l'énergie mécanique inutilisée présente en abondance dans l'environnement (vibrations, déformations liées à des mouvements ou à des flux d'air…). Ils peuvent ainsi contribuer à rendre ces capteurs autonomes en énergie. Sous la forme de nanofils (NF), les matériaux piézoélectriques offrent une sensibilité qui permet d'exploiter des sollicitations mécaniques très faibles. Ils sont également intégrables, éventuellement sur substrat souple. Dans cette thèse nous nous intéressons au potentiel des nanofils de matériaux semi-conducteurs piézoélectriques, tels que ZnO ou les composés III-V, pour la conversion d'énergie mécanique en énergie électrique. Depuis peu, ceux-ci ont fait l'objet d'études relativement nombreuses, avec la réalisation de nanogénérateurs (NG) prometteurs. De nombreuses questions subsistent toutefois avec, par exemple, des contradictions notables entre prédictions théoriques et observations expérimentales. Notre objectif est d'approfondir la compréhension des mécanismes physiques qui définissent la réponse piézoélectrique des NF semi-conducteurs et des NG associés. Le travail expérimental s'appuie sur la fabrication de générateurs de type VING (Vertical Integrated Nano Generators) et sur leur caractérisation. Pour cela, un système de caractérisation électromécanique a été construit pour évaluer les performances des NG réalisés et les effets thermiques sous une force compressive contrôlée. Le module d'Young et les coefficients piézoélectriques effectifs de NF de GaN; GaAs et ZnO et de NF à structure coeur/coquille à base de ZnO ont été évalués également dans un microscope à force atomique (AFM). Les nanofils de ZnO sont obtenus par croissance chimique en milieu liquide sur des substrats rigides (Si) ou flexibles (inox) puis sont intégrés pour former un générateur. La conception du dispositif VING s'est appuyée sur des simulations négligeant l'influence des porteurs libres, comme dans la plupart des études publiées. Nous avons ensuite approfondi le travail théorique en simulant le couplage complet entre les effets mécaniques, piézoélectriques et semi-conducteurs, et en tenant compte cette fois des porteurs libres. La prise en compte du piégeage du niveau de Fermi en surface nous permet de réconcilier observations théoriques et expérimentales. Nous proposons notamment une explication au fait que des effets de taille apparaissent expérimentalement pour des diamètres au moins 10 fois plus grands que les valeurs prévues par simulation ab-initio ou au fait que la réponse du VING est dissymétrique selon que le substrat sur lequel il est intégré est en flexion convexe ou concave.

General Introduction

Energy autonomy in networks of small sensors is one of the key quality parameter for end-users. It is even critical when addressing applications in structures health monitoring (avionics, machines, building…), or in medical or environmental monitoring applications.

There are many sources of energy that can be harvested, depending of the specific environment. For structure and environmental monitoring, a large number of sensors increase the response quality. But their number can become an issue either because of the amount of wiring or because of battery management cost. Harvesting energy from the environment can bring a smart solution where each node could ideally become self-powered, or in other word, energetically autonomous. For implantable medical sensors, the autonomy is even a more crucial requirement. Piezoelectric materials make it possible to exploit the otherwise wasted mechanical energy which is abundant in our environment (e. g. from vibrations, deformations related to movements or air fluxes). Thus, they can contribute to the energy autonomy of those small sensors. In the form of nanowires (NWs), piezoelectric materials offer a high sensibility allowing very small mechanical deformations to be exploited. Piezoelectric NWs have recently provided a promising improvement for electronics, sensing and energy harvesting nanosystems [1][2][3]. Among them, semiconducting NWs have attracted more and more attention due to their excellent piezoelectric properties, large-scale synthesis and compatibility with Si based integration. The piezoelectric generators based on vertically integrated ZnO NWs (VING) have presented a great potential in harvesting the mechanical energy from the environment ever since they were first demonstrated [3]. An increasing number of publications have recently bloomed about these nanostructures and promising nanogenerators (NGs) have been reported (Fig. I). However, there remain many contradictions between experimental results and our theoretical understanding of ZnO NW-based devices when realistic doping levels are considered. Chief among them are (1) decent and length-dependent experimental performance of ZnO NWs [4], while anticipations based on analytical and computational study shows that the output of NWs under compression are reduced to a few millivolts and are expected to present length-independent performance due to the screening effect [5,6]; (2) enhanced piezoelectric coefficients [7], which are measured for ZnO NWs with diameters much larger than anticipated by ab-initio method [8]; and (3) dissymmetric piezoelectric response of bent NGs under tensile and compressive strain by experimental observation [9].

In this thesis, the work was mainly focused on the piezoelectric semiconducting NWs, such as ZnO, GaAs and GaN, and on their implementation into NGs. We concentrated on one of the most promising NG structure based on vertically integrated NWs (the so-called VINGs). As shown in Fig. II, the study targeted three aspects: measurements of mechanical and electromechanical properties of individual piezoelectric NWs using AFM techniques; integration of ZnO NW arrays on different substrates to fabricate NGs and their characterization; and computational simulation study for NGs. The investigations will be introduced and discussed in three chapters: (1) In chapter I: we described the background of researches on semiconducting piezoelectric NWs for energy harvesting and sensing: the autonomous system and sensor networks.

The physical basics of piezoelectricity were also introduced. Piezoelectric NGs integrating semiconducting NWs were considered as a solution to self-powering. (2) In chapter II: we used Finite element method (FEM) as the tool for simulation studies on ZnO NWs based NGs. Piezoelectricity and semiconductor physics were coupled in the simulations. We investigated NGs with various matrix materials under compression and bending, where material properties for nanoscale geometry were also considered. We also put forward the theory of surface Fermi level pinning to explain the difference existing between the theoretical results and experimental observations. (3) In chapter III: to investigate the ability of energy harvesting, we conducted electromechanical characterization on both individual NWs and NGs. ZnO NWs were synthesized by the chemical bath deposition method in our lab. They were grown on Si wafer and stainless steel foil, and then embedded into different matrix to form rigid and flexible NGs. AFM assisted techniques were applied to individual ZnO, GaN, GaAs and ZnO based core-shell NWs. We also built a measurement system to characterize the piezoelectric response of NGs under controlled compression. For the NGs working under flexion, we perform preliminary measurements, which demonstrate the surface Fermi level pinning hypothesis.

Chapter I From Piezoelectricity towards Nanogenerators for Autonomous System I.1 Energy harvesting for autonomous system

As the technologies develop fast during the recent decades, the emergence and increasing importance of low-energy consuming and portable/wireless miniature electronics have surfaced. One example of such kinds of devices is wearable medical and autonomous assistive devices [START_REF] Yang | Converting Biomechanical Energy into Electricity by a Muscle-Movement-Driven Nanogenerator[END_REF][START_REF] Mateu | Optimum Piezoelectric Bending Beam Structures for Energy Harvesting using Shoe Inserts[END_REF][START_REF] Riemer | Biomechanical energy harvesting from human motion: theory, state of the art, design guidelines, and future directions[END_REF]. In many cases, such devices are operated with wired or wireless sensor-transducer-actuator configurations that are powered by batteries [START_REF] Mallela | Trends in cardiac pacemaker batteries[END_REF][START_REF] Lanmuller | Multifunctional Implantable Nerve Stimulator for Cardiac Assistance by Skeletal Muscle[END_REF]. However, batteries need to be either replaced or recharged periodically and have limited lifetime, as well as the difficulty in miniaturization. Besides, in some cases the cost of wiring could be remarkable. For instance a study have evaluated the cost of installing wiring to each sensor in a commercial building at $200, while a typical cost of a wireless sensor node could be lower than $10 [START_REF] Beeby | Energy harvesting for autonomous systems[END_REF]. Efforts are required in two aspects: (1) minimize energy requirements without losing functionality; (2) harvest ambient energy to recharge the batteries, or even to directly power the specific electrical loads. The combination of low power circuits, new materials integration and 3D processing technologies make possible the development of autonomous systems. These autonomous systems harvest energy from various energy sources depending on the environment, such as light, heat, or mechanical vibration. The design of autonomous systems includes an energy harvester, an energy management unit to rectify the power, an energy storage unit (a microbattery or a supercapacitor) that stores the harvested energy and delivers the power required to switch on function units like sensors and transceivers (Fig. 1.1) [START_REF] Wang | Self-Powered Nanosensors and Nanosystems[END_REF]. Energy harvesting can power a wide variety of autonomous systems such as wireless sensors [START_REF] Gilbert | Comparison of energy harvesting systems for wireless sensor networks[END_REF][START_REF] Esu | Feasibility of a fully autonomous wireless monitoring system for a wind turbine blade Renew[END_REF], biomedical implants [START_REF] Hannan | Energy harvesting for the implantable biomedical devices: issues and challenges[END_REF], military monitoring devices for harsh combat or training conditions [START_REF] Cremers | Military: Batteries and Fuel Cells Encyclopedia of Electrochemical Power Sources[END_REF], structure-embedded instrumentation [START_REF] Mascarenas | Experimental studies of using wireless energy transmission for powering embedded sensor nodes[END_REF], remote weather station [START_REF] Sharma | Cloudy Computing: Leveraging Weather Forecasts in Energy Harvesting Sensor Systems[END_REF], and electronic devices such as portable calculators, watches, and Bluetooth headsets. Taking the wireless sensor network as an example, where battery lifetime is the major limitation in its performance, one can evaluate the value of energy autonomy. For a wireless sensor node with basic functionality of sending the data to a remote location for processing, the minimum power requirements can be estimated using a mixture of currently available off-the-shelf technology, and devices that are the current state-of-the-art in research. Three basic elements are considered: the STLM20 temperature sensor from ST Micro [START_REF]Anon 2006 Ultra-low current 2.4 V precision analog temperature sensor datasheet[END_REF], An ADC reported by Sauerbrey et al. [START_REF] Sauerbrey | A 0.5-v 1--μW successive approximation adc[END_REF], and an IEEE 802.15.4a standard-compliant ultra-wide-band transmitter from IMEC [25]. By assuming a low data rate (1 kbps), Mitcheson et al. have suggested a total power consumption for the sensor node of 10 μW -20 μW, or even 1μW -2 μW or less if the other components are also duty cycled [START_REF] Mitcheson | Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices[END_REF]. This level of power can be harvested by ever smaller structures and, eventually, nanostructures.

I.2 Semiconductor based energy harvesters

Energy harvesting is with no doubt a very attractive technique for a wide variety of autonomous systems. Several methods of energy harvesting, such as photovoltaics (PV), thermoelectric generators, electromechanical transducers, are suitable for autonomous system corresponding to various working environments. The typical characteristics of some common energy-harvesting transducers are summarized in Table 1.1, where the available power of various ambient energy sources is compared [START_REF] Yildiz | Potential Ambient Energy-Harvesting Sources and Techniques[END_REF]. Driven by the need of lower cost (wireless) and higher integration, energy harvesting with nanostructures emerges. Among them, the energy harvester based on semiconductor NWs and nanosheets attracts more and more attention due to its possibility of further miniaturization and compatibility with IC integration. In the next subsections, we will describe briefly the most promising technologies for energy harvesting.

I.2.1 Photovoltaics (PV)

A PV cell is a solid state device that converts the energy of light directly into electricity by the photovoltaic effect. When photons are absorbed, they transfer their energy to electrons in the filled valence band (VB) and promote these electrons to higher energy states in the empty conduction band (CB). As there are no energy states in the band gap, only photons with energies above the band gap can cause the transfer of electrons from the VB into the CB. Thus, absorbed photons in semiconductors create pairs of negative electrons (in the CB) and positive holes (in the VB). In a solar cell, photo electrons and photo holes formed upon absorption of light separated by electric field and move to opposite sides of the cell structure, where they are collected and can feed a load circuit.

First generation solar cells are typically synthesized using inorganic wafer materials such as silicon. Of the 1.7 × 10 TW of solar energy that reaches the Earth's surface, approximately 600 TW is of practical value, and 60 TW of power could be generated by using solar farms that are only 10% efficient [START_REF] Schiermeier | Energy alternatives: Electricity without carbon[END_REF]. Accounting for 90 % of the market, they are currently the mainstream solar cells and have found applications through small-scale devices such as solar panels on roofs, pocket calculators and water pumps. Second-generation PV cells were developed during the mid-1970s. These cells are mostly composed of thin-film of amorphous polycrystalline compound semiconductors [START_REF] Carabe | Thin-film-silicon solar cells[END_REF]. These devices are initially designed to be high-efficiency, multiple junctions PV cells (or tandem cells) [START_REF] Dimroth | High-efficiency solar cells from III-V compound semiconductors[END_REF]. However, these cells have a lower efficiency than the wafer-based Si solar cells, but with a higher cost. Third generation solar cells are the cutting edge of solar technology. They are broadly defined as semiconductor devices that do not rely on the conventional p-n junction. Most third-generation solar cells are still in the research stage and tend to contain dye-sensitised solar cells (DSSCs), heterojunction cells, quantum dot cells, polymer solar cells, and hot carrier cells [START_REF] Hardin | The renaissance of dye-sensitized solar cells[END_REF]. Based on nanostructures they optimize the efficiency and considerably decrease the production costs. For instance the efficiency of DSSCs that are sensitised by Ru compounds adsorbed on nanocrystalline TiO 2 has reached 11% -12% [START_REF] Chiba | Dye-Sensitized Solar Cells with Conversion Efficiency of 11.1%[END_REF][START_REF] Buscaino | A mass spectrometric analysis of sensitizer solution used for dye-sensitized solar cell[END_REF]. The maximum efficiencies for all solar conversion technologies are presented in Fig. 1.2 [36].

Overall, PV energy conversion is a well-known integrated circuit compatible technology that offers higher power output levels, when compared with the other energy-harvesting mechanisms. Nevertheless, its power output is strongly dependent on environmental conditions; in other words, varying light intensity.

I.2.2 Thermoelectric generators

The thermoelectric effect, also referred to as the Seebeck effect, is the direct conversion of temperature differences to electric voltage and vice-versa. A thermoelectric device creates a voltage when there is a temperature gradient on each side. Conversely, when a voltage is applied to it, it creates a temperature difference.

Thermoelectric generators (TEGs) are simply thermoelectric modules that convert a temperature gradient across the device, and resulting heat flow through it, into a voltage via the Seebeck effect. The reverse of this phenomenon, known as the Peltier effect, produces a temperature differential by applying a voltage and is familiarly used in thermoelectric coolers (TECs).The polarity of the output voltage is dependent on the polarity of the temperature differential across the TEG. Reversing the hot and cold sides of the TEG will reverse the output voltage polarity.

The efficiency of thermoelectric material, which determines the performance of the TEG, is often described by a dimensionless number called the figure-of-merit ZT, ZT = σS 2 T/κ, where T is the absolute temperature, σ and κ are the electrical and thermal conductivity, respectively, and S is the Seebeck coefficient. Materials with high ZT are desired in thermoelectric generator design; in practice, however, it is difficult to increase ZT because increasing S often leads to simultaneous decreasing σ and increasing σ also leads to increasing κ by the Wiedemann-Franz law. In bulk thermoelectric materials, Bi 2 Te 3 alloys have the highest ZT at about 1.0 at 300 K. over the three decades before 1990, there has been only a 10% increase in ZT because the change of one of its parameters adversely affects the other. In 1993, Hicks and Dresselhaus demonstrated that ZT > 2 can be achieved by low-dimension materials such as quantum well and quantum wire [START_REF] Hicks | Thermoelectric figure of merit of a one-dimensional conductor[END_REF][START_REF] Hicks | Effect of quantum-well structures on the thermoelectric figure of merit[END_REF]. Since then, there is a possibility to realize micro-thermoelectric generators (μTEGs) [START_REF] Hauser | Elaboration de super-réseaux de boîtes quantiques à base de SiGe et développement de dispositifs pour l'étude de leurs propriétés thermoélectriques[END_REF][START_REF] Stein | Croissance et caractérisation de super-réseaux de boites quantiques à base de siliciures métalliques et SiGe pour des applications thermoélectriques[END_REF].

A μTEG composed of n-type and p-type Bi 2 Te 3 NW arrays was fabricated by Wang et al. [START_REF] Wang | A new type of low power thermoelectric micro-generator fabricated by nanowire array thermoelectric material[END_REF]. The NW arrays were grown by electrochemical deposition of Bi 2 Te 3 into the nanopores of alumina template. The measurements showed that the Seebeck coefficient α of p-type and n-type Bi 2 Te 3 NW arrays with a diameter of about 50 nm was about 260 and -188 μV/K respectively at 307 K. Yang et al. designed a μTEG adopting TSMC0.35μmBiCMOS process with two poly-silicon layers, one poly-SiGe layer and three metal layers (3P3M) [START_REF] Yang | Application of quantum well-like thermocouple to thermoelectric energy harvester by BiCMOS process Sensors[END_REF]. In Yang's work, μTEGs with different lengths and weights were tested and the one with the size 60 μm×4 μm had the largest power factor 0.251 μW/cm 2 K 2 and voltage factor 10.042 V/cm 2 K. Compared with similar works [START_REF] Strasser | Micromachined CMOS thermoelectric generators as on-chip power supply Sensors[END_REF][START_REF] Huesgen | Design and fabrication of MEMS thermoelectric generators with high temperature efficiency Sensors[END_REF][START_REF] Yang | Development of a thermoelectric energy harvester with thermal isolation cavity by standard CMOS process Sensors[END_REF], this CMOS integrated μTEG has an outstanding power factor as well as the voltage factor. Meanwhile, n-Bi 2 Te 3 and p-(Bi 1-xSbx)Te 3 thermoelectric thin films have also been used as pressure and gas concentration sensors [START_REF] Giani | Thermoelectric microsensor for pressure and gas concentration measurement[END_REF]. Similarly, Al khalfioui et al. realized anemometers based on periodic structures elaborated by flash evaporation technique on polyimide substrate using Bi 2 Te 3 -Sb 2 Te 3 (P) and Bi 2 Te 3 -Bi 2 Se 3 (N) materials which have a high figure of merit [START_REF] Al Khalfioui | Anemometer based on Seebeck effect Sensors[END_REF].

Similar to PV cells, the μTEG also has a limitation with the working environment. The power generation is largely dependent on the temperature gradient that the environment can offer.

I.2.3 Mechanical-electrical conversion for autonomous system

Besides light and thermal sources, energy from vibrations, human movements, impacts or any other mechanical source is very present in daily applications and can be exploited. Table 1.2 shows how much energy is available and yet wasted from ambient vibrations. It is then interesting to develop an effective way to absorb the mechanical energy from the ambient and convert it into electrical energy.

Devices, which are possessing most of the market, to harvest the mechanical energy are based on electrostatic effect, electromagnetic effect and piezoelectric effect. Electrostatic devices are easily integrated using MEMS technologies, but the fact that they typically require an initial charge and the low energy density that they produce have limited their use to research without industrial applications, to the best of our knowledge. Electromagnetic devices have a higher power densities but are difficult to integrate because of limitations on magnets miniaturizations, for this reason, only bulky devices have been commercialized [48]. Piezoelectric transduction offer a good compromise in terms of power densities and compatibility with Si integration and nowadays industrial MEMS harvesters can be found in the market [START_REF]MicroGen Systems[END_REF]. Typical piezoelectric harvesters use bulk ceramic materials (as PZT [START_REF]Piezo Ceramic Technology[END_REF]) or thin films (as AlN [START_REF] Van Schaijk | Piezoelectric AlN energy harvesters for wireless autonomous transducer solutions[END_REF]). [3]. Later the word "NG" was cited by other ultra-small energy harvesting systems that can convert mechanical, microwave, biochemical, thermal energy into electricity [START_REF] Bisotto | Microwave based nanogenerator using the ratchet effect in Si/SiGe heterostructures[END_REF][START_REF] Hansen | Hybrid nanogenerator for concurrently harvesting biomechanical and biochemical energy[END_REF]. Recently, this concept has also been used for the emerging triboelectric NGs (TENGs).

I.2.3.1 Triboelectric nanogenerators (TENG)

TENGs are devices taking advantage of the triboelectric effect to convert movements into electric power. The triboelectric effect, also known as triboelectric charging, is a type of contact electrification in which certain materials become electrically charged after they come into frictional contact with a different material. For example, when thin films of PET plastic and a metal come into contact with each other, both of them are charged. A current will flow between them, which can be harvested to charge a battery.

As shown in Fig. 1.3, there are four fundamental principle modes for TENGs: (1) vertical contact-separation mode; (2) in-plane contact-sliding mode; (3) single-electrode mode; and (4) freestanding triboelectric-layer mode [START_REF] Wang | Triboelectric nanogenerators as new energy technology for self-powered systems and as active mechanical and chemical sensors[END_REF]. The first triboelectric generator was fabricated by stacking two polymer sheets, PET and Kapton, with metal films deposited on the top and bottom of the assembled structure [START_REF] Fan | Flexible triboelectric generator[END_REF]. Such a flexible polymer generator gave an output voltage of up to 3.3 V at a power density of ∼10.4 mW/cm 3 . More recently, the two contact surfaces have been patterned with nanoscale structures to increase the surface area, thus the friction between the materials. A TENG was developed by utilizing the contact electrification between a polytetrafluoroethylene (PTFE) thin film and a layer of TiO 2 nanomaterial (NW and nanosheet) array [START_REF] Lin | Enhanced triboelectric nanogenerators and triboelectric nanosensor using chemically modified TiO2 nanomaterials[END_REF]. TENGs have been applied for a variety of self-powered sensing system, such as vibration detection [START_REF] Zhong | Fiber-Based Generator for Wearable Electronics and Mobile Medication[END_REF], tracking of a moving object (location, velocity and acceleration) [START_REF] Chen | Triboelectric Nanogenerators as a Self-Powered Motion Tracking System[END_REF][START_REF] Han | Self-powered velocity and trajectory tracking sensor array made of planar triboelectric nanogenerator pixels[END_REF][START_REF] Su | Triboelectric sensor for self-powered tracking of object motion inside tubing[END_REF] or the fine displacement in MEMS [START_REF] Zhou | Nanometer resolution self-powered static and dynamic motion sensor based on micro-grated triboelectrification[END_REF]. This concept to harvest energy is very revolutionary because of its simplicity in terms of materials and fabrication. One possible drawback on this kind of devices is the working principle using movable parts in contact or friction, which could affect the devices lifetime and reliability.

I.2.3.2 Piezoelectric nanogenerators (PENG)

The other way to convert mechanical movement into electrical power is to use the piezoelectric effect. Piezoelectric materials can work in two different ways depending on the contact:

(1) With conductive contacts, the conduction current is modulated by the strain and is proportional to the polarization-induced charges. In this case, the integrated material can only work as a sensor, and it requires a power supply to work. (2) With insulating or Schottky contacts (or in the case of an insulating piezoelectric material), a displacement current is generated when there is a change in strain. The current is then proportional to the time variation of the polarization induced charge.

There is no need for an external power supply and piezoelectric generators usually work in this way, acting as either mechanical energy harvesters or self-powered mechanical sensors. Table 1.3 compares different mechanical energy harvesting techniques according to their complexity, energy density, size, and encountered problems. We focused on the PENG in this thesis. Details will be introduced in the following sections. The name "Piezoelectricity" was first proposed by Hankel [START_REF] Hankel | Uber die aktinound piezoelektrischen eigenschaften des bergkrystalles und ihre beziehung zu den thermoelektrischen[END_REF] in 1881 to describe a phenomenon discovered a year before by the Pierre and Jacques Curie brothers. The prefix "piezo" means pressure in Greek, thus the meaning of the whole word is "electricity by pressure". Apparently, the phenomenon found in their experiments was that positive and negative charges appeared on several parts of the crystal surfaces when compressing the crystal in different directions. It was analyzed according to the crystal symmetry. In 1881, one year after their discovery, the Curie brothers testified the existence of the reverse effect, predicted by Lippmann in the same year. Basically, the rule is that if certain materials are able to generate an electric charge due to a stress, they would also deform mechanically, under similar circumstances, in an electric field. In a word, piezoelectricity describes the ability of some materials to convert between mechanical and electrical energy.

I.3.2 The piezoelectric effect

The above description of the two processes was summarized as the direct and reverse piezoelectric effect. It can be explained by the arrangement of ions in the crystal structure. Fig. 1.4a shows a 2D lattice scheme of a simple two-element molecule material (AB). In a static state, the gravity centers of the negative and positive charges of each molecule coincide. Thus, their "macro" effects on the crystal are reciprocally cancelled. As a result, the molecule behaves electrically neutral in this way. When the material is placed in a stress field, its internal atomic structure can be deformed. The positive and negative gravity centers of the molecules are thusly separated and form little dipoles (Fig. 1.4b-c). Dipoles with opposite directions inside the material are mutually cancelled, leaving a distribution of a linked charge appearing on the surfaces. That is how the material is polarized. The polarization creates an electric field inside the material, which can be used to transform the mechanical energy stored in the material into electrical energy.

I.3.3 Piezoelectric materials

Piezoelectric materials refer to a series of materials that can exhibit piezoelectric, pyroelectric or ferroelectric effect. In general, all of the materials undergo a small physical deformation when subjected to an external force, an electric field, or a temperature change. If the deformation results in a change in electric polarization, we say it gives rise to the occurrence of the piezoelectric, ferroelectric or pyroelectric effects. In fact, the specific symmetry of the crystal unit cell determines whether the material exhibits these effects. Based on orientation only, the lattice structures of crystals are divided into 32 point groups.

The relationship between polarization behavior and crystal structure is shown in Fig. 1.5. 11 classes are centrosymmetric, thus nonpolar and do not possess a finite polarization or dipole moment. The other 21 classes are noncentrosymmetric, possessing no center of symmetry, which is the necessary requirement for the occurrence of piezoelectricity. However, one of the 21 classes, though classified as the noncentrosymmetric class, possesses other combined symmetry elements, thus rendering no piezoelectricity. In half of the left 20 classes, the polarization can be induced by a mechanical stress. The representative material is quartz. The other half is permanently polared and thus can have piezoelectric as well as pyroelectric effects by possessing spontaneous polarization. ZnO, CdS and most of the III-V compounds belong to this category. A subgroup within these 10 classes possesses not only spontaneous polarization, but also reversible polarization. This last category exhibits all three effects-ferroelectric, piezoelectric, and pyroelectric, such as PZT, PMN-PT and PVDF.

I.4 PENGs for energy harvesting or sensing

Harvesting ambient mechanical energy at the nanometer scale holds great promises for powering small electronics and achieving self-powered electronic devices. Actually, PENGs are widely used for energy harvesting and sensing. Up till now, two kinds of mechanical stress field have been applied to the piezoelectric NWs. In the first way, the NWs are strained along their axes. While in the second way, the NWs are bent, generating potential difference between the sides of the NW. Most of the applications can be sorted by these two families.

I.4.1 PENG strained along NW's axis

PENGs working in this way have contacts on the two ends of the NWs to collect the potential. Therefore the NWs can be connected in parallel as what they do for laterally integrated NGs (LING) and vertically integrated NGs (VING).

I.4.1.1 Laterally integrated NGs (LINGs)

A first demonstration of using a single ZnO NW as a NG was reported in 2006 by Wang and his group [3]. Later laterally packaged NGs with either a single wire or bonded NWs appeared with the development of fabrication techniques [START_REF] Yang | Power generation with laterally packaged piezoelectric fine wires[END_REF][START_REF] Xu | Self-powered nanowire devices[END_REF][START_REF] Hu | High-Output Nanogenerator by Rational Unipolar Assembly of Conical Nanowires and Its Application for Driving a Small Liquid Crystal Display[END_REF]. In a single wire generator (SWG), a single ZnO NW is fixed by silver paste on a flexible polyimide film as a doubly-clamped beam (Fig. 1.6a). When a SWG is stretched and released with the strain around 0.05% -0.1%, the generated open-circuit voltage reaches 20 mV -50 mV [START_REF] Yang | Power generation with laterally packaged piezoelectric fine wires[END_REF]. Laterally grown ZnO NWs are fabricated using masks on the top surface of the ZnO seed layer that guided the NWs to grow on the side walls [START_REF] Qin | Growth of Horizonatal ZnO Nanowire Arrays on Any Substrate[END_REF][START_REF] Xu | Patterned growth of horizontal ZnO nanowire arrays[END_REF]. The maximum output voltage peak of this structure is 1.26 V [START_REF] Xu | Self-powered nanowire devices[END_REF]. This value has been improved by using 30 µm long, 1 µm wide rational unipolar assembly of conical ZnO wires dispersed randomly on a polymer matrix [START_REF] Hu | High-Output Nanogenerator by Rational Unipolar Assembly of Conical Nanowires and Its Application for Driving a Small Liquid Crystal Display[END_REF]. The model of the device was a capacitor-like plate structure with ZnO conical NWs packaged by PMMA as dielectric media, with one end fixed and a transverse mechanical force applied at the other end. The potential difference between the top and bottom electrodes of such a generator was calculated as a function of the NW density that the voltage was as high as 2.5 V when the density was 9×10 5 mm -2 [START_REF] Hu | High-Output Nanogenerator by Rational Unipolar Assembly of Conical Nanowires and Its Application for Driving a Small Liquid Crystal Display[END_REF]. The same group reported an effective approach, named scalable sweeping-printing-method, for fabricating flexible high-output LING from vertically aligned ZnO NWs (Fig. 1.6b). The reported peak output power density can reach ~11 ⁄ [START_REF] Zhu | Flexible high-output nanogenerator based on lateral ZnO nanowire array[END_REF]. This high output power can be comparable to actual MEMS and macro-devices (see Table 1.1), although better figures-of-merit are required to compare the different performance and technologies, for instance including the mechanical input (strain, acceleration, force…). Another group has built a LING based on PZT nanofibers, which were laterally suspended between the Pt wires and packaged with a thick layer of polydimethylsiloxane (PDMS) as high output NGs (Fig. 1.7a) [START_REF] Chen | 1.6 V nanogenerator for mechanical energy harvesting using PZT nanofibers[END_REF]. Fig. 1.7b shows a typical voltage output of this NG by periodic knocking of the PDMS surface. The potential amplitude increased monotonically with the strain applied to the PDMS slab. The highest output potential was ~1.6 V. In another work, similar structure was built as high output NGs, where PZT nanoribbons were printed onto the surface of a PDMS slab and interdigitated electrodes (with 25 μm spacing) were patterned on top of the nanoribbon arrays (Fig. 1.7c) [START_REF] Qi | Nanotechnology-enabled flexible and biocompatible energy harvesting[END_REF]. Frequency-dependent piezoelectric output is shown in Fig. 1.7d and e. Higher output produced by higher frequency taping is possibly due to fundamental piezoelectric theory relating current to strain rate [START_REF] Sirohi | Fundamental Understanding of Piezoelectric Strain Sensors[END_REF][START_REF] Chang | Direct-write piezoelectric polymeric nanogenerator with high energy conversion efficiency[END_REF]. At a 3.2 Hz taping frequency, the open-circuit voltage reached ~ 25 mV and the short-circuit current was ~ 40 nA, thus the optimal output power was ~ 10 nW for the NG with a size of ~ 1 cm 2 . Although these PZT NGs have a promising performance, they need to be poled by applying an electric field in advance. Vertically integrated NG (VING) structure is designed to harvest compressive and bending mechanical energy. It was first used in a self-powered system with wireless data transmission by Wang and his group, where the mechanical energy is harvested and converted into electrical energy, then stored in a capacitor to drive the other devices: sensors, data processors or data transmitters in the system (Fig. 1.8) [START_REF] Hu | Self-powered system with wireless data transmission[END_REF]. The VING structure presented in their work is composed of a five-layer flexible plate with PMMA surrounded ZnO NWs grown vertically on both sides of a polymer substrate and electrodes deposited on both top and bottom of the plate. Compared to lateral structures, VING fabrication is far easier with few lift-off steps. Several substrates can be used (Si, plastics, metals, etc.) and large scale production is possible [3,[START_REF] Choi | Mechanically Powered Transparent Flexible Charge-Generating Nanodevices with Piezoelectric ZnO Nanorods[END_REF][START_REF] Van Den Heever | The performance of nanogenerators fabricated on rigid and flexible substrates[END_REF][START_REF] Ebrahimi | Electrochemical Detection of Piezoelectric Effect from Misaligned Zinc Oxide Nanowires Grown on a Flexible Electrode Electrochim[END_REF][START_REF] Khan | Mechanical and piezoelectric properties of zinc oxide nanorods grown on conductive textile fabric as an alternative substrate[END_REF][START_REF] Chen | Gallium nitride nanowire based nanogenerators and light-emitting diodes[END_REF]. An ultrathin PENG with a total thickness of ~ 16 µ m was fabricated as an active or self-powered sensor for monitoring local deformation on a human skin [9]. The super-flexible NG was based on ZnO NWs with an anodic aluminum oxide (AAO) as an insulating layer (Fig. 1.9a-b). The AAO layer was grown on an ultrathin Al foil prior to the growth of ZnO NWs. This could lead to high-sensitivity and durability of the NG as well as high-throughput process due to the covalent bonds by sharing oxygen atoms and the increased surface contact area between the AAO and the ZnO seed layer by the nanopores of the AAO layer. This NG could be pasted on the human eyelid and was able to detect the motion of the eyeball (Fig.

I.4.2 PENG working with bent NWs

Bent piezoelectric NWs generate a potential difference between the opposite sides: the contractive side and the extensive side (Fig. 1.10). The problem to harvest energy with bent NWs is how to place the contact. The first trial was to integrate a Pt coated serrated electrode with vertically aligned ZnO NWs to convert ultrasonic waves into electricity, as schematically shown in Fig. 1.11a [START_REF] Wang | Direct-current nanogenerator driven by ultrasonic waves[END_REF]. The ultrasonic wave drove the electrode up and down to bend and/or vibrate the NWs. The serrated electrode acted as an array of metal tips to create, collect, and output electricity from bent NWs. A cross section SEM image of the packaged NW arrays is shown in Fig. 1.11b. The output power per unit of area was 10 mW/cm 2 . This type of NG built with the NWs grown on an area of 1 cm 2 has been demonstrated to be able to operate up to 1000 of nanodevices that are fabricated with one NW or nanotube [START_REF] Huang | Logic Gates and Computation from Assembled[END_REF][82][START_REF] Chen | Bright infrared emission from electrically induced excitons in carbon nanotubes[END_REF].

(a) (b) Another work trying to make use of the bent piezoelectric NWs for sensing application is accomplished by E. Perez [START_REF] Perez | Matrice de nanofils piézoélectriques interconnectés pour des applications capteur haute résolution : défis et solutions technologiques[END_REF]. He designed and fabricated a force sensitive pixel consists of an individual ZnO NW, selectively grown on a material stack representative of the targeted process, and with side electrodes (Fig. 1.12).

I.4.3 Nanopiezotronics

Besides the two major sorts of working modes, a few researches have been done by using conductive contacts and piezotronic effect. Piezotronic effect is using the piezopotential created in materials with piezoelectricity as a "gate" voltage to tune/control the charge carrier transport properties. It is used to fabricate a new class of electronic components, such as piezoelectric field-effect transistors (PE-FETs) and piezoelectric diodes (PE diodes) and sensors. These devices form the fundamental components of nanopiezotronics. Wang et al. reported a PE-FET designed by connecting a ZnO NW across two electrodes that can apply a bending force to the NW [2]. The electric field generated by the piezoelectric effect across the NW serves as the gate for controlling the electric current flowing through the NW.

I.5 Conclusion

In this chapter, we illustrated the importance and promising future of energy harvesting techniques. By harvesting energy from the environment, it can provide power to a variety of autonomous systems for wireless sensor networks, biomedical implants, or wearable personal electronics. We also introduced different energy harvesting methods based on semiconductors, such as PV cells, TEGs and different mechanical energy harvesters. As last, we focused on the fundamental and applications of PENGs, which is the main device studied and developed in this thesis.

Chapter II Analytical and Modeling Study of Piezoelectric

Nanowires and Nanogenerators

Analytical and computational modeling studies are important tools in the investigation within nanoscale, where experimental tools could be partially confined by the resolution of manipulation or the sensitivity of signal acquirements. In this chapter, we first introduce the modeling tools that are widely used in nanoscale researches. Secondly, analytical and modeling studies on material properties and piezoelectric response of individual piezoelectric semiconducting NWs reported in literature are discussed, according to which merits of NWs are explained. Finite element method (FEM) is the modeling tool that we use for our work on NW-based NGs. It is divided into three parts: first, NG cells integrating intrinsic piezoelectric NWs are investigated with various matrix under compression and bending, where material properties for nanoscale geometry are also considered; second, the existence and influence of the screening effect as coupling the piezoelectric and semiconducting physics are testified; and finally, we put forward the theory of surface Fermi level pinning to explain the difference existing between the theoretical results and experimental observations.

Although experimental studies have probed either electrical or mechanical behavior of NWs, the characterization of the coupling properties still faces challenges such as the manipulation of individual NW, the contact resistance between the sample and the measurement tools, the sensitivity of output electrical signals. In fact, different or even contrary results have been highlighted by measuring piezoelectric coefficient d 33 using different tools and methods. [7,[START_REF] Christman | Piezoelectric measurements with atomic force microscopy[END_REF][START_REF] Fan | Template-assisted large-scale ordered arrays of ZnO pillars for optical and piezoelectric applications[END_REF][START_REF] Scrymgeour | Polarity and piezoelectric response of solution grown zinc oxide nanocrystals on silver[END_REF][START_REF] Zhu | Piezoelectric characterization of a single zinc oxide nanowire using a nanoelectromechanical oscillator[END_REF] Compared with the bulk value 12.4 pm/V of ZnO [7,[START_REF] Christman | Piezoelectric measurements with atomic force microscopy[END_REF], piezoresponse force microscopy (PFM) method conducted on ZnO nanorods with diameters 150 nm -500 nm revealed an effective coefficient from 4.41 pm/V to 7.5 pm/V, smaller than the bulk value [START_REF] Fan | Template-assisted large-scale ordered arrays of ZnO pillars for optical and piezoelectric applications[END_REF][START_REF] Scrymgeour | Polarity and piezoelectric response of solution grown zinc oxide nanocrystals on silver[END_REF]. In contrast, a resonance shift method conducted on a 230 nm ZnO NW gave out a value of 12000 pm/V, thus 1000 times the bulk value [START_REF] Zhu | Piezoelectric characterization of a single zinc oxide nanowire using a nanoelectromechanical oscillator[END_REF].

Since contradictory observation results are partially dependent on the measurement methods that differ, as well as the materials involved in the substrate and probe contacting the NW, theoretical and computational studies offer a help to explore the physical principles of piezoelectric NWs. Simulation tools function at different levels, from atomic structure to continuum media. First-principles calculations are employed to investigate the piezoelectricity in semiconducting piezoelectric NWs at the atomistic level, while finite element method (FEM) is used to study the electromechanical behavior of both individual NWs and NWs based devices. Besides, Molecular dynamics (MD) and continuum models are also applied to related studies in piezoelectric field. Details of these simulation tools are introduced in Appendix I.

II.1 Study of piezoelectricity for intrinsic NWs

Piezoelectricity describes the ability of some materials to convert between mechanical and electrical energy. Piezoelectric materials are polarized under mechanical strain and the polarization is proportional to the strain. This is the direct piezoelectric effect. The converse effect is that a crystal is strained when an electric field is applied to it.

II.1.1 First-order of piezoelectricity

Continuum media models are used to deduce the piezoelectricity. In the first-order theory, the polarization is described as = ∑

, where the indexes µ, α, β stand for the x, y, and z axes of the Cartesian coordinate system. The mechanical and electrical behavior of a piezoelectric material can be modeled by two governing equations [START_REF] Sodano H A | A Review of Power Harvesting from Vibration Using Piezoelectric Materials Shock Vib[END_REF],

= - 2.1 = + 2.
2 where σ is the stress, ε is the strain, E is the electric field, D is the electric displacement, [c] is the elasticity matrix, described by the tensor, = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

In the case of ZnO, = 209.7GPa , = 121.1GPa , = 105.1GPa , = 210.9GPa, = 42.47GPa, = 44.29GPa are measured for a thin film [START_REF] Bateman | Elastic moduli of single crystal zinc oxide[END_REF]. [START_REF] Ashkenov | Infrared dielectric functions and phonon modes of high-quality ZnO films[END_REF]. The mechanical equilibrium condition is given by,

-∇σ = -∇( ) + ∇( ) = -∇( ) -∇ ∇ = 2.3
where f v is the mechanical body force and equal to 0 in a static system. Considering the Poisson's equation in dielectric materials, ∇ = 0 ∇( ) + ∇( ) = 0 2.4 the coupling equations that express the piezoelectric effect in semiconductors are then written as:

∇( ) + ∇ ∇ = 0 ∇ ∇ -∇( ) = 0 2.5
For the rest of the modeling study involving ZnO material properties, we will use the parameters mentioned above unless otherwise stated. Besides, second-order of piezoelectricity and flexoelectricity will not be considered in our simulation work for the moment.

II.1.2 Second-order of piezoelectricity and flexoelectricity

Second-order piezoelectricity, also defined as nonlinear piezoelectricity was first put forward by Cibert et al. in 1992 and applied to CdTe [START_REF] Cibert | Piezoelectric fields in CdTe-based heterostructures[END_REF][START_REF] André | Nonlinear piezoelectricity: The effect of pressure on CdTe[END_REF]. The piezoelectric coefficient of CdTe-based quantum wells measured at large lattice mismatch was more than three times larger than the value reported for bulk CdTe [START_REF] André R | Non-linear piezoelectric effect in CdTe and CdZnTe[END_REF]. They measured a piezoelectric field that behaved a nonlinear dependence on the elastic strain. Subsequent theoretical calculations showed that the piezoelectric tensor in CdTe strongly depended on the hydrostatic pressure, but very little on the traceless strain [START_REF] Dal Corso | Nonlinear piezoelectricity in CdTe[END_REF]. Bester et al. demonstrated the existence of second-order (nonlinear) piezoelectricity in III-V compounds and established the theoretical framework in which the second-order piezoelectric coefficient tensor was simplified in the wurtzite symmetry [START_REF] Bester | Effects of linear and nonlinear piezoelectricity on the electronic properties of InAs∕GaAs quantum dots[END_REF][100][START_REF] Prodhomme | Nonlinear piezoelectricity in wurtzite semiconductors[END_REF]. They determined the three first-order and the eight second-order piezoelectric coefficients for AlN, GaN, InN and ZnO by using a finite difference technique in combination with Density Functional Perturbation Theory (DFPT) within Local Density Approximation (LDA). The second-order piezoelectric tensor is associated with the second term in Eq. 2.6:

= + 2.6
where e ijk is the third-rank proper piezoelectric coefficient tensor of the unstrained material, while e ijklm is a fifth-rank tensor defined below. The Greek indexes µ, α, β, γ and λ stand for the x, y and z axes of the Cartesian coordinate system. The six independent components of the strain tensor are given in the Voigt notation as:

= = = = 2 = 2 = 2
Using Latin letters (j,k,...) for the Voigt index, the polarization component can then be written as:

= + 2.7
where represents the first-order strain-induced piezoelectric tensor. Then we have the definition of nonlinear piezoelectric coefficient, which depends on the strain,

( ) = = + 2.8
A more specific research on the nonlinear piezoelectricity of ZnO NWs was proposed by Al-Zahrani et al. [102]. Density Functional Theory (DFT) calculated equilibrium values were fitted to the following equation:

= + + 2 ∥ + ∥ + + ∥ 2.9
which expressed the strain dependence of the magnitude of the total piezoelectric polarization in the direction orthogonal to the growth plane. In this particular case with cylindrical NW, = = ∥ , = are strain parallel and perpendicular to the c-axis respectively. The dependence of the total polarization on strain in the range -0.08 to +0.08 of both linear and nonlinear models showed that the main feature of nonlinear polarization was always indicating either less negative or more positive values compared to the linear model. The linear and nonlinear models were tested in a ZnO NW subjected to a bending force. With the same strain range, the polarization on a cross section changed from -0.08 C/m 2 to 0.06 C/m 2 for the nonlinear model and from -0.12 C/m 2 to 0 C/m 2 for the linear model (Fig. 2.1). The polarization difference was up to 15%, which was consistent with the calculation in the literature [START_REF] Prodhomme | Nonlinear piezoelectricity in wurtzite semiconductors[END_REF]. The nonlinear piezoelectricity played an important role in semiconducting piezoelectric NWs at high strain. Our study did not include this effect, because the strain on the models was relatively small, where the second-order of piezoelectricity had a weak influence. Another interesting phenomenon has been observed that a non-uniform strain field or the presence of strain gradients could locally break inversion symmetry and induce polarization even in centrosymmetric crystals [103]. This is the flexoelectric effect. The flexoelectric coefficient exhibits a nonlinear interaction with the piezoelectric coefficient. Since it has a strong size dependency, a nonlinear increase of 3 -4 times in the effective piezoelectric coefficient was suggested with decreasing NW diameter [START_REF] Wang | Piezoelectric nanogenerators-Harvesting ambient mechanical energy at the nanometer scale[END_REF]105]. The study on bending ZnO NWs showed that this enhancement became significant when the diameter was below 50 nm [105]. For a bending BaTiO 3 beam, 500% enhancement over bulk properties induced by the flexoelectricity existed only for a beam thickness of 5 nm [103]. In our simulation, the diameter of ZnO NWs was above 50 nm. Besides, instead of bending, the ZnO NWs were actually compressed or elongated along their c-axis, therefore less strain gradient could be converted to polarization by flexoelectric effect.

Although both second-order piezoelectricity and flexoelectricity are not applicable to our case for the moment, it is still very interesting to include these effects in future simulations for a better understanding of the physical principles.

II.1.3 Mechanical properties and scaling rules for NWs

To assess the merits of using piezoelectric NWs in upcoming technologies, a simple analytical model explains the geometry scaling rules for NWs. An individual cylindrical NW is bent by a force F perpendicular to the central axis (Fig. 2.2a) or compressed by a force F in direction of the central axis (Fig. 2.2b) with the bottom constrained to the ground. By applying a fixed force, the radius and the aspect ratio dominate the generation of the strain and strain energy within the NW.

(a) (b)

Strain along z axis:

_ = • 4 • • ( -)
Strain along z axis: Hinchet et al. investigated the strain, stiffness and deformation of ZnO NWs with the size scaling down at a given bending force [START_REF] Hinchet | Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration[END_REF]. Curves in Fig. 2.3 were plotted as a result of analytical calculation with the linear assumption (i.e. the Young's modulus is a constant). Specifically, the strain is proportional to , and the deformation is proportional to . By reducing the scaling factor, namely the size of the NW, the strain increases fast. Thus we can either obtain a larger polarization with the same force for thinner NW, or bend a thinner NW with smaller force. This is how a NW can benefit from scaling down.

= • 1 • Maximum deflection: = 4 3 • • ( -) • Maximum deformation: = • • Strain energy: = 2 3 • • ( -) • Strain energy: = 1 2 • • • Figure 2.
In fact, a FEM simulation of a NW having a radius 25 nm and a length 600 nm (geometry parameters chosen to compare with fabricated NWs in experiments) shows that the mechanical deformation enters nonlinear region when the force exceeds 20 nN. With a nonlinear deformation, the strain generated inside the NW has been increased by around 1.6 times at 80 nN (typical force applied by AFM tip in characterization of piezoelectric NWs) compared to the linear case shown in Fig. 2.3 [START_REF] Hinchet | Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration[END_REF]. This example clearly reveals the necessity of considering mechanical nonlinear effect in NWs. In another opinion, the surface bond saturation, rather than bulk nonlinear elastic effects, was considered to be responsible for the size effects of ZnO nanostructures [START_REF] Zhang | Young's moduli of ZnO nanoplates: Ab initio determinations[END_REF]. Then Agrawal et al. studied the elasticity size effects in ZnO NWs with a combined experimentalcomputational approach [START_REF] Agrawal | Elasticity size effects in ZnO nanowires--a combined experimental-computational approach[END_REF]. The authors measured NWs with diameters ranging from 20.4 nm to 412.9 nm by applying a uniaxial tensile load using a nanoscale materials testing system inside a TEM and calculated the Young's modulus of NWs with diameter ranging from 5 nm to 20 nm. The results are presented in Fig. 2.4, where the Young's modulus decreases from 194 GPa to 169 GPa as the NW diameter increases from 5 nm to 20 nm, and then it monotonically decreases from 160 GPa to 140 GPa and finally converged to this bulk value (140 GPa) as the diameter increases from 20 nm to 400 nm. This size effect is due to surface relaxation and long-range interactions present in ionic crystals, resulting in surfaces much stiffer than bulk [START_REF] Agrawal | Elasticity size effects in ZnO nanowires--a combined experimental-computational approach[END_REF]. Agrawal's experimental-computational results are consistent with the size effect reported by Chen et al. [START_REF] Chen | Size Dependence of Young's Modulus in ZnO Nanowires[END_REF].

Figure 2.3 Variation of Young's modulus with wire diameter (the dashed line shows the experimentally reported bulk value of ∼140 GPa). [START_REF] Agrawal | Elasticity size effects in ZnO nanowires--a combined experimental-computational approach[END_REF] Although the geometry size of the model considered in first-principles calculations is quite different, Yvonnet et al. reported a similar nonlinear elasticity in wurtzite ZnO NWs [START_REF] Yvonnet | Characterization of surface and nonlinear elasticity in wurtzite ZnO nanowires[END_REF]. They computed by ab initio method the Young's modulus that decreases from 420 GPa to 158 GPa as the diameter increases from 0.3 nm to 10 nm (Fig. 2.4a). Qi et al. demonstrated opposite size effects on the pristine and hydrogen passivated (H-passivated) ZnO NWs from the first-principles calculation conducted in a tetragonal supercell [START_REF] Qi | Different mechanical properties of the pristine and hydrogen passivated ZnO nanowires[END_REF]. Their results prove that the Young's modulus of pristine ZnO NWs is larger than the bulk ZnO and decreases from 210 GPa to 160 GPa as the diameter increases from 0.7 nm to 1.6 nm. In contrast, for the H-passivated ZnO NWs, the Young's modulus is smaller than the bulk ZnO and increases from 70 GPa to 85 GPa as the diameter increases from 1.1 nm to 2.0 nm (Fig. 2.4b). The underlying mechanism of discrepancy is the coupling of both core nonlinear effect and surface stress effect. The latter effect leads to significant axial elongations for pristine NWs and contractions for H-passivated NWs leading to the stiffening or softening of ZnO NWs.

It is worth to point out, for all the first principle work, the Young's modulus shows a size effect for NWs with a diameter of a few nanometers. As the diameter exceeds this range, the Young's modulus converges to the bulk value. However, in Espinosa's study, the experimentally measured Young's modulus shows that the size effect starts from 100 nm. ZnO NWs with diameters ranging from 0.3 nm to 2.8 nm by employing first-principles methods [START_REF] Xiang | Piezoelectricity in ZnO nanowires: A first-principles study[END_REF]. The LDA of the exchange correlation functional was used for the calculations. The piezoelectric constant increased monotonically along with the decrease of ZnO NW radius. These size effects were studied later in both ZnO and GaN NWs with radius ranging from 0.6 nm to 2.4 nm by Espinosa et al. [8]. First principles-based DFT calculations were performed with generalized gradient approximation (GGA) using the Perdew -Burke -Ernzerhof (PBE) functional and the revised PBE (RPBE) functional with double-ζ polarization (DZP) orbital basis sets. Their results show that GaN NWs present a larger and more extended size dependence than ZnO and that piezoelectric constants can be improved by 2 orders of magnitude compared to the bulk values [START_REF] Catti | Full piezoelectric tensors of wurtzite and zinc blende ZnO and ZnS by first-principles calculations[END_REF]116], if the NW diameter is reduced to less than 1 nm [8]. Other piezoelectricity calculations of ZnO, GaN and AlN NWs based on first-principles are compared in Table 2.1 to Table 2.3, where is the effective piezoelectric constant. These investigations are highly dependent on the chosen functionals. In addition, only a few hundreds of atoms (a few nanometers in diameter) are evaluated due to computational limitations. Here we have a similar contradiction as what is with the Young's modulus. According to the calculation, piezoelectric coefficients are enhanced when the NW diameter is as small as a few nanometers, which does not consist with experimental results [8].

II.1.5 Piezoelectric response of individual intrinsic NWs

Initially researchers consider the piezoelectric NWs, such as ZnO NWs, as intrinsic semiconductors. Thus most of the studies deal with it by using physics of dielectric materials.

II.1.5.1 Bending individual intrinsic ZnO NWs

Wang et al. first proposed a continuum model for simulating the electrostatic potential in a laterally bent ZnO NW with diameter 50 nm and length 600 nm [START_REF] Gao | Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics[END_REF]. A perturbation technique is introduced with the assumption that no free charge exists in the NW. To simplify the analytical solution, the NW is considered to be an insulator and to have a cylindrical shape and isotropic elastic constants. The maximum potential at the surface of the NW is calculated by Eq. 2.10,

( , ) = ± 1 1 + -2(1 + ) -2 1 2.10
where κ is the dielectric constant, is the lateral force, E is the Young's modulus, e is the linear piezoelectric coefficient, ν is the Poisson's ratio and is the NW radius. Fig. 2.5 shows the potential distribution for the ZnO NW at a lateral bending force of 80 nN. The voltage drop created across the cross section of the NW is around ± 0.3 V with the compressive side having negative voltage and the tensile side having positive voltage, which is high enough to support the working mechanism of NGs [3,120]. They also point out that if the experimental elastic modulus [START_REF] Chen | Size Dependence of Young's Modulus in ZnO Nanowires[END_REF][START_REF] Song | Elastic property of vertically aligned nanowires[END_REF] and piezoelectric coefficient [7] are used in the above calculations, the potential would be multiplied by a factor of 3 -4. Hinchet et al. also put forward an optimized configuration of electric contacts for bent NWs [START_REF] Hinchet | Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration[END_REF] (Fig. 2.7a). The potentials generated in the "bottom-bottom" and the "top-bottom" configurations are compared in Fig. 2.7b. The potential difference is linear in the "bottom-bottom" configuration and approximately fits to bF+cF 2 in the "top-bottom" configuration where is the bending force applied to the NW. Larger sensitivities would be achieved with a top-bottom contact configuration. However, such configuration remains technologically out-of-reach to date and would lose linearity for high forces.

Perez et al. designed a representative elementary pixel of an arrayed force-sensing device based on individual ZnO NW using the "bottom-bottom" electrode configuration [START_REF] Perez | Static finite element modeling for sensor design and processing of an individually contacted laterally bent piezoelectric nanowire[END_REF]. The pixel is constituted by a silicon base substrate, a ZnO seed-layer, one vertical ZnO NW and two gold metallic electrodes placed at the NW base (Fig. 2.8a). In their work, effects of the NW-electrode distance and the electrode thickness due to fabrication techniques were studied (Fig. 2.8b). They concluded that output voltage of several hundred millivolts could be obtained in technologically relevant corporation as response to 80 nN force.

II.2 FEM modeling of NGs based on intrinsic piezoelectric NWs

Individual NWs provide typically very low power. Sun et al. [START_REF] Sun | Fundamental study of mechanical energy harvesting using piezoelectric nanostructures[END_REF] proposed a dynamic analysis on individual NWs showing that the power generated by single NWs varied from 10 -3 pW to 1 pW with different damping ratios in vibration. To increase the energy generated, NWs are mostly integrated laterally [START_REF] Xu | Self-powered nanowire devices[END_REF][START_REF] Qin | Growth of Horizonatal ZnO Nanowire Arrays on Any Substrate[END_REF][START_REF] Xu | Patterned growth of horizontal ZnO nanowire arrays[END_REF][START_REF] Hu | Self-powered system with wireless data transmission[END_REF][START_REF] Yang | Characteristics of output voltage and current of integrated nanogenerators[END_REF], and vertically [START_REF] Hu | Self-powered system with wireless data transmission[END_REF][START_REF] Choi | Mechanically Powered Transparent Flexible Charge-Generating Nanodevices with Piezoelectric ZnO Nanorods[END_REF][START_REF] Van Den Heever | The performance of nanogenerators fabricated on rigid and flexible substrates[END_REF][START_REF] Ebrahimi | Electrochemical Detection of Piezoelectric Effect from Misaligned Zinc Oxide Nanowires Grown on a Flexible Electrode Electrochim[END_REF][START_REF] Khan | Mechanical and piezoelectric properties of zinc oxide nanorods grown on conductive textile fabric as an alternative substrate[END_REF][START_REF] Chen | Gallium nitride nanowire based nanogenerators and light-emitting diodes[END_REF] on the substrate to form piezoelectric composite materials.

II.2.1 State of the art

NWs can be integrated into NGs using two methods: LING and VING.

II.2.1.1 Modeling study on LING

The development and applications of LING have been introduced in Chapter I. It developed from SWG, which consists of one ZnO micro-rod fixed by silver paste on a flexible polyimide film as a doubly clamped beam. The maximum output voltage peak of this structure was 1.26 V [START_REF] Xu | Self-powered nanowire devices[END_REF]. This value was improved by using rational unipolar assembly of conical ZnO NWs [START_REF] Hu | High-Output Nanogenerator by Rational Unipolar Assembly of Conical Nanowires and Its Application for Driving a Small Liquid Crystal Display[END_REF]. The model of the device was a capacitor-like plate structure with ZnO conical NWs packaged by PMMA as dielectric media, with one end fixed and a transverse mechanical force applied at the other end (Fig. 2.9a and b). Assuming that the simulation was conducted without considering the coupling between the piezoelectric field and the inductive charges in the electric plates under the first-order approximation, the model of a paired intrinsic NW with opposite c axes was analyzed. The potential difference between the top and bottom electrodes of such a generator was calculated as a function of the NW density and the voltage was as high as 2.5 V when the density was 9×10 5 mm -2 . In their work, the piezopotentials inside the two conical NWs are opposite in sign under compressive strain, but with a small separation in the charge centers in z direction, which is the fundamental mechanism for creating the inductive charges at the top and bottom electrodes (Fig. 2.9c-e).

The calculation for cylindrical NWs with zero conical angle (Fig. 2.9f) showed that the conical shape is the key for the device to work correctly.

II.2.1.2 Modeling study on VING

Theoretical and computational studies have been done to investigate the physical basics and the optimization guideline of VING design. Hinchet et al. explored the working principle of VING structure in compression mode and put forward the design and guideline rules for the performance improvement by using FEM simulations [START_REF] Hinchet | Design and guideline rules for the performance improvement of vertically integrated nanogenerator[END_REF]. The VING is composed of NG cells each including a single intrinsic ZnO NW surrounded by PMMA matrix material under an applied compressive pressure (1 Mpa) (Fig. 2.10a). The energy conversion mechanism was divided into three steps: mechanical energy transfer, mechanical to electrical energy conversion and, finally, electrical energy transfer to the output circuit (Fig. 2.10b). To simplify the simulation, the authors started with an individual NG cell coupling the piezoelectric equations for the NW and the mechanical and electrostatic equations for PMMA and electrodes. For comparison, the geometry parameters of the NW were taken from Ref [START_REF] Gao | Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics[END_REF] (also see Fig. 2.10a) and varied, as well as the geometry ratio (defined as NW diameter/cell size), to optimize the NG performance. The divergence of simulation results from the analytical calculation indicated a complex 3D effect arising from the non-homogenous structure.

(a) (b) The yield (η) has been calculated for each step using the parameters of (a). d x , E x and ε x are the thickness, Young modulus and dielectric constant of layer x. Index eq indicates that the corresponding layer is modeled as a uniform equivalent medium. T is the stress and e 33 the piezoelectric coefficient relevant to this strain configuration. [START_REF] Hinchet | Design and guideline rules for the performance improvement of vertically integrated nanogenerator[END_REF] Further simulations considering multiple NG cells (NG matrix) were further studied [5]. The piezoelectric potential increased from 20 mV to 70 mV and approached saturation as the NG matrix size increased from 1 cell × 1 cell to 15 cells × 15 cells, indicating that edge effects and 3D dielectric losses were reduced by a matrix size of around 200 NWs (Fig. 2.11a and b). Compared to a bulk ZnO layer, the NG cell generated a piezoelectric potential and electric energy varying as a function of the geometry ratio. The potential peak appeared at a geometry ratio equal to 0.4, while the energy peak appeared at 0.5. For geometry ratio of 0.5, the piezoelectric potential was as high as 3.3 times of the bulk ZnO layer, and the electric energy was about 5.6 times of the bulk layer generator (Fig. 2.11c-e). The author also tested different materials as the top insulating layer, among which Si 3 N 4 featured the best trade-off between the mechanical energy loss and electric energy loss because of its large Young's modulus (250 GPa) and relatively high permittivity (9.7). It is worth to point out that the authors demonstrated the decrease of energy generation for larger diameter NW and the approach of a saturation value with the increase of the NW length. Semiconducting properties were then introduced into the FEM simulation. Given the size of NWs, full depletion of free charges approximation was applied as the doping level was smaller than 5×10 18 cm -3 . The screening was then caused by the fixed ionized dopants and decreased the piezoelectric potential generated by ZnO NWs from 68 mV to 1.4 mV as dopant concentration increased from 1×10 12 cm -3 to 1×10 18 cm -3 . The above simulations used the bulk piezoelectric coefficients. Thus the piezoelectric potential could be increased to 123 mV if the piezoelectric coefficient of ZnO NWs measured experimentally at nano scale was used [7].

(a) (b)

(c) (d) (e)

II.2.1.3 Alignment of NWs in VING

In the modeling study of VING, NWs are usually considered to possess perfect vertical orientation and unified polarity. Although perfectly aligned NWs have been successfully fabricated [128], to our knowledge, only slightly inclined piezoelectric NWs have been used to develop mechanical transducers [5]. In fact, the tempering effect on the potential generation does exist due to the inclination of the NWs. We have discussed about this effect particularly in one chapter of the book Future Trends in Microelectronics: Journey into the Unknown [START_REF] Tao | Will composite nanomaterials replace piezoelectric thin films for energy transduction applications? Future Trends in Microelectronics: Journey into the Unknown[END_REF]. The reference NG structure was formed by ZnO NWs (600 nm long) immersed on PMMA with a top insulator layer of Si 3 N 4 (100 nm thick), which was found optimal compared to PMMA top layer [5]. A single cell was evaluated under a compression of 1 MPa, including an increasing number of NWs having different inclination angles with respect to the ideal vertical case, starting from 1 NW up to 64 NWs. NWs were assumed to grow along the c-axis in all the FEM simulations, which was important to define their piezoelectric properties; this had been done by defining these properties with respect to a rotated Cartesian axis, aligned with each inclined NW. In this section, material properties of ZnO thin film were used for the simulations.

a. Individual VING composite cell including a single NW Fig. 2.12a shows the absolute value of the potential generated by the individual composite cell integrating an inclined NW in function of the inclination angle. Two simulation conditions are confronted: taking into account the Cartesian axis rotation to correct the c-axis or without the axis rotation. As the inclination angle is low (below about 5°) the curves are very close to each other and a small error is produced if the c-axis correction is neglected (maximum error of 2% below 5° and 8% below 12°), then the error increases with the inclination angle reaching a maximum of  85%. An optimal inclination angle can also be observed when the inclination angle is lower than 5°, increasing slightly the absolute electric potential at the top electrode. Then the potential is greatly reduced reaching a reduction of 50% for an inclination of  30°. A comparison of the results with and without c-axis correction for a specific angle is depicted in Fig. 2.12b and c.

b. Individual VING composite cell including 2 NWs

When 2 NWs were included in a single cell, several possibilities of inclinations were evaluated. To facilitate the study, only one inclination following the xz-plane was considered. A first series of simulations were conducted with only one inclined NW (Fig. 2.13a). The absolute value of the electric potential at the top electrode in function of the inclination is shown in Fig. 2.13b. In general the results are similar to the previous case with a single NW, with an optimal inclination close to 5°. This same behavior is observed if the inclination angle is defined along the yz-plane instead of the xz-plane (Fig. A second set of simulations were conducted inclining both NWs on the cell only at small angles between 0° and 12° on the xz-plane at different situations as described on Table 2.4. The results shows no clear trend, in some cases the electric potential is slightly increased (increase of 1%) compared to the ideal situation (≈ 69mV) and in some cases the potential is highly decreased (reduction of 17%). More NWs per cell are needed to see if a trend is observed. In order to verify the trend found with the simulations including 4 NWs, cells including 36 and 64 ZnO NWs were simulated (Fig. 2.15). The absolute value of the electric potential at the top electrode in both cases is close to 59mV, representing a reduction of 14% from the ideal case. We expect that these simulations represent better the real trend because of the greater number of NWs composing actual devices. Only small inclinations angles have been considered (<12°), for this reason and because of the increasing number of NWs, these simulations have been made without correcting the c-axis of the NWs, thus the results underestimate slightly the electric potential generated (estimated at 8%). As a conclusion, the approach of considering a small number of NWs in a composite cell is only applicable if the NWs are vertical, providing the maximum electric potential. If real cases are considered with slightly inclined NWs, a large number of NWs in the cell is required to obtain appropriate simulation results. These simulations also show that integrating slightly inclined piezo NWs would reduce the electric potential generated by as much of 14% compared to the integration of vertical NWs. [START_REF] Tao | Will composite nanomaterials replace piezoelectric thin films for energy transduction applications? Future Trends in Microelectronics: Journey into the Unknown[END_REF]

Table 2.4 Output electric potential (absolute value) of cells including two inclined

II.2.2 FEM simulations for VING with intrinsic ZnO NWs

To study the performance of the VING structure, we conduct computational simulations on intrinsic ZnO NWs based nano-composites in both compression and flexion modes. Matrix materials and ZnO properties are varied to compare with conventional thin film generators.

II.2.2.1 Material parameters for ZnO NWs

The material parameters of ZnO presented in section II.2.1 are measured on ZnO thin films. These parameters have been used for ZnO NWs in our modeling research because they are widely accepted due to the mature and convincing measurement techniques [START_REF] Bateman | Elastic moduli of single crystal zinc oxide[END_REF][START_REF] Carlotti | Acoustic investigation of the elastic properties of ZnO films[END_REF][START_REF] Ashkenov | Infrared dielectric functions and phonon modes of high-quality ZnO films[END_REF]. However, as 1D material, NWs usually have parameters that differ from the bulk material, including dielectric constant, piezoelectric coefficient, stiffness constant, etc.

a. Dielectric constant of ZnO NWs

Yang et al. [START_REF] Yang | Size Dependence of Dielectric Constant in a Single Pencil-Like ZnO[END_REF] used scanning conductance microscopy (SCM) to measure the dielectric constant of a single pencil-like ZnO NW with the diameters ranging from 85 nm to 285 nm (Fig. 2.16a). As the diameter decreases, the dielectric constant of ZnO NW was found to decrease from 6.4 to 2.7, which was much smaller than that of the bulk ZnO of 8.9.

b. Piezoelectric coefficient (d 33 ) of ZnO NWs

Zhao et al. used PFM to measure the effective piezoelectric coefficient (d 33 ) of an individual (0001) surface dominated ZnO nanobelt lying on a conductive surface [7]. Based on references of bulk (0001) ZnO and x-cut quartz, the effective piezoelectric coefficient d 33 of ZnO nanobelt (360 nm in width and 65 nm in thickness) was found to be frequency dependent and varied from 14.3 pm/V to 26.7 pm/V, which is much larger than that of the bulk (0001) ZnO of 9.93 pm/V (Fig. 2.16b).

c. Young's modulus and stiffness constant of ZnO NWs

Size effect of the Young's modulus of ZnO NW has been discussed in section II.2.3. Computational -experimental combination results showed that the Young's modulus presented significant increase when the diameter was smaller than 50 nm. On the other hand, the stiffness is also related to the surface status of the ZnO NW. Since those results are not fully validated, we still use the mechanical parameter of ZnO thin film in our simulations. To sum up, in the rest of section II.3, we will use = 2.7 and = 26.7 ⁄ as "nano dielectric constant" and "nano piezoelectric coefficient" of ZnO NWs.

d. Material parameters of matrix materials

In our simulation, different matrix materials have been used. Their Young's modulus, Poisson ratio and dielectric constant are listed in Table 2.5.

a. Model description

For VING in compression mode, the core function part of the simplified model (named NG cell) is one NW surrounded by matrix material, where the input pressure on the top surface is equal to the one on the whole structure (Fig. 2.17). Lateral surfaces are confined by symmetry boundary conditions, which represents that there are identical NG cells surrounding the target one. In this case, the NW is immerged into a layer of PMMA, which protects it from electrical leakage or short circuits that could occur because of the semiconducting properties of ZnO NW, but also gives the device robustness. Then, top and bottom surfaces are defined as electrodes to harvest the electrostatic energy generated. When the device is compressed, part of the input mechanical energy is stored inside the core piezoelectric NW, and then it is converted into electric energy through direct piezoelectric effect. Finally, the electric energy is driven out by the external circuit (not shown here). The initial cell size is 100 nm × 100 nm × 750 nm, with NW radius R = 25nm, and length L = 600 nm. The size is varied with the changing geometry ratio (NW diameter/cell width). The compressive pressure is 1 MPa. The electrical and piezoelectric properties of ZnO are varied respectively to study their influence. As mentioned above, the mechanical properties have a great scatter, so we do not consider the variation of ZnO elastic modulus for current simulations.

b. Effect of material properties of ZnO NWs

Fig. 2.18a shows the absolute value of the output potential varying with the previously defined ratio. The thin film model generated a potential around 10 mV. When the model of the composite NG cell was considered, the potential increased by 8 times (at ratio = 0.4) even though the NW was assumed to have the same properties as thin film [START_REF] Bateman | Elastic moduli of single crystal zinc oxide[END_REF][START_REF] Carlotti | Acoustic investigation of the elastic properties of ZnO films[END_REF][START_REF] Ashkenov | Infrared dielectric functions and phonon modes of high-quality ZnO films[END_REF]. The simulation results are corresponding to Ronan's modeling on the same NG cell. [5] The changing trends are the same and the optimum also appears at ratio = 0.4 in his work. There is a slight difference on the absolute value due to the selection of material parameters. The enhancement was due to the soft matrix PMMA, which concentrated the strain inside ZnO. Besides, because of the 3D dielectric losses and the deviation of the strain field around the NWs, a smaller size ratio improved the storage of mechanical energy to the NG but reduced the electrical energy stored. In contrast, a high size ratio increased the capacity to store electrical energy in the NG, at the expense of reducing mechanical energy storage (Fig.

2.18b

). The trade-off of these two contradictory effects formed a potential curve with a peak at ratio = 0.4. Since the dielectric constant decreases with the NW radius [START_REF] Yang | Size Dependence of Dielectric Constant in a Single Pencil-Like ZnO[END_REF], the electric energy loss through the top insulating layer is smaller in NG cell. With the increase of ratio, the dielectric constant became the major factor that influences the output potential. As a result, the potential of the NG cell with nano dielectric constant kept increasing with the size ratio. For the cell with nano piezoelectric coefficients, the potential curve followed the changing trend of the cell with thin film properties, but increased by roughly two times. Finally, the potential of NG cell with NW properties was enhanced by 22 times compared to thin film model and by 2.4 times compared to the NG cell with thin film properties. The electric energy was calculated from the potential and the equivalent capacitance of this structure. The maximum shifted to higher geometry ratio because of larger capacitance (Fig.

2.18c). We defined the energy conversion ratio/efficiency as, energy conversion ratio = × 100%

Apparently, the energy conversion ratio was increased by as high as 5.9 times considering dielectric constant and piezoelectric coefficient of ZnO NWs (Fig. 2.18d). This magnification could reach 212 compared to ZnO thin film. Besides, there was also a shift of optimum geometry ratio compared to NG with thin film properties as nano piezoelectric constant and nano dielectric constant were considered respectively, while this shift was negligible for NG combining both NW piezoelectric and dielectric properties.

II.2.2.3 VING working under bending (intrinsic ZnO NWs)

As mentioned above, VING can work also in flexion mode. Here we extended the study to the flexion mode using a thin plate as a mechanical transducer. The hydrostatic pressure generated a force bending the membrane, compressing the NW from the sidewalls. Under strain, the NW active layer of the VING structure generated a potential difference which can be used to power an external circuit by means of a capacitive displacement current.

a. Model description and working principle

VING structure working in flexion mode was actually integrated on flexible metallic foils (25 μm) acting like a bottom electrode as well, bended by a hydrostatic pressure as a doubly clamped plate (Fig. 2.19a). The VING structure was the same as when it was integrated on Si wafers, NWs grown on a seed layer being embedded in a matrix sandwiched by electrodes (Fig. 2.19b). Similarly, only a NG cell of the device was considered (Fig. 2.19c) with appropriate boundary conditions for fast and reliable FEM modeling. When the device membrane was under bending as shown in Fig. 2.19a, the NG cell was compressed laterally and extended along the c-axis (Fig. 2.19c). Since the NW/PMMA layer was far from neutral plane, we assumed that the cell had a quasi-constant strain at sidewalls along z direction when the device was bent by a hydrostatic pressure (100 Pa). The initial cell size was 100 nm × 100 nm × 750 nm, with NW radius R = 25 nm, and length L = 600 nm. The size varied with the changing geometry ratio (NW diameter/cell width). The ZnO material parameters varied as in compression mode and their effects were discussed. Then different matrix materials were used based on the simulation using ZnO nano properties. In all studies, simulation with a ZnO thin film was included as a reference. The main issue compared to previous studies on the compression mode remains how the energy is transferred and converted. In the core cell, the energy conversion mechanism has been divided into 3 steps [START_REF] Hinchet | Design and guideline rules for the performance improvement of vertically integrated nanogenerator[END_REF]: mechanical energy transfer, mechanical to electrical energy conversion and, finally, electrical energy transfer to the output circuit. In the first step, the total input mechanical energy ξ is considered to be composed of two parts. One ( ) is the energy stored in the seed layer and the top insulating layer, and the other ( ) is the energy stored in the NW/PMMA compound. The energy that reaches the NW is used in the piezoelectric transfer process ( ). Thus, the mechanical energy transfer efficiency is expressed as

= ( + ) ⁄
, where is supposed to be a constant. Thus the major influencing factor is the ratio of and , whose reciprocal increases with (w 1 E NW )/(dE PMMA ) where w 1 and d are geometrical parameters (see Fig. 2.20a) and E is the Young Modulus. The energy conversion efficiency of the second step depends on the NW's electromechanical properties and is proportional to the square of piezoelectric strain constant e 33 2 (Fig. 2.20b) [START_REF] Hinchet | Design and guideline rules for the performance improvement of vertically integrated nanogenerator[END_REF]. The third step brings dielectric losses to our device with the efficiency ( ) defined as 1/(1+L 1 ε 2eq /L 2 ε 1 ), where d is a geometrical parameter (Fig.

b. Effect of material properties of ZnO NWs

The output potential of the NG cell with thin film properties increased with the size ratio (Fig. 2.21a). This increase was fast when the geometry ratio was low due to the increasing piezoelectric functional cores. Then the potential variation tended to be stable as a result of more functional cores and larger equivalent dielectric constants. Finally the increase of ZnO overcame the other effects and further enhanced the potential. NG cells with nano properties showed different behaviors in this case. The NG cell with only nano piezoelectric coefficients generated a higher potential at a geometry ratio around 0.4. On the other hand, NG cell with nano dielectric constant presented a monotonic increasing potential with geometry ratio. Since the nano dielectric constants of ZnO is smaller than PMMA, the electric energy loss decreased as the quantity fraction of ZnO increased (Fig. 2.21c). Under the combination influence of nano piezoelectric constants and dielectric constants, the NG cell showed a similar changing trend compared to the one using thin film properties, but with an increase of 3.5 times. Since the volume ratio of matrix material in the whole plate was small, the influence on the strain energy was negligible (Fig. 2.21b). As a result, the energy conversion ratio followed the changing trend of electric energy and achieved an optimum value at ratio = 0.5 for NG with NW properties (Fig.

c. Effect of matrix material

Although using "nano" properties improved the energy conversion and potential generation of VING in flexion mode, the performance was not as good as ZnO thin film generators based on the simulation results. However, the performance of this composite material can be further improved by using different matrix materials.

Analysis was focused on the displacement, the strain tensor and the electric potential distributions. The hardness of the matrix material resulted in two different types of distribution of the displacement and the strain. When a soft matrix material (PMMA) was used, the matrix was more compressed than the NW as indicated by the displacement distribution (Fig. 2.22a). The strain tensor distribution (Fig. 2.22b) shows that strain was concentrated in the matrix material instead of the NW. The opposite resulted from using a hard matrix (Al 2 O 3 ) (Fig. 2.22c) and strain was concentrated in the NW (Fig. 2.22d). This is consistent with the mechanical energy transfer efficiency (η m ). As the Young's modulus of the matrix material increases, the efficiency increases. More mechanical energy is transferred into the core NW by using hard matrix, influencing the final potential and energy generation. As a result, the potential generated was higher than the thin film starting from a ratio = 0.3 -0.5, and reached a value that was 1.5 -2.5 times larger than the ZnO thin film (Fig. 2.23a). Since the improvement was majorly due to the increase of input strain and the reduction of electric energy loss, potential and electric energy both increased with the geometry ratio. More details have been discussed in a previous modeling study on a similar NG cell with ZnO NWs but using thin film properties [132]. To clarify the energy transfer process, Young's modulus, Poisson's ratio and relative permittivity of matrix materials were varied independently. The former two parameters mainly influenced the mechanical energy transfer and slightly affected the piezoelectric energy transfer. The relative permittivity affected the electrical energy transfer to the output circuit. Mechanical and electrical parameters of real matrix materials are listed in Table 2.5 in section II.3.2.1. First, the effects of Young's modulus and Poisson's ratio on the potential generation were compared (Fig. 2.24a). The curves were plotted against one parameter while the two others were kept equal to that of PMMA. As the value of Young's modulus spanned from 3 GPa (PMMA) to 400 GPa (Al 2 O 3 ), the potential increases from 0.8 V to 4.4 V. In contrast, varying from 0.17 to 0.40, the change of Poisson's ratio only brought a potential difference of 1 V. The relationship between the relative permittivity and the electric potential was more complex. In fact, the relative permittivity of the matrix material was not the direct factor that influenced the electrical energy transfer process. Efficiency η e decreased with increasing ε eq of the matrix/NW compound. Here ε eq was not a linear combination of the permittivity of the NW and the matrix. As a result, the potential curve reached a maximum value when the permittivity was close to 2.5 (Fig. 2.24b). Considering that the relative permittivity of real matrix materials varied from 2.09 (SiO 2 ) to 9.7 (Si 3 N 4 ), the potential variation is less than 0.5 V. In the simulation, the effect of Young's modulus was more significant than the effects of Poisson's ratio and relative permittivity.

II.2.3 Placement of the top electrode for VING in flexion mode

A preliminary mechanical simulation of bending a doubly-clamped membrane showed that the strain on the active layer was negative in the middle of the membrane (in compression) and positive in the rest of the membrane (in extension) (Fig. 2.25). The potential generated in such condition without considering the top metallic contact will follow the strain, positive in the compressive part and negative in the extensive part. In real conditions, a metallic contact is necessary to produce an electrical contact to an external circuit. Including this contact on the simulation (floating potential condition), such device would generate a potential close to 0 V because the positive potential compensated the negative one. Thus, this structure is not appropriate for a transducer. We came up with an improved structure presented in Fig. 2.26. It consisted of a thin layer of piezoelectric material integrated only in the central part of the membrane. In this case a positive potential (Fig. 2.28a) was generated which could be used by electrical load. Adding a metallic contact on top of the whole structure created an equipotential condition reducing the voltage generated to 50% of the maximum potential generated without contact. This was further improved by adding the metallic layer only in the region where the piezoelectric material was integrated. This move increased the potential of 30% (see Fig. 2.28a) thus increasing the energy conversion efficiency. In another case, we tried to collect potential from both the compressive and extensive regions on the membrane. This design included a piezoelectric layer on those regions as illustrated in Fig. 2.27. The voltages generated at the side electrodes (see Fig. 2.28b) can be added using a series connection in order to boost the potential and the global energy conversion efficiency. This simulation also showed that the reduction of the length of the piezoelectric layer by 2 times towards the maximum of strain increased the voltage 1.2 times, but also reduced the equivalent capacitance of the structure 2 times, thus reducing the overall energy produced. This new structure with 3 electrodes (lateral electrode length L = 2 mm) increased the voltage generated up to 2 times and increased the conversion efficiency up to 12 times compared to the structure with the single piezoelectric layer in the middle of the membrane. The reason of this improvement is the increase in the global capacitance of the device and the voltage.

II.3 Coupling of piezoelectric and semiconducting properties in NGs

Initially linear mechanical and piezoelectric NW and NG models were built to evaluate the NW capabilities as the functional element for emerging electromechanical devices within self-powered nanosystems. However, many of the piezoelectric NWs are semiconductors, such as ZnO, GaN and GaAs NWs. Under this circumstance, the semiconducting properties need to be considered, because they are responsible for screening effects that influence energy harvesting and sensing.

II.3.1 The screening effect in individual NW

Although intrinsic III-N and ZnO are generally considered as insulators due to their middle-wide band gap, in fact, those NWs are doped during the synthesis by defects and impurities, either purposefully for achieving certain functionality or through accidental doping due to the growth mechanism [134][START_REF] Gao | Compensation mechanism in N-doped ZnO nanowires[END_REF][START_REF] Lee | Depletion width engineering via surface modification for high performance semiconducting piezoelectric nanogenerators[END_REF][START_REF] Sinha | Synthesis and enhanced properties of cerium doped ZnO nanorods[END_REF][START_REF] Kim | Electrical transport properties of individual gallium nitride nanowires synthesized by chemical-vapor-deposition[END_REF][START_REF] Fan | Very low resistance multilayer Ohmic contact to n-GaN[END_REF]. Semiconducting properties need to be included in the simulations on piezoelectric NWs since dopants play a role in the conductivity of the specimen and therefore influence the electromechanical response. Gao and coworkers investigated the behavior of free charge carriers in a bent piezoelectric n-type ZnO NW under thermodynamic equilibrium conditions by inducing donors into the model [START_REF] Gao | Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire[END_REF]. The Gauss's law was combined with the mechanical equilibrium and the direct piezoelectric effect, as the free charge carriers would redistributed due to the electric field established by the polarization. The authors studied distributions of the piezoelectric potential, free electron concentration and activated donor center concentration varying at different doping levels (0.6 × 10 17 cm -3 ≤ N D ≤ 2.0 × 10 17 cm -3 ), assuming a flat Fermi level and a homojunction between the ZnO NW and the substrate. The results (shown in Fig. 2.29) lead to a conclusion that when an n-type ZnO NW is bent, the compressive side preserves the negative voltage, while the tensile side with positive potential is partially screened by free electrons. The charge carriers are accumulated at the tensile side and the compressive side is largely depleted. Besides, in order to compare with the situation when ZnO is considered as an insulator without any free charge carriers, the authors have made a high temperature approximation (T = T high = 300000K) and achieved a result that is consistent with their former work in ref [START_REF] Gao | Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics[END_REF]. Similar effects were also tested in Araneo's simulations [141]. ZnO NWs of cylindrical and truncated conical shapes with typical doping levels were laterally bent by very small input forces of 442 nN. For the cylindrical NWs, the piezopotential was increasingly screened as doping level was larger, and meanwhile, the dissymmetry between the smaller reduction of the negative voltage and the larger one of the positive voltage increased. Unlike the cylindrical NWs, the output piezopotential for a doped conical NW was comparable or even higher than for a purely dielectric NW if the doping level was around the typical effective-donor concentration 10 17 cm -3 . for different donor concentrations 0.6 × 10 17 cm -3 ≤ N D ≤ 2.0 × 10 17 cm -3 . Reprinted with permission [START_REF] Gao | Equilibrium potential of free charge carriers in a bent piezoelectric semiconductive nanowire[END_REF].

In this work, Romano et al. [6] performed a theoretical and finite element analysis of a vertically compressed NW under equilibrium conditions and considering a finite electrical conductivity. The simulation model was composed by a cylindrical ZnO NW grounded and fixed at its base and compressed by a uniaxial force along the z axis, surrounded by air (Fig. 2.30). The far-field boundary conditions were set as a conductive thin film at the bottom of the NW and zero electric field far away from the NW. The authors computed the output piezopotential while varying the donor concentration, the geometry, the input force and the surrounding medium. The results identified that the output potential was screened by free electrons. The reduction of the piezopotential was dependent on the donor concentration. The influence of the dielectric medium was also discussed. For a NW with low doping level (e.g. N D = 1 × 10 16 cm -3 ), the reduction of piezopotential induced by the small dielectric constant of a certain medium (e.g. PMMA) was negligible, while for a close-to-intrinsic NW the reduction could be significant.

Generally, the screening effect resulting from the free charge carriers could be useful for sensing applications as reported [START_REF] Zhao | Biomolecule-adsorption-dependent piezoelectric output of ZnO nanowire nanogenerator and its application as self-powered active biosensor[END_REF][START_REF] Nie | The conversion of PN-junction influencing the piezoelectric output of a CuO/ZnO nanoarray nanogenerator and its application as a room-temperature self-powered active H₂S sensor[END_REF]. However, it decreases the energy generation in the piezoelectric NW. Efforts have been done to reduce the influence of this effect by manipulating the depletion region. In Romano's work, the authors calculated the depletion region in the longitudinal direction, where the depletion width was much smaller than the length of NWs. Under full depletion approximation, there is no voltage drop outside the depletion region, which offers a lenient requirement for the length of NWs. Their results provide important guidelines for the design of high-efficiency PENGs. However, we wanted to re-examine these results in view of our own device configuration.

II.3.2 The screening effect in VINGs

To study the screening effect in the NGs, we introduced this effect into FEM modeling using FlexPDE software. We modify Eq. 2.5 by coupling the Poisson equation for semiconductors, ∇ = -2.12 = ( -+ -) 2.13 where is the total charge density, is the electron carrier density, is the hole carrier density, is the acceptor density, is the dopant density and is the elementary charge. With Eq. 2.8, we can obtain the coupling equation of piezoelectric and semiconductor physics as,

∇(

)

+ ∇ ∇ = 0 ∇ ∇ -∇( ) = ( -+ - ) 2.14
In our simulation, the ZnO NW is considered as n-type semiconductor. Therefore Eq. 2.14 is further simplified by setting equal to zero,

∇( ) + ∇ ∇ = 0 ∇ ∇ -∇( ) = ( -- ) 2.15
Similar to what happens in individual NW, the piezopotential generated by a NG cell is also influenced by the screening effect. A 2D NG cell model representing a nanowall generator under compression was simulated while the doping concentration of the ZnO NW varied from 10 to 10 (Fig. 2.31a). Piezopotential collected on the top of the structure is shown in Fig. 2.31b. At extremely low doping level ( 10), the domain of the NW was fully depleted and polarization charges existed without being screened by free electron charges and by few fixed charges from dopants. In this case, the piezopotential was close to that of the same NG structure integrating an intrinsic ZnO NW.

Then the dopants increased with the doping level, and started to screen the polarization charges. When the doping level reached = 10 , the piezopotential was already reduced to a quarter of the intrinsic value. At > 10 , the piezopotential was almost fully screened by both free charges and fixed dopants.

II.4 Surface Fermi level pinning (SFLP) effect

Based on the analytical and modeling study on the screening effect in NGs, the real NG device would have fatal problems in supplying electric power since the standard doping level of ZnO NWs is from 10 to a few of 10 . However, several critical issues have not been readily addressed since contradictory observations from analytical and experimental results exist . Chief among them are: (1) decent and length-dependent performance of ZnO NWs [4], while anticipations based on analytical and computational study showed that the output of NWs under compression were reduced to a few millivolts and presenting length-independent performance due to the screening effect [5,6]; (2) enhanced piezoelectric coefficients [7], which were measured for ZnO NWs with diameter beyond the size effects anticipated by ab-initio method [8]; and (3) dissymmetric piezoelectric response of NGs under tensile and compressive strain [9]. One possible explanation to these issues is the Surface Fermi Level Pinning (SFLP) effect.

II.4.1 SFLP effect on semiconducting NWs

When the periodic structure of a crystal lattice is terminated at a surface, electronic states particular to the surface are created. Surface states can be true surface states with wave functions which are peaked near the surface plane and which decay in amplitude away from the surface. They may result, with typical energies inside the gap between the valence band and the conduction band. In fact, surface states emerge from the conduction and valence band since the total number of states is conserved. The "gap" between a conduction and valence band is connected in the imaginary k-plane. Moreover, the nature of this state (i.e. its orbital character and symmetry) smoothly varies between that of the conduction band (which might be, say, 4s orbitals) and the valence band (which might be 3p orbitals). In imaginary k-space, there must therefore be some crossover point, where donor-like states and acceptor-like states switch over to one another. If the Fermi level lies above this energy, it quickly concentrates electrons there in real space. If it lies below, it concentrates holes. So for the semiconductor to be locally charge-neutral, the Fermi level must lie at this crossover point ---it's pinned, hence the name Fermi level pinning. The crossover point ---the charge neutrality level is the Fermi-level pinning location. This effect commonly exists at the surface of III-V and II-VI semiconductor compounds [START_REF] Chakrapani | Electrochemical pinning of the fermi level: Mediation of photoluminescence from gallium nitride and zinc oxide[END_REF][START_REF] Lüth | Solid Surfaces, Interfaces and Thin Films[END_REF][START_REF] Van Weert | Large redshift in photoluminescence of p -doped InP nanowires induced by Fermi-level pinning[END_REF]. At the surface of ZnO NWs, oxygen molecules adsorbed are negatively charged ions by capturing the free electron from n-type ZnO and form a low-conductivity depletion layer near the surface, where the screening effect is crippled [START_REF] Lüth | Solid Surfaces, Interfaces and Thin Films[END_REF][START_REF] Kind | Nanowire ultraviolet photodetectors and optical switches[END_REF][START_REF] Li | Oxygen sensing characteristics of individual ZnO nanowire transistors[END_REF][START_REF] Li | Electronic transport through individual ZnO nanowires[END_REF][150][151].

The depletion phenomenon has been investigated on the cross-section of the NW. As shown in Fig. 2.32a, for a NW with large radius, the region close to the lateral wall is depleted and a neutral core exists in the center. While a NW with small radius can be fully depleted. The critical radius for fully depleted NW at N D = 10 18 cm -3 was calculated to be around 50 nm. Then Mouis et al. gave out a guideline on the relationship between the NW size, doping level and depletion region by analytical work from a pure semiconducting point of view using the assumption of SFLP [START_REF] Mouis | Title Materials Research Society (MRS) Spring Meeting & Exhibit[END_REF]. Fig. 2.32b presents the analytical depletion width as a function of the donor concentration and the radius of ZnO NWs. For a NW with a high doping level, the radius should be small to achieve a full depletion on the cross-section of the NW; and vice versa, for a NW with large radius, the doping level should be lower than the one with small radius. For instance, a ZnO NW with a radius of 25 nm would be fully depleted and could be less influenced by the screening effect if its doping level was lower than 5×10 18 cm -3 .

(a) (b) In the modeling, both intrinsic and n-doped ZnO NWs (N D = 10 16 cm -3 -10 18 cm -3 ) were investigated. To compare with the NG cell having free Fermi level, two different situations were studied, where Fermi level was pinned only on top surface (for qualitative comparison with Romano's work) and on all surfaces (to consider a more realistic case). Equivalent surface charge was applied on top surface, and on all surfaces (Fig. 2.33). In 2D axisymmetric cylindrical coordinates, we have strain components:

= ( ) = ⁄ = ( ) = ( ) + ( )

2.16

Where r, and z are the cylindrical coordinates, and are the displacements in r and z directions, respectively. Then the expression of strain σ components is derived as,

= + + + ( ) = + + + ( ) = + + + ( ) = + ( )
2.17

If we consider a system in the mechanical static state (body force = 0), the governing equations are, (r direction):

( • ) -+ ( ) = 0 2.18 (z direction):

( • ) + ( ) = 0 2.19
For the semiconductor Poisson equation, we have the polarization vector as, = ( , )

2.20 = 2.21 = + + 2.
22 Then the Poisson equation can be written with the form,

∇ ∇ - = ( -- ) 2.23
In a static system, if we define the potential as V when there is no mechanical input and when there is a mechanical input, the piezoelectric potential is:

∇ ∇ = ( -- ) 2.24 ∇ ∇ - = ( -- ) 2.25 = - 2.26

II.4.2.2 Electrical boundary conditions

The bottom of the NG cell is electrically grounded and equilibrium potential condition is applied to the top simulating the electrode. In the modeling of SFLP, an equivalent surface charge was used on the interfaces between the NW and the matrix as,

• = 2.27
Two assumptions could be used to calculate the equivalent surface charges.

a. Fermi level pinned at mid-gap

To simplify the simulation, the Fermi level is supposed to be pinned at mid-gap and described by an equivalent surface charge on the interface between the NW and the matrix. The surface potential is defined as,

= 2 - 2.28
where E g is the band gap of the bulk ZnO (3.37 eV), N D is the doping concentration, k B is the Boltzmann constant and T is the room temperature. The equivalent surface charge can be approximated by its expression calculated under planar assumption,

= -2 | | 2.29
which is used at the boundaries of the NW. The depletion width can be estimated by, = -2.30

b. Surface trap density

In the second assumption, the surface charge is calculated based on a given density of slow traps on the surface. For low trap density, this assumption is corresponding to a free Fermi level on the surface. For larger than 5 × 10 , calculated from the surface trap is equivalent to Fermi level pinned at mid-gap with planar assumption when we deal with wide NWs. This second assumption has the advantage of being self-consistent when we consider thin NWs. The following simulation results were obtained using this assumption with = 5 × 10 .

II.4.2.3 Mechanical boundary conditions a. 2D axisymmetric NG cell under compression

We can transform the cuboid NG cell into cylindrical model in two ways (Fig. 2.35a and b). In order to avoid overlap with other cells, the model in Fig. 2.35a is more appropriate in the 2D axisymmetric simulation. Some boundary condition problems come along with this transformation. As discussed in section II.3, for the 3D cuboid NG cell model under compression, we introduce symmetry boundary conditions on the side walls assuming there is an identical cell on the other side, which is the case in periodic arrays. This symmetry boundary condition is no longer suitable to our cylindrical model because there are only 4 lines (drawn in Fig. 2.35a) which have zero displacement in radial direction (r direction), on the lateral wall of the new cell. On the other hand, the lateral wall is actually not a fully free surface also due to the constraint of the outer imaginary cuboid. Two models were simulated with free and fixed lateral walls, respectively. The comparison of the results showed that there is a variation of the output piezopotential of less than 5% which does not influence the variation trends (Fig. 2.36). In other words, there is some flexibility in their boundary condition, and we decided to use mechanically free boundary condition for the NG cell under compression. For the NG cell under bending, the modification is more significant. Here we assume a flexible NG disk with all-clamped edge, which is bent by hydrostatic pressure (Fig. 2.37a). In this case, we can have a prescribed displacement all over the lateral wall in the cylindrical NG cell located in the center of the disk. In section II.3.2.3, we analyzed the VING with intrinsic NWs under bending, in those simulations the input strain in the NG cell was considered a constant. However, the strain component in the R direction (strain R) of the cell is not uniform (Fig. 2.37b). Actually it varies linearly along the c-axis (Fig. 2.37c). For short NWs (L = 600 nm), the difference between the top and the bottom of the cell is about 5%. This value will increase with the total length of the cell and it can approach 20% in the model containing long NW (L = 2 μm). Therefore, the input strain R is expressed as = + • . To keep consistent with the deformation of the NG cell under compression, the input strain of bending NG is first considered to create an expansion in the R direction as shown in Fig. 2.37c, thus positive input strain/displacement.

II.4.3 SFLP effect in VING under compression

The NG cell model used in this section is similar to what has been used in section II.3, with a NW being embedded in PMMA matrix on a seed layer. The geometry ratio (the NW diameter/the NG cell width) was fixed at 0.5. The thickness of the top insulating layer and the seed layer were 100 nm and 50 nm, respectively. The radius and length of the NW were varied. The cell was compressed by a pressure of 1 MPa.

II.4.3.1 NW with normal radius (R=100nm)

SFLP effect creates depletion zone inside the NW extending from the interface towards the neutral center. The NW with a radius of 100 nm and a length of 600 nm was considered in the initial simulation, which is commonly obtained using chemical bath deposition (CBD). Fig. 2.38 shows qualitative maps of the polarization, potential and free electron carrier of NG cell under compression mode with SFLP on the top surface and on all surfaces, respectively. Three doping levels were chosen to present the changing trend. In the case of top SFLP, the NW was depleted from the top and the polarization in depleted zone played an important role in creating the output potential. The depletion width increases as the doping concentration decreases. As a result, the piezopotential was enhanced significantly at lower doping level. In the other case, where the equivalent surface charge was applied to all surfaces of the NW, the piezopotential was further improved. The depletion appeared not only on the top of the NW, but also on the lateral walls. At low doping level (10 16 cm -3 ), the NW was fully depleted, and therefore the potential was only screened by dopants. As the doping concentration increased, the neutral zone started from the center and extended to the lateral walls. Fig. 2.39a summarizes the piezopotential variation with the doping concentration for different SFLP conditions. As discussed in section II.4 previously, the screening effect would attenuate the potential generation even at quite low doping level. This was verified once again in the 2D axisymmetric model. We built a reference model by assuming the ZnO NW as an intrinsic semiconductor, thus only dielectric properties were considered. Compared to this reference, potential generated by the NG based on n-doped NW is reduced to 5% without any SFLP effect with N D = 10 16 cm -3 . Then we assumed that SFLP only existed on the top surface, and the potential was found out to be enhanced by 10 times at the same doping level. This magnification reached 15 times at the same doping level, if the Fermi level was also pinned at the lateral surface of the NW. Up to 10 17 cm -3 , the potential generated by the NW with SFLP was 50 times larger than the one with free Fermi level, and it accounted for 94% of the reference cell with insulating ZnO. Thus we find that the existence of SFLP largely expands the utilization of ZnO NWs with normal doping concentrations.

The average length of ZnO NWs synthesized by the CBD method in our group was around 2 μm. Therefore we also run a series of simulations on the NG cell with longer NW (R = 100 nm, L = 2 μm). Fig. 2.39b shows the output piezopotential of the NG cell varying with the doping concentration of the NW. Apparently, the screening effect was more significant in a longer NW. Although the absolute value remained the same, the potential of n-type NW with free Fermi level was reduced by 98.6% compared to insulating NW at low doping level. Similarly, for the NG with FLP on all surfaces, the piezopotential was still equal to the one for insulating NW at doping level as high as N D = 10 17 cm -3 . Consistently, in the cases with free surface Fermi level and top SFLP, the output was the same for both lengths, consistently with Romano's report [6]. In contrast, with insulating ZnO, the piezopotential increased with the length. By considering realistic doping levels with SFLP from all surfaces, the piezopotential was also found length-dependent and increased with the length. II.4.3.2 NW with small diameter FEM simulations were also carried out for thinner NWs with 25 nm radius and 600 nm length (Fig. 2.40). For free Fermi level and top SFLP cases, the piezopotential kept the consistent negative sign due to the negative polarization on the top zone. According to the relation between the depletion width and the surface charge, NWs were nearly fully depleted at normal doping level (N D = 10 16 cm -3 -10 18 cm -3 ) from the sidewall in conditions with SFLP on lateral surface. As a result, the potential generated with all SFLP was almost equal to the one obtained with reference ZnO NW. = 5 × 10 .

II.4.3.3 Geometry influence

When increasing the length of the NW and keeping all other parameters constant, the NG with top SFLP showed almost no variation in response (Fig. 2.41a). This has also been reported in Romano's work [6]. However, it became interesting to increase the length for NGs with SFLP on all surfaces, because a large response was obtained even at high doping levels. Fig. 2.41b shows that the piezopotential is enhanced by 3. On the other hand, an improvement can be expected from the decrease of the NW radius. With top SFLP, the smaller the NW radius was, the higher the piezopotential became (Fig.

2.42a).

With FLP on all surfaces, a large response was obtained even at doping level as high as 10 18 cm -3 for thin NWs (Fig. Fig. 2.43 shows a more clear effect of NW radius. For a NW with a length of 2 μm, as long as the radius was small enough to form a fully depleted case, the NW could be considered as an insulating one. The potential would increase slowly with the decreasing NW radius. Then as the radius got large to form a neutral core inside the NW, the potential decreased fast. Therefore, decreasing the NW radius has the effect of increasing the maximum piezo-response but more importantly of increasing the range of acceptable doping level towards higher values. = 5 × 10 .

II.4.3.4 Comparison with the ZnO thin film

For reference, a ZnO thin film model with the thickness of 2 μm was also simulated in compression mode. For the ZnO thin film, the only interface where the SFLP effect exists is the top surface. As shown in Fig. 2.44, NG cell with top SFLP had a slightly larger response than the thin film under the same pressure, because the strain in NG cell was larger due to soft matrix material. However, the problem of screening effect was still dominant. In contrast, with SFLP on all surfaces of the NW, the piezopotential was largely improved compared to a ZnO thin film in compression mode. At N D = 10 17 cm -3 , the potential generated by the NG cell was as high as 7 times of the one generated by the thin film. While at N D = 10 16 cm -3 , the potential was improved by a factor of 9.

II.4.4 SFLP effect in VING under bending

The NG cell model used in this section is the same as in compression mode. The geometry ratio (the NW diameter/the NG cell width) is also fixed at 0.5. The thickness of the top insulating layer and the seed layer is 100 nm and 50 nm, respectively. The radius and length of the NW are going to be changed. The input strain of the cell is calculated from a disk bending by a pressure of 100 Pa. With SFLP on all surfaces, the piezopotential reached 55 mV and kept this value as the doping level increased to 10 cm (Fig. 2.46). Within this range of doping levels, the NW was fully depleted. As the doping level continued to increase, the potential went through a slow decrease, which, unlike the wide NW, allowed NW with much higher doping concentration to be used as the generator. Besides, a similar effect of NW radius as in compression mode could also be observed. In the case of top SFLP, the model with the thinner NW generated higher piezopotential due to the strain that was concentrated more to the NW. In the case with SFLP on all interfaces, a smaller NW radius was able to enlarge the doping levels that could be used for NG devices. As a result, the SFLP effect had a more significant influence on the NW with a high aspect ratio.

II.4.4.4 Non symmetric performance

Until now, all the NG cells under bending were simulated with the pressure applied in the same direction as shown in Fig. 2.48a. Named after the strain state on the lateral wall of the cell, it is called stretching bending. Correspondingly, we have the other way to apply the bending pressure, which we called contractive bending (Fig. 2.48b). In fact, a non-symmetric performance exists in the NGs under contractive and stretching bending. In the model where R = 100 nm and L = 2 μm, by plotting the ratio between the contractive potential and the stretching potential, we found that it has been always over 1 (Fig. 2.48c). It means that there is a feedback influence of the surface charge on the potential generation. The negative charges on the surface can act as a contractive strain, confining the NG cell from the lateral extension. This feedback is weak when the doping concentrations is small, but it becomes obvious as the doping level increases. We will see in chapter III that a non-symmetry was also found in the experimental move.

(c)

II.5 Conclusion

In this chapter, we mainly discussed analytical and computational modeling research on piezoelectric semiconducting NWs and NGs. In particular, ZnO NW is studied for its brilliant future in electromechanical application ever since 2006. The modeling investigation also started a decade ago as a powerful tool to design devices and guide the experimental activity. Most of the modeling work focused on individual NWs, developing from regarding the NWs as dielectric material to considering the screening effect of doped semiconductors. However, very few work had been done on the NW composites before our group. We started to investigate the piezoelectric behavior of VINGs based on ZnO NWs working under compression in 2010. Due to spontaneously doping during the synthesis, free carriers exist in ZnO NWs, which screen large part of the piezopotential generated. In the absence of SFLP, the piezopotential can be considered as fully cancelled for doping level higher than 10 cm , compared with the experimental doping level of 10 cm to 10 cm . Meanwhile, a few tens to a few hundred millivolts of output potential can still be observed in electromechanical measurements. R. Hinchet in our group worked on this field by coupling solid mechanics and electrostatic physics. He put forward an assumption that for thin NWs (R ≤ 25nm) the NG cell can be treated as dielectric material due to full depletion by SFLP, so that the only screening effect came from ionized dopants. In my thesis work, I reconsidered this assumption by taking SFLP into account in the framework of full coupling between semiconducting and piezoelectric equations. It turned out that the full depletion assumption did not hold for all dimensions and doping level.

With SFLP on all surfaces, several observations from the simulation work fit the experimental results in the literature and are able to explain the contradiction which had been existing between the theory and experiments. Firstly, piezoelectric response of the NG cell did present a geometry dependency due to SFLP, indicating that better performance would come up with NWs with larger length and aspect ratio. Secondly, compared with ZnO thin film, NG cells generated higher potential, because they possessed more surfaces where SFLP contributed to decrease the screening effect. It offered a possible explanation to the higher piezoelectric coefficient experimentally measured for ZnO NWs. Finally, a non-symmetric performance of NG devices working in flexion mode was observed with SFLP in the simulation. A summary of major breakthroughs in modeling researches is presented below (Fig. 2.49).

Chapter III Electromechanical Characterization of Piezoelectric

Nanowires and Nanogenerators

Although analytical and computational studies are helpful to analyze physical principles and provide guidelines for experiments, it is of prime importance to carry out the experimental work, with mechanical and electromechanical measurements, in order to assess our understanding of the operation mechanisms and to characterize the performance of piezoelectric NWs and NGs. This chapter starts with a short presentation of device fabrication. Vertical ZnO NW arrays were synthesized using chemical bath deposition and were then integrated to fabricate the NGs. After that, we give an overview of the methods that have been used to characterize the mechanical and electromechanical properties of piezoelectric NWs and NGs. We report on our measurement of the apparent Young's modulus and of the effective piezoelectric coefficients of semiconducting NWs using AFM-based techniques. We conducted as well electromechanical measurements on the rigid and flexible NGs introduced in Chapter III in order to evaluate their respective performance for energy generation. Finally, we end up with the observation of a dissymmetry, consistent with our simulation results, in the response of flexible NGs depending on bending direction.

III.1 Synthesis of ZnO NWs and NGs

The NGs under study were fabricated in the IMEP-LaHC cleanrooms. The process was adapted from the one previously developed during Ronan Hinchet's thesis, based on literature. Although some adjustments and variations were explored, our aim in this thesis was not to develop a new process but rather to have our own source of devices and to have the flexibility of changing technological parameters as required by our studies. In this work, ZnO NW arrays were grown on rigid p-type (100) Si wafer (500 μm) and flexible stainless steel foil (25 μm) using chemical bath deposition (CBD) method. We fabricated ZnO NW arrays with controlled morphology by adjusting the thickness of the seed layer, the precursor concentration, the temperature and the growth time.

Then we designed the process to integrate the NWs into NGs. It was divided into three steps. First, the matrix and top layer material deposited. PMMA, Si 3 N 4 and Al 2 O 3 with controlled thickness were used for different NGs. This process aimed at finding the material that could provide best performance. Second, a 200 nm thick aluminum thin film was deposited on the top of PMMA by evaporation. The cross section view of the VING by this step is shown in Fig. 3.1a. The last step to build a working NG device was to package it with external electrodes and Cu wires. The top external electrode was an Al or Cu flat plate stuck on the evaporated Al thin film by silver paint to protect the surface from mechanical damage. The bottom external electrode was a conductive Al tape stuck on a glass plate and connected with the substrate by silver paint. Both external electrodes also offered a position to connect the wires so that the main specimen was kept flat.

The VING integrated on a Si wafer could only work under compression (Fig. 3.1b), while the one on stainless steel foil could also work under flexion (Fig. 3.1c). More details about the NW morphology control, growth issue discussion and techniques for matrix deposition will be presented in Appendix II.

III.2 Electromechanical measurement techniques for piezoelectric NWs and NGs

III.2.1 Nanomechanical characterization methods

Nano technologies have been used to investigate the mechanical properties of piezoelectric NWs, including MEMS in situ SEM/TEM [START_REF] Agrawal | Elasticity size effects in ZnO nanowires--a combined experimental-computational approach[END_REF][START_REF] Agrawal | Experimental-computational investigation of ZnO nanowires strength and fracture[END_REF][START_REF] Desai | Mechanical properties of ZnO nanowires Sensors Actuators[END_REF][START_REF] Bernal | Effect of growth orientation and diameter on the elasticity of GaN nanowires. A combined in situ TEM and atomistic modeling investigation[END_REF][START_REF] Brown | Tensile measurement of single crystal gallium nitride nanowires on MEMS test stages Sensors Actuators[END_REF], nanoindentation [START_REF] Huang | In situ nanomechanics of GaN nanowires[END_REF][START_REF] Feng | A study of the mechanical properties of nanowires using nanoindentation[END_REF][START_REF] Yang | Nanomechanical characterization of ZnS nanobelts[END_REF][START_REF] Li | Mechanical Properties of ZnS Nanobelts[END_REF], resonance techniques [START_REF] Chen | Size Dependence of Young's Modulus in ZnO Nanowires[END_REF][START_REF] Huang | In situ mechanical properties of individual ZnO nanowires and the mass measurement of nanoparticles[END_REF][163][164][165][START_REF] Gao | Higher-order harmonic resonances and mechanical properties of individual cadmium sulphide nanowires measured by in situ transmission electron microscopy[END_REF][START_REF] Gaevski | Non-catalyst growth and characterization of a -plane AlGaN nanorods[END_REF][START_REF] Kim | Determination of Mechanical Properties of Single-Crystal CdS Nanowires from Dynamic Flexural Measurements of Nanowire Mechanical Resonators[END_REF], AFM cantilever in situ SEM/TEM [169-173] and AFM based instruments [START_REF] Wen | Mechanical Properties of ZnO Nanowires[END_REF][START_REF] Ni | Young's modulus of ZnO nanobelts measured using atomic force microscopy and nanoindentation techniques[END_REF][START_REF] Chen | Mechanical elasticity of vapour-liquid-solid grown GaN nanowires[END_REF][177][START_REF] Ni | Elastic modulus of single-crystal GaN nanowires[END_REF][START_REF] Xiong | Force-deflection spectroscopy: A new method to determine the young's modulus of nanofilaments[END_REF]. These measurement methods can be sorted according to the loading mode, namely uniaxial tension or compression, and bending-based, where bending (either static or in resonance) and buckling are employed. Uniaxial methods operate by applying a controlled deformation at one end of the NW, while measuring the load at the other end [START_REF] Agrawal | Elasticity size effects in ZnO nanowires--a combined experimental-computational approach[END_REF][START_REF] Agrawal | Experimental-computational investigation of ZnO nanowires strength and fracture[END_REF][START_REF] Desai | Mechanical properties of ZnO nanowires Sensors Actuators[END_REF][START_REF] Bernal | Effect of growth orientation and diameter on the elasticity of GaN nanowires. A combined in situ TEM and atomistic modeling investigation[END_REF][START_REF] Brown | Tensile measurement of single crystal gallium nitride nanowires on MEMS test stages Sensors Actuators[END_REF]. Strain is usually measured by imaging of the sample, for example using in situ an electron microscope (SEM/TEM). Bending and buckling methods are usually easier to implement but data interpretation is more complex. Controllable nanostructure bending is achieved by atomic force microscopy (AFM), which also provides measurement of force, either in the lateral [START_REF] Wen | Mechanical Properties of ZnO Nanowires[END_REF] or vertical directions [START_REF] Ni | Young's modulus of ZnO nanobelts measured using atomic force microscopy and nanoindentation techniques[END_REF] or by a nano-manipulator pushing the NW until it buckles [START_REF] Xu | Mechanical properties of ZnO nanowires under different loading modes[END_REF].

III.2.2 Characterization of piezoelectricity in NWs

The piezoelectricity is an electromechanical coupling. There are two ways to characterize piezoelectric materials, the direct and reverse effect. The most common methods for characterization of direct piezoelectricity in nanostructures usually involve bending or stretching the material with in situ measurement of the charge or electric potential. This is challenging because the charges or voltages tend to be small, which requires ultra-sensitive electronics. To give an example of such a measurement, charge generation from a suspended and doubly clamped single-crystal BTO NW has been studied under periodic tensile mechanical load. This method provided a tes a controlled experimental method for measuring the direct piezoelectric effect in nanostructures Conversely, the measurement of reverse piezoelectric effect in nanostructures has mostly been performed by means of piezoresponse force microscopy (PFM) [181][START_REF] Kolosov | Nanoscale visualization and control of ferroelectric domains by atomic force microscopy[END_REF][183][START_REF] Wang | One-dimensional ferroelectric monodomain formation in single crystalline BaTiO3 nanowire[END_REF][START_REF] Wang | Ferroelectric and piezoelectric behaviors of individual single crystalline BaTiO3 nanowire under direct axial electric biasing[END_REF]. This method takes advantage of the scanning and cantilever deflection measurement capabilities of the AFM. Fig. 3.3 schematically shows a set-up for probing the 3D piezoelectric tensor of a single c-axis GaN NW from the work of Jolandan et al., where scanning probe microscopy (SPM) was used exploiting the reverse piezoelectric effect [186]. The set-up consists of an AFM system, extended electronics including a lock-in amplifier, and a function generator (Fig. 3.3a). The NW was measured using two methods. In Fig. 3.3b, the NW is shown on an insulating surface with its two ends clamped by electric contacts, which are used to apply an axial electric field. In this configuration, electric field was generated by adding a voltage the two electric contacts. Twist of the cantilever measured the axial displacement, corresponding to strain , and the bending of the cantilever measured the out-of-plane displacement, corresponding to strain and , to obtain and , respectively. In the second configuration (Fig. 3.3c), the NW was placed on a conductive substrate acting as an electric ground. An electric voltage was applied between a conductive AFM probe and the grounded substrate to induce a transverse electric field in the NW. Torsion of the cantilever measured the displacement along the NW axis, corresponding to , to obtain An AC voltage is applied between these electrodes, resulting in an axial electric field. The long axis of the NW is placed perpendicular to the AFM cantilever. (c) In this configuration the NW is laying on a Si substrate coated with a conductive Au layer. The electric field is applied between the tip of the conductive AFM probe and the grounded substrate. Torsion of the cantilever measures the induced shear strain allowing identification of d 15 .

[186]

III.2.3 Characterization techniques at IMEP-LaHC

Our group introduced an improved method using AFM allowing the direct bending of cantilevered NWs without using clean room techniques to prepare the as grown samples [START_REF] Xu | An improved AFM cross-sectional method for piezoelectric nanostructures properties investigation: application to GaN nanowires[END_REF]. This method (Fig. 3.4) allows a precise selection of a NW including its state before and after the experiment. The application of a controlled force at a specific location of the NW allows us to combine the mechanical and piezoelectric measurements. A high input impedance preamplifier is required to improve the voltage measurement accuracy. The detailed working principle will be discussed in next sections. Besides, we also built a set-up to characterize the piezoelectric performance of the NG device under compression. With precise force control, the relationship between the applied force and generated potential was established. This will be detailed in section III.4.

III.3 Mechanical and electromechanical characterization of individual

NWs using AFM techniques

III.3.1 Young's Modulus measurement of piezoelectric NWs

The method to measure the Young's modulus of NWs evolves from the solid mechanical physics in a one-end clamped beam. Scaling down to the nano scale, some variables, such as the deflection of the beam, can no longer be measured directly. Ergo we make a transform of the Euler-Bernouilli equations, which describes the relationship between the deflection of the beam and the applied load.

III.3.1.1 Physical principle of Young's modulus measurement

The scheme (Fig. 3.5) shows the principle of the Young's modulus measurement by the AFM probe. The substrate is placed perpendicular to the AFM sample holder (z direction), so that the NW vertically grown on it will be along the x direction. The force is applied in the z direction by the AFM tip. The manipulation process contains two steps: firstly, a topographic scanning image is made of the sample surface to locate the object; secondly, a small force (~10 nN) is used to control the deflection of the object. The governing equation of a cantilever beam is,

• • ∆ ( ) = ( ) 3.1
where E is the Young's modulus, the curve ∆ ( ) describes the deflection of the beam in the z direction at position x, I is the area moment of inertia and M is the bending moment.

For position within the strained region (0 ≤ x ≤ L), the bending moment is,

( ) = + • + --• ( -) 3.2
To solve this equation, the geometry boundary conditions are given as, ∆ | = 0; ∆ = 0 (at the clamped end) 3.3

= 0; = 0 (at the free end) 3.4 At the free end, L is the distance from the clamped end to the point where the force is applied. Then the deflection of the beam at 0 ≤ x ≤ L is expressed as,

∆ ( ) = 6 • ( -3 ) 3.5
The absolute deflection at the force position is,

|∆z| = • 3 3.6
The force F is calculated by the product of the deflection of the AFM cantilever ∆ and the spring constant k (shown in Fig. 3.5), = × ∆ 3.7 In the measurement, we fix the total deflection Z (the deflection of the AFM cantilever and the beam combined) to a constant, and then the deflection of the beam can be calculated from,

|∆ | = -∆ 3.8 Finally, we obtain the following formula for the Young's modulus,

E = 3 × 1 |∆ | ⁄
3.9

III.3.1.2 Calibration of polycrystalline silicon beam as a reference

To verify our approach for the Young's modulus measurement, a NEMS nano-switch consisting of a source (S), two gates (G), two drains (D) and a cantilever made of polycrystalline Si beam has been used in the first test (Fig. 3.6a). Top view SEM image (Fig. 3.6b) presents the structure of the nano-switch. The Si beam is a rectangular block with dimensions: width a equal to 450 nm, the depth b equal to 900 nm and the total length L tot of 20 um, with = . The measurement of Young's modulus uses the AFM tip as the force source. By fixing the total deflection (deflection of the AFM cantilever and the Si beam combined) and monitoring the deflection of the AFM cantilever, we can calculate the force applied to the beam and thus the Young's modulus at different positions along the beam. Fig. 3.7 shows the AFM topographic image of the Si beam and the positions where the force was applied (red arrows). The point signed by the black arrow was selected to be the reference "zero point", because this point was located at the fixed end, where the deflection stayed to be zero under pressure. The effective length of the Si beam was considered to be the distance from the "zero point" to other points. As the effective length L increased, the deflection of the AFM cantilever decreased, on the other hand, the deflection of the Si beam increased because of the reduction of rigidity (shown in Fig. 3.8a). To obtain the spring constant of the Si beam, we plotted the Δz/F curves for each point and applied a linear fitting on them (Fig. 3.8b). According to Eq.3.9, we plotted the Young's modulus-force position curve of the Si beam (Fig. 3.9a). The Young's modulus increased along the beam and then became flattened, approaching and becoming stable to 150 GPa when the tip position moved to the free end. This value is in the range reported in the literature. The Young's modulus of polycrystalline Si film varies from 120 GPa to 200 GPa depending on different measuring methods [START_REF] Schneider | Non-destructive characterization and evaluation of thin films by laser-induced ultrasonic surface waves[END_REF][START_REF] Tabata | Mechanical property measurements of thin films using load-deflection of composite rectangular membranes[END_REF][190][191]. One reasonable explanation of the variation of E along the beam is that the Si beam is over-etched during the fabrication process at the fixed end, so that the actual effective length L' is larger than the measured effective length L (Fig. 3.9b). This effect has larger influence when the measurement is done near the fixed end, resulting in the underestimated Young's modulus. In (Fig. 3.9a), a correction based on this over-etching problem is displayed with the red dash line. Therefore, we only considered points that belonged to the remaining three-quarter of the beam. As we can see, the Young's modulus measurement method is suitable to beam structure with large aspect ratio.

III.3.1.3 Young's modulus of long GaAs NWs

As demonstrated above, when we use the AFM technique to measure the Young's modulus of micro beam structures, the results is close to the literature. However, the limitation of this method is also evident taking into account the aspect ratio of the beam (the length over the radius) which should be large. Besides, the measurement accuracy of the geometry becomes a significant factor influencing the result of Young's modulus as the tested structures scale down to nano scale. Here we apply this method to long GaAs NWs grown on Si wafers by our colleagues (J. Penuelas) from Institut des Nanotechnologies de Lyon (INL) of Ecole Centrale de Lyon (ECL) using solid-source molecular beam epitaxy (ss-MBE) method. SEM images show the morphology of the long GaAs NW arrays (Fig. 3.10a). The length is about 8 μm and the diameter varies from 160 nm to 220 nm. The AFM scanned a small region of the cross section containing several GaAs NWs (Fig. Here we consider the NW as a cylindrical beam with = , where d is the diameter of the NW. The deflection of the AFM cantilever is proportional to the total deflection (Fig. 4.11b and 3.12b). Since point 0 is at the root of the NW, the AFM cantilever deflection is equal to the total deflection at this position. Then the difference between the tip deflection of each point and point 0 is actually the deflection of the NW. With Eq. 3.7 and 3.9, we plot the curves of NW deflection versus the bending force (Fig. 3.11c and 3.12c). By applying linear fitting to these curves, we obtain the important factor ∆ / to calculate the Young's modulus. The Young's modulus of long GaAs NWs is plotted in Fig. 3.13. It increases with the length L and saturates at around 80 GPa, while the value of bulk GaAs is 85.5 GPa [192]. This confirms the validity of our approach.

III.3.2 Piezoelectric response of individual NWs

To investigate the properties of piezoelectric free-standing nanostructures, appropriate tools as well as convenient methods are required. Wang et al provided an approach to study the piezoelectric properties of nanostructures using AFM [3]. They plotted a potential map as the AFM tip swept across the vertical aligned ZnO NW arrays. In this method, the deformation of the NW cannot be precisely controlled, and damage will be done to the NWs. Our electromechanical measurements on individual NWs with controlled force were realized by improving the existing set-up. Based on the Young's modulus measurement, an electrical circuit including an amplifier and an oscilloscope have been introduced to monitor the potential drop between the NW and the substrate while it is bent [START_REF] Xu | An improved AFM cross-sectional method for piezoelectric nanostructures properties investigation: application to GaN nanowires[END_REF].

III.3.2.1 Principle of electromechanical measurement on individual NWs a. Experimental set-up

The experiments were carried out at room temperature and normal atmosphere pressure by using AFM (with a high performance controller Digital Instruments Dimension 3100 from Veeco) and high frequency oscilloscope (Fig. 3.14a). The circuit of the whole device is schematically shown in Fig. 3.14b. When the NW is bent, strain induced polarization creates an electric field across the NW and charges are accumulated at the surface. Since the substrate of the NWs is electrically grounded, the potential generated by the NW can be measured. As the samples to be tested (GaN, GaAs and ZnO NWs) are semiconductors with wide band gap and a Schottky contact exists between the tip and the NW, a voltage preamplifier is required to improve voltage measurement accuracy.

(a) (b)

b. Theoretical piezoelectric response of individual bending NW

Theoretical analysis on bending individual piezoelectric NW has been studied by many researchers. Details are discussed in Chapter II. As a reference to our piezoelectric measurements by the AFM, an equation should be considered [START_REF] Gao | Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics[END_REF],

( , ) = ± 1 1 + -2(1 + ) -2 1 3.10
where is the maximum potential at the surface of the NW at the tensile (T) side with positive sign, is the maximum potential at the contractive (C) side with negative sign. F is the lateral bending force. If we define the effective piezoelectric coefficient under bending as, = -2(1 + ) -2 3.11 Eq. 3.10 and 3.11 can be simplified as,

( , ) = ± 1 1 + 1 × 3.12
For certain NWs, if the dielectric constant, Young's modulus and geometry factors are known, the equations above can be written as, For n type semiconductors, a Schottky barrier is the potential energy barrier for electrons which builds at a metal-semiconductor junction. It is proportional to the difference of the metal work function Φ and the semiconductor electron affinity , ≈ Φ -3.14 However, for real semiconductor surfaces, there will be additional energy states on the surface of a semiconductor because the perfectly periodic lattice ends at the surface and many bonds are not satisfied. These states can have a very high density and create a narrow distribution of energies within the band gap. The nature of these metal-induced gap states and their occupation by electrons tend to pin the Fermi level at a specific position in the band gap, which is the metal-induced Fermi level pinning effect. When the density of surface states is high, as it typically is, the potential barrier that develops is dominated by the location of the surface states in the semiconductor band gap, rather than by the work function of the metal,

≈ E - ln 3.15
where f is a factor to describe the position of the pinned Fermi level. In our AFM measurements, the probe of an AFM tip was coated with PtSi (details in Appendix III).

III.3.2.2 GaN NWs grown by MBE method

The GaN NWs that we tested were prepared by our colleagues (R. Songmuang) at Néel Institute in Grenoble. Fig. 3.15 shows the SEM and AFM images of undoped GaN NW arrays. The diameter of GaN NWs was 150 nm -200 nm, while the length was from 600 nm to 800 nm. The white cross signs in Fig. 3.15b represent the positions where the AFM tip contacts the NW and applies a force on it. During the measurement, the ramp force applied on the three points was controlled by the piezo response system of the AFM. The maximum value was set to a constant (~ 2.3 μN). The saturation piezopotential generated by the single GaN NW changed from 0.84 mV to 0.6 mV as the force position approached the root (the fixed end) (Fig. 3.16a). As the tip moved from point 1 to point 3, the effective length of the NW decreased. The deflection of the NW also decreased and resulted in lower potential. Take the potential signal of point 1 as the example: we analyzed the relationship between the potential and the force (Fig. 3.16b). When the applied force was smaller than 480 nN, the oscilloscope could not acquire any piezoelectric response. By continuing to increase the force, a proportional increase appeared in the potential. This threshold resulted from the Schottky barrier between the GaN surface and the PtSi coating of the AFM probe. The electron affinity of GaN is 4.1 eV [193]. By assuming the PtSi coating has a (001) orientation, its work function is 4. 96 eV [194]. Using these values, the analytical barrier height is 0.86 eV. The experimental results show a value around 0.83 eV existing in the PtSi-GaN contact [START_REF] Liu | Thermally stable PtSi Schottky contact on n-GaN[END_REF]. This means that in our experiment, before detecting any piezoelectric signal, the NW needs to lower the potential barrier by generating a potential. In the GaN NWs, this has been reached for an applied force larger than 400 nN. Fig. 3.18a presents the quasi-linear relationship between the maximum deflection of the NW and the force. This corresponds to Eq. 4.5, which describes that the maximum deflection is proportional to the bending force. Fig. 3.18b shows the measured potential as a function of deflection and force. A threshold was also observed in this case although at a lower force of 54 nN (NW deflection about 4.5 nm) In this case, to estimate the potential barrier, we considered: the electron affinity of GaAs is 4.07 eV [START_REF] Sze | Physics of Semiconductor Devices[END_REF] and the band gap is 1.27 eV at 300K [START_REF] Shenai | Optimum semiconductors for high-power electronics[END_REF]. Similar to the case of GaN, the surface states dominates the potential barrier. According to Eq. 4.15, with = 0.6~0.7, theoretical is about 0.76 . This result was consistent with the measurements.

for GaAs being smaller than for GaN, a lower force was needed before acquiring a piezo signal. The total deflection being controlled by a ramp plot, the tip deflection increased linearly with the total deflection (Fig. 3.20a). The relationship between the NW deflection and the force was deduced from the cantilever deflection and spring constant (Fig. 3.20b). With small deflection, potential generated by ZnO NW was larger than for ZnO/PZT NWs, although the saturation value was only 20% of the latter (Fig. 3.20c). Meanwhile, beyond threshold, ZnO/PZT NWs produced a larger potential compared to ZnO NWs with the same bending force (Fig. 3.20d). The ZnO/BTO core-shell NWs were fabricated by the same CVD method in the same group as ZnO/PZT NWs. To start with, the ZnO NWs were grown on one Si substrate by CBD.

Then the sample was cut into two parts. For one of them, a BTO coating was deposited and the remaining part was kept for reference. As shown in Fig. 3.21a and b, the diameter of the ZnO NWs varied from 70 nm to 190 nm. As for ZnO/BTO core-shell NWs, the typical diameter was about 300 nm, with a wide distribution, from 200 nm to as much as 500 nm.

The typical length of ZnO and ZnO/BTO NWs was 3 μm and 4 μm, respectively. Target NWs were located by the AFM topographic scanning and then bent by the cantilever at chosen position (Fig. 3.21c and d). The electrical response was plotted in Fig. 3.21e and f. When the ramp force was applied to the NW repeatedly, potential pulses were generated by both samples. The maximum force applied was 120 nN for ZnO NWs and 300 nN for ZnO/BTO NWs. The maximum output of ZnO NWs was around 6.5 mV, while that of ZnO/BTO NWs could reach more than 30 mV. The BTO shell was deposited in an attempt to improve the piezoelectric response of the ZnO NWs. To compare the piezoelectric behavior of both kinds of NWs, two individual NWs were chosen as representative. According to the relationship between cantilever deflection and total deflection (Fig. 3.22a), we could verify that NW deflection was proportional to bending force (Fig. 3.22b). Since the BTO shell was coating ZnO NW, the area moment of inertia increased significantly due to the enlarged radius ( ∝ ). Therefore, by applying the same force, the deflection of the ZnO NW was much larger than that of the ZnO/BTO NW. However, with the same deflection, the ZnO/BTO NW generated a larger potential (Fig. 3 An experiment on bending one ZnO/BTO NW at the same position with different forces was carried out to verify the force threshold. Despite the already mentioned reproducibility issue, it can be observed that the saturation potential decreased significantly as the force reduced from 320 nN to 250 nN (Fig. 3. 23a andb). When the force approached 200 nN, the potential tested was close to zero. This is consistent with the threshold found in Fig.

b. Comparison among different piezoelectric NWs

Fig. 3.25 synthesizes all the results shown in previous measurements and compares the piezoelectric response of different NWs. GaN, GaAs and ZnO NWs were compared in Fig. 3.25a. ZnO NWs with a cylindrical cross section came from Institut des Nanotechnologies de Lyon, cited as ZnO cylindrical. ZnO NWs with hexagonal cross section were fabricated in our group, later cited as ZnO hexagonal. Apparently, the ZnO NWs generated higher potential than GaN and GaAs NWs. The threshold of these potential curves was related to the Schottky barrier height of the NW-PtSi contacts and the piezoelectric coefficients. The higher the barrier was, the larger was the threshold. Correspondingly, the piezoelectric behavior of ZnO-based NWs were also modified by depositing different shells, and even by the NW morphology (Fig. Further analysis of effective piezoelectric coefficients under bending should be investigated containing the material properties and the geometry. Table 3.1 lists the Young's modulus and dielectric constant of GaN, GaAs, ZnO, BTO and PZT materials reported in the literature. The values have been measured on thin film samples. From these parameters we deduced the effective Young's modulus and the effective dielectric constant / of core-shell NWs using linear combination of each material property according to their volume ratio. The radius R was measured by AFM. The factor * defined in Eq. 3.13 was then calculated by using , and R (Table 3.2). The effective piezoelectric coefficient under bending shown in Table 3.2 was calculated to evaluate the electromechanical properties of these NWs (Fig. 3.26). 3.2 with a log scale. The best effective piezoelectric coefficients were observed in ZnO/BTO and ZnO/PZT core-shell NWs. In general, the core-shell NWs had larger than homostructure NWs. On the other hand, compared with GaAs and ZnO NWs, these core-shell NWs obviously had a larger threshold force, indicating that they were not sensitive to small force.

III.4 Piezoelectric response of NGs under compression

Although the mechanical and electromechanical measurements of individual NWs helped us to understand their material properties and piezoelectric response, the performance of integrated NWs, namely NGs, is different. We need specific measurement configurations and set-up to characterize the NG devices. In this section, devices that are characterized will be named after their serial number. Only the parameter required for the discussion will be mentioned, while other details will be listed in Appendix II.

III.4.1 Electromechanical measurement at room temperature

We built a system to realize the measurement of the piezoelectric response of the NG while accurately controlling the compressive force which is applied on it. The set-ups worked at room temperature.

III.4.1.1 Measurement set-up and working principle

Fig. 3.27 presents the measurement set-up that we developed to measure the output potential of rigid NGs under compression. The main components are the actuator, the sample holder, the force load and the force sensor (Fig. 3.27a). The sample holder is supported and moved by a PC-controlled linear actuator, whose position can be adjusted in three directions (x, y and z) manually. Above the sample holder, there is a ceramic rod acting as the force load to apply pressure on the sample during the measurement. The ceramic rod is in contact with a force sensor, which measures the force applied between the rod and the sample holder (or the sample on it). The electrodes of the sample connect to the voltage, current and charge preamplifiers via a transmission unit. Then the output electrical signal of the preamplifier is converted into a digital signal by an analog to digital converter (ADC) which is connected to a PC. Besides, two softwares based on Labview platform were developed to control the actuator and to acquire the force and voltage signals ( As the strain variation stops, the flowing charges start to compensate the polarization charges inside the NW, which results in exponential decay of both voltage and current signals. This is similar to a capacitor discharge in a resistive load. Finally, when force is released, change in polarization charges and charge transfer process occurs.

In our measurement, the sample holder was connected to the actuator with a sphere joint (see Fig. 3.29a). The purpose was to adjust the perpendicularity of the applied force on the sample, but its presence produced an overshoot on the compressive force (see Fig. 3.30a) However, the releasing force do not present this overshoot and it is well controlled by the actuator. For this reason, the voltage and current measured in section III.4 and III.5 were taken from the response to force release.

b. Instantaneous power

III.4.1.3 Piezoelectric response of NGs under compression at room temperature

The performance of NG devices working at room temperature has been studied first. Open circuit voltage and short circuit current were measured to characterize the NG devices. The output power was also calculated using a variable resistive load.

a. Effect of fabrication parameters: top PMMA layer and precursor concentration

The thickness of the top insulating layer played an important role in determining the NG performance. To keep the functional device un-damaged, we were unable to measure the thickness of the top layer via a cross-section SEM image. Therefore we deduced the thickness by combining measurement results from the reference devices and the theoretical thickness vs. spin speed parameters in the data-sheet. The reference devices were prepared with the same PMMA deposition method, but they were cut to obtain the cross section images. Table 3.3 shows the distribution of potential generated by different NGs according to the PMMA thickness and applied force. In general, NGs with densely packed NWs (geometry ratio larger than 0.8 due to precursor concentration of 50 mM) had a lower performance in potential generation. This is consistent with the modeling results reported previously in our group [5,[START_REF] Tao | FEM modeling of vertically integrated nanogenerators in compression and flexion modes 10th Conference[END_REF]. Meanwhile, because PMMA features low hardness and small dielectric constant, the control of top PMMA layer thickness is critical. With too thin a layer, short circuit forms between ZnO NWs and the top electrode, and reduces performance. Conversely, thick layers decrease the capacitance and reduce performance as well, although for a different reason. This is what is observed in Fig. 3.31 where generated piezopotential is plotted as a function of PMMA thickness for given force of 1.5 N.

b. RC circuit analysis

Graton et al. proposed an equivalent circuit model of the VING that took into account the effect of the polymer matrix on the mechanical and electrical behavior of the generator (Fig. 3.32a) [205]. In their approach, several approximations on the elastic and electric field allowed to consider the NW/polymer composite as an effective homogeneous medium whose physical properties are expressed in terms of , the volume fraction of piezoelectric material and = 1 -, the volume fraction of polymer. The electrical branch containing the output voltage and current (right part of the circuit) is a RC circuit with characteristic capacitance ̅ and resistance . With our measurement set-up, the electrical load is the impedance of the voltage amplifier when we measure the open circuit voltage. We can also make an estimation of ̅ according to the equation given by Graton et al.[205],

̅ = ̅ 3.17 ̅ = - 2 ( + ) + ( + ) + 3.18
where is the dielectric constant, A is the surface of electrodes, is the length of the NW (ergo the thickness of the NW/PMMA composite layer), is the piezoelectric coefficient and is the stiffness components. The superscript s represents the properties of ZnO NWs, and the overline is used for effective parameters. For our NG samples, there is an extra insulating layer on the top of the composite, which can be considered as a capacitance connected in series with ̅ . Therefore we add,

1 ̅ = 1 ̅ + 3.19
where is the thickness of top PMMA layer. With the NW density equal to 2 × 10 , and the average radius equal to 60 nm, we get = 0.23. Since the Young's modulus of PMMA is in the range of 1.8 GPa to 3 GPa, we calculate the effective capacitance of NG sample In24B as, ̅ = 5.9 ∼ 8.6 × 10 3.20 The effective capacitance can also be evaluated through the measured voltage. For a NG device working under compression, once the strain is changed, a displacement current flows through the electrical load. As shown in Fig. 3.32b, the voltage yields the formula for exponential decay,

( ) = exp (- ̅ ) 3.21 ln ( ) = - ̅ 3.22
The slope = -33.58 of Eq. 3.22 is measured from the curve in the inset of Fig. 3.32b. The impedance of the voltage amplifier is 100 MΩ, so the effective capacitance is,

̅ = - = 3.0 × 10 3.23
Both theoretical and experimental effective capacitance values of the NG are around the order of 10 . The difference may result from the assumption made for the analytical calculation. For example, the analytical calculation is actually dealing with a NG made up of a lattice of equally spaced vertically aligned NWs fully entangled in a polymer matrix. While in the real case, the morphology and the alignment are not perfect and the PMMA matrix is unable to fulfill all the space in the lattice.

III.4.2 Electromechanical measurement with thermal cycles

Piezoelectric materials based electronics have been used in a plethora of industrial fields. The environments that these devices are required to serve in are becoming more demanding, with ambient temperatures being driven higher. For instance, one application where piezoelectric materials are used at higher temperatures, is an innovative approach for thermal energy harvesting put forward by Puscasu et al. contained a first step of thermo-mechanical conversion by a bimetal oscillating between a hot and a cold surface and a second step of electromechanical conversion by a piezoelectric material, when snapped by the bimetal [START_REF] Puscasu | An innovative heat harvesting technology (HEATec) for above-Seebeck performance[END_REF]. Therefore, it is interesting to evaluate the thermal effect on the performance of the piezoelectric NGs.

III.4.2.1 Measurement set-up and working principle

To realize such a measurement, we refitted our set-up by adding a temperature control system. A thermoelectric generator module (Peltier generator) was inserted below the metallic sample holder (Fig. 3.33a) to heat the sample. The Peltier generator was controlled by a temperature controller with an external power supply (Fig. 3.33b). The microcontroller West 4100+ allowed the Peltier to heat up or cool down the NG sample by switching on and off the power supply depending on the feedback of the temperature sensor stuck on the sample holder. Fig. 3.34a shows the connection of all these elements. The Peltier module in the heating system is sandwiched between two aluminum plates. The NG device is placed on the aluminum layer in contact with the hot side, while the sphere joint is under the aluminum layer in contact with the cold side (shown in Fig. 3.34b).

III.4.2.2 Piezoelectric response of NGs with thermal cycles

The thermal study (Fig. 3.35a) of the NG devices was based on a thermal cycle including heating and cooling down. Within one thermal cycle, the device was heated from the room temperature to several temperature plateau values ( , and ) and then cooled back to again. At each step, the temperature was kept stable for a period to allow for open circuit voltage, short circuit current, and output power measurements. Most of the study has focused on NG No4. Different thermal cycles were performed on the device and its performance was evaluated. First, the device NG No4 was subjected by the thermal cycles with = 50℃ , = 80℃ and = 90℃. The compression force was 2 N. We measured the open circuit voltage of this device before and after each thermal cycles. The initial potential was around 50 mV. During each thermal cycle, the potential was improved as the temperature increased from to . After each cycle, we recorded the potential when the device was completely cooled down. As shown in Fig. 3.35b, the potential generated by NG No4 were further improved by repeating the thermal cycles. By the end of the third cycle, the potential reached 500 mV, 10 times the initial value. Apparently, the thermal cycle induced improvement was progressive. Meanwhile, we observed that this thermal-based enhancement had a long-term effect. The open circuit voltage decreased to 290 mV three month after the thermal treatment and came back to the initial value (50 mV) after as long as six months. Six months later we conducted another thermal treatment on the same device, with = 30℃, = 50℃ and = 70℃, and = 2 N. During the first thermal cycle, the open circuit voltage increased from 50 mV to 75 mV. One could easily perceive a distinct improvement of 50 % for V oc (Fig. 3.36a). This was lower than the first experiment with thermal treatment, because the temperature of each steps was also lower. This variation of the performance also existed in other NG devices, such as NG In29A (Fig. 3.36b). The increase of V oc for this latter device reached 7 times. According to our results, this thermal-based enhancement was repeatable and commonly found in the NGs.

III.4.2.3 Temperature influence on NG performance with electrical load

The piezoelectric response of NG No4 connected to an electrical load was also studied during the thermal cycle. Fig. 3.37 presents the measurement results of the first thermal cycle. Three steps of the thermal cycle were selected: before the cycle, (70℃), and after the cycle. Both the potential (Fig. 3.37a) and the instantaneous power (Fig. 3.37b) increased as the temperature arose from room temperature to 70 ℃. After cooling down, the values were still larger than initial ones. The optimum load of this device after one thermal cycle was around 50 MΩ.

III.4.3 Comparison between NGs and PZT generator

As a mature piezoelectric ceramic, PZT is widely used for passive sensing, active transmitting and mechanical displacement applications. Actually PZT is a good traditional piezoelectric material with a much larger piezoelectric constant than that of piezoelectric semiconductors. Thus commercial approaches for piezoelectric energy harvesters based on PZT in bulk or thin film forms have been realized for several years. However, PZT has several drawbacks: (1) it needs to be pre-polarized before getting into application; (2) it is difficult to obtained in thin film and hard to be compatible with CMOS techniques; (3) it contains Pb which is toxic. It is interesting to make the comparison between our NG with a commercial PZT disk generator.

The measurement of the voltage and power of NG No4 was taken three months after the first thermal treatment (see section III.4.2.2). Both the NG and PZT disk generator were compressed by a 5 N force. As the resistive load changed from a few kΩ to 1 GΩ, the voltage increased with the resistance and tended to saturate at the value of open circuit voltage (0.29 V). The instantaneous power was calculated according to the potential on the load. Unlike the voltage variation, the instantaneous power presented an obvious optimum value of 13 nW at = 1 MΩ. Considering the volume of the NG, the power density could reach 85 μW/cm 3 (Fig. 3.38a). Meanwhile, we also characterized the performance of the PZT disk generator as a reference. Fig. 3.38b shows the voltage and instantaneous power of this PZT device. The voltage followed the same trend as the NG, but with a much larger saturation value of 2.4 V. On the other hand, although the PZT device performed an optimum power of 2 μW at = 0.5 MΩ, its actual volume was much larger than that of the NG. Geometry, piezoelectric coefficient and power density of both generators are compared in Table 3.4. While the piezoelectric constant of PZT is 40 times larger than that of ZnO, the volume power density of the latter was 3.4 times higher due to the small effective thickness. According to what was observed for NGs working under compression, we started to consider that it would be interesting to characterize the performance of flexible NGs under bending. In the next section we will present experimental results on this characterization.

III.5 Piezoelectric response of NGs under bending

VING integrated on flexible stainless steel foil can also work under bending. It would give us better understanding of the physical principles to measure the potential with accurate deflection control. However, building this set-up is beyond what could be addressed in the timeframe of a thesis. Therefore, this section presents our very first results, obtained manually. They give a basic understanding of flexible NGs operation and are very useful for further developments.

III.5.1 Measurement Set-up of NGs under bending

During the measurement, the voltage signal generated by bending was acquired by an oscilloscope. Since the impedance of the oscilloscope (1 MΩ) is large compared to that of our flexible NGs (a few tens of kΩ), the measured voltage can be regarded as the output piezopotential of the NG.

The NG device was bent by two methods. In the first method, one edge of the plate was clamped and we used airflow with a pressure of 0.5 psi to bend the device periodically at the other edge with an approximated deflection of about 1 cm (Fig. 3.39a). In the second method, the device was bent manually as shown in Fig. 3.39b with the deflection less than 1 cm. Fig. 3.39c and d present the piezoelectric response to periodically applied deflection of the same NG bent by the airflow and manually, respectively. Although the fluctuation of the voltage pulse was attenuated by the airflow bending, the maximum output potential of both measurements was around 20 mV. In31A, In32A, In35A and In20B were grown with the same process and parameters. Then different PMMA deposition procedures were selected to construct the matrix and the top insulating layer, resulting in a difference in the thickness. The four devices were bent manually with an estimated deflection of 0.5 cm. As shown in Fig. 3.40a, the potential reduced from 0.15 V to 0.024 V as the top layer thickness increased. On the other hand, the reproducibility of the potential generation was improved by increasing the top insulator thickness (Fig. 3.40b). When the top layer was thin, the charge leakage tended to be dominant due to the short circuit. To investigate the optimum design for NGs working under bending, Al 2 O 3 and Si 3 N 4 were selected as the matrix and top insulating material. To compare with PMMA, the NGs were bent manually with a deflection approximatively equal to the one with PMMA. The potential generated by the NG packaged with Al 2 O 3 was stable and the peak value was around 1 V (200% of improvement compared to PMMA) as shown in Fig. 3.41a. It was higher than most of devices with PMMA, and comparable with the best one. Meanwhile, the NG with Si 3 N 4 as packaging material generated stable potential of 0.6 V (100% of improvement compared to PMMA) (Fig. 3.41b).

To achieve functional NGs with PMMA matrix, we needed top PMMA layer thicker than one micrometer, otherwise the performance would be crippled due to the short circuit threat. On the other hand, thick top layer reduced the generated potential by up to 84%. The compromise existing between the thin and thick layers led to a difficulty in the synthesis control. Compared to the PMMA, the thickness of the Al 2 O 3 and Si 3 N 4 top layers was about 300 nm. This is consistent with our simulation which predicted that a thinner and harder insulating material would enhance the NG performance

III.5.2.3 Non-symmetric potential generation phenomenon

As mentioned in Chapter II, a non-symmetric performance was observed for the NGs under bending thanks to these preliminary electromechanical measurements on NGs built on stainless steel foil. The NGs were bent manually downwards (Fig. 3.42a) or upwards (Fig. However, the VING works as a capacitor in generating the potential. The change of the capacitance in bending mode was significant compared to how it performed in compression mode. Therefore, the measured potential was not only the piezoelectric potential. It was actually composed of capacitance change induced fluctuation and the piezoelectric signals.

In fact, we conducted a measurement, under the same experimental circumstances, on a device where no ZnO NWs were integrated, but only with PMMA layers. The result showed that there was still this capacitance change induced fluctuation (Fig. 3.44a). Then we tried to bend the VING device with a quick move. The piezoelectric signal showed itself as a typical displacement voltage signal before the influence of capacitance (Fig. Still it was extremely difficult to obtain a piezopotential precise and reproducible enough via bending manually. There is a clear need for a more controlled experimental set-up, which is presently under development in the framework of a following thesis.

III.6 Conclusion

In this chapter, we first discussed the mechanical and electromechanical response of individual NWs. An AFM was used to directly bend cantilevered NWs to characterize their Young's modulus and the piezoelectric response. We demonstrated that the Young's modulus measurement could be used for beam-like nanostructures with large aspect ratio by bending the free end with a controllable force. The piezoelectric response was measured simultaneously, as the voltage signal was acquired by a high input impedance preamplifier through conductive AFM tips. The potential -force relation was established in this way, offering a method to calculate the effective piezoelectric coefficients. In our work, III-V NWs, such as GaN and GaAs NWs, were characterized. ZnO and ZnO based core-shell heterostructure NWs were also measured and compared. In our experiments, ZnO NWs presented larger effective piezoelectric coefficients than III-V NWs, among which the core-shell ZnO/BTO and ZnO/PZT NWs provided a concept to improve even more the piezoelectric properties. Secondly, we characterized rigid and flexible NGs integrating ZnO NWs immerged into an insulating material (PMMA, Si 3 N 4 or Al 2 O 3 ). Concerning the NG devices (on Si), we built a system to measure their energy generation performance under compression by acquiring the open circuit voltage, short circuit current and instantaneous power with resistive load. Thermal control was also added to this set-up (<80°C). We found that the temperature of the working environment influenced the output. The generated potential and power were improved when the devices under compression are subjected to thermal cycles, including a rise in temperature and cooling down to ambient temperature. After three of these cycles, the potential and power were increased by 10 and 300 times, respectively. The improvement of the performance was studied over time. It was found that the performance of the devices returned to its initial value after 6 months.

Flexible NGs were also characterized with preliminary experiments, using manual bending or airflow to provide the bending force. Although simple, these tests provided guidelines about how to improve the performance. For instance, we verified that it was beneficial to use a harder material allowing top layer to be thinned without the risk of short circuit formation between NWs and top electrode. Finally, the non-symmetric performance predicted by the computational study (Chapter II) seemed to be observed experimentally. However, for further investigation with flexible NGs, we need to build a set-up with accurate control of the deflection, so that we can obtain the deflection-potential relationship, as well as more quantitative analysis for the non-symmetric performance. In fact, this new bending set-up is under development for an accurate and reproducible characterization. Only then, it will be possible to determine if the non-symmetry between upward and downward bending observed in experiments has the same origin as in our simulation.

Conclusions and perspectives

Development of technologies expedites the emergence of low-power consuming and wireless miniature electronics, from wireless sensor networks to portable personal electronic products. Most of the cases, these system and devices are powered by batteries and/or wired. Sometimes, this can be very costly. On one hand, batteries need to be either replaced or recharged periodically and have limited lifetime. It seems easy for some sensor networks. For example a 46-node battery-powered sensor network have been deployed to measure the dynamics of the Golden Gate Bridge. However, when it comes to the border monitoring, a large number of sensors (> 1000) is required at the border between US-Mexico [START_REF] Beeby | Energy harvesting for autonomous systems[END_REF]. On the other hand, wiring can be negative to spread the application of sensor networks. For instance, wiring each sensor in a commercial building can increase the cost by 20 times compared with the use of wireless sensors. Therefore, efforts are required for autonomous system where ambient energy is harvested to recharge the batteries or even to directly power other units, such as sensor, ADC or transmitter.

Among variety of energy harvesting methods, electromechanical transducers based on piezoelectric effect have attracted much attention. Conventional thin film piezoelectric devices can satisfy the power supply requirements with high generation and high energy conversion efficiency. Piezoelectric generators using ceramic compounds (such as PZT) can generate high voltages (up to 100 V [START_REF] Park K Il | Highly-efficient, flexible piezoelectric PZT thin film nanogenerator on plastic substrates[END_REF]) and have a high direct coupling efficiency between the mechanical and electrical energy (up to 80% [208]). Driven by the demand of miniaturization and compatibility with the IC/MEMS industry, PENGs based on semiconducting NWs came into sight ten years ago. Although piezoelectric semiconductor NWs might not be able to generate voltage as high as the ceramic thin film finally, they have their own strengths for energy harvesting in autonomous system. In fact, based on current research, a PENG might be able to meet the power consumption of a simple sensor node, which can work with energy supply of 1 or 2 μW for a low data rate.

The objective of this thesis was the study of physical principles and piezoelectric responses of semiconducting NWs including III-V compounds, ZnO, ZnO core-shell heterostructure NWs, and ZnO NWs based VINGs. The study was divided into two main aspects: computational simulation study for VING devices, and the characterization of individual piezoelectric NWs using AFM techniques and PENGs using a set-up built by ourselves. The integration of VINGs based on ZnO NW arrays were prepared in our group. The CBD method was used to grow ZnO NWs on both p-type Si wafers and stainless steel foils. Then they were vertically integrated into dielectric matrix and top insulating layer. These NWs and NGs were characterized, together with other samples from our cooperators.

Most of the simulation work in the literature is focused on individual NWs, developing from regarding the NWs as dielectric material to considering the screening effect of doped semiconductors. However, very few work had been done on the NW composites before our group. To better understand how the piezoelectric NWs could work in a VING structure, we built NG cell models, which consisted of a single NW immerged in an insulating matrix with proper boundary conditions, for VING working in compression and flexion modes. First, the ZnO NW used for the NG cell was assumed to be insulating, meaning only dielectric material properties included besides the piezoelectricity. Under this circumstance, we analyzed the working principle of VINGs and investigated the effect of matrix materials with an explanation from both mechanical and electrical aspects (section II.2). In fact, due to unintentionally doping during the synthesis, free carriers screened large part of the piezopotential generated by ZnO NWs. Simulation results showed that the piezopotential could be considered as fully cancelled for doping level higher than 10 cm . Yet a few tens to a few hundred millivolts of output potential can still be observed in electromechanical measurements. By taking SFLP into account in the framework of full coupling between semiconducting and piezoelectric physics, we gave possible explanations to several unaddressed issues: (1) better performance would come up with NWs with larger length and aspect ratio even with high doping level; (2) NG cells generated larger potential compared to ZnO thin film even with a diameter larger than predicted by first-principle calculations; (3) a non-symmetric performance of NG devices working in flexion mode was observed with SFLP in the simulation.

Although analytical and computational researches helped us to understand the physical principle and provided the guideline of experimental activities, mechanical and electromechanical measurements is indispensable in the study of piezoelectric NWs and NGs. In this thesis, the Young's moduli and electromechanical responses of individual NWs were characterized under AFM. The Young's modulus of GaAs NWs with high aspect ratio was measured by bending the free end with a controllable force. The piezoelectric response was measured simultaneously as the NW was deformed. Consequently, the potential -force relation was established in this way, offering a method to calculate the effective piezoelectric coefficients. GaN, GaAs, ZnO and ZnO based core-shell heterostructure (ZnO/PZT, ZnO/BTO) NWs were measured and compared. ZnO NWs presented larger effective piezoelectric coefficients than III-V NWs, among which the core-shell ZnO/BTO and ZnO/PZT NWs provided a concept to improve even more the piezoelectric properties.

Meanwhile, we moved the electromechanical characterization to the device level for a more direct evaluation. We built a system to measure the energy generation performance of NGs under controlled compression and temperature by acquiring the open circuit voltage, short circuit current and instantaneous power with a variable resistive load at different temperatures (< 80 °C). The performance of the devices was affected by the temperature. After several cycles of compression under heating and going back to ambient temperature, the performance of rigid NGs could be improved up to 10 times in open circuit voltage and 280 times in power generated.

Flexible NGs were also characterized. Preliminary results were obtained by bending the samples manually or under air flow keeping approximatively the same deformation. The brief results revealed mainly two key points: first, a harder matrix could improve the energy generation performance as predicted in the simulation; and second, the non-symmetric responses were observed in most of the functional flexible NGs, self-consistent with the SFLP theory we put forward in section II.4. To achieve more accurate measurements, a new characterization set-up for controlled and reproducible bending is actually under development.

Limited by what could be addressed in the timeframe of a thesis, several questions remain to be answered. For example, the effective piezoelectric coefficients tested by the AFM were lower than the theoretical values, which might be resulted from the doping conditions. If we assume that the NWs are doped at a normal level, then why can we still observe several to several tens of millivolts generation? Does SFLP confine the screening effect here? In the thesis, we observed this interesting and promising enhancement of NG performance due to thermal treatment. Then the questions come up. Does the effect of this thermal treatments repeatable? Does the thermal treatment change the characteristic, other than potential and power, of the NG, for instance, the optimum load? And the most important one ---what is the physical principle of this change? A possible answer to the last one is the surface trap, requiring further investigation of the surface state between ZnO and PMMA.

In addition to researches for better understanding of the fundamentals, exploiting new application of PENGs could also be interesting for autonomous system. Since friction or contact between the electrodes/piezoelectric material and the substrate is inevitable during the operation of the PENG. This can drive a TENG with the electrostatic induction, thus offering a possibility to combine TENG with PENG to supply more power to drive electronics and to realize self-powered active sensors. A hybrid piezoelectric-triboelectric NG can be an effective way to harvesting mechanical energies. emerged as one of the first simulation methods from the pioneering applications to the dynamics of liquids by Alder and Wainwright and by Rahman in the late 1950s and early 1960s. Due to the revolutionary advances in computer technology and algorithmic improvements, MD has subsequently become a valuable tool in many areas of physics and chemistry.

MD simulations are increasingly being used to study the mechanical behavior, such as the uniaxial tension, failure strain and Young's modulus of nanostructures [START_REF] Gall | The Strength of Gold Nanowires[END_REF][215][216][START_REF] Branício | Large deformation and amorphization of Ni nanowires under uniaxial strain: A molecular dynamics study[END_REF][START_REF] Komanduri | Molecular dynamic simulations of uniaxial tension at nanoscale of semiconductor materials for micro-electro-mechanical systems (MEMS) applications[END_REF][START_REF] Ju | A molecular dynamics study of the tensile behaviour of ultrathin gold nanowires[END_REF]. Besides, more specific simulations are conducted on piezoelectric NWs. Size effects, defects, and elastic properties of ZnO and GaN NWs investigated through MD models are supportive to their assets of the application in energy conversion [START_REF] Kulkarni | Orientation and size dependence of the elastic properties of zinc oxide nanobelts[END_REF][START_REF] Dai | Molecular dynamics simulation of ZnO nanowires: size effects, defects, and super ductility[END_REF][221][222][START_REF] Agrawal | Investigation of ZnO nanowires Strength and Fracture[END_REF].

 Continuum modeling Some physical phenomena can be modeled assuming that materials exist as a continuum, which means the matter in the body is continuously distributed and fills the entire region of space it occupies. A continuum is a body that can be continually sub-divided into infinitesimal elements with properties being those of the bulk material. Continuum mechanics deals with physical properties of solids and fluids which are independent of any particular coordinate system in which they are observed.

The piezoelectric response of a macroscopic 3D system is well described by the continuum Landau Devonshire model. This model does not adequately describe the piezoelectric response of a one-dimensional system because the 1D Coulomb kernel is a short range potential. People demonstrate that this short range kernel leads to new physical effects in nanotubes and NWs [224]. To overcome the scale independency of the classical continuum theory, many high-order theories, such as the strain gradient theory [START_REF] Zhao | Nonlinear microbeam model based on strain gradient theory[END_REF][START_REF] Akgöz | Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams[END_REF], couple stress theory [START_REF] Akgöz | Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams[END_REF]227], micropolar theory [228], nonlocal elasticity theory, [START_REF] Eringen | On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves[END_REF][START_REF] Eringen | Nonlocal polar elastic continua[END_REF] etc., are developed to characterize the size effects in the nanostructures by introducing an intrinsic length scale. Moreover, aspect ratio effect and surface effects of piezoelectric NWs are also investigated using advanced continuum models. [224,[231][232][START_REF] Samaei | Timoshenko beam model for buckling of piezoelectric nanowires with surface effects[END_REF]  Finite element method

The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations (PDE), which is originally developed for solving solid mechanics problem in the 1940s by Richard Courant. FEM solves an equation by approximating continuous quantities as a set of quantities at discrete points. These quantities are usually called elements and the joint points of the elements are named as nodes (Fig. Nowadays FEM are used in the mechanical, thermal, fluidic, electrostatic or even chemical reaction problems. For complex geometry and boundary condition, these PDEs cannot be solved with analytical methods, where an approximation of the equations can be constructed, typically based upon different types of discretizations. For example, a function is the dependent variable in a PDE (i.e., temperature, electric potential, pressure, etc.). The function can be approximated by a function using linear combinations of basis functions according to the following expressions:

≈ =
Here, denotes the basis functions and denotes the coefficients of the functions that approximate with (Fig. I.2b). Many physics laws are expressed by mathematical equations that can be solved with FEM. For example, the conservation laws such as the law of charge conservation, mass conservation and momentum conservation are all expressed by the continuity equation in differential form:

+ ∇ • = σ I.1
where  ρ is the amount of the quantity per unit volume,  j is the flux of the quantity,  t is time,  σ is the generation of the quantity per unit volume per unit time. Terms that generate (σ > 0) or remove (σ < 0) the quantity are referred to as a "sources" and "sinks" respectively. The differential equations express a small change in a dependent variable with respect to a change in an independent variable (x, y, z, t). In the case of the continuity equation, ρ is the dependent variable, while x, y, z and t are the independent variables. In Cartesian 3D coordinate system, the divergence of the flux j is denoted by:

∇ • = + + I.2
Furthermore, the flux usually can be described by the constitutive relation: = -∇ I.3 In the above equation, k represents the related factors and has different physical meanings in different conservation laws. Eq. 2.1-2.3 state that as a PDE, the continuity equation includes the derivatives of more than one independent variable, each of them represent a change in one direction out of several possible directions. If we know the value of ρ at a time t 0 , and the value of ρ or j at certain position (x 0 , y 0 , z 0 ), we can apply the initial condition and boundary conditions for Eq. 2.1. In many situations, PDEs cannot be resolved with analytical methods to give an expression such as = ( , , , ). Ergo an alternative option is to search for approximate numerical solutions through numerical models. This is the reason of the wide application of FEM simulations. deposition, and low-damage dry etching using inductively coupled plasma (ICP).

Ra et al. first demonstrated the feasibility of the various applications based on semiconductor oxide NW devices fabricated by the NSL method [START_REF] Ra | Fabrication of ZnO nanowires using nanoscale spacer lithography for gas sensors[END_REF]. According to Ra's work, it is easily to find that the NWs obtained by NSL method are well aligned and are usually laterally integrated to the substrate. These NWs can also have controlled geometry with ultra-long or sub-10 nm thin morphology, determined by the mature thin-film deposition techniques. On the other hand, these features also exclude some application fields, such as vertically integrated devices for mechanical sensing and energy harvesting. In fact, NSL techniques are largely used in the fabrication of individual-NW electronics and chemical or biological sensing devices [242,[START_REF] Choi | Fabrication of sub-10-nm silicon nanowire arrays by size reduction lithography[END_REF].

AII.1.1.2 Inductively coupled plasma reactive ion etching (ICP-RIE)

Reactive ion etching (RIE) is a directional etching process utilizing ion bombardment to remove material. This etch process is commonly used in the manufacturing of printed circuit boards and other micro fabrication procedures; the process is performed in a vacuum chamber and aggressively etches in a vertical direction. Horizontal etching is purposefully minimized in order to leave clean, accurate corners. Generally, RIE uses chemically reactive plasma to remove material deposited on wafers. The plasma is generated under low pressure (vacuum) by an electromagnetic field. High-energy ions from the plasma attack the wafer surface and react with it.

The plasma comes from variable power sources, among which the ICP is involved in the fabrication of miniature structures, such as NWs. The ICP is employed as a high density source of ions which increases the etch rate, whereas a separate RF bias is applied to the substrate (silicon wafer) to create directional electric fields near the substrate (Fig. II.2a). In conventional RIE etching, the physico-chemistry cannot be controlled to make low damage processes, because the density and the energy of the radicals cannot be separately adjusted. This is the main advantage of the ICP-RIE etching that uses a RF source power to ionize the gas, and another RF chuck power (called RF platen power) to control the energy of the radicals. This ICP-RIE system achieves more anisotropic and low-damage etch profiles.

It has been reported that III-V compounds, silicon and even carbon NWs can be obtained by ICP-RIE techniques [START_REF] Zhao | Nanometer-scale vertical-sidewall reactive ion etching of ingaas for 3-D III-V MOSFETs[END_REF][START_REF] Yu | Gallium Nitride Nanorods Fabricated by Inductively Coupled Plasma Reactive Ion Etching[END_REF][START_REF] Behnam | Nanolithographic patterning of transparent, conductive single-walled carbon nanotube films by inductively coupled plasma reactive ion etching[END_REF][START_REF] Wang | High optical quality GaN nanopillar arrays[END_REF][START_REF] Jalabert | High aspect ratio GaAs nanowires made by ICP-RIE etching using Cl2/N2 chemistry[END_REF][START_REF] Hausmann | Fabrication of diamond nanowires for quantum information processing applications Diam[END_REF][START_REF] Huang | Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching[END_REF]. Jalabert et al. reported an experimental study of GaAs etching by ICP-RIE based on Cl 2 :N 2 chemistry [START_REF] Jalabert | High aspect ratio GaAs nanowires made by ICP-RIE etching using Cl2/N2 chemistry[END_REF]. To obtain high aspect ratio GaAs NWs, they prepared GaAs samples with arrays of microstructures (lines and dots) made by electron beam lithography, followed by a lift-off of a 30 nm thick Ni film. Then GaAs NW arrays of 1 μm high and 30 nm in diameter were fabricated by ICP-RIE with Ni mask as the catalyst on top (Fig. II.2b). Compared to pure semiconductor NWs, ICP-RIE techniques are more suitable to NWs with longitudinal heterostructures or even individual NW based electronics. Huang and his coworkers reported a novel method to fabricate GaN-based nanorod light emitting diodes (LEDs) with controllable dimension and density using self-assemble Ni and Ni/Si 3 N 4 nano-masks and ICP-RIE [START_REF] Huang | Fabrication of GaN-based nanorod light emitting diodes using self-assemble nickel nano-mask and inductively coupled plasma reactive ion etching[END_REF]. A 300 nm Si 3 N 4 thin film layer was deposited on GaN-based LED heterostructure film, followed by a Ni layer with the thickness ranging from 5 to 15 nm. The sample was subsequently rapid thermal annealing (RTA) under flowing N 2 and then etched using a planar type ICP-RIE system (Fig.

AII.1.2 Bottom-up method

Based on existent research, bottom-up mechanisms can be grouped into two different basic categories each with two subcategories. One is based on the suppression of crystal growth in two directions to create one-dimensional structures, as is the case for selective area epitaxy (SAE) and oxide-assisted growth (OAG). SAE employs a mask layer with well-defined openings, out of which wires grow in a layer-by-layer mode (Fig. II.3a). The fact that growth continues one-dimensionally also above the mask layer, in contrast to lateral overgrowth, is attributed to the formation of slowly growing side facets with a low surface energy. [START_REF] Ikejiri | Mechanism of catalyst-free growth of GaAs nanowires by selective area MOVPE[END_REF] For this kind of growth, no seed particle is used. OAG is based on the use of the semiconductor and one of its oxides. During growth, phase separation occurs, leading to a core of the semiconductor material, which is simultaneously covered by a passivating shell of its oxide (Fig. II.3b), suppressing lateral growth [START_REF] Zhang R Q | Oxide-Assisted Growth of Semiconducting Nanowires[END_REF]. Unlike other NWs, the OAG NWs have almost always oxide sheath. The quality of these NWs hinges on how effectively the oxide is segregated from the core to the peripheral surface of the droplet during growth.

The second group of 1D growth mechanisms is based on a significant local increase of growth velocity in one direction, in many cases caused by a particle at the NW top [START_REF] Wacaser | Preferential interface nucleation: An expansion of the VLS growth mechanism for nanowires[END_REF]. For these particle-assisted growth (PAG) schemes, we may distinguish between seed particles containing elements constituting the wire (homo-particle assisted growth, Fig. II.3c), and seed particles of a different material (hetero-particle assisted growth, Fig. II.3d). In both cases, supersaturation of the growth system leads to material crystallizing rapidly at the particle/crystal interface. The seed particle can be either liquid (vapor-liquid-solid growth, VLS) or solid (vapor-solid-solid growth, VSS). Some researches consider that it is more accurate to name the seed particle "quasi-liquid" or "quasi-solid" (vapor-quasi-liquid-solid growth or vapor-quasi-solid-solid growth, VQS) as it does not remain unchanged in liquid (or solid) phase during the whole growth of NWs. However, the basic principle is the same. Oxide-assisted growth. The semiconductor and its oxide are adsorbed on the surface, creating nucleation centers which separate into a semiconductor core and a passivating oxide shell. (c) Homo-particle growth. A seed particle is formed consisting of one or all elements used for wire growth. During growth both length and diameter increase as the seed particle size is variable. (d) Hetero-particle growth. A seed particle (typically Au) is deposited prior to growth. During heating to growth temperature the seed particle alloys with the substrate and/or material from the gas phase. Particle size during growth is nearly constant [START_REF] Mandl | Growth mechanism of self-catalyzed group III-V nanowires[END_REF].

AII.1.2.1 Nanopole template-assisted growth

Nanopole template-assisted growth belongs to the first group, where the crystal growth in lateral direction is suppressed to create 1D structures. It has been shown to be effective for the fabrication of ordered NW arrays of metals or semiconductors. As dry method, it possesses advantages such as strict geometry control, versatility on different components and ease of dopant control. Thurn-Albrecht et al. has reported a method to rapidly and reliably fabricate NW arrays with densities in excess of 1 terabit per square inch, based on the self-assembled morphology in diblock copolymer thin films (Fig. II.4) [START_REF] Thurn-Albrecht | Ultrahigh-density nanowire arrays grown in self-assembled diblock copolymer templates[END_REF]. Another template ---Anodic aluminum oxide (AAO) ---is commonly used in the template-assisted growth of ZnO NWs [START_REF] Kovtyukhova | Layer-by-layer self-assembly strategy for template synthesis of nanoscale devices[END_REF][START_REF] Liu | High-density, ordered ultraviolet light-emitting ZnO nanowire arrays[END_REF]. AAO template can provide ordered porous structures with channel diameters ranging from 10 to 200 nm. As a thermally and chemically stable template, the growth of ZnO NWs in it could use solution-based methods, such as electroplating [START_REF] Li | Ordered semiconductor ZnO nanowire arrays and their photoluminescence properties[END_REF], electrophoretic deposition [START_REF] Wang | Preparation and characterization of nanosized ZnO arrays by electrophoretic deposition[END_REF], sol-gel [START_REF] Lakshmi | Sol-Gel Template Synthesis of Semiconductor Nanostructures[END_REF], and hydrothermal processes [START_REF] Shi | Photoluminescence of ZnO nanoparticles in alumina membrane with ordered pore arrays[END_REF]. AII.1.2.2 Methods based on VLS mechanism Among various PAG approaches used to grow NWs, most of them are based on VLS mechanism [START_REF] Wu | Direct observation of vapor-liquid-solid nanowire growth[END_REF] using chemical vapor deposition (CVD), metal organic chemical vapor deposition (MOCVD) [START_REF] Novotny | InP nanowire/polymer hybrid photodiode[END_REF], molecular beam epitaxy (MBE) [262], or laser-assisted catalytic growth [START_REF] Gudiksen | Growth of nanowire superlattice structures for nanoscale photonics and electronics[END_REF]. The VLS mechanism was proposed in the 1960s-1970s for large whisker growth [264,265], which later was developed for the growth of semiconductor NWs. The VLS mechanism relies on a vapor phase precursor of the NW material, which impinges on a liquid phase seed particle, from which unidirectional NW growth proceeds. The choice of an appropriate seed material has the benefit of allowing control over the diameter of the NWs produced, while the seed material can also significantly affect the crystalline quality of the NW [266,267]. According to the homologous or heterologous properties of the seed particle, the VLS growth is usually sorted as metal-catalyzed growth and self-catalyzed growth.

(a) Metal-catalyzed VLS mechanism

In the past decade, NWs of a variety of materials have been fabricated using VLS growth mechanism assisted by hetero-particles. Metal seed particles are widely used for NW growth on VLS mode, preferentially Au nanoparticles (sometimes Mn and Ni nanoparticles are also used) [START_REF] Martelli | On the growth of InAs nanowires by molecular beam epitaxy[END_REF][269][START_REF] Li | Nanowire electronic and optoelectronic devices[END_REF][START_REF] Hsieh | Time-course gait analysis of hemiparkinsonian rats following 6-hydroxydopamine lesion[END_REF]. The yields are well-controlled by modulating the size, position or pattern of seed particles.

The VLS process can be divided into two main steps: 1) the formation of a small liquid droplet, and 2) the alloying, nucleation, and growth of the NWs. The growth starts on a clean, defect-free surface of a substrate, which is a semiconductor wafer in most cases. At first, metal clusters are deposited on the substrate; techniques for patterning control will be involved in this part. As pointed out above, gold is the metal catalyst used in most works. A thin layer of gold is deposited on the Si substrate followed by a short-time heating at about 700 ºC until the Au layer melts to form small droplets and combine with Si atoms. Then the substrate is heated in a reaction tube of chamber until the metal clusters melt and form liquid droplets, also called collectors. In order to lower the temperature used in the heating, the prevalent method is to replace the pure metal with an alloy of the metal and semiconductor materials, which could reach the suitable temperature in the range of 300 -1100 °C according to the target NWs. In a second step, a gas containing the elements of NWs flows through the reaction tube. The NWs grow at the interface of the collectors and the surface of the substrate.

(b) Self-catalyzed VLS mechanism

Nevertheless, for the combination with Si technology, this is problematic due to Au forming deep level traps in Si. Contamination and undesired dopants brought by hetero-particles strict the application of NWs to a great extent. Thus homo-particle assisted growth (or "self-catalyzed growth", SCG) attracts much more interests than ever before. The yields of this growth mechanism are usually called "self-catalyzed" or "self-catalytic" NWs, while the whole process, from the deposition of homo-particles to the particle-induced growth, can be considered as "self-organization system". The VLS growth of self-catalyzed NWs through supersaturation and precipitation at the liquid-solid interface can be explained by considering the composition-temperature phase diagram of the binary system.

Besides, some routes belonging to the second group make use of the intrinsic property of the target material without particle-assistance, such as various chemical bath deposition (CBD) methods.

AII.2 Chemical bath deposition method for the growth of ZnO NWs

For the synthesis of ZnO NWs in our lab, chemical bath deposition (CBD) or so-called hydrothermal growth method has been used. CBD method has been proved effective and convenient in preparing ZnO NW arrays due to their low growth temperature, low cost and potential for scale up. Moreover, a remarkable diversity of ZnO 1D nanostructure, with different and controllable morphologies, can be obtained simply by changing the precursor chemicals, their concentrations, and/or the growth temperature.

AII.2.1 Seed layer assisted growth mechanism

Among all the CBD methods developed for the synthesis of ZnO NWs and nanorods, such as hydrothermal decomposition [START_REF] Li | Fabrication of ZnO nanorods and nanotubes in aqueous solutions[END_REF][START_REF] Peterson | Epitaxial chemical deposition of ZnO nanocolumns from NaOH solutions[END_REF], electrochemical reaction [START_REF] Yang | Electrochemical route to the synthesis of ultrathin ZnO nanorod/nanobelt arrays on zinc substrate[END_REF] and template-assisted sol-gel processes, seed layer assisted growth provide an effective route to increase the length and aspect ratio. Using ZnO thin film as the seed layer effectively lowers the interfacial energy between the ZnO nucleation and the substrate [START_REF] Tian | Complex and oriented ZnO nanostructures[END_REF]. The nucleation barrier is thus reduced, facilitating the growth of small-diameter ZnO NWs. Meanwhile, the orientation and doping status of the seed layer will dominate the orientation of NWs due to an epitaxial growth mechanism to improve the vertical alignment, and influence the semiconducting properties of NWs due to the diffusion of free carriers.

In the growth process, Zn 2+ and OH -are provided by hydration of zinc nitrate hexahydrate (Zn(NO 3 ) 2 •6H 2 O) and hexamethylenetetramine (HMTA). When the precursor solution is heated, hydrothermal reactions can occur as follows:

( ) ( ) + 6 ↔ + 2 + 6 II.1 ( ) + ∆ ↔ 6 ( ) + ( ) II.2 ( ) + ↔ + II.3
where ( ) is HMTA or Hexamine. Here, Zn 2+ are known to react readily with OH - to form more soluble Zn(OH) 2 complexes, which act as the growth unit of ZnO nanostructures. Finally, ZnO is obtained by decomposition of Zn(OH) 2 . Therefore, the key chemical reactions involved in hydrothermal synthesis process is as:

+ 2 ↔ ( ) ( ) II. 4
( ) ↔ ( ) + II.5 When the concentration of ZnO has reached supersaturation, ZnO crystal nuclei form and then grow according to the growth habit of ZnO crystals. ZnO crystal exhibits partial polar characteristics, and in a typical Wurtzite structure the (0001) plane is the basal polar plane. It is terminated by Zn and (0001 ) plane terminated by O, resulting in the divergence of surface energy for large polar surfaces. Other nonpolar planes have lower surface energy compared to the polar basal plane. [276] Under thermodynamic equilibrium condition, the facet with higher surface energy is usually small in area, while the lower energy facets are larger. In a word, the direction perpendicular to the smaller facet is fast in growth and the directions perpendicular to larger facets correspond to slow growing rates thus dominate the final morphology [START_REF] Tang | Size-Controllable Growth of Single Crystal In(OH) 3 and In 2 O 3 Nanocubes[END_REF]. For the ZnO crystal, the growth rates V along the normal directions of different index planes are described as follows: V(0001) > V(101 0) > V(101 1 ) > V(101 1) > V(0001 ), thus nanorod/wire type morphologies are frequently obtained. It is believed that, in the chemical bath, HMTA would preferentially attach to the non-polar facets of the NWs, thereby exposing only the (0001) plane for epitaxial growth [START_REF] Sugunan | Zinc oxide nanowires in chemical bath on seeded substrates: Role of hexamine[END_REF]. Thus it helps the NW to have a more preferential growth along the [0002] direction.

AII.2.2 Growth process of ZnO NWs on rigid and flexible substrates

In this work, ZnO NWs were grown on rigid p-type (100) Si wafer (500 μm) and flexible stainless steel foil (25 μm). The synthesis process and morphology control will be discussed in this section.

AII.2.2.1 Growth procedures

We prepared both substrates with square shapes for easy handling and testing. The Si wafer was immersed into diluted HF acid to remove the top SiO 2 layer. Both substrates were then cleaned by immersion into acetone (3 min), ethanol (3 min) and deionized water (5 min), then they were dried by N 2 gas. Fig. II.5a presents the scheme of the ZnO NW synthesis procedure. Firstly, a ZnO thin film as the seed layer was deposited covering the entire surface by ALD method. Secondly, the specimen was fixed on a rectangular glass holder by kapton tape. To prevent the possible short circuit due to the falling down ZnO NWs grown on the edges, the tape covered about 0.1 cm width from four edges of the specimen as shown in

AII.2.2.3 Deposition of the seed layer

ZnO seed layers can be deposited by many methods such as ALD, magnetic sputtering, spin coating and "bath dip" chemical methods. To achieve ZnO thin film with controllable orientation and good quality, we mainly used ALD technique in the deposition. ALD is an advanced thin film coating method which is used to fabricate ultrathin, highly uniform and conformal material layers for several applications. ALD uses sequential, self-limiting and surface controlled gas phase chemical reactions to achieve control of film growth in the nanometer/sub-nanometer thickness regime. Due to the film formation mechanism -the gases won't react until in touch with the surface which means the film growth proceeds by consecutive atomic layers "up" from the surface -the ALD film is dense, crack-, defect-and pinhole-free and its thickness and structural and chemical characteristics can be precisely controlled on atomic scale. ALD process is digitally repeatable and it can be performed at relatively low temperatures. This gives the possibility to construct not only single material layers but also doped, mixed, or graded layers and nanolaminates, whereas low process temperature allows coating of also sensitive materials such as plastics and polymers.

A basic schematic of the ALD process including four steps is shown in Fig. II.6a. In step 1, precursor A (in pink) is added to the reaction chamber containing the material surface to be coated by ALD. After precursor A has adsorbed on the surface, any excess is removed from the reaction chamber (step 2). Precursor B (in blue) is added (step 3) and reacts with precursor A to form one monolayer of compound AB on the surface (step 4). Precursor B is then cleared from the reaction chamber and this process is repeated as a cycle until a desired thickness is achieved.

Most of ZnO seed layers in our experiments were deposited by using ALD instruments shown in Fig. II.6b. The reaction was completed in the main reaction chamber. In the process, the precursor A is the deionized water, while the precursor B is the Diethyl zinc. Precursor delivery temperature was around 150 °C. The growth temperature of ZnO seed layer was 250 °C. Argon gas was used as a carrying gas with a flow speed of 40 sccm. The chemical reaction in the chamber was given below:

( ) + → + 2 ( ) II.6
The thickness of the seen layer obtained by ALD method is around 40 nm.

AII.3.2 Matrix and top insulating layer deposition

Polymers are first used as the buffer matrix and insulating layer in the VINGs to enhance the mechanical robustness and flexibility. [START_REF] Hu | Self-powered system with wireless data transmission[END_REF] In our earliest experiments, PMMA is used for VINGs working under both compression and bending. Later, different dielectric materials with higher rigidity and relative permittivity are included in the fabrication to improve the performance and to validate the computational studies described in sections II.2.2 of chapter II [5,132].

AII.3.2.1 PMMA deposition with spin coating method

a. Spin coating process Spin coating generally involves the application of a thin film evenly across the surface of a substrate by coating a solution of the desired material in a solvent while it is rotating. The substrate is coated by the solution and then rotated at high speed so that the majority of the ink is flung off the side. The rotation of the substrate at high speed also means that the centripetal force combined with the surface tension of the solution pulls the liquid coating into an even covering. Finally, the solvent is evaporated to leave the desired material on the substrate in an even covering.

To deposit PMMA matrix, we used MicroChem 495PMMA A2 and A6 Resists, each containing 2% and 6% of PMMA dissolved in Anisole, and a primer Hexamethyldisilazane (HMDS). Several processes were selected to control the thickness of the PMMA layer. The first step in the whole procedure was to deposit the primer with a spin speed of 1000 rpm and a spin time of 45 s to improve the adhesion between the resist and the sidewalls of NWs. The matrix was deposited using A2 resist and the top insulating layer was using A6 resist. In both cases, the resist "inks" were deposited on the surface of the sample, and rest for 90 s. Then the spin coating worked with certain spin speed and time. Finally the sample was placed on a hot plate at 180 ˚C for 90 s. This process was repeated several times to achieve desirable thickness. [START_REF] Wang | Self-Powered Nanosensors and Nanosystems[END_REF] shows the progressive change of the morphology as the default thickness increases. By comparing the diameters of Al 2 O 3 coated NW and pure ZnO NW, one can observe that the thickness of Al 2 O 3 thin film on the sidewalls is smaller than the top layer (default thickness). When the default value is 15 nm, the side thickness is around 10 nm. This difference is enhanced by the increase of ALD cycles. As the thickness reaches 310 nm, the Al 2 O 3 forms an top insulating layer covering the entire surface of ZnO arrays. In this case, the side thickness is supposed to be 150 nm.

AIII.3 AFM probes used for mechanical and electromechanical measurements

An AFM probe has a sharp tip on the free-swinging end of a cantilever that is protruding from a holder [282]. The dimensions of the cantilever are in the scale of micrometers. The radius of the tip is usually on the scale of a few nanometers to a few tens of nanometers. The cantilever holder, often 1.6 mm by 3.4 mm in size, allows the operator to hold the AFM probe assembly with tweezers and fit it into the corresponding holder clips on the scanning head of the AFM. Most AFM probes are made of Si, but borosilicate glass and silicon nitride are also in use. Depending on the interaction under investigation, the tip surface of the AFM probe needs to be modified with a coating. Due to the nano-scale force modulation (few hundreds of nN) and the small piezopotential (few tens of mV) to be tested in our electromechanical measurements, the tip must be conductive with a metallic or metallic alloy coating. The force constant of the probe should be specially tailored for the force modulation yielding very high force sensitivity while simultaneously enabling tapping mode and lift mode operation. The combination of soft cantilever and fairly high resonance frequency enables stable and fast measurements with reduced tip-sample interaction.

a. Platinum Iridium (PtIr5) AFM probes

Initially we used PtIr probes, which have overall metallic coating (PtIr5) on both sides of the cantilever to increase the electrical conductivity of the tip (Fig. III.2a). These AFM probes are designed for non-contact or soft tapping mode imaging. The PtIr5 coating is an approximately 25 nm thick double layer of Chromium and Platinum Iridium5 on both sides of the cantilever. The tip side coating enhances the conductivity of the tip and allows electrical contacts. The detector side coating enhances the reflectivity of the laser beam by a factor of about 2 and prevents light from interfering within the cantilever. The coating process is optimized for stress compensation and wear resistance. The bending of the cantilever due to stress is less than 3.5% of the cantilever length. The tip has a radius of curvature better than 25 nm and the tip height is around 10 -15 µm.

Résumé en français

Chapter IV Générateurs piézoélectrique à base de nanofils semi-conducteurs : simulations et études expérimentales L'alimentation en énergie des réseaux de capteurs miniaturisés pose une question fondamentale, dans la mesure où leur autonomie est un critère de qualité de plus en plus important pour l'utilisateur. C'est même une question cruciale lorsque ces réseaux doivent assurer une surveillance d'infrastructure (avionique, machines, bâtiments…) ou une surveillance médicale ou environnementale. La qualité de la surveillance environnementale ou d'infrastructure peut être améliorée en utilisant un grand nombre de capteurs. Cependant, ce nombre peut devenir un problème en raison de la quantité du câblage ou en raison du coût de gestion de la batterie. Pour de telles applications, la récupération d'énergie à partir de l'environnement peut apporter une solution intelligente où devenir chaque noeud pourrait idéalement s'auto-alimenter, ou en d'autres termes, énergétiquement autonome. Selon l'environnement spécifique de l'application, de nombreuses sources d'énergie peuvent être converties en électricité : l'énergie solaire, la chaleur ou les mouvements mécaniques entre d'autres. Les matériaux piézoélectriques permettent d'exploiter l'énergie mécanique inutilisée présente en abondance dans l'environnement (vibrations, déformations liées à des mouvements ou à des flux d'air…). Sous la forme de nanofils (NFs), les matériaux piézoélectriques offrent une sensibilité qui permet d'exploiter des sollicitations mécaniques très faibles. Les NFs piézoélectriques ont récemment fourni un ingrédient prometteur pour l'électronique, la détection et les nanosystèmes de récupération d'énergie. Parmi eux, les NFs semi-conducteurs ont attiré l'attention en raison de leurs excellentes propriétés piézoélectriques, de leurs techniques de synthèse à grande échelle, de leur intégration possible sur CMOS ou sur substrat souple et de la commodité de moduler leurs propriétés électriques par le dopage.

Dans cette thèse nous nous intéressons au potentiel des nanofils de matériaux semi-conducteurs piézoélectriques, tels que ZnO ou les composés III-V, pour la conversion d'énergie mécanique en énergie électrique. Notre objectif est d'approfondir la compréhension des mécanismes physiques qui conditionnent la réponse piézoélectrique des NF semi-conducteurs et des dispositifs associés pour les applications de récupération d'énergie. Pour atteindre ces objectifs, nous avons travaillé à la fois sur des simulations théoriques et sur des travaux expérimentaux. Le travail expérimental a consisté, d'une part, à fabriquer et caractériser des matériaux composites intégrant des NFs de ZnO alignés verticalement et, d'autre part, à caractériser les propriétés électromécanique des NFs individuels (ZnO, GaN, GaAs…) en utilisant un microscope à force atomique (AFM). Les études théoriques ont été basées sur la Méthode des Eléments Finis (FEM), en tenant compte du couplage complet entre les effets mécaniques, piézoélectriques et semi-conducteurs, y compris les porteurs libres. En prenant en compte le piégeage du niveau de Fermi à la surface (SFLP) des NFs, nous avons réussi à concilier pour la première fois des observations théoriques et expérimentales de la littérature.

Après un bref rappel sur quelques concepts de base sur les dispositifs piézoélectriques, les sections suivantes résumeront brièvement mon travail de thèse. Sur le plan théorique, je présenterai le cadre théorique et discuterai les résultats de la simulation. Ensuite, les sections expérimentales présenteront les résultats obtenus sur des NF individuels, ainsi que la fabrication et la caractérisation des nanogénérateurs à base de NF.

IV.1 De l'effet piézoéléctrique aux nanogénérateurs

Pierre et Jacques Curie découvrent l'effet piézoélectrique en 1880. Cet effet décrit la relation qui existe entre une déformation mécanique et la création d'une charge électrique dans certains matériaux. Un an plus tard, les frères Curie ont prouvé l'existence de l'effet inverse, qui venait d'être prédit par Lippmann: un champ électrique produit une déformation mécanique dans ces matériaux. Les matériaux piézoélectriques typiques comprennent le quartz, les semi-conducteurs tels que ZnO et les composés III-V, les céramiques comme PZT et BTO ou des polymères comme le PVDF.

Selon la facon dont ils sont connectés électriquement, les matériaux semi-conducteurs piézoélectriques peuvent fonctionner de deux manières différentes:

(3) Avec des contacts conducteurs, le courant de conduction est modulé par la déformation et est proportionnel aux charges induites par la polarisation. Dans ce cas, le matériau intégré ne peut fonctionner que comme un capteur, et il nécessite une alimentation pour travailler. (4) Avec des contacts isolants ou Schottky (ou dans le cas d'un matériau piézoélectrique isolant), un courant de déplacement est généré en cas de changement de contrainte. Le courant est alors proportionnel à la variation temporelle de la charge induite par la polarisation. Il n'y a pas besoin d'une alimentation externe et les générateurs piézoélectriques travaillent habituellement de cette façon, agissant soit comme des récupérateurs d'énergie mécanique (ou générateurs piézoélectriques), soit comme des capteurs mécaniques auto-alimentés. Les NFs piézoélectriques peuvent être intégrées pour construire des générateurs piézoélectriques, également connus sous le nom de nanogénérateurs (NG). Ils peuvent être soit intégrés latéralement (conduisant à ce que l'on appelle LING, pour les nano-générateurs latéralement intégrés) ou verticalement (menant à ce que l'on appelle VING, pour les nano générateurs verticalement intégrés). Dans ma thèse, la structure VING a été choisie en raison de sa performance par rapport au LING, et parce qu'elle est plus simple à fabriquer et plus robuste.

IV.2 Étude analytique et modélisation de Nanofils et Nanogénérateurs piézoélectriques

La modélisation analytique et la simulateur numerique sont des outils importants dans l'investigation des propriétés à l'échelle nanométrique, où les outils expérimentaux pourraient être partiellement limités par la résolution de la manipulation ou la sensibilité de l'acquisition du signal. Dans cette section, je vais discuter des effets des propriétés mécaniques, électriques et semi-conductrices sur la performance des VINGs.

La methode de éléments finis (FEM) a été l'outil que j'ai utilisé pour mon travail sur les NGs à base de NFs. Le domaine de simulation a été réduit à une cellule élémentaire du NG, consistant en un seul NF entouré d'une matrice diélectrique, avec substrat et contacts. Des conditions aux limites appropriées ont été utilisées pour représenter le comportement de l'ensemble du dispositif NG. Deux modes de fonctionnement ont été étudiés, la cellule NG travaillant en compression ou en flexion. Le travail théorique a été divisé en deux parties. Notre premier objectif était de trouver des lignes directrices permettant l'optimisation des réponses du NG. Pour cela, nous avons effectué une série de simulations FEM, où la géométrie du NG et le matériau de la matrice ont été modifiés. Nous avons également évalué l'influence des propriétés du ZnO, afin de tenir compte de la différence entre les coeffients du matériau massif et ceux trouvés à l'échelle nanométrique par certains auteurs. Nous avons constaté que l'optimisation dépendait du mode de fonctionnement. En résumé (Fig. Pour cette optimisation, le ZnO a été considéré comme intrinsèque. Cependant, les NFs de ZnO fabriqués par croissance chimique (CBD -Chemical Bath Deposition) sont normalement dopés de type N. Cela nous amène à la deuxième contribution théorique de cette thèse, où nous qvons tenu compte du couplage complet entre les propriétés piézoélectriques et semi conducttrices. En accord avec les quelques articles qui considèrent ce couplage, on a constaté que la réponse piézoélectrique du VING devrait être proche de zéro pour les niveaux de dopage expérimentaux, ce qui est contraire aux observations. Nous avons proposé de rechercher l'origine de cette différence dans le fait que le niveau de Fermi est très vraisemblablement piégé à la surface de ZnO. Cette thèse présente pour la première fois une étude de simulation du potentiel piézoélectrique généré à partir des NFs de ZnO où le piégeage du niveau de Fermi à la surface a été prise en compte (par une charge de surface comme condition de frontière à l'interface entre le ZnO et la matrice diélectriaque). La Fig. 4.2 donne une illustration qualitative du mécanisme physique impliqué lorsque le niveau de Fermi à la surface est piégé à mi-intervalle sur toutes les interfaces entre le NF et le matériau matriciel. On peut voir que le piézo-potentiel n'est généré que dans les zones de dépletion, tandis que les porteurs libres écrantent la charge de polarisation dans les zones neutres. Avec le SFLP, la zone de déplétion peut s'étendre sur toute sa longueur du NF, même pour des niveaux de dopage assez importants (dans la plage de 10 17 cm -3 pour des NFs de 200 nm de diamètre). Avec cette hypothèse, plusieurs observations de la simulation correspondent maintenant qualitativement aux résultats expérimentaux de la littérature. Nous croyons que le SFLP est la clé pour résoudre les contradictions qui ont été trouvées entre la théorie et les expérimentations. Plusieurs conclusions ont été tirées de ce travail. Premièrement, le SFLP a introduit une dépendance géométrique plus réaliste de la réponse piézoélectrique de la cellule NG, avec une amélioration de performance pour des NFs plus longs et plus minces. Deuxièmement, par rapport aux couches minces de ZnO, les cellules NG ont généré un plus grand potentiel, parce que la structuration dans les NFs a augmenté l'épaisseur globale de la région qui est influencée par le SFLP. Cet effet pourrait même expliquer pourquoi un plus grand coefficient piézoélectrique est mesuré pour les NFs de ZnO. Enfin, avec le SFLP, on a constaté que les dispositifs NG fonctionnant en flexion présentaient une performance non symétrique lors de la flexion vers le haut ou vers le bas, comme cela a été observé dans les expériences.

IV.4 Conclusions and perspectives

Dans cette thèse, des simulations par éléments finis ont été réalisées pour étudier l'optimisation de VING par un fonctionnement en compression ou en flexion. Ils ont également été utilisés pour étudier les effets des propriétés semi-conductrices de ZnO, parmi lesquels le SFLP induit par les pièges lents de surface a présenté son importance pour la performance. Outre la modélisation, nous avons réussi à fabriquer des VING sur différents substrats et différentes matrices diélectriques. Enfin, nous avons caractérisé la réponse piézoélectrique des NFs individuels et des VING. Les NFs ZnO ont montré une bonne sensibilité à une force, ainsi ils sont un bon choix pour les VINGs. Les mesures de la production d'énergie et des effets de recuit avec les VING en mode de compression ont illustré leurs avantages en tant que generateurs d'énergie. De plus, nous avons observé quelques résultats qui pourraient être intéressants pour la suite comme le rôle bénéfique d'un réactif à haut température.

Du point de vue matériau, les NFs à structure coeur/coquille à base de ZnO pourraient être une clé pour améliorer les performances des dispositifs VING, mais également d'autres applications utilisant des NFs semi-conducteurs piézoélectriques. Ils nous permettent de tirer profit des forts coefficients piézoélectriques de la coquille céramique (PZT, BTO), sans la difficulté de fabriquer des NFs en céramique ou le besoin d'utiliser des champs électriques élevés pour polariser ces structures.

Pour le futur, nous envisageons d'améliorer les hypothèses utilisées dans la description des propriétés des materiaux. Les propriétés mécaniques non linéaires, la piézoélectricité du second ordre et la flexoélectricité doivent être prises en compte. De plus, l'effet dynamique du piège de surface joue également un rôle important.

Finalement, un banc de mesure automatique devrait être développé pour mieux caractériser les dispositifs flexibles fonctionnant en mode de flexion.

  Mots-clés: Récupération d'énergie, Nanofils piézoélectriques semi-conducteurs, Nanogénérateurs, Piégeage du niveau de Fermi, Microscopie à force atomique, Mesures électromécaniques IX Résumé en français ......................................................................................................... --Chapter IV Générateurs piézoélectrique à base de nanofils semi-conducteurs : simulations et études expérimentales ............................................................................ --IV.1 De l'effet piézoéléctrique aux nanogénérateurs ............................................ --IV.2 Étude analytique et modélisation de Nanofils et Nanogénérateurs piézoélectriques ........................................................................................................ --IV.3 Caractérisation électromécanique de Nanofils et de Nanogenerators piézoélectriques ........................................................................................................ --IV.4 Conclusions and perspectives ......................................................................... --

Figure I

 I Figure I Number of publications on "piezoelectric nanowires" and "piezoelectric nanogenerators" in Google Scholar between years 2006 and 2015.

Figure

  Figure II Researches and activities of the thesis.

Figure 1 . 1

 11 Figure 1.1 Schematic of an autonomous system.

Figure 1 . 2

 12 Figure 1.2 Chart of photovoltaic cell development from 1975 to 2015. [36]

Figure 1 . 3

 13 Figure 1.3 The four fundamental modes of TENGs: (a) vertical contact-separation mode; (b) in-plane contact-sliding mode; (c) single-electrode mode; and (d) freestanding triboelectric-layer mode. [54]

Figure 1 . 4

 14 Figure 1.4 Simple molecular model for explaining the piezoelectric effect: (a) unperturbed molecule; molecule subjected to (b) a compressive stress, and (c) a tensile stress. (adapted from [64])

Figure 1 . 5

 15 Figure 1.5 Classification of crystals showing the classes with piezoelectric, pyroelectric, and ferroelectric effects.

Figure 1 . 6

 16 Figure 1.6 (a) Design of a SWG on a flexible substrate.The piezoelectric fine wire lies on a polymer (Kapton) substrate, with both ends tightly bonded to the substrate and outlet interconnects. Mechanical bending of the substrate creates tensile strain and a corresponding piezoelectric potential in the wire, driving electrons through the external load.[START_REF] Yang | Power generation with laterally packaged piezoelectric fine wires[END_REF] (b) Scheme of LING with demonstration of the output scaling-up when mechanical deformation is induced, where the "±" signs indicate the polarity of the local piezoelectric potential created in the NWs.[START_REF] Zhu | Flexible high-output nanogenerator based on lateral ZnO nanowire array[END_REF]

Figure 1 . 7

 17 Figure 1.7 (a) Schematic view of the PZT nanofiber generator. (b) Voltage output measured when a small Teflon stack was used to impart an impulsive load on the top of the PZT nanofiber generator. The inset in (b) shows the schematic of a Teflon stack tapping on the NG. [70] (c) Illustration of a flexible energy harvesting device, composed of a Kapton plastic substrate, PZT nanoribbons, and patterned interdigitated electrodes. Measured (d) open-circuit voltage and (e) short-circuit current as a function of tapping frequencies. [71]

Figure 1 . 8

 18 Figure 1.8 NG composed of a five-layer flexible plate with PMMA surrounded ZnO NWs grown vertically on both sides of a polymer substrate and electrodes deposited on both top and bottom of the plate. [74]

Figure 1 . 9

 19 Figure 1.9 (a) Scheme of the super-flexible NG based on ZnO NWs with AAO as an insulating layer. (b) Cross section SEM image of the super-flexible (c) NG. Super-flexible NG as an active sensor for detecting the motion of a human eye ball. The NG attached a right eyelid was driven by moving the eye ball from right (R), center (C), and to left (L) or from L, C, and R. Output voltage measured under (d) slow and (e) rapid eye movement. [9]

Figure 1 . 10

 110 Figure 1.10 Potential distribution in a bent NW as a result of the piezoelectric effect.

Figure 1 .

 1 Figure 1.11 ZnO NW-based PENGs. (a) Schematic diagram showing the design and structure of the NG. (b) Cross-section SEM image of the NG showing the integration of aligned NWs and the top electrode.Inset shows an NW that is forced by the electrode to bend.[START_REF] Wang | Direct-current nanogenerator driven by ultrasonic waves[END_REF]

Figure 1 .

 1 Figure 1.12 (a) schematic showing the modulation and (b) SEM top view image of a force sensitive pixel based on individual ZnO NW. Adapted from[START_REF] Perez | Matrice de nanofils piézoélectriques interconnectés pour des applications capteur haute résolution : défis et solutions technologiques[END_REF]

Fig. 1 .Figure 1 .

 11 Figure 1.13 (a) Principle of the PE-FET, in which the piezoelectric potential across the NW created by the bending force F replaces the gate in a conventional FET. The contacts at both ends are conductive. [86] (b) Corresponding I-V characteristics of the ZnO NW for different bending cases. This is the I-V curve of the PE-FET. [2] (c) The principle of the piezoelectric gated diode, in which one end is fixed and enclosed by a metal electrode, and the other end is bent by a moving metal tip. Both have Ohmic contact with ZnO. The piezoelectric potentialat the tensile surface acts like the p-n junction in a conventional diode.[86] (d) The sequence of SEM images of the ZnO NW at various bending angles and the corresponding I -V characteristics.[START_REF] He | Piezoelectric Gated Diode of a Single ZnO Nanowire[END_REF]

  [e] is the piezoelectric coefficient with the form, 51 ± 0.04 ⁄ , = 1.22 ± 0.04 ⁄ , = -0.45 ± 0.02 ⁄ are measured for ZnO thin film[START_REF] Carlotti | Acoustic investigation of the elastic properties of ZnO films[END_REF]. [κ] is the dielectric constant, are values of bulk ZnO

Figure 2 .

 2 Figure 2.1 (a) Dependence of the total polarization (C/m2) on strain in the range -0.08 to +0.08 according to the classic linear model (LM) and nonlinear (quadratic) model (NLM). (b) Variation of the polarization (C/m2) in a cross-section of a ZnO NW. The perpendicular (parallel) strain varied from -2.8% (+2.8%) to +2.8% (-2.8%). The calculated polarization of the NLM is on the left half and the LM on the right. [102]

2

 2 Schematic of cylindrical NW under (a) bending and (b) compression.

Figure 2 . 3

 23 Figure 2.3 Effect of the size scaling down of a ZnO cantilever in terms of axial strain, axial deformation and stiffness under fixed lateral force (80 nN). The reference NW (scaling factor a = 1) features r = 25 nm and L = 600 nm).[START_REF] Hinchet | Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration[END_REF]

Figure 2 . 4

 24 Figure 2.4 (a) Young's modulus of wurtzite ZnO NWs obtained by full ab initio calculations and continuum model. [112] (b) Young's modulus of the pristine and H-passivated ZnO NWs as a function of the diameter.The inset is the equilibrium axial lattice constant L 0 (% strain from bulk) of two kinds of NWs as a function of the diameter.[START_REF] Qi | Different mechanical properties of the pristine and hydrogen passivated ZnO nanowires[END_REF]

Figure 2 . 5

 25 Figure 2.5 (a) side and (b) cross-sectional piezoelectric potential distribution for a ZnO NW with diameter of 50 nm and length of 600 nm at a lateral bending force of 80 nN. [120]

Figure 2 . 6

 26 Figure 2.6 (a) Configurations of electrodes: top-total (TT), bottom left (BL), bottom right (BR), bottom total (BT), bottom center (BC) and top-center (TC) contacts.[122] (b) Viewand schematic of a cylindrical NW (radius 150 nm and length 2 µm) surrounded by free space and subject to compressive force.[START_REF] Araneo | Piezo-semiconductive quasi-1D nanodevices with or without anti-symmetry[END_REF] (c) Piezopotential along the entire axis of the NW with floating and grounded base.[START_REF] Araneo | Piezo-semiconductive quasi-1D nanodevices with or without anti-symmetry[END_REF]

Figure 2 . 7

 27 Figure 2.7 (a) Schematics of contact design for a sensor. (b) Piezopotential varies with the bending force in the linear and nonlinear cases.In bottom contact configuration, the potential increases following a linear law (a = 7.3×10 6 V/N), whereas in the "top-bottom" contact case, ∆V=bF+cF 2 with b = 7.5±0.1×10 6 V/N and c = 3×10 13 V/N 2 .[START_REF] Hinchet | Scaling rules of piezoelectric nanowires in view of sensor and energy harvester integration[END_REF]

Figure 2 . 8

 28 Figure 2.8 (a) Schematics of the force-displacement sensing device pixel based on a vertical piezoelectric ZnO NW with contact (δ = 0) and non-contact (δ 0) electrode placement. (b) Potential distribution in the pixel for a 124 nm top displacement (F = 80 nN). Impact of NW-electrode distance and electrode thickness is presented.[START_REF] Perez | Static finite element modeling for sensor design and processing of an individually contacted laterally bent piezoelectric nanowire[END_REF]

Figure 2 . 9

 29 Figure 2.9 Schematic model showing (a) the conical NWs based LING device and (b) the setup for measuring the energy conversion. The conical NWs are under compressive strain during the deformation. (c) The unit cell and model used for calculating the potential distribution across the top and bottom electrodes of the NG with the presence of a pair of conical NWs. The corresponding cross sections, at which the potential distributions were exhibited, are indicated by dashed lines. The results are shown in (d) and (e), respectively.(f) Cross section output potential induced by perfect cylindrical NWs (e.g., zero conical angle).[START_REF] Hu | High-Output Nanogenerator by Rational Unipolar Assembly of Conical Nanowires and Its Application for Driving a Small Liquid Crystal Display[END_REF]

Figure 2 .

 2 Figure 2.10 (a) Structure of the VING before and after vertical compression. (d=thickness). Structure and dimensions of the NG cell in the reference case. The applied pressure is 1 MPa. (b) Diagram of the VING working principle.The yield (η) has been calculated for each step using the parameters of (a). d x , E x and ε x are the thickness, Young modulus and dielectric constant of layer x. Index eq indicates that the corresponding layer is modeled as a uniform equivalent medium. T is the stress and e 33 the piezoelectric coefficient relevant to this strain configuration.[START_REF] Hinchet | Design and guideline rules for the performance improvement of vertically integrated nanogenerator[END_REF]

Figure 2 .

 2 Figure 2.11 (a) FEM simulation of the distribution of the electric potential generated by 15 cells × 15 cells NG matrix embedded with PMMA and Si 3 N 4 , surrounded by air and strained under 1 MPa. (b) Difference of electric potential generated at the top electrode by a NG surrounded by air as a function of the NG matrix size. (c) Schematics of different NG structures using various materials and NWs densities. (d) Electric potential, and (e) electric energy of a NG core cell using different top insulating materials, function of the NWs density as the ratio parameter, also compared with a thin ZnO layer. Reprinted with permission [5].

Figure 2 . 12 FEM

 212 Figure 2.12 FEM Simulation results for a VING individual composite cell as a function of the inclination angle to the vertical axis. A single ZnO NW is integrated inside the individual cell. (a) Absolute value of the piezoelectric potential generated. (b) Electric potential (mV) inside an individual cell taking into account the c-axis correction and (c) neglecting the c-axis correction.[START_REF] Tao | Will composite nanomaterials replace piezoelectric thin films for energy transduction applications? Future Trends in Microelectronics: Journey into the Unknown[END_REF]

Figure 2 .

 2 Figure 2.13 FEM simulations results of a single VING cell with 2 NWs with inclination angles on the xz plane: a) Displacement (nm) of one cell under compression including one vertical NW and one NW inclined at an angle of 11°. b) Electric potential at the top electrode of a single cell in function of the inclination angle to the vertical axis of one NW. c) Displacement (nm) of one cell under compression composed of one vertical NW and one NW inclined at an angle of 11° on the yz plane. [129]

  ZnO NWs in function of different sets of inclinations angles (lower than 12°) to the vertical axis. [129] NWs inclination conditions (<12°) Electric potential (mV) Ideal condition (vertical NWs) 68.9 Inclination towards the outside of the cell (different angles) 63.5 Inclination towards the middle of the cell(same angles) 68.3 Inclination towards the same side of the cell(small different angles) 69.5 Inclination towards the same side of the cell(same angles) 69 Inclination towards the same side of the cell(large different angles) 62.3 Inclination towards the outside of the cell(same small angles) 69.4 Inclination towards the outside of the cell(same large angles) 57 c. Individual VING composite cell including 4 NWs. In the case of 4 inclined NWs inside a composite cell, 4 different cases are simulated with inclination angles below 12° (see Fig. 2.14). The obtained potentials at the top electrode are presented in the same Figure. In this case a systematic reduction of the electric potential is observed, ranging from 1 to 13%.

Figure 2 . 14

 214 Figure 2.14 Results of the deformation (nm) of the individual cell with 4 ZnO NWs representing the different conditions of the simulations (with sets of inclinations angles lower than 12° to the vertical axis). The electric potential (absolute value) at the top electrode is presented for each condition. The simulated electric potential for the ideal condition with vertical NWs is 68.9mV for comparison. [129]

Figure 2 .

 2 Figure 2.15 FEM simulations results of the displacement (nm) of different single cells under compression with inclination angles below 12°. The electric potential (absolute value) at the top electrode is presented for each simulation: a) single cell composed of 36 ZnO NWs, b) single cell composed of 64 ZnO NWs.[START_REF] Tao | Will composite nanomaterials replace piezoelectric thin films for energy transduction applications? Future Trends in Microelectronics: Journey into the Unknown[END_REF]

Figure 2 .

 2 Figure 2.16 (a) Diameter dependence of the dielectric constant in the single pencil-like ZnO NW: (blue dot) experimental results, (red solid line) fitted results by core-shell composite NW model, and (green dashed line) dielectric constant of bulk ZnO. [130] (b)Frequency dependence of piezoelectric coefficient of ZnO nanobelt, bulk (0001) ZnO, and x-cut quartz. Only the piezoelectric coefficient of ZnO nanobelt is frequency dependent.[7]

Figure 2 . 17

 217 Figure 2.17 Scheme of (a) a composite piezoelectric material vertically integrated on a metallic substrate and (b) the NG cell in compression mode.

Figure 2 .

 2 Figure 2.18 (a) Absolute value of potential, (b) surface density of elastic strain energy, (c) surface density of electric energy of NG cells working in compression mode using ZnO thin film properties, nano dielectric, piezoelectric constants and NW properties combining nano dielectric and piezoelectric constants, respectively. Results using a ZnO thin layer were calculated as reference.

Figure 2 .

 2 Figure 2.19 (a) Scheme of VING plate working under bending. [131] (b) Cross-section view of the VING structure. (c) Scheme of NG cell when the device is working under bending. [131]

11 Figure 2 . 20

 11220 Figure 2.20 Schematic of energy transfer process within a NG cell at the center of a bending VING plate. (a) Mechanical energy transferred into ZnO NW. (b) Mechanical energy stored in the NW converted into electrical energy due to the piezoelectric effect. (c) Electrical energy transfer to the output circuit.

Figure 2 . 21

 221 Figure 2.21 Absolute value of (a) potential, (b) surface density of elastic strain energy, (c) surface density of electric energy and (d) energy conversion ratio of NG cells working in flexion mode using ZnO thin film properties, nano dielectric constant, nano piezoelectric constant and NW properties respectively. Results using a ZnO thin layer were calculated as reference.

Figure 2 . 22

 222 Figure 2.22 Topview map of (a) displacement and (b) strain tensor when PMMA is used. Topview map of (c) displacement and (d) strain tensor when Al 2 O 3 is used.

Fig. 2 .

 2 Fig. 2.23 displays the simulation results of NG cells using PMMA, SiO 2 , Si 3 N 4 , and Al 2 O 3 as matrix material respectively, as well as the comparison with a ZnO thin film. With higher rigidity, SiO 2 , Si 3 N 4 , or Al 2 O 3 matrix enhanced the input strain of the NG cell while the whole NG membrane was still bended by 100 Pa pressure (Fig. 2.23b). With larger relative permittivity, they reduced the energy loss passing through the top insulating layer (Fig. 2.23c).As a result, the potential generated was higher than the thin film starting from a ratio = 0.3 -0.5, and reached a value that was 1.5 -2.5 times larger than the ZnO thin film (Fig.2.23a). Since the improvement was majorly due to the increase of input strain and the

Figure 2 . 23

 223 Figure 2.23 Absolute value of (a) potential, (b) surface density of elastic strain energy, (c) surface density of electric energy and (d) energy conversion ratio of NG cells working in flexion mode using PMMA, SiO 2 , Si 3 N 4 , and Al 2 O 3 as matrix material respectively. Results using a ZnO thin layer were calculated as reference.

Figure 2 .

 2 Figure 2.24 (a) Potential changing trend with the increasing Young's modulus and Poisson's ratio of matrix materials. (b) Potential changing trend with the increasing relative permittivity of matrix materials. [132]

Figure 2 .

 2 Figure 2.25 (a) Deformation and side view of the reference piezoelectric transducer (not in scale) under a pressure of 100 Pa (the deformation is exaggerated in this figure). (b) Surface strain on the active layer of the membrane piezoelectric transducer under a pressure of 100 Pa [133].

Figure 2 .

 2 Figure 2.26 Improved structure integrating a piezoelectric layer in the middle of the membrane (not in scale). a) Structure without a top electrode, b) structure including an electrode on top of the whole membrane, c) structure including an electrode only over the position of the piezoelectric layer.

Figure 2 .

 2 Figure 2.27 Further improvement of the transducer structure. In this case separate layers of piezoelectric materials are integrated in the regions were the strain is negative and positive.

Figure 2 .

 2 Figure 2.28 (a) Simulation results of the basic structure integrating a piezoelectric layer in the middle of the membrane. (b) Simulation results of the potential generated by a side piezoelectric layer. The other two piezoelectric layers where left without electrode to simplify the modeling. The resulting potential of the 3 electrodes can be connected in series in order to boost the electric potential.

Figure 2 .

 2 Figure 2.29 (a) Piezoelectric potential, (b) parameter η, (c) free electron concentration n, and (d) activated donor center concentration N D + cross the NW (R = 25 nm, L = 600 nm)

Figure 2 . 30

 230 Figure2.30 Piezoelectric potential distribution for a 1 × 10 16 cm -3 -doped ZnO NW with R = 150 nm and L = 4 μm pressed by a uniaxial compressive force (along the z axis).[6]

Figure 2 .

 2 Figure 2.31 (a) Scheme of a 2D NG cell model with geometry factors. (b) Piezopotential generated by a 2D NG cell model under compression simulated while the doping concentration of the ZnO NW varies from 10 to 10 .

Figure 2 . 32

 232 Figure 2.32 Scheme of the FLP assumption with (a) energy band diagram, and depletion domain distribution of cylindrical NWs with large and small radius. (b) Depletion width as a function of the donor concentration and the radius of ZnO NWs, calculated with the assumption of mid-gap Fermi level pinning.[START_REF] Mouis | Title Materials Research Society (MRS) Spring Meeting & Exhibit[END_REF]

Figure 2 .

 2 Figure 2.33 Scheme of NG cell model with equivalent surface charge applied to the boundaries as SFLP assumption. Models with FLP on top surface, on side surfaces and on all surfaces will be used in the following simulations.

Figure 2 .

 2 Figure 2.34 Schematic of 2D axisymmetric cylindrical model of the NG cell.

Figure 2 . 35

 235 Figure 2.35 Transformation of NG cell geometry from 3D cuboid model to 2D axisymmetric cylinder model. In the cross section view, (a) the circle is inscribed in the square and (b) the square is inscribed in the circle.

Figure 2 .

 2 Figure 2.36 Comparison of piezopotential generated by 2D axisymmetric NG cell under compression with fixed and free lateral walls (SFLP on all surfaces are applied)

Figure 2 .

 2 Figure 2.37 (a) Schematic of a flexible NG disk with all-clamped edge. Scheme of (b) the central NG cell in a bending device and (c) the strain X distribution on its sidewalls.

Figure 2 . 38

 238 Figure 2.38 Maps of polarization, potential and carrier concentration for NG cell with SFLP (a) on top interface and (b) on all interfaces, containing a NW with a radius of 100 nm and a length of 600 nm. = 5 × 10 .

Figure 2 . 39

 239 Figure 2.39 Piezopotential of NG cell having free Fermi level, FLP on top surface, FLP on lateral surfaces and on all surfaces, with a radius of 100 nm, and a length of (a) 600 nm; (b) 2 μm. = 5 × 10 .

Figure 2 .

 2 Figure 2.40 Piezopotential of NG cell having free Fermi level, FLP on top surface, FLP on lateral surfaces and on all surfaces, with a radius of 25 nm, and a length of 600 nm. = 5 × 10 .

Figure 2 . 41

 241 Figure 2.41 Geometry effect of the NW length on the output of the NG cell. Piezopotential comparison between NW with 600 nm length and 2 μm length in the case of (a) SFLP on top surface and (b) SFLP on all surfaces. = 5 × 10 .

Figure 2 . 42

 242 Figure 2.42 Geometry effect of the NW radius. Piezopotential comparison between NW with 100 nm and 25 nm radius in the case of (a) SFLP on top surface and (b) SFLP on all surfaces.= 5 × 10 .

Figure 2 . 43

 243 Figure 2.43 Variation of the piezopotential in function of the NW radius for N D = 10 17 cm -3 . = 5 × 10 .

Figure 2 . 44

 244 Figure 2.44 Piezopotential generated under compression (1 MPa) by a ZnO thin film cell with top SFLP, a NG cell with SFLP on all surfaces. The NW of the NG cell has a radius of 100 nm, and a length of 2 μm. = 5 × 10 .

II. 4 . 4 . 1 Figure 2 . 45

 441245 Figure 2.45 Piezopotential of NG cell having free Fermi level, FLP on top surface, and on all surfaces, with a radius of 100 nm, and a length of (a) 600 nm; (b) 2 μm. = 5 × 10.

Figure 2 . 46

 246 Figure 2.46 Piezopotential of NG cell in function of the doping concentration when the NW has free Fermi level, SFLP on top surface, and on all surfaces.= 5 × 10 .

Figure 2 . 47

 247 Figure 2.47 Comparison between the piezopotential generated by thin film with FLP effect on top surface, and NG cells with FLP effect on all surfaces in flexion (extensive bending) mode. The NW of the NG cell has R = 100 nm, L = 2 μm and = 5 × 10 .

Figure 2 .

 2 Figure 2.48 Schematics of NG plates under (a) stretching and (b) contractive bending. (c) Non-symmetric performance of the NG under contractive and stretching bending in FEM modeling. = 5 × 10 .

Figure 3 . 1

 31 Figure 3.1 (a) Cross-section view of SEM image showing the VING structure. Image of packaged NG device for working (b) under compression and (c) under flexion.

Figure 3 . 2

 32 Figure 3.2 (a) Schematic showing the experimental setup for the piezoelectric charge detection from an individual BTO NW. Inset shows the SEM image of the suspended NW under test. (b) Acquired output signal from the charge amplifier for a BaTiO 3 NW under a periodic tensile load.[180]

.Figure 3 . 3

 33 Figure 3.3 Schematics showing the setup for probing the 3D piezoelectric tensor of a single c-axis GaN NW. (a) The experimental setup includes an AFM, a function generator, and a lock-in amplifier. (b) Configuration for measuring d 33 and d 13 . The NW is laying on Si substrate with an insulating SiO 2 layer. The NW is clamped at two ends by metals contacts.An AC voltage is applied between these electrodes, resulting in an axial electric field. The long axis of the NW is placed perpendicular to the AFM cantilever. (c) In this configuration the NW is laying on a Si substrate coated with a conductive Au layer. The electric field is applied between the tip of the conductive AFM probe and the grounded substrate. Torsion of the cantilever measures the induced shear strain allowing identification of d 15 .[186]

Figure 3 . 4

 34 Figure 3.4 Direct piezoelectric measurement by lateral bending. (a) The experimental setup, including a high impedance preamplifier, and AFM probe. (b) Measured electric potential from an individual GaN NW vs. applied force.[START_REF] Xu | An improved AFM cross-sectional method for piezoelectric nanostructures properties investigation: application to GaN nanowires[END_REF]

Figure 3 . 5

 35 Figure 3.5 Schematic principle of the Young's modulus measurement conducted using an AFM tip.

Figure 3 . 6

 36 Figure 3.6 (a) 3D schematics and (b) top view SEM image of polycrystalline Si beam based nano-switches. Width a and depth b of the Si beam are marked in the figure.

Figure 3 . 7

 37 Figure 3.7 AFM topographic image of the Si beam. The red arrows marked the position of the applied force.

Figure 3 . 8

 38 Figure 3.8 (a) The deflection of the AFM cantilever varying with the total deflection Z, (b) The deflection of the Si beam varying with the force applied at different positions.

Figure 3 . 9

 39 Figure 3.9 (a) Calculated Young's modulus along the Si beam with error bar. The red dash line presents the assumed correction by considering over-etching in fabrication. (b) Schematics showing geometry of the poly-Si beam when there is over-etching.

Figure 3 .

 3 Figure 3.10 (a) SEM image and (b) 3D AFM topographic image of GaAs NW arrays.

Fig. 3 .

 3 Fig. 3.11a and 3.12a shows the AFM topographic image of two NWs and the positions where the force was applied (red arrows). Similar to Si beam measurement, the effective length L of the different points is defined by the distance between each point and point 0.

Figure 3 .Figure 3 .

 33 Figure 3.11 (a) AFM image of the GaAs NW. The red arrows mark the position of the applied force on the first NW. (b) Deflection of the AFM cantilever varying with the total deflection Z, and (c) deflection of NW No1 varying with the force applied at different positions.

Figure 3 .

 3 Figure 3.13 Young's modulus of GaAs measured at different positions on the NW. Property of bulk GaAs is taken as a reference.

Figure 3 .

 3 Figure 3.14 (a) Photo of the measurement set-up for characterizing individual piezoelectric NWs. (b) The experimental setup, including a high impedance preamplifier, and AFM probe [187].

  barrier of the PtSi-semiconductor NW contact

Figure 3 .

 3 Figure 3.15 (a) SEM image of undoped GaN NWs; (b) AFM topographic image of undoped GaN NWs. The cross symbols mark the positions where bending force is applied.

Figure 3 .

 3 Figure 3.16 (a) Piezopotential generated by bending the GaN NW with a force of 2.3 μN at three positions (point 1, 2 and 3 in Fig. 3.15) along it. The blue curve displays the force applied on the NW and the red curve represents the potential signal acquired by the oscilloscope. (b) The piezopotential generated by bending NW varies with the applied force.

Figure 3 . 17

 317 Figure 3.17(a) and (b) AFM topographic images of two ultra-long GaAs NWs with cross marks where the bending force is applied. (c) and (d) Piezoelectric response of GaAs NWs. The blue curve describes the force applied on the NW and the red curve represents the potential signal acquired by the oscilloscope.

  Figure 3.17(a) and (b) AFM topographic images of two ultra-long GaAs NWs with cross marks where the bending force is applied. (c) and (d) Piezoelectric response of GaAs NWs. The blue curve describes the force applied on the NW and the red curve represents the potential signal acquired by the oscilloscope.

Figure 3 .Figure 3 .

 33 Figure 3.18 (a) Relationship between the maximum efficient deflection and the bending force. (b) Piezopotential generated by the bending of the NW varies with the efficient deflection/ applied force.

Figure 3 . 20

 320 Figure 3.20 Analysis of the comparison between ZnO NW and ZnO/PZT NW. (a) Cantilever deflection increases linearly with the total deflection which is controlled by a ramp plot. (b) NW deflection is proportional to the bending force. Piezopotential varies with (c) NW deflection and (d) bending force.

Figure 3 .

 3 Figure 3.21 SEM cross-section view images of (a) ZnO NW arrays and (b) ZnO/BTO core-shell NW arrays. AFM topographic images of (c) ZnO NWs and (d) ZnO/BTO core-shell NWs with cross symbols marking where the bending force is applied. Piezoelectric response of (e) ZnO NWs and (f) ZnO/BTO core-shell NWs. The blue curve describes the force applied on the NW and the red curve represents the potential signal acquired by the oscilloscope.

Figure 3 . 22

 322 Figure 3.22 Analysis of the comparison between ZnO NW and ZnO/BTO NW. (a) Cantilever deflection increases linearly with the total deflection which is controlled by a ramp plot. (b) NW deflection is proportional to the bending force. Piezopotential varies with (c) NW deflection and (d) bending force.

Figure 3 . 23

 323 Figure 3.23 Piezoelectric response of ZnO/BTO NW under ramp bending force of (a) 320 nN and (b) 250 nN.

Figure 3 .

 3 Figure 3.24 AFM topographic images of ZnO NWs for periodic bending (a) at one fixed point and (b) at several points along the NW with white symbols marking where the bending force is applied. (c) Piezoelectric response of ZnO NW shown in (a). (d) Piezoelectric response of ZnO NW shown in (b).

Figure 3 . 25

 325 Fig.3.25 synthesizes all the results shown in previous measurements and compares the piezoelectric response of different NWs. GaN, GaAs and ZnO NWs were compared in Fig.3.25a. ZnO NWs with a cylindrical cross section came from Institut des Nanotechnologies de Lyon, cited as ZnO cylindrical. ZnO NWs with hexagonal cross section were fabricated in our group, later cited as ZnO hexagonal. Apparently, the ZnO NWs generated higher potential than GaN and GaAs NWs. The threshold of these potential curves was related to the Schottky barrier height of the NW-PtSi contacts and the piezoelectric coefficients. The higher the barrier was, the larger was the threshold. Correspondingly, the piezoelectric behavior of ZnO-based NWs were also modified by depositing different shells, and even by the NW morphology (Fig.3.25b).

Figure 3 . 26

 326 Figure 3.26 Effective piezoelectric coefficients of different NWs.

Fig. 3 Figure 3 . 27 Figure 3 .Figure 3 .Fig. 3 .

 3327333 Fig.3.27 presents the measurement set-up that we developed to measure the output potential of rigid NGs under compression. The main components are the actuator, the sample holder, the force load and the force sensor (Fig.3.27a). The sample holder is supported and moved by a PC-controlled linear actuator, whose position can be adjusted in three directions (x, y and z) manually. Above the sample holder, there is a ceramic rod acting as the force load to apply pressure on the sample during the measurement. The ceramic rod is in contact with a force sensor, which measures the force applied between the rod and the sample holder (or the sample on it). The electrodes of the sample connect to the voltage, current and charge preamplifiers via a transmission unit. Then the output electrical signal of the preamplifier is converted into a digital signal by an analog to digital converter (ADC) which is connected to a PC. Besides, two softwares based on Labview platform were developed to control the actuator and to acquire the force and voltage signals (Fig.3.27b).

Figure 3 . 30

 330 Figure 3.30 Typical piezoelectric response of NGs to periodic compressing/releasing force. (a) The compressing signal is larger due to the force overshoot. (b) Typical shape of the electrical signal pulse obtained after load release.

Figure 3 . 31

 331 Figure 3.31 Potential influenced by the top PMMA insulating layer as the NG is compressed by a force of 1.5 N.

Figure 3 .

 3 Figure 3.32 (a) Schematic representation and equivalent electrical circuit of a VING. [205] (b) Potential generated by one force pulse decaying exponentially with time. The inset presents the RC time constant.

Figure 3 . 33

 333 Figure 3.33 Electromechanical measurement set-up under controlled temperature (a) Image of main components including the actuator, sample holder, force sensor, thermoelectric generator module (Peltier generator) and temperature sensor installed above the metallic holder. (b) Image of set-up to characterize rigid NGs under compression with temperature control system.

Figure 3 .

 3 Figure 3.34 (a) Schematics of the temperature control system. (b) Schematic of integrating the Peltier module into the sample holder.

Figure 3 .

 3 Figure 3.35 (a) Schematic of the process within one thermal cycle. (b) Open circuit potential generated by NG No4 at room temperature before and after each thermal cycles.

Figure 3 .

 3 Figure 3.36 (a) Open circuit voltage generated by NG No4 at each temperature step during the first thermal cycle. (b) Open circuit voltage improved by the temperature increase of NG In29A in the first cycle.

Figure 3 .

 3 Figure 3.37 (a) Potential and (b) instantaneous power generated by the NG device at room temperature, 70℃ and after cooling down within one thermal cycle.

Figure 3 .

 3 Figure 3.38 Potential, instantaneous power and power density generated by (a) ZnO NW based NG (NG No4) and (b) reference PZT commercial disk vary with the electric load

Figure 3 . 39

 339 Figure 3.39 Schematics of flexible NGs bent (a) by the airflow and (b) manually. Voltage signal acquired by the oscilloscope of flexible NGs bent (c) by the airflow and (d) by hands.

Figure 3 .

 3 Figure 3.40 (a) Potential generated by NGs varies with the thickness of the top layer. (b) Potential generated by flexible NGs with PMMA matrix and top insulating layers. NGs consist of NWs grown under the same conditions, but with different PMMA deposition process.

Figure 3 . 41

 341 Figure 3.41 Potential generated by flexible NGs with (a) Al 2 O 3 and (b) Si 3 N 4 matrix.

Figure 3 .Figure 3 .

 33 Figure 3.42 Flexible NG in the characterization bent (a) downwards (contractive bending) and (b) upwards (stretching bending), respectively.

3

 3

Figure 3 .

 3 Figure 3.44 (a) Potential of reference device without ZnO NWs, bent manually. (b) Piezopotential of VING device bent manually with quick deformation.

Figure I. 2

 2 Figure I.2 (a) Continuous quantity approximated by typical elements and nodes. (b) Function (solid blue line) approximated with (dashed red line), which is a linear combination of linear basis functions ( is represented by the solid black lines). The coefficients are denoted by through .

  Figure II.1 (a) Schematic diagram illustrating the fabrication processes of the ZnO NW device based on NSL: 1) thermal SiO 2 deposition, 2) α-carbon deposition (etch-stop layer), 3) PECVD of SiO 2 (sacrificial layer), 4) sacrificial layer patterning, 5) ZnO ALD, 6) top view after ZnO plasma etching, 7) sacrificial layer removal, and 8) ZnO NW device after metal electrode deposition. (b) Field-emission SEM image of ZnO NW arrays fabricated by NSL. The width and height of the ZnO NW were 70 and 100 nm, respectively. [241]

Figure

  Figure II.2 (a) Schematic of ICP-RIE instruments. (b) SEM image of GaAs NW arrays etched by ICP-RIE with Ni as the mask with Cl 2 :N 2 of 8:1, at 5 mTorr, 60 -500 W of RF platen and source powers, respectively [248]. (c) Schematic illustration of GaN-based nanorod LEDs' process: using Ni/Si 3 N 4 as nano-masks formation. The reaction products after RTA and ICP-RIE etching, leading to the formation of GaN-based nanorod LEDs. (d) SEM image of GaN-based nanorod LEDs samples made by etching at fixed the RTA temperature 850 ℃, annealing time 1 min, Cl 2 /Ar flow rate of 50/20 sccm, ICP/Bias power of 400/100W, and chamber pressure of 0.67Pa for 3 min of etching time [250].

Figure II. 3

 3 Figure II.3 Schematic representation of the four basic NW growth mechanisms: (a) Selective area epitaxy. An epitaxial layer nucleates in openings of a mask layer and continuously grows in height. Its lateral growth is restricted by low-energy facets. (b)Oxide-assisted growth. The semiconductor and its oxide are adsorbed on the surface, creating nucleation centers which separate into a semiconductor core and a passivating oxide shell. (c) Homo-particle growth. A seed particle is formed consisting of one or all elements used for wire growth. During growth both length and diameter increase as the seed particle size is variable. (d) Hetero-particle growth. A seed particle (typically Au) is deposited prior to growth. During heating to growth temperature the seed particle alloys with the substrate and/or material from the gas phase. Particle size during growth is nearly constant[START_REF] Mandl | Growth mechanism of self-catalyzed group III-V nanowires[END_REF].

Figure II. 4

 4 Figure II.4 Schematic representation of high-density NW fabrication in a polymer matrix.(a) An asymmetric diblock copolymer annealed above the glass transition temperature of the copolymer between two electrodes under an applied electric field, forming a hexagonal array of cylinders oriented normal to the film surface. (b) After removal of the minor component, a nanoporous film is formed. (c) By electro-deposition, NWs can be grown in the porous template, forming an array of NWs in a polymer matrix.[START_REF] Thurn-Albrecht | Ultrahigh-density nanowire arrays grown in self-assembled diblock copolymer templates[END_REF]

Figure II. 5

 5 Figure II.5 (a) Scheme presenting the growth procedure of ZnO NW arrays by CBD method. (b) Specimen fixed on a glass holder with four edges covered by kapton tape. (c) Specimen tilted face down in the precursor solution.

Figure II. 6 Figure II. 8 Figure II. 9 Figure II. 10 FigureFigure

 68910 Figure II.6 (a) Schematics of basic reaction principle of ALD process. (b) Image of ALD instruments.

  b. Thickness control Currently, we are not able to measure the thickness of the top PMMA layer without damaging the sample. However, based on the experimental-theoretical combination diagram (Fig. II.14), we can estimate the thickness as listed in Table 3.1.

Figure II. 14

 14 Figure II.14 Experimental-theoretical combination diagram of the dependence of the thickness on the spin speed for A6 resist.

Al 2 O

 2 3 thin film was deposited by ALD using water and Tri Methyl Aluminum (TMA) () as precursors, which may be employed for the controlled deposition using the two-half reactions:[START_REF] Dillon | Surface chemistry of Al2O3 deposition using Al(CH3)3 and H2O in a binary reaction sequence[END_REF]281] mechanisms are summarized in Fig. II.15. Theoretically, the thickness of the film per deposition cycle should be typically 1 monolayer, in this case, 0.18 nm per cycle.

Figure II. 15

 15 Figure II.15 Mechanisms for the surface chemistry of Al 2 O 3 controlled deposition using TMA and H 2 O in a binary reaction sequence.[START_REF] Dillon | Surface chemistry of Al2O3 deposition using Al(CH3)3 and H2O in a binary reaction sequence[END_REF]

Figure II. 16

 16 Figure II.16 Top-view SEM images of ZnO NWs embedded into Al 2 O 3 matrix and top insulating layer with a thickness of (a) 0 nm, (b) 15 nm, (c) 50 nm, (d) 140 nm, (e) 205 nm, and (f) 310 nm.

Figure III. 1

 1 Figure III.1 Schematic of the structure and feedback system of AFM, presenting the working principle.

Figure III. 2

 2 Figure III.2 SEM image of the AFM tip with (a) PtIr5 coating and (b) PtSi coating.

Figure 4 . 1

 41 Figure 4.1 Potentiel (en valeur absolue) généré par des cellules NG fonctionnant (a) en compression et (b) en flexion. Les matériaux de matrice sont PMMA, SiO 2 , Si 3 N 4 et Al 2 O 3 respectivement. Les résultats obtenus avec une couche mince de ZnO sont indiques pour référence. (c) Optimisation de la configuration du VING en modes compression et flexion.

Figure 4 . 2

 42 Figure 4.2 Cartes de polarisation, potentiel et concentration de porteurs pour les cellules NG avec SFLP sur toutes les interfaces. Nit = 5  10 11 cm -2 V -1 . Le rayon du NF est de 100 nm et la longueur est de 600 nm. Le matériau de la matrice est le PMMA.

Figure 4 . 3

 43 Figure 4.3 (a) Vue en coupe de l'image MEB montrant la structure du VING. Image du dispositif NG finale pour travailler (b) en compression et (c) en flexion.

Figure 4 . 4

 44 Figure 4.4 (a) Principe de fonctionnement du système de caractérisation électromécanique des NFs piézoélectriques individuels. (b) Images topographiques AFM des NFs ZnO. (c) Réponse piézoélectrique des NFs ZnO.

Figure 4 . 5

 45 Figure 4.5 (a) Réponse piézoélectrique typique de VING sous compression. (b) Potentiel de circuit ouvert généré par un VING à température ambiante avant et après chaque cycle thermique.

Figure 4 . 6

 46 Figure 4.6 Potentiel de sortie de VING sous flexion manuelle composée d'un effet capacitif et d'une réponse piézoélectrique.

Table 1 . 1

 11 Characteristics of common energy-harvesting transducers (adapted from Yildiz et al.

	[27])

Table 1 . 2

 12 Mechanical energy available from the ambient environment and human activities Inspired by the recent observation of superior material properties of nanostructures, eletromechanical transducers based on NWs and nanosheets are developed to meet the need of miniature autonomous systems with high integration. The concept of Nanogenerator (NG) technology was first introduced by Wang et al. in 2006 as they fabricated a NG based on piezoelectric effect

		Energy source	Order of magnitude of potential power density ( ⁄ )
		Washing machine	58
	Mechanical	Microwave oven	23
	vibration	External windows	2.8
		Refrigerator	0.35
		Human motion	10 ~ 10 3
		Airflow	~ 10 2
		Acoustic noise	~ 0.1

Table 1 . 3

 13 Comparison of mechanical energy harvesting techniques (adapted from[START_REF] Yildiz | Potential Ambient Energy-Harvesting Sources and Techniques[END_REF])

		Complexity of process	Energy density	Current size	Problems
							Very high voltage and
	Electrostatic Low	4	⁄		Integrated	need of adding charge
							source
	Electro-magnetic	Very high	24.8	⁄		macro	Very low output voltage
	Piezoelectric High	35.4	⁄		macro	Low output voltage
	TENG	In the lab	31.2	⁄	[55]	Integrated/ macro	high output voltage but low output current, durability problem
	PENG	In the lab	33	⁄	[62]	Integrated/ macro	Low output voltage, stability problem
	I.3 Fundamentals of piezoelectricity

I.3.1 What is piezoelectricity?

Table 2 .

 2

	1 Effective first-principles piezoelectric parameter	(in C/m 2 ) of ZnO NW, with
				different diameters (in nm).
	Atoms Diameter (nm)	12 0.3	48	108	192 →	300	432	588 3.9 bulk ∞	Refs.
		LDA	4.83 4.39 4.49 4.74 4.68			3.47 [114]
	Functionals	PWGGA 1 CRYSTAL	4.78 4.07						3.99 [117]
		RPBE	50.4 18.1						1.18	[8]
		PWGGA		7.32 3.96 3.12 2.82 2.50 2.36 1.70 [118]
	Table 2.2 Effective first-principles piezoelectric parameter	(in C/m 2 ) of GaN NW, with
				different diameters (in nm).
	Atoms Diameter (nm)	12 0.3	48	108	192 →	300	432	588 3.8	∞ bulk	Refs.
		PSP 2 1	51.0 23.3						0.255 [8]
	Functionals	PSP2 PBE0	25.8	7.6 6.00 3.13 2.36				0.554 [8] 1.15 [118]
		PWGGA		5.30 2.70 2.03 1.72 1.54 1.43 0.94 [118]
	Table 2.3 Effective first-principles piezoelectric parameter	(in C/m 2 ) of AlN NW, with
				different diameters (in nm).
	Atoms Diameter (nm)	12 0.3	48	108	192 →	300 432 588 3.8	∞ bulk	Refs.
		PWGGA 8.53 5.14 4.59 4.63				4.19 [117]
	Functionals	PBE PBE0	8.66 5.17 9.15 4.87 3.73				4.24 [117] 1.86 [118]
		PWGGA		8.69 4.62 3.53 3.03 2.75 2.57 1.73 [118]

Table 2 . 5

 25 Mechanical and electrical parameters of different matrix materials.

		PMMA	SiO 2	Si 3 N 4	Al 2 O 3
	Young's modulus (GPa)	3	73.1	250	400
	Poisson's ratio	0.40	0.17	0.23	0.22
	Relative permittivity	3.0	2.09	9.7	5.7

II.2.2.2 VING working under compressive pressure (intrinsic ZnO NWs)

Table 3 . 1

 31 Young's modulus E and dielectric constant / of GaN, GaAs, ZnO, BTO and PZT materials. Data is taken form thin film measurement.

	Material			GaN	GaAs	ZnO		BTO	PZT
	E (GPa)			181 [198]	85.5 [192]	129	128 [199]	125-190 [200]
	/				9.5 [201]	13.1 [192]	7.77 950-1200 [202,203] 650 [204]
	Table 3.2 Effective Young's modulus	, effective dielectric constant	/ , radius
	R, factor * , effective piezoelectric coefficient		and force threshold	of GaN,
	GaAs, ZnO, ZnO/BTO and ZnO/PZT NWs.	and	are deduced from Table 3.1
						with linear combination.
		NWs		GaN GaAs	ZnO Cylindrical	ZnO Hexagonal	ZnO/BTO ZnO/PZT
	E eff (GPa)		181	85.5	129		129		128	146
		/			9.5	13.1	7.77		7.77		714	289
	R (nm)		54	118	109		116		142	143
	* (	•	⁄	•	) 3.50	2.53	2.92		2.74		0.03	0.06
	e eff ( ⁄ )	0.004	0.01	0.085		0.236		9.572	5.076
		(nN)		420	54	80		80		200	150
	Fig. 3.26 plots	of Table

Table 3 . 3

 33 Distribution of potential generated by NGs with different geometry ratio according to the top layer thickness and applied force.

	Series number	PMMA thickness (μm)	Potential (mV)	Precursor concentration (mM)	Force (N)
	In28B	0.5	20.7	30	1.5
	In29A	1	26.1	30	1.5
	In24A	1	37.0	30	3
	In24B	1.2	61.6	30	3
	In19B	1.3	10.9	30	3
	In27A	1.2	21.0	50	6
	In27D	1.8	12.1	50	6
	In26C	1.8	11.7	50	1.5

Table 3 . 4

 34 Piezoelectric constant, geometry parameters and power density of PZT device and NG No4

	Sample	d 33 (pC/N)	t (μm)	A (cm 2 )	P (nW)	P/t (μW/cm)	P/A (μW/cm 2 )	P d (μW/cm 3 )
	PZT	400	250	3.14	2000	80	0.64	25
	VING	9.93	1.5	1	13	93	0.014	85

Table II .

 II 1 VING samples with different PMMA deposition speeds. Estimated and measured thickness is listed. The acceleration time is 9 s, and the spin time is 60 s. The substrates are Si wafer, unless otherwise illustrated.

	Sample reference	A2 (rpm) 750	1000	A6 (rpm) 900 850	750	Estimated thickness (μm)	Growth concentration (mM)
	In028B	x2	x1			0.5
	In029A	x2	x2			1
	In024A	x2	x2			1
	In024B	x2		x2		1.2
	In027A	x2		x2		1.2
	In027D	x4		x3		1.8
	In026C	x2		x3		1.8
	In031A	x2	x2			1
	In032A	x2	x3			1.5
	In035A	x4	x4			2
	In020B	x4		x4		2.4
						Measured
						thickness
						(μm)
	In026B	x4		x2		1.2
	In019B	x2		x2		1.3
	In018B	x2			x2	1.5
	AII.3.2.2 Al 2 O 3 deposition with ALD method
	a. Deposition mechanism

Exchanged functionals of Crystal software: Perdew-Wang'91 (PWGGA)

Pseudopotentials (PSP) functional

Acknowledgements

Xavier Mescot, Martine Gri, Antoine Gachon, Corinne Perret

Appendix I: Tools for Computational Modeling  First principle calculation method First principle approach is a way to study the ground-state properties and excitation spectrum of a multiple-electron system, by searching eigenfunctions and eigenvalues of the Hamiltonian with a parameter-free approximation. Generally, the first-principles approach is suitable to small molecules without any adjustable parameters. However, severe approximations have to be induced to solve it for the problem with many electrons. The most successful first-principles method is the density functional theory (DFT) within the local (spin-) density approximation (L(S)DA) [START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF]210], where the multiple-body problem is mapped into a non-interacting system with a one-electron exchange-correlation potential which is approximated by that of the homogeneous electron gas. LDA has proved to be very efficient for extended systems, such as large molecules and solids.

Recently, many researchers have access to the possibility of predicting ferroelectric and piezoelectric behavior of solids by first-principles techniques. A number of diverse bulk properties, elastic constants, polarization, and piezoelectric constants of the zinc-blende (ZB) and wurtzite (WZ) III-V nitrides AlN, GaN, and InN, are predicted from first principles within DFT using the plane-wave ultra-soft pseudopotential method, within both LDA and generalized gradient approximation (GGA) to the exchange-correlation functional [211]. Then the complete piezoelectric tensors of both the ZB and WZ polymorphs of ZnO and ZnS have been computed by ab initio periodic linear combination of atomic orbitals (LCAO) and DFT methods [START_REF] Catti | Full piezoelectric tensors of wurtzite and zinc blende ZnO and ZnS by first-principles calculations[END_REF]212]. Later the first principles studies approach to III-V and II-VI NW structures using hexagonal atom positions similar to the model shown in Fig. I.1 [8,[START_REF] Xiang | Piezoelectricity in ZnO nanowires: A first-principles study[END_REF][START_REF] Mitrushchenkov | Piezoelectric Properties of AlN , ZnO , and Hg x Zn 1 -x O Nanowires by First-Principles Calculations[END_REF][START_REF] Hoang | First-principles based multiscale model of piezoelectric nanowires with surface effects[END_REF][START_REF] Zhao | First-principles calculations of AlN nanowires and nanotubes: atomic structures, energetics, and surface states[END_REF].  Molecular dynamics modeling Molecular dynamics (MD) modeling is concerned with the description of the atomic and molecular interactions that govern microscopic and macroscopic behaviors of physical systems. The atoms and molecules interact for a fixed period of time to give a view of the dynamical evolution of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are calculated using interatomic potentials or molecular mechanics force fields. MD Appendix II: Fabrication of Piezoelectric Semiconducting Nanowire Arrays and Vertical Integrated Nanogenerators Two basic methods are involved in the synthesis of semiconducting NWs: top-down method and bottom-up method. Chemical bath deposition (CBD) belongs to the latter and has been used to grow ZnO NWs in our group. In this chapter, we mainly introduce how to fabricate ZnO NWs and to integrate the NGs based vertically aligned ZnO NW arrays. Concerning the ZnO NWs, detailed processes are described, while X-ray diffraction (XRD) and SEM techniques are used to assist the morphology control. Then the ZnO NW arrays are embedded into different dielectric matrices using several techniques such as the spin coating, the sputtering and the atomic layer deposition (ALD), covered by a metal electrode.

AII.1 Synthesis techniques of piezoelectric semiconductor NWs

From the analytical and computational study to the application in real life, controlled fabrication of NWs with desired longitudinal or axial structures is critical to integrating NWs into various application platforms [START_REF] Thurn-Albrecht | Ultrahigh-density nanowire arrays grown in self-assembled diblock copolymer templates[END_REF][START_REF] Novotny | InP nanowire/polymer hybrid photodiode[END_REF][236][START_REF] Wu | Semiconductor Nanolasers and NanoLEDs[END_REF]. Nowadays there are many different methods for fabricating semiconductor NWs. They are commonly placed into two categories, namely, the top-down and bottom-up approaches. The top-down approach relies on dimensional reduction through selective etching and various nanoimprint techniques. While the bottom-up approach starts with individual atoms and molecules and builds up the desired nanostructures.

AII.1.1 Top-down methods

Top-down etching techniques have been used for fabricating large devices with complex vertical structures for a long time. Their merits focus on well aligning, positioning, integrating and interfacing NWs to macro systems with high yields and repeatability.

AII.1.1.1 Nanoscale spacer lithography (NSL)

Spacer patterning is a technique employed for patterning features with line width smaller than can be achieved by conventional lithography. In the most general sense, the spacer is a layer that is deposited over a pre-patterned feature, often called the mandrel. The spacer is subsequently etched back so that the spacer portion covering the mandrel is etched away while the spacer portion on the sidewall remains. Direct patterning techniques using spacer lithography (SL) have been reported to avoid the problems associated with the alignment of the NWs [START_REF] Hua | Polymer imprint lithography with molecular-scale resolution[END_REF][START_REF] Ge | Cross-linked polymer replica of a nanoimprint mold at 30 nm half-pitch[END_REF][START_REF] Liu | Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids[END_REF]. Large-density NW arrays of complex vertical structures could be fabricated by using these approaches with sizes of tens of nanometers and a lateral resolution of about 2 nm. These methods are expected to be more plausible and suitable for the large-scale manufacturing of NW-based devices. NSL consists of photolithography, thin film could lead to reduced performance on the integrated devices. The concentration change in the solution during the reaction could be responsible for part of it. To solve these problems, we need further study of the synthesis techniques.

AII.3 Fabrication of rigid and flexible VINGs based on ZnO NWs

The fabricated ZnO NWs need to be integrated into a device packaged for further characterization and application. In this section I will describe the process of integration and improvement of the fabricated devices including new dielectrics as matrix material for the composite.

AII.3.1 Process from NW arrays to VINGs

The process from NW arrays to VING device working under compression can be divided into three steps (Fig The bottom external electrode is a conductive Al tape stuck on a glass plate and connected with the substrate by silver paint. Both external electrodes also offer a position to connect the wires so that the main specimen is kept to be flat. The integration of VING working under bending is more simple. It follows the same process as the VING under compression, but as the substrate is already metallic, the bottom contact is taken directly from it.

AII.3.3 Top Al electrode deposition with evaporation method

After the deposition of matrix and top insulating layer, a 200 nm Al thin film was deposited on the top of the sample by electron beam evaporator as an electrode. The electron gun current was 180 mA, giving a deposition rate of 0.25 nm/s.

AII.4 conclusion

In this work, we have successfully synthesized vertically aligned ZnO NWs on both p-type Si wafer and stainless steel foil by CBD methods. The vertical alignment corresponded to the c-axis of ZnO lattice. Influence of growth process parameters were discussed and a preliminary guideline on the morphology control was given. Contact mode AFM operates by scanning a tip attached to the end of a cantilever across the sample surface while monitoring the change in cantilever deflection with a split photodiode detector. The tip contacts the surface through the adsorbed fluid layer on the sample surface. A feedback loop maintains a constant deflection between the cantilever and the sample by vertically moving the scanner at each (x, y) data point to maintain a "set point" deflection. By maintaining a constant cantilever deflection, the force between the probe and the sample remains constant.

b. Non-contact mode AFM

The cantilever is oscillated at a frequency which is slightly above the cantilever's resonance frequency typically with an amplitude of a few nanometers (<10nm), in order to obtain an AC signal from the cantilever. The probe does not contact the sample surface, but oscillates above the adsorbed fluid layer on the surface during scanning The cantilever's resonant frequency is decreased by the van der Waals forces, which extend from 1nm to 10nm above the adsorbed fluid layer, and by other long range forces which extend above the surface. The decrease in resonant frequency causes the amplitude of oscillation to decrease. The feedback loop maintains a constant oscillation amplitude or frequency by vertically moving the scanner at each (x, y) data point until a "set point" amplitude or frequency is reached. The distance that the scanner moves vertically at each (x, y) data point is stored by the computer to form the topographic image of the sample surface.

c. Tapping mode AFM

Tapping mode AFM operates by scanning a probe attached to the end of an oscillating cantilever across the sample surface. The schematic in Fig. III.1 explains the working principle. The cantilever is oscillated at or slightly below its resonance frequency with an amplitude ranging typically from 20nm to 100nm. The probe lightly "taps" on the sample surface during scanning, contacting the surface at the bottom of its swing. The feedback loop