Alberto Rua

Diana Taborda

Chapter IV: Multilayer Energy harvesting fabrication Chapter V: Towards SPS sintering route

Keywords: [MEMS; Couche épaisse, Récupération d'énergie, piézoélectrique, SPS] Printed ceramic Piezoelectric MEMS for Energy Harvesting: towards Spark Plasma Sintering of multilayers [MEMS, Thick-film, Energy harvesting, Piezoelectric, SPS]

This work would not have been possible without the help of numerous people that I would like to thank warmly. They contributed not only to the scientific aspect but also to the human aspect during these years. First of all I would like to thank my two supervisors, Hélène Debeda and Catherine Elissalde, for their constant support, compromise and their scientific expertise to improve and guide my work. It was a pleasure to work with them, for their expertise in their respective scientific field, but also for their very human

General Introduction

Nowadays, an increasingly growing technology trend concerns an "intelligent world" where countless numbers of autonomous wireless sensing devices continuously monitor and provide information to control our environment. The concept of this intelligent world is in constant evolution. So far, this includes "wireless sensor networks (WSN)," "ambient intelligence," and, more recently, "the Internet of Things (IoT)." It is estimated that more than a trillion of sensors are used around the world. The majority of these sensors are powered by batteries which have limited lifetime and that have to be periodically replaced or recharged. This operation can be an issue for human intervention. Therefore, the availability of energy-autonomous technologies, able to capture and store part of the energy available in the surrounding environment and to power the WSNs could speed up the wide diffusion of efficient and cost-effective WSN applications. Furthermore, these energy-autonomous technologies need to attain requirements such as small scale dimensions, low-cost, high reliability. In this context, increasing attention has been focused in the last two decades on the recovery of energy from ambient energy sources such as light, heat and mechanical vibrations. This new field of research is referred to as Micro Energy Harvesting. An Energy Harvester can be defined as a device or system that captures (or harvests) ambient energy in the environment and converts it into electricity. Large-scale renewable power generation such as solar cell arrays and wind turbine generator can be considered as forms of energy harvesting. However, sensors networks need a smaller scale, requiring power in the range of 10-100s of microwatts. The overall dimensions of micro energy harvesters are usually in the millimeter or centimeter range but the transducers performing the electromechanical conversion are not always at the microscale. Based on these considerations, the realization of miniaturized Energy Harvesters (EHs) taking advantage of MEMS (Micro Electro Mechanical Systems) technology is a solution full-filling both energy-autonomy and miniaturization/integration requirements. Also, aside thermoelectric and pyroelectric materials, piezoelectric compounds seem to be good candidates for the capture of small amounts of wasted energy ie. mechanical vibrations in our surroundings (human activity, machinery, car, etc.). Piezoelectric energy conversion is in fact displayed as the most interesting option for vibration energy harvesting MEMS, mainly due to its output power and compatibility with MEMS technologies.

With vibration piezoelectric EHs, the transformation from mechanical to electrical energy is obtained through the direct piezoelectric effect. The resulting energy can be stored after using a rectifier and DC-DC converter circuit. In general, one can abridge an energy harvesting system in three main steps: (1) capture the mechanical stress from vibration source, (2) converting the mechanical energy into electrical energy by direct piezoelectric transduction, and (3) processing and storing the generated electrical energy. Different approaches can be explored to optimize the extracted power, depending upon the aimed frequency (<100 Hz for ambient vibrations) and the sensor to power. These approaches cover a broad range of research field, from material science, going through mechanics, MEMS technologies until electronics.

In this context, this thesis aims to develop a MEMS EH structure capable of harvesting mechanical vibrations and converting them into electricity using piezoelectric transduction. Among inorganic compounds, PZT (PbZr x Ti 1-x O 3 ) and its derivate presents larger electromechanical properties than other piezoelectric inorganic or polymer materials. It remains preferentially used due to its outstanding properties despite its hazardous lead content. Also, for MEMS piezoelectric vibration EHs, the realization of screen-printed piezoelectric thick film layers (10<thickness (µm)<400) at a low cost can be automated and adapted to large volumes. Implementation of the piezoelectric MEMS achieved with a single printed technology, presents actually the following advantages: accessibility in the micro-manufacturing (stacking of layers showing various nature, geometries and dimensions) and choice flexibility of materials (piezoelectric, electrodes or substrates). However, recent works have shown that the electromechanical properties of PZT thick-films remain lower than those of the ceramic, mainly because of the too important residual porosity of the screen-printed layers. To improve the densification of both the piezoelectric material and the multilayer, we have selected the Spark Plasma Sintering (SPS) technique that combines the application of a uniaxial pressure and a pulsed electric current. The efficiency of SPS to densify (relative density higher than 95%) at low temperature and in short time a broad range of materials (from nanomaterials to multimaterials), is now fully recognized. Furthermore, optimization of the EH design with a complex geometry and the use of flexible substrate can be exploited to maximize power output. Such approaches are also in line with the current trend towards energy savings.

In this specific context, an interdisciplinary work has been conducted during this thesis work, for which three central and complementary axis can be defined (1) The first axis is focused on the thick film piezoelectric fabrication by screen-printing. The process has been carried out in a cleanroom at the IMS laboratory. (2) The second axis consists on the Spark Plasma Sintering based investigations targeting the densification of screen-printed structures at the ICMCB laboratory, (3) Finally, axis 3 includes all the characterizations of the active piezoelectric material and the EH system, carried out in between the two laboratories ICMCB and IMS. Collaborative projects with University of Waterloo and Paris-Sud University are a part of this axis. They are focused on the performance tests and electrical circuit design of complex EH structure. A flowchart illustrating the interdisciplinary nature of the thesis work as well as the various collaborations is proposed in Figure 1. Chapter one presents the state of the art on the different types of energy harvesting sources and energy conversion principles. The mechanical energy harvesting is then detailed by introducing the different types of electromechanical transducers highlighting the piezoelectric transduction. Different processes used for piezoelectric MEMS are then shown with a special focus on EH using flexible metallic substrates and PZT thick films. Qualitative comparisons of the most relevant piezoelectric EH are carried out.

Chapter two describes first the thick film technology and the different steps inherent to the process. The basics of sintering are then briefly proposed with particular emphasis on conventional technique and Spark Plasma Sintering.

Chapter three presents the different techniques and methods used to characterize the raw piezoelectric material and the fabricated piezoelectric ceramics and printed components. Characterizations are oriented on structural, microstructural and interfaces related aspects as well as dielectric and electromechanical properties.

Chapter four focuses on the EH fabrication consisting of a multilayer structure where electrodes and piezoelectric material are printed on a metallic substrate. The choice of the materials, the optimization of the fabrication of the EH with a complex geometry developed at the University of Waterloo are justified. A microstructural analysis is conducted through the comparison of different PZT based structures: a bulk ceramic, a printed disk and a cantilever (representative of the complex structure). Specific attention is paid to the effects of the passive metallic substrate on both microstructural features and functional properties. Dielectric and electromechanical characteristics and power output performance are finally investigated.

Finally, chapter five explores the SPS as a sintering route for the densification in one-step of the multilayer printed EH structure. First, the sintering conditions of the active material PZT are optimized with as a main objective to densify PZT without adding sintering aid and without additional post-sintering annealing. To do this, our approach based on the use of a carbonate protective layer is presented. Then the challenging transfer towards the sintering of the EH multilayer structure by Spark Plasma Sintering constitutes the second part of this chapter. This manuscript ends with the general conclusions, including some perspectives for future work and experiments. 1 A primary battery is designed to be used once and discarded, and not electrically recharged and reused as secondary cells (rechargeable battery).

The main objective of this first chapter is to define the background and the context related to energy harvesting. The beginning is dedicated to the available energy harvesting sources. Then the mechanical energy harvesting will be engrossed, presenting the different transductions methods with their general principle, main advantages, and drawbacks. Furthermore, piezoelectric energy harvesting (PEH) will be encompassed and carefully explained from its basics until recent advances in PEH devices, highlighting mainly the material and fabrications techniques.

Context

Many of nowadays applications would not be possible without progress in miniaturization and reduction of the power consumption of electronics (10's nW -100's μW of power [1]). This is illustrated by the progress in Wireless Sensor Network (WSN) technology for smart systems. Further advances in smart sensors and WSN tend to be even more embedded and mobile in the future. However, the power supply of the sensor nodes raises some serious challenges for the widespread implementation of WSN. As the sensors need to be wireless, the power is usually provided by primary or secondary batteries 1 . Nevertheless batteries have some unavoidable drawbacks. The most important one for application in WSN's is that the energy is inherently limited. As a result, the periodical replacement for long term operations can compromise the complete integration and size of the system and in some cases is not even possible, due to the difficult access of the sensor location [2]. Advances in WSN technologies have enable different solutions for battery-less autonomous sensors and network systems. Harvesting solutions using different energy sources such as heat, radio-waves, light or vibrations are promising [3].

Harvesting from environment vibrations using Micro-Electromechanical System (MEMS) energy harvesters is one of the most promising option, since it addresses both issues, autonomy and miniaturization, and allows large energy to volume ratio production by scavenging energy from external vibrations [4].

Energy harvesting sources

The purpose of an energy harvesting is to reuse or recover energy from different available sources that can be found in our surroundings (Figure I-1). These sources can be divided into different types: solar energy, wind energy, thermal energy, acoustic energy, mechanical energy and electromagnetic radiation. This section explains the basic principle of the main types of energy harvesting, highlighting their major advantages and drawbacks, as well as their positioning related to power performance.

Solar energy

Solar energy generators are a well-developed technology used for large-scale energy generation (milliwatts to megawatts). Solar energy cells or photovoltaic modules generate electrical power by converting solar radiation directly into electricity using semiconductors [5]. The generated electricity can be used for many applications, such as grid systems, water heaters and outdoor lamps. There exist many other different applications mainly found in portable products, such as calculators, watches, or monitoring sensor nodes [6]. In an outdoor environment on a sunny midday, the power density of the solar radiation on the earth's surface is about 100 mW/cm 3 , making solar energy one of the most effective energy harvesting methods. Nevertheless, solar energy becomes less suitable for indoor environments due to the drop in power density to a value as low as 10 μW/cm 3 . Solar cells are developed using silicon technologies, and are divided in two major categories: single-crystal silicon and polycrystalline thin-films. The efficiency of single-crystal silicon cells in between 12 to 25%. Polycrystalline thin-films and amorphous silicon solar cells are commercially available and have lower cost and efficiency than singlecrystal silicon cells [7]. Most recently organic solar cells (OSC) consisting mainly in polymer materials have been studied because it is potentially cost-effective for photovoltaic applications. With polymers, molecular engineering (e.g. changing the length and functional group of polymers) can change the band gap, allowing for electronic tunability. The optical absorption coefficient of organic molecules is high, so a large amount of light can be absorbed with a small amount of materials, usually on the order of hundreds of nanometers. However low efficiency, low stability and low strength compared to inorganic photovoltaic cells remain challenging [8].

Wind energy

Wind energy uses the air flow through wind turbines to provide mechanical power to turn electric generators. It is a mature energy source used in large-scale electric power generation for grid applications. Recently, micro wind generators (micro-WGs) have been proposed as energy-harvesting for indoor or autonomous systems (Figure I-2) [6]. Micro-WGs can generate several milliwatts of power, which is relatively large in the scope of energy harvesting. Nevertheless wind power depends on environmental conditions. In fact, wind generators depend directly on the torque generated through wind and not all locations have strong winds conditions, moreover their large dimensions are inconvenient for integration on a microelectronic scale.

Reducing the size of WGs is difficult because of the wind power density and wind turbine mechanism size limitations.

Thermal energy

Thermal energy can be divided in two types: pyroelectric and thermoelectric. Concerning pyroelectric generator, a voltage is generated by heating or cooling pyroelectric materials. Pyroelectric materials possess a spontaneous polarization, a temperature variation in these materials leads to a shift in atomic positions changing the polarization and giving rise to a voltage. Thermoelectric generators (TEGs) are based on the thermoelectric effect which produces a direct conversion of temperature into electric voltage and vice versa. A thermoelectric generator basically consists of a thermocouple, which comprises p-type and ntype semiconductors and produces an electrical current proportional to the temperature difference between hot and cold junctions [6]. In metals and semiconductors, charge carriers are free to move and when a temperature gradient exists in a material, the mobile charges at the hot part diffuse to the cold one, resulting in a net charge and an electricc potential (Figure I-3). The best thermoelectric materials are heavily doped semiconductors. The output voltage of TEGs is in the range of several millivolts, achieved using compacted structures with large number of thermocouples. Thermoelectric generators are mainly solid-state devices and their efficiency is often lower than 10%. TEGs are suitable for small distributed power generation in energy harvesting applications such as power plants in order to convert waste heat into additional electrical power and in automotive applications such as thermoelectric generators (ATGs) to increase fuel efficiency and for bio-WSNs [9]. The major drawback is the rejected heat that must be evacuated. It requires an additional heat dissipation mechanism and thus a larger area. commercial TEG with a output power of 6.21 µW for a temperature increase of 73°K (1MC04-030-15_TEG from PL Engineering Ltd, Russia).

Acoustic energy

Acoustic or sound energy harvesters (AEHs) convert high and continuous acoustic waves from the environment to electrical energy using an acoustic transducer or a resonator. AEHs reported in literature can be divided in two types, electromagnetic and piezoelectric based.

The energy available in acoustic energy sources can be converted into electrical energy with a Helmholtz or quarter-wavelength resonator integrated with an energy transduction mechanism (piezoelectric transductions using a piezoelectric membrane or electromagnetic transduction using a structure integrated of a permanent magnet with a coil).

In a Helmholtz resonator, the incident acoustic pressure wave oscillates the lumped air located at the neck (Figure I-4 (a)). The downward motion of the neck's air increases the pressure of air in the cavity; however, due to the upward motion, the pressure of the cavity's air decreases. This system can be modeled as a spring-mass-damper system as shown in Figure I-4 (b). The pressure amplitude in the cavity is always higher than that of the incident acoustic wave. Hence, the fluctuating cavity's pressure triggers the energy transduction mechanism to produce the power [10]. This same principle applies for the quarter-wavelength resonator, but for a tube structure with just one open end as depicted in Figure I-4 (c). Here one-third of the tube's length near the open end acts as a neck and the remaining portion of the tube behaves like the cavity similar to the Helmholtz resonator, but the amplification factor of the quarter-wavelength resonator is relatively higher than the Helmholtz resonator for the same volume.

The power produced by the piezoelectric AEHs ranges from 0.68 pW to 30 mW, whereas for the electromagnetic AEHs the range is 1.5-1.96 mW. Although output power can reach the mW scale, such energy can only be recovered in very noisy environments. Acoustic resonators are still vastly used for both noise attenuation and sound augmentation [10], [11]. [10] ), and (c) scheme of a quarter-wavelength resonator.

Mechanical energy

Conversion of mechanical energy into electrical energy can be obtained from kinetic sources, such as vibrations, mechanical stresses, deformations, high-pressure motors, etc. The principle of mechanical energy harvesting is to convert the energy of the movements and mechanical oscillations of a spring-mass component mounted inside the energy harvesting, into electrical energy. This type of mechanical energy harvesting is based mainly on three principles of transduction: piezoelectric, electrostatic and electromagnetic, which will be further presented in section 3 of this chapter. The frequency of mechanical excitation depends on the source which can be generated by the human body movements or by any vibrating structure.

For human movements, it represents a few tens of Hz, while for machine vibrations, the frequency range is in the range 30-1000 Hz, with vibration amplitudes that may be low (<0.1 g). Some applications for mechanical energy harvesters, which include the energy for powering the implantable medical or wearable devices have been for instance proposed. Shenck and Paradiso at the MIT Media Laboratory (Massachusetts, USA) [11] proposed a pioneer vibration energy harvesting unit made of a shoe-mounted piezoelectric generator with a complete subsequent power conditioning circuit . The unit uses the human movement as vibration source.

The circuit supports an active RF tag that is able to transmit a short-range, 12-bit wireless identification (ID) code, while the wearer walks. (Images from [12])

Electromagnetic energy

Electromagnetic energy can be divided in:

 Conversion of Radio Frequency (RF) electromagnetic waves into electricity based on a rectifying antenna. The energy can be recovered either from RF energy sources such as radio, television, mobile phones and WiFi communications, or from electromagnetic signals generated at a specific wavelength. For this type of energy harvesting the power generated depends on the distance between the RF transmitter and the generator.

 Resonant energy harvesting using kinetic energy to induce magnetic-field-flux variation on a fixed coil to generate energy. The principle is based on the transfer of electrical energy between two coils resonating at the same frequency. The magnitude of the magnetic field variation is proportional to the current of the power wire [1] [13].

Summary on energy harvesting sources

The Table I-1 shows the power density that can be extracted with the energy sources presented in the previous paragraphs. The harvested power is limited by the size of the energy harvesting system. In order to maintain the small dimensions requirements of microsystems, it is necessary to take into account the maximum output power density of such energy harvesting system. Because of their limited volume, energy harvesting microstructures (volume <1cm 3 ) cannot therefore power high energy consumption devices such as smartphones or laptops (200 mW -40 W). However, they are ideal for providing the energy needed to operate simple pressure, acceleration or temperature sensors (1-10 μW).

Table I-1: Energy sources with power density harvested [6]. Therefore converting mechanical energy from ambient vibration into electrical energy is a very interesting approach to power wireless sensor nodes,since it provides a power solution that can meets the requirements of size limitations. Moreover the source can be found almost anywhere where wireless sensor networks may potentially be deployed. In the framework of this thesis we will focus on this type of energy harvesting.

Energy source

Mechanical energy harvesting

A mechanical energy harvesting system usually involves three elements (Figure I-7):

 The mechanical-mechanical converter that captures the energy. The best suited capture device is a mechanical oscillator with a proof (or seismic) mass [14].

 The energy converting transducer; the energy is usually transferred to the transducer with the proof mass. Note that in some systems the mechanical-mechanical converter and the transducer can be a single element.

 The electronic circuit to power the electronic load.

Mechanical conversion principle

Oscillator

Vibration of a rigid body can be caused by several factors such as unbalanced mass in a system, tear and wear of materials and can occur in almost all dynamical systems. Most commonly, vibration energy harvester can be simply modeled as a second-order spring-mass system. The characteristics of the energy harvester can be described by a damping constant and the natural frequency of the system. This simple equivalent model based on linear system theory was proposed by Williams and Yates [15] [18]. The governing equation of motion of a lumped spring mass system can be written as:

𝑀𝑧̈+ (𝑏 𝐸 + 𝑏 𝑀 )𝑧̇+ 𝑘𝑧 = -𝑀𝑦̈ (Eq. 1.1)

where 𝑧 is the spring deflection, 𝑦 the input displacement, 𝑀 the mass, 𝑏 𝐸 the electrically induced damping coefficient, 𝑏 𝑀 the mechanical damping coefficient, and k the spring constant.

Assuming that the external base excitation is sinusoidal given as y(t)= Ysin ωt , with ω the input frequency the solution of the equation 1.1. is:

𝑧(𝑡) = ( 𝜔 𝜔 𝑛 ) 2 √[1 -( 𝜔 𝜔 𝑛 ) 2 ] 2 + (2𝜁 𝑇 𝜔 𝜔 𝑛 ) 2
𝑌 sin(𝜔𝑡 -𝜙) (Eq. 1.2) where Y is the amplitude of vibration and 𝜔 𝑛 is the natural frequency of spring mass system, 𝜁 𝑇 is the combined damping factor (𝜁 𝑇 = 𝜁 𝐸 + 𝜁 𝑀 ) and 𝜙 the phase angle between output and input. From Eq. 1.2 the maximum amplitude |𝑧| is found at the resonant frequency and is inversely proportional to the resulting damping. Moreover, the lower the resonance frequency, the higher the amplitude.

The natural resonant frequency of a spring mass system is defined as:

𝜔 𝑛 = √𝑘 𝑀 ⁄ (Eq. 1.
3)

The phase angle can be expressed by: 𝜙 = arctan ( 𝐶𝜔 𝑘 -𝜔 2 𝑀) ) (Eq. 1.4)

The quality factor can be then defined by the ratio of the amplitude of the mass z with the amplitude of the resonant excitation y at the resonant frequency  0 , as followed :

𝑄 = 𝑧 𝑦 | 𝜔=𝜔 0 = 𝑀𝜔 0 𝑏 𝐸 + 𝑏 𝑀 = 1 2(𝜁 𝐸 + 𝜁 𝑀 ) = 1 2𝜁 𝑇 (Eq. 1.5)
Consequently, from Eq. 1.5, the lower total damping factor, the greater the quality factor Q.

Output power in mechanical energy harvesting

The power converted to the electrical system is equal to the power extract from the mechanical system by 𝑏 𝐸 , the electrically induced damping. The average harvested electrical power can be obtained from the product of velocity and force on the mass, described by:

𝑃 = 1 2 𝑏 𝐸 𝑧̇2 (Eq. 1.6)
Therefore taking into account the already described equations, the magnitude of the average power |𝑃|dissipated by the energy harvester is:

|𝑃| = 𝑀𝜁 𝐸 𝜔 𝑛 𝜔 2 ( 𝜔 𝜔 𝑛 ) 3 𝑌 2 (2𝜁 𝑇 𝜔 𝜔 𝑛 ) + (1 -( 𝜔 𝜔 𝑛 ) 2 ) 2 (Eq. 1.7)
where Y is the displacement magnitude of input vibrations. When the generator is at resonance, ω = ω n . The maximum dissipated power becomes:

|𝑃| = 𝑀𝑌 2 𝜔 𝑛 3 4𝜁 𝑇 (Eq. 1.8)
According to the relationship of mass, acceleration magnitude and resonant frequency previously observed, higher mass and higher acceleration result in higher output power. The maximum power delivered to the electrical domain is inversely proportional to the damping factor. Thus, when designing a vibration-based micro-generator in order to achieve maximum power output, it is important to design the generator with a high Q factor working at its resonant frequency. In addition, due to the nature of vibrations and since the output power is inversely proportional to the resonant frequency of the generator for a given acceleration, it is generally preferable to operate at the lowest available fundamental frequency, since acceleration levels associated with environmental vibrations tend to reduce with increasing frequency [17].

Transduction mechanisms

In mechanical energy harvesting, a particular transduction mechanism is used to extract electrical energy from motion. So far, existing vibration transducers are commonly based on three different conversion mechanisms: electromagnetic [18], electrostatic [19] and piezoelectric [20]. In few cases the effect of magnetostriction [21] has been investigated as well.

The transduction mechanism can generate electrical energy by exploiting the relative displacement or strain based on the spring-mass system described previously.

Electromagnetic energy conversion

Electromagnetic energy conversion is based on Faraday's law of electromagnetic induction discovered by Michael Faraday in 1831. This law describes the interaction of a magnetic field with an electric circuit to produce an electromotive force (EMF), a phenomenon called electromagnetic induction and produced across an electrical conductor in a varying magnetic field. In an electromagnetic generator, permanent magnets are used to produce strong magnetic field and a coil is used as electric conductor [22]. Two systems can be differentiated, one with a moving magnet and permanent coil ( Where ε is the electromotive force (EMF) and Φ is the magnetic flux. Power is extracted when the generator is loaded to a resistance allowing a current to flow in the coil. This current produces its own magnetic field, opposing the field that induces it. The interaction between the field generated by the induced current and the field from the magnets creates a force that opposes the motion [6]. The open-circuit voltage V out , which is generated by a linear electromagnetic generator, can be described as followed:

𝑉 𝑜𝑢𝑡 = 𝑁𝐵𝐴 𝑐𝑜𝑖𝑙 𝜈 (Eq. 1.10)
Where N is the number of turns in the coil, B is the magnetic strength of the magnet, 𝐴 𝑐𝑜𝑖𝑙 is the cross-sectional area of the coil, and 𝜈 is the velocity of the magnet as it goes through the coil. An electromagnetic generator is characterized by high output current level at the expense of low voltages [22]. Moreover Beeby et al., have stated that electromagnetic energy harvesters perform better in macro-scale than in micro-scale, due to the use of discrete permanent magnets, therefore it is challenging to incorporate electromagnetic energy harvesters with the MEMS fabrication process [24].

Electrostatic energy conversion

Electrostatic harvesting of mechanical energy is based on varying vibration-dependent capacitance of variable capacitors (varactors) [25][26]. Electrostatic energy conversion scheme is depicted in Figure I-11. The capacitance varies between maximum and minimum values through mechanical vibrations. If the charge on the capacitor is constrained, charge moves from the capacitor to a storage device or to the load as the capacitance decreases. Thus, mechanical energy is converted into electrical energy. The voltage V across the capacitor is expressed by Eq. (1.11), where Q is the charge, d is the gap or distance between plates, A is the area of the plate, and  is the dielectric constant of the free space.

𝑉 = 𝑄𝑑 𝐴

(Eq. 1.11)

The energy stored in the capacitor is expressed by:

𝐸 = 𝑄 2 2𝐶
(Eq. 1.12)

Where C is the capacitance.

Increasing the voltage or the charge increases the energy stored in the capacitor. Thus, energy transfer schemes can be classified as either charge-or voltage-constrained conversion; these two types of energy transfer schemes are adopted in various works [13].

Figure I-11: Scheme of an electrostatic generator, where E represents the produced energy, q the charges and V t the voltage across the capacitor. (Image from [27])

Piezoelectric energy conversion

The piezoelectric conversion is based on the piezoelectric effect characteristic of some materials. This effect can be defined in a general way as the conversion of mechanical energy into electrical energy (direct effect) or the conversion of electrical energy into mechanical energy (inverse effect). Piezoelectric coupling provides a two-way conversion between mechanical energy and electrical energy. The constitutive equations for a piezoelectric material are expressed by: 𝛿 = 𝜎 𝑌 + 𝑑𝐸 (Eq. 1.13)

𝐷 = 𝜀𝐸 + 𝑑𝜎 (Eq. 1.14)
where δ is the mechanical strain, σ is the mechanical stress, Y is the Young's modulus of the material, d is the piezoelectric strain coefficient, E is the electric field, D is the electrical displacement (charge density) and ε is the dielectric constant of the piezoelectric material. Piezoelectric energy harvesters are typically simple structures such as unimorph or bimorph cantilevers, or double-clamped beam. Figure I-12 shows a scheme of a bimorph piezoelectric cantilever [28][29] [30]. However, bimorph cantilevers are less adapted in terms of manufacturability considering existing micro-fabrication processes [3]. As a result, MEMS cantilevers mostly have a unimorph configuration. A seismic mass is usually attached at the tip of the cantilever to adjust the resonant frequency to the available environmental frequency, usually below 100Hz [16][31] [32].

Piezoelectric conversion has the simplest structure among the three transducers (electromagnetic, electrostatic, piezoelectric). Moreover they can produce appropriate voltages for electronic devices. However, the mechanical properties of the piezoelectric material may limit overall performance and lifespan of the generator.

Comparison of the different energy conversion mechanisms

Advantages and disadvantages of each type of conversion mechanisms are summarized in Table I

-2.
In general the main drawbacks of electromagnetic transducers are their difficulty to be integrated into MEMS fabrication process and their low energy density that limits the fields of applications. Since electrostatic and piezoelectric transducers are compatible with MEMS technologies, they are more suitable to be used in micro-or nano-scale systems while electromagnetic transducers are suitable for macro-scale systems.

The main disadvantage of electrostatic generators is the voltage source requirement to initiate the conversion process because the capacitor must be charged to an initial voltage. Moreover Roundy et al. [33] calculated the theoretical maximum energy density of the different transducers and it was concluded that piezoelectric and electromagnetic transducers have similar energy density which is about 10 times higher than that of electrostatic transducers. Therefore piezoelectric energy conversion is displayed as the most interesting option for vibration energy harvesting MEMS. This is mainly due to its output power and compatibility with MEMS technologies. Nevertheless the challenge remains to guarantee good mechanical properties of the piezoelectric material since they can limit overall performance and lifespan of the generator. The root of the word piezo means pressure; hence, the original meaning of the word piezoelectricity is "pressure electricity", the ability of some materials to develop an electric charge proportional to a mechanical stress [34]. This definition ignores the fact that the piezoelectric effect is reversible, allowing the generation of a deformation proportional to an applied voltage. Piezoelectricity was discovered by Pierre and Jacques Curie in 1880 in single crystals such as Rochelle salt and quartz. It is only in 1946 that scientists discovered that the barium titanate BaTiO 3 is piezoelectric [34]. With its increased sensitivity and higher operating temperature, PbZrTiO 3 (PZT) soon replaced BaTiO 3 in many existing devices and is still the most widely used piezoceramic today. With the apparition of Internet Of Thing (IOT) and because of the brittleness of the piezoceramics, piezoelectric composites and polymers are nowadays more and more studied for instance for wearables because of their flexibility and conformability [35]. However, their properties remain lower than those of the piezoceramics [36]. The piezoceramics can be found in a broad range of applications using either the direct or inverse piezoelectric effect. They are present in every day, for example in cleaning application for jewelry, glasses or teeth using generators of ultrasonic applications, but also in high-end technology markets such as medical technology, semiconductor technology or mechanical and automotive engineering . Some examples of applications are listed below:

 Transducers for sound and ultrasound in air (microphones, intruder alarm system, loudspeakers, etc).  Sensors (pressure, accelerometers, chemical, ultrasonic sensors for medical applications, etc), Structural Health Monitoring (SHM),  Actuators, motors, transformers, Energy harvesting applications are also more and more needed with the growing of this intelligent world surrounding us. For vibration piezoelectric energy harvesters, the direct piezoelectric effect is involved. Basics on piezoelectric effect are given in the next paragraph. The existence of piezoelectricity is due to the lack of a center of symmetry in the unit cell of the crystal. Consequently, as a result of the stress, a net movement of the positive and negative ions with respect to each other produces an electric dipole (polarization). This piezoelectric effect is linear and reversible, and the sign of the produced charge depends on the direction of the stress (tensile or compressive). Figure I-14 illustrates the origin of the piezoelectric effect. The link between piezoelectricity and crystal symmetry has been clearly established. Among the 32 crystallographic classes, 21 do not possess a center of symmetry and 20 of these are piezoelectric. Some piezoelectric crystals, like the quartz only develop the polarization when the force is applied, while others are already polarized without pressure applied. The wellknown materials barium titanate (BaTiO 3 ), lead titanate (PbTiO 3 ) or lead zirconate titanate (PbZrTiO 3 ) belong to the family of piezoelectric materials which exhibit reversible polarization: they are ferroelectric materials. However, the spontaneous polarization in polycristalline materials such as ceramics is random and a polarization process (or "poling" process) is necessary to obtain a macroscopically piezoelectric ceramic. During this process, the domains within grains can orient in the direction of the direct electric field applied at a temperature slightly below the Curie temperature . A remanent polarization is thus achieved within the polycrystalline material after the removal of the field [37].

Description and origin of the piezoelectric effect

Configurations of piezoelectric energy harvesters

Generally, micro-scale piezoelectric energy harvesters are designed either in a unimorph or bimorph cantilever structure, where electroded piezoelectric films or ceramics are bonded onto the cantilever substrate. In some cases different electrode arrangement ie. interdigitated electrodes can be also used (Figure I-16 (b-c)) [32]. Due to the symmetry, directions at right angles to the polar axis are equivalent and can be referred as "1" directions. The direction of the applied stress can be either along the polar axis (3-direction) or at right angles to it (1direction), resulting in two common piezoelectric energy harvesting configurations, 33-mode and 31-mode, as illustrated in Figure I-16 (a). The 33-mode means that the compressive stress/strain is applied parallel to the 3-direction, while the voltage is generated along the same axis. In the 31-mode, the stress/strain is applied perpendicular to the polar axis and the direction of the generated voltage is at the right angle of the applied force [39][40]. The open circuit voltage of the piezoelectric is expressed by:

𝑉 𝑜𝑐 = 𝑑 𝑖𝑗 𝜖 𝑟 𝜀 0 𝜎 𝑖𝑗 𝑡 (Eq. 1.15)
Where 𝑑 𝑖𝑗 is the piezoelectric coefficient, 𝜎 𝑖𝑗 the mechanical stress, 𝑡 the distance between electrodes and, 𝜖 𝑟 and 𝜀 0 are the relative dielectric constant and the permittivity of vacuum, respectively. In general the output voltage for the 33-mode energy harvester is expected to be higher than that of the 31-mode (d 33 >d 31 ) [32]. However, 33 mode is not suitable for energy harvester mainly because of limited strain due to high stiffness, and high frequency operation. The 31 mode configuration is hence usually preferred for vibration energy harvesters [30].

Piezoelectric materials properties requirements for energy harvesting

It is obvious that piezoelectric energy harvesting performance depends in a large extend on the properties of the piezoelectric material. Another important characteristic is the squared electromechanical coupling coefficient k 2 . It represents a convenient and direct evaluation of the ability of the piezoelectric material to convert one form of energy to another. It is defined as follow:

𝑘 2 = 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙𝑒𝑛𝑒𝑟𝑔𝑦𝑠𝑡𝑜𝑟𝑒𝑑 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙𝑒𝑛𝑒𝑟𝑔𝑦𝑎𝑝𝑝𝑙𝑖𝑒𝑑 = 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙𝑒𝑛𝑒𝑟𝑔𝑦𝑠𝑡𝑜𝑟𝑒𝑑 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙𝑒𝑛𝑒𝑟𝑔𝑦𝑎𝑝𝑝𝑙𝑖𝑒𝑑 (Eq. 1.16)
The ways to calculate this electromechanical coupling coefficient in different piezoelectric resonators will be further described in chapter 3.

Even if the electromechanical coupling coefficient indicating the energy conversion ability is a relevant criteria to choose the piezoelectric material, the Figure -of merit (FOM) should be taken into account to compare different materials for energy harvesting applications [33][41]. This FOM applicable for materials, but not for devices, is defined as the electrical energy density divided by the mechanical deformations:

𝐹𝑂𝑀 = 𝑑 2 𝑌 2 𝜀 = 𝑒 2 𝜀 (Eq. 1.17)
Where 𝑌 is the elastic modulus, 𝜀 the permittivity (or dielectric constant of the material) and e the piezoelectric stress coefficient of the material.

To get a high FOM, a compromise can be found considering both permittivity values and piezoelectric performances. As an illustration, the FOM of PZT ceramics can be tuned according to the composition and thus the properties. Undoped PZT is rarely used for applications. A range of properties can be obtained by acceptor or donor doping on A and/or B sites of the perovskite ABO 3 . Acceptor-doped PZT (K + , Fe 3+ ,.. ) are called "hard" PZT due to compensating defects (oxygen vacancies) that stabilize the domain structure which in turn becomes difficult to be reoriented (difficult poling). Donor doped PZT (La 3+, Nb 5+, ), on the contrary are compensated by electrons or lead vacancies and are easy to pole. They are called "soft", exhibiting high piezoelectric coefficients, high permittivity and dielectric losses [37]. According to the targeted applications (sensors, actuators, etc…), higher or lower permittivity values may be desired. Table I-3 summarizes the main properties to consider for a piezoelectric material. [42]. These piezoelectric materials can be in single crystal (bulk or thin films) or polycrystalline forms (ceramics, thin or thick-films). PZT single-crystal are difficult to grow, but others lead based perovskite can be grown such as (Pb(Mg,Nb)O 3 -PbTiO 3 (PMN-PT). They can be sealed on a steel cantilever as shown by Badel et al [43]. As a result a 20-fold improvement in harvested power was displayed compared to PZT ceramic.

Ceramics used in energy harvesting application, mostly PZT, are currently thinned to get more flexibility to the energy harvester, and then bonded on the passive substrate, often metallic [3].

For MEMS devices, polycrystalline PZT thin films are currently grown by sol-gel or sputtering on the passive substrate [32][44] [45].

Lead-free materials such as AlN and ZnO cannot compete with PZT and this is one of the reasons why PZT is commercialized by companies, and researches focused on PZT based applications are still very active. However lead free perovskite materials for energy harvesting is a hot topic and it is worth noting that among different options, KNN has displayed interesting results in both thin film and ceramic forms [46]. Nanomaterials can be used for the development of stretchable nanogenerators, in particular ZnO, GaN, PZT and BaTiO (Images from [52])

Table I-4 summarizes the properties of the main piezoelectric materials used for energy harvesting applications. Although good piezoelectric properties are required, the ultimate performance of generators devices will not depend only on the material but also on the complete material/structure assembly system and on the chosen technological processes.

Micro-fabrication technologies for energy harvesting MEMS

An important aspect when developing energy harvesting devices concerns the deposition and patterning of the piezoelectric materials with high crystalline quality and controlled morphology. Piezoelectric thin deposition usually refers to silicium techniques including several deposition techniques such as: sol-gel, sputtering, epitaxial growth, laser ablation processes, etc. The piezoelectric PZT is the most largely used combined with the use of silicon on insulator (SOI) wafer or bare silicon. The unimorph microcantilever design in the 31-mode with a proof mass is by far the most employed structure, due to its simplicity and very good sensitivity. where a silicon based microcantilever including a polycrystalline PZT sol-gel thin film is fabricated [39]. For 31-mode energy harvesting applications, the choice of the bottom electrode will influence the crystalline texture, the quality, and properties of the piezoelectric film. PZT/Pt/Ti/SiO 2 /Si is the most widely applied deposition sequence, where a homogeneous (111) texture of the platinum (Pt) is commonly used to obtain a homogeneous nucleation of the same perovskite orientation [59]. The titanium (Ti) is used as an adhesion layer and additionally it plays an important role in the diffusion phenomena [60]. Also, with this sol-gel process used for PZT deposition, layer of µm thickness needs tens of monolayers deposition. (Images from [39])

Piezoelectric thick films with high piezoelectric coefficients are advantageous to improve the output performances. Thick piezoelectric layers with thicknesses ranging from 10 to 100µm can be obtained by different deposition techniques: screen-printing, sol-gel process, electrophoretic deposition, tape-casting, or aerosol deposition [2][4] [61]. Most of the piezoelectric energy harvesters with thick films are reported on a Si substrate [62]- [65]. However Si substrate can be easily broken and presents limitations such as low vibration amplitudes [3]. Flexible and compliant piezoelectric energy harvesters are more and more studied to overcome the brittleness and rigidity of the substrate and/or the piezoelectric materials. There are several feasible approaches aiming to address this requirement, such as the use of organic piezoelectric materials [66], thin films growth on flexible substrates [67], [68], nanowires growth on flexible substrates [51][69], [70], and "pattern-transfer" methods (i.e., first growing and/or patterning films on rigid substrates, and then transferring the patterns to plastic substrates) are some of the proposed options. The growth transfer process is considered to be one of the most common approach for the flexible piezoelectric energy harvesters. They can be achieved by transferring high piezoelectric perovskite thin films from rigid substrates to flexible organic ones using the soft-lithographic technique, laser lift-off process, or solution-based sacrificial layer methods. Park et al [67] presented the concept of the laser lift-off based growth-pattern-transfer process for the piezoelectric thin-film energy harvester (Figure I-21). The final PZT thin film NanoGenerator (NG) on a single thin plastic substrate converts a high-output performance of ∼200 V and ∼150 µA•cm -2 from the slight mechanical deformations. The short-circuit current generated from a large-area NG (3.5 cm × 3.5 cm) reached up to ∼ 8 µA. The design of the devices and the chosen process depend on the required performances for a given application (frequency, acceleration, required power) and on the expected costs. Alternative processes are thus proposed. In particular thicker piezoelectric layers combined with flexible substrates (for instance metallic substrates) may be nowadays preferred to achieve higher power. Here, because of application requirements for this thesis work (flexibility, mechanical reliability, low cost, good integration), the energy harvester to develop is based on a metallic substrate with PZT thick-film. In the following section examples of EH using metallic substrates and/or PZT thick-films are hence shown.

Metallic substrate based energy harvesting devices

Common piezoelectric EH are millimeter size cantilevers, unimorph or bimorph with two pieces of bulk piezoelectric material sandwiching a metallic stainless substrate [30]. Thinning of the bulk bonded ceramic is moreover proposed to bridge the 1 to 100 µm gap which lies between bulk and thin film components. Once thinned, these bulk ceramics can be micro-structured on metallic supports [71], but also on silicon substrates as reported by Aktakka et al, 2011 [63]. With a bimorph harvester with a 50µm PZT layer of thinned bulk ceramic reported on a stainless substrate ( These processes require additional micromachining, grinding and/or polishing of the bulk ceramics which needs finally to be manually assembled. An interesting alternative is the use of thick-film processes to fabricate the PZT transducer (screen-printing, sol-gel process, electrophoretic deposition, tape-casting or aerosol deposition). For instance, screen-printed piezoelectric thick-films implemented on stainless steel platforms have been shown to deliver power of ~240µW harvested at 66.2Hz with an acceleration of g=2.8m.s -2 (0.3g) [START_REF] Zhu | A credit card sized self powered smart sensor node[END_REF] With the same acceleration, free-standing piezoelectric thick-films (bimorph structure) fabricated on a silicon sacrificial substrate provide ~3 µW at 250Hz though power of ~50µW is measured at 242Hz for g=13.7m.s -2 (1.4g) [4]. For piezoelectric energy harvesting, stainless steel (SS) substrate is so far the most popular metallic substrate because of its relatively low Young's modulus. Other metallic substrates are also studied such as brass, copper, nickel or aluminum [61][74]. Performances of some selected vibration piezoelectric EH using metallic substrates (SS substrate mainly) can be compared in Table I-6. The different materials and technologies or processing (piezoelectric layer, substrate, proof mass) are detailed.

Conclusion

In general, energy harvesting offers significant advantages and opportunities for the development of smart applications (smart cities, smart homes, smart health, smart agriculture, intelligent transportation, industry, security, marine, and so on). It is a promising option for creating an enhanced class of autonomous self-powered terminal nodes that can operate for much longer periods of time without the need of battery charges. It can also induce cost savings by significantly delaying battery replacement and the energy harvesting solutions can further increase the robustness in all IoTs applications.

MEMS piezoelectric energy harvesters at the ~mm 3 dimensions can lead to battery-less autonomous sensors systems and networks if 10-100 μW of power can be extracted from the ambient vibration continuously, robustly and at low cost. Various types of harvester configurations, piezoelectric materials, and fabrication techniques have been explored. However, the domain of MEMs energy harvesting still faces some challenges as for instance the use of new kind of materials (organic or bio piezoelectric [START_REF] Gaur | A bio-based piezoelectric nanogenerator for mechanical energy harvesting using nanohybrid of poly(vinylidene fluoride)[END_REF]) or processes. Also, a large number of approaches have been proposed to enhance the power output and broaden the working frequency bandwidth: These approaches concern the:

 Nature and processing of the active material to increase its properties (densification optimization for instance for PZT layers as seen in this state of art).

 Nature of the passive substrate: Tendency for flexible substrates with good mechanical reliability and wearable applications. Substrates with better thermo-mechanical compatibility with the active material for ensuring high-quality of the structure interfaces [START_REF] Oh | Fabrication of piezoelectric polymer multilayers on flexible substrates for energy harvesting[END_REF][80].

 Structure design: complex geometries have been explored to reduce resonant frequencies and increase strain [3][81]. Multi-frequency harvesting are also found, these one aim to achieve multiple resonant frequency in order to broaden the operating range by structure, geometries, and number of spring-mass hierarchies modifications [27]  Hybrid mechanism: structures using more than one transduction mechanism piezoelectric-electromagnetic, piezoelectric -electrostatic [START_REF] Paprotny | Electromechanical energy scavenging from current-carrying conductors[END_REF][27], or using combined different sources, i.e. solar -vibrations [27] Figure I-24: A typical hybrid VEH configuration integrated with piezoelectric and electromagnetic mechanisms. (Image from [39]  Non-linear harvesting mechanism : different dynamic response that increases the frequency bandwidth by hardening or softening the resonance characteristics of the beam structure [START_REF] Hajati | Ultra-wide bandwidth piezoelectric energy harvesting[END_REF]  Electrical circuit design: used for both increasing power output and broadening the frequency bandwidth [29].

In the frame work of this thesis work, the two approaches explored for power enhancements will be the geometry design, and the active material processing. Furthermore the hybrid piezoelectromagnetic mechanism will be explored. Thick-film technology was introduced in the 1950s for the fabrication of the hybrid thick-film circuit when the replacement of the printed circuit board process was envisaged. A hybrid thickfilm circuit comprises integrated circuits, discrete passive components and thick-films (conductors, resistors or dielectrics) reported on a substrate, being a ceramic substrate in most of the cases [1]. The use of thick-film technology was nevertheless overshadowed in the 1960s by thedevelopment of silicon technology. It found again popularity in the 1980s with the arrival of Surface Mounted Technology (SMT), SMT devices being reported on circuit boards using screen-printed solder paste. Nowadays, thick films are not only used in hybrid circuits but also in sensors, actuators and MEMS [1].

Chapter Thick-film technology and Sintering

Basics of the process

One of the characteristics of the thick-film technology is the film deposition method, also called screen-printing. This additive process, classically recognized as a kind of art, was updated and modernized in order to be used as a scientific tool for microelectronic technology. The main evolutions are the screen materials and the more sophisticated screen-printer equipment. With this technique, conductive, resistive and dielectric layers of a controlled thickness (from 1 µm to a few tens of microns per deposit) with line definition until 100 µm can be printed. Figure II-2 illustrates the principle of the screen-printing process.

The screen is typically made with a specific mesh fabric attached with tension to a metallic frame. The mesh is coated with an ultra-violet (UV) sensitive emulsion, and the desired pattern is produced by photolithography on this emulsion. During printing, the screen is held at a constant distance from the substrate, typically 0.5 mm. The ink (or paste) is applied to the upper surface of the screen. Then, the squeegee traverses the screen under pressure (Figure II-2). The screen is hence in contact with the substrate, and the ink is forced through the open areas of the screen mesh. At this step, due to the surface tension between the ink and the substrate, a deposit of the paste in the desired pattern on the substrate is obtained, and the screen is moved away from the substrate. It is important to notice that the rheological properties of the paste are critical to achieve a good definition of the final deposited layer. This will be further detailed in the section devoted to pastes.

The next stage of the process is to dry the deposited layer to remove the organic solvents from the paste. Finally, as the paste contains fine powders, it must be exposed to a high temperature in order to form a solid layer; this is referred to sintering.

Evolutions of the screen-printing process

Among numerous technologies nowadays available for printing films in microelectronics, screen-printing is the simplest, most flexible and cheapest process. The most valuable advantages of screen-printing are the low investment required in equipment and the large choice of materials, including substrates and pastes. It allows valorization of the properties of materials and development of applications in the field of passive components, sensors and actuators. Nevertheless, standard screen-printing technology presents a line width limited to 100 µm. Modifications of standard screen-printing have been therefore proposed for integration purpose or performance improvement. Polymer thick-films represent, for instance, important achievements leading to various applications on flexible substrates [3]. The screen-printing has also been recently considered for MEMS by using a sacrificial layer [4].

Screens 1.2.1 Screen characteristics

The function of the screen is to define the pattern of the printed film and to control its thickness.

The screens are made of mesh fabric attached to a metallic frame and characterized (Figure II-4) by:

 The wire diameter d that depends on the type of fabric.

 The number of wires per inch (mesh count M). This mesh count and the filament diameter determine the resolution of the deposit. In general, a typical mesh count might be 200 wires per inch i.e. 200 meshes.

 The ink passage zone which is the opening of mesh O. It depends on the mesh count and on the filament diameter. In general, the opening of the mesh must be 3 to 5 times greater than the maximum diameter of solid particles in the paste.

 The thickness of the mesh fabric is a function of the tension of the mesh fabric on the frame. The tension varies from 8 to 30 N/cm.

 The emulsion covering part of the fabric, of thickness 𝐸 𝑓 , chosen according to the final desired thickness (see deposition section 1.5). Note that, for specific applications (e.g. solder paste deposition, or any application where important thickness is required and the definition of deposit is not a limitation) metallic stencil can replace the mesh screen. The stencil is made of a stainless steel foil micro-machined by laser, and its thickness is typically between 100 and 250 µm.

Screen manufacture

The design of the printed circuit can be completed with the different available commercial software packages. CleWins4 has been selected in the framework of this thesis. Design guidelines such as track width (minimum 100 µm), track spacing (minimum 150 µm), fiducials shape (circular or cross) (Figure II-6 (left)), and size must be taken into account depending on the selected screen. When the UV photolithography step is led, an accurate photo-plotter has to be used to print the design on a plastic sheet (Clicherie, Pessac France). Another option is to send the generated files (extension .cif) to fabricate the screen directly (Marabu Bondy France or DB Products, Savigny, France). Once the screen fabric is attached to the metallic frame, the light-sensitive emulsion must be deposited on it before the UV photolithography exposure. Direct emulsion process and direct film method are the typical methods [5].

Direct film method is used here, where an UV sensitized film (negative film from MS Capillary Film -Murakami, Tokyo, Japan) is attached to a transparent sheet of polyester backing. The emulsion supported on the backing film is first placed on the screen (Figure II-5). After heating 1 h at 40 °C, the backing film is removed, and the emulsion can be UV exposed with the pattern mask before its development in water. The UV exposure time varies according to the mesh size and thickness of the polymer film (between 5 µm and 100 µm). For a 325 meshes screen with a 50 µm thick emulsion, the exposure time is for instance 40 s. The complete assembly for the screens fabrication is described onFigure II-6 (right).

Substrates

In classical thick-film technology, the substrate is the mechanical support for the printed layers, which must provide electrical insulation. Other properties should be considered, depending on the final aimed applications: dielectric properties (permittivity and dielectric strength), thermal properties (thermal conductivity, thermal coefficient of expansion, melting point, etc.), mechanical properties (Young's modulus, strength, etc.), density, and cost [6]. The well-known substrate materials used in classical thick-film technology are ceramic substrates, but for sensors, actuators or MEMS applications, other substrates can be preferred such as organic, silicon or metallic substrates.

Ceramic

Some well-known substrate materials used in thick-film technology are the alumina (Al 2 O 3 ), beryllium monoxide (BeO) and aluminium nitride (AlN) ceramics. However alumina is the most common substrate used in the vast majority of worldwide commercial hybrid circuits. Purity of alumina substrate can be found from 96 to 99%. The remaining percent corresponds to magnesia and silica, which improve the densification. A good compromise is obtained in terms of electrical, thermo-mechanical and chemical properties. Moreover, it provides a low-cost solution. Beryllium monoxide has a high thermal conductivity and is used in applications where rapid heat removal is required. It is, however, a very toxic material and is therefore only used in limited applications. Aluminium nitride is mainly an alternative for BeO, with a high thermal conductivity and also improved mechanical properties such as higher flexural strength [6].

Silicon

Silicon, standard in microelectronics for integrated circuits (IC) can be also used in thick-film technology to integrate thick-films having specific properties for sensors or actuators, while keeping the integration of electronic circuits. Silicon or silicon on insulator wafers (SOI) can be simply used as a support during the thick-film process prior to the release of the thick-film [7][8]. Also, as for silicon MEMS, silicon membranes can be prepared by either volume or surface micromachining before the screen-printing step [9]. Koch et al. screen-printed for instance PZT and electrodes on a 70 µm silicon membrane for micropump application [10].

Organic

Organic and flexible printed electronics are becoming more and more popular [11]. Polymer (PET polyethylene, PEN Polyethylene naphtalate or PI polyimide) and even paper substrates can support printed based pastes [12]. Cermet thick-film pastes are not compatible with these organic substrates and special polymer thick-film pastes should hence be selected. Whereas the temperature of operation of these substrates is typically in the range 120-150 °C, the maximum processing temperature (curing of the polymer pastes) is usually limited to  200 °C, except for PI for which 400 °C can be reached.

Metallic

Insulated metals have been successfully used in hostile environment because of their mechanical strength, good thermal properties, shielding character and low cost potential. Porcelain enamel which are steel substrates coated with a glassy layer of thickness (100µm) is an example of such substrate. Nevertheless, it presents drawbacks such as temperature limitation, and complex fabrication process [13]. Stainless steel substrates covered by a screen printed dielectric layer or a tape can be an option and have been successfully used for heating or energy harvesting [14] [15].

In this work, stainless steel substrate will be used to support the printed piezoelectric layers. It has a lower Young's modulus than alumina or than silicon and is hence more attractive for energy harvesting application. It can be found at different thicknesses (<250 m).

Pastes

The study of the rheology of screen printing inks is of great interest since the quality of the obtained deposits depends on the viscosity of the inks.

Basics on rheology

Isaac Newton established the fundamental law of rheology, introducing the notion of viscosity [16]. Let us consider a liquid situated between two flat and parallel surfaces, one of which is in motion in relation to the other (Figure II-7). The speed of a fluid point differs from adjacent planes to a d𝑣 quantity when moving vertically from a dy quantity. This defines the speed gradient (D), also called as the shear speed, which is expressed by:

𝐷 = d𝑣 d𝑦 ⁄ (s -1 ) (Eq. 2.1)
The shear stress is defined by: τ = 𝐹 𝑆 (Dyne. 𝑐𝑚 -2 in CGS, or Pa in S. I. ) (Eq. 2.2)

Where F is the force necessary to overcome the sum of friction forces existing between two neighboring planes (called viscosity forces), and S the surface.

The viscosity is then defined as the ratio between these two quantities:

𝜂 = 𝜏 𝐷 (Pa. s in S. I. or Poise in CGS, 10 poi = 1 Pa. s) (Eq. 2.3)
Therefore, the viscosity depends on the nature of the liquid itself (viscosity forces) and the shear stress. Different rheological behaviors can be found:

 The Newtonian behavior: the viscosity is independent of the speed gradient. Pure liquids often exhibit this type of behavior (water, mineral oil, molasses, etc.).

 The pseudo-plastic or rheo-fluidifying behavior: the viscosity decreases when the speed gradient increases. This is the common behavior of liquids with several phases, at least one of which is solid.

 The dilatant behavior (or rheo-thickening): the viscosity increases when the speed gradient increases, conversely to the pseudo-plastic behavior. This behavior is rare but occurs for highly concentrated suspensions.

All these behaviors are reversible. However, for a constant gradient speed, if the viscosity varies, i.e. it decreases as a function of time, the behavior is said to be thixotropic. The opposite effect is called anti-thixotropic.

Rheology of a screen-printing paste

For an excellent printing quality, an ideal screen printing paste (or ink) must have a pseudoplastic and moderate thixotropic behavior, in order to ensure:

 An adapted fluidity when passing through the screen (i.e., fast printing under squeegee pressure),  Fast settling of the film in the desired geometry after removal of the squeegee and good ink smoothing.

The viscosity of the paste will hence be modified during each step of the printing process, as described inFigure II-8. The main stages, where the speed gradient strongly varies, are the following:

 Before agitation, the viscosity of the ink must be high to keep the particles in suspension before use. The paste is homogenized with a spatula (10 -2 s -1 <D<1 s -1 ).

 During screen printing, the ink is subjected to shearing stresses due to the passage of the squeegee. The viscosity must decrease with the applied shearing stresses so that the ink passes through the screen (10<D<1000 s -1 and η <50 Pa.s for D ~100 s -1 ).

 Once the deposit has been made, the ink must be "coated" or "smoothed" in order to remove the trace from the screen. The viscosity should slowly return to its original value to allow the ink to smooth in time (10 -1 <D<1 s -1 ); this is the thixotropic behavior.

Paste composition

Two types of pastes (or inks) can be considered: the so-called "mineral" inks with generally firing temperatures between 500 and 1100 °C, and the so-called "polymer" inks, developed for low temperature applications, whose consolidation by polymerization is carried out below 200 °C. Polymer inks will not be detailed, but rather that of mineral inks consisting of a mineral and an organic phase.

Mineral phase

The mineral phase differentiates each ink as it defines the final function of the screen-printed layer. It contains:

 The active material in the form of a powder generally calibrated from 0.1 to 10 microns. It provides to the printed layer its final properties (conductor, resistive, insulator, magnetic, piezoelectric, etc.). Commercial conductive inks are manufactured from silver, gold, platinum powders, or from metals alloys from these metals (Ag-Pt, Ag-Pd, Ag-Pd-Pt, Au-Pt, etc.). The films characteristics (sinterability, conductivity and solderability) are strongly affected by size and shape of metal particles. Finally, resistive inks usually consist of ruthenium dioxide (RuO 2 ) or ruthenate (Bi 2 Ru 2 O 7 or PbRu 2 O 6 ), with different proportions of glasses. For other applications as sensors, a myriad of metal oxides can be used (SnO 2 , WO 3 , ZnO, ZrO 2 , etc.) [17] .

 Additives or dopants are introduced in small quantities and may be used to adjust physico-chemical and electrical properties, or to reduce the sintering temperature, promoting adhesion, etc.

 The mineral binder: it is generally a glass frit which has a softening point in the range 400-600 °C. Hence, during the firing temperature, the viscosity of the glass is low enough to assist the sintering of the mineral part. This glass being liquid will wet both the substrate and the grains. During cooling, this phase solidifies and ensures the cohesion of the layer and its adhesion to the substrate. Its coefficient of thermal expansion should be as close as possible to that of the substrate. Silica glasses with a large amount of Pb are often present in thick-film resistors and often in conductors. New pastes are nevertheless developed to follow the RoHS directives (Restriction of the use of certain Hazardous Substances as Pb Bi, Cd, etc).

Organic phase

It is a mixture of volatile solvents and polymers or resins. It provides a homogenous suspension of the particles in the paste and the suitable rheological properties for the printing stage. It should also temporarily ensure the cohesion of the mineral part after the printing process and be removed entirely in the following steps of the process (drying and sintering).

The most straightforward formulation of organic vehicle used in previous work [18] for feasibility studies is based on terpineol-type solvents and cellulose type resins. A well-known formulation of paste is ethylcellulose dissolved by terpineol and butyl carbitol solvents. Most of the solvents are removed during drying (120 °C-150 °C) while organic binders are only removed by firing in air atmosphere at temperature ranging from 150 °C to 550 °C. Acrylic resins are alternative to ethylcellulose for paste compositions requiring nitrogen firing, as they depolymerize when heated. The relative fractions of these ingredients depend on both the shape and nature of the inorganic part.

When using polymer pastes, the thick films are not fired at high temperature, unlike conventional inorganic pastes. The glassy binder is indeed substituted by a thermosetting resin which purpose is to ensure the cohesion of the layer. A drying or drying and curing step at a temperature in the range from 150 °C to 300 °C will then give to the printed layer its final structure. Several types of resins can be found:

 Phenolic resins: they have very good dielectric properties, but they can also be used as conductive inks when loaded with metallic powders.

 Epoxy resins: they have similar properties to those of phenolic resins.

 Polyimide resins: they have a higher curing temperature; they resist at higher temperatures providing hence a more reliable and stable system because of a higher temperature resistance.

For polymer-based conductors, silver powder is the most common additive, for polymer-based resistors, a mixture of carbon black, graphite and silver powders is used; finally polymer-based dielectrics include a pigment and inorganic filler. In this thesis, for the EH layer, mineral pastes will be used: PZT based paste will be home-made, whereas electrodes based on Au will be provided by ESL (Electro Science laboratory www.electroscience.com, further information in chapter 4). The specific preparation of the PZT ink used in this work will be later explained in chapter 4. Also, a low temperature paste based on epoxy and carbonate will be prepared to be used as sacrificial or protective layer. The preparation of this paste will be given in chapter 5.

Paste preparation 1.4.4.1 Milling

Before incorporating the active powder into the organic phase, a milling step is necessary if the grain diameter is not adapted (> 10 µm) or if large agglomerates are present. A uniform distribution of precursors is hence obtained. This process is carried out during 12 h using 30 g of powder with 40 g of ethanol and 13 agate spheres per jar. A speed of 400RPM is used during milling. The grain size is checked out before and after milling by a laser diffraction spectrometry analysis. Afterwards the powder is dried at 40 °C in an oven.

Powder mixing

If the mineral phase powder is based on two or more powders (active material and/or additives and/or mineral binder), the powders must be mixed before adding the organic phase. They are first weighted with a precision Sartorius balance. A minimum of 10 g is required for the further organic incorporation step. The mixture is then placed in a plastic container with agate spheres (10 mm ∅) and ethanol solvent. The containers are then introduced in a Turbula shaker mixer (Turbula System Schatz Mixing is carried out during 7 h at a frequency of 101 min -1 . The homogenized solution is then dried at 40 °C in an oven.

Organic phase incorporation

Finally, the organic binder is added to the powder mixture in order to provide a desired viscosity for the thick-film paste.

The mixture (organic and mineral phases) is first blended manually in a mortar with the suitable proportions which vary typically between 10 to 20% vol. Then it is transferred in a three roll mill (EXAKT 80 at IMS) (Figure II-12 (left)). The used gap is typically of 2 mm. The dispersion control of the ink is carried out during 5 cycles with a speed

of the three roll mill between 18-58 RPM.

Control of the viscosity

If the viscosity is not well adapted, the rheological properties of the ink will not be suitable, for example high η doesn't let the ink smooth after printing (section 1.4.2). Hence, the viscosity needs to be controlled after the paste preparation, by printing tests and measurements with a rheometer. The rheometer used is a parallel plate cone-type measurement system which consists on a cone structure with an angle α (lower than 1°) respecting the horizontal plane of its position ( The rheometer used is a CARRIMED parallel plate cone-type measurement system present at ELORPrinTec-Université de Bordeaux. The shear speed D varies between 10 -1 and 10 4 s -1 . The viscosity measurement range for this system is between η = 0.1 and η= 5.10 3 Pa. s.

Deposition 1.5.1 Squeegee

The squeegee is a flexible blade. Its function is to transfer the paste through the screen and onto the screen. Lifetime of the squeegee and screen are linked to squeegee's material, shape and pressure applied during the printing. Squeegees must be also resistant to the solvents and pastes used in thick-film processing. Common squeegees are in polyurethane or neoprene, with hardness in the range 50-90 durometers [5]. For stencil screens, metallic squeegees are recommended. Photographs of a typical squeegee and the corresponding blade are shown inFigure II-14.

The squeegee construction used in this work is shownFigure II-14 (a), with an angle of attack of 45°.

Figure II-14: (a) Photographs of the polyurethane squeegee used in this work, (b) and the metallic squeegee for stencil screens.

Screen-printing machine and critical parameters

The screen-printing equipment used at IMS laboratory is a DEK Horizon 03IX, which includes an automated sight-reading and alignment system. A photo of the DEK is shown inFigure II-15. Different parameters need to be carefully optimized in order to obtain a good deposition:

 Alignment and fiducials: The alignment of the screen and substrate is crucial so that the paste can be printed at the desired position. This is ensured via the video recognition of circular fiducials of 1 mm diameter. These fiducials are incorporated into the screen patterns and filled up with silver epoxy resin (ESL1901, Annex 1) to facilitate their recognition. The fiducials are also printed on the stainless steel substrate holder. A blue dielectric ink (ESL4924, Annex 2) sintered at 850 °C is used for this purpose. The contrast with the substrate must be strong for a good alignment. However, slight inaccuracies in the automatic alignment have been noted so a constantly manual verification of the alignment is required.

 Off-contact distance: Screen printing requires the screen to be slightly separated from the substrate. The "off-contact distance" also known as "snap-off distance" should be kept to a minimum to prevent image distortion. This off-contact distance is required to prevent the screen from adhering to the substrate which would cause separation problems and damage print quality. Off-contact distance allows the mesh to come in contact with the substrate only at the printing edge during the printing. Off contact distances of 0.5 mm -3.0 mm are common and values of 0.1 mm -0.2 mm is possible with stainless steel masks.

Excessive off-contact distance generates print quality and alignment problems. In most situations, the best off-contact distance is the lowest one. Off-contact distance is controlled by the distance between the platform substrate and the screen.

 Squeegee pressure: Optimization of the squeegee pressure is necessary, since this one can limit the amount of paste transferred, and thus the thickness. It also affects the definition and uniformity of the print. The optimal pressure depends on the paste viscosity, screen tension, and off-contact distance (distance between squeegee and substrate). Squeegee pressure is also very critical when superposition of layers is made, high pressures can damage the previous printed layers. Pressure load values ranged from 1to 20 kg.

 Squeegee speed: This parameter affects directly the thickness of deposit and depends on the rheological properties of the paste. At higher speed, a smaller amount of paste is transferred and as a result the layer thickness is lower. Squeegee print speed values range from 10 to 200 mm/s.

 Printing direction: Printing should be carried out in the direction of the longest possible length of the patterns in order to have a more homogenous deposit. If two layers are printed next to each other, the printing order has to be taken into account since this affects the shape of the junction.

 Emulsion thickness and screen mesh: The setting of the screen-printer associated with the screen mesh and its emulsion thickness determines the final deposited thickness and its precision. Examples of screens are given in Table II-3. For a film deposited with a given screen, the thickness of the deposit (T) can be approximated by the relation (2.4):

𝑇 = 0.5𝐸 𝑡 + 𝐸 𝑓 (Eq. 2.4)
Where E t and E f correspond to thicknesses of the fabric and the emulsion, respectively [5].

Table II-  Separation speed: This is the speed at which the substrate is separated from contact of the screen after printing. This is rather a consequence of the off-contact distance for mesh screens, but may be a problem in the case of the stencil screen where too low speed can generate some uniformities of the deposit. The speed usually used is 1 mm/s.

Table II-4 reports some characteristic parameters impacting both the printed thickness and the resolution [5].

Table II- In this thesis work, the screen and its emulsion and each of the parameters (off contact-distance, separation speed, squeegee pressure, and speed) have been optimized experimentally to reach the desired thickness and resolution (Table II-5). It is worth noting that the values for the squeegee pressure and speed are an approximation from the different deposition processes carried out since these parameters depend on the ink viscosity, which was observed to be very sensitive to slight temperature changes and lifespan. Even under controlled conditions (clean room), these two parameters need to be readapted beforehand to each deposition. Separation Speed 1 mm/s

Drying

After the screen-printing and the paste smoothing, the film has to be dried at temperatures between 120 °C and 150 °C in a conventional oven. During this stage, the most volatile organic solvents are removed. The thickness of the layer can be decreased of approximately 50%, this value depends on the proportion of organic vehicle. If the component is a multilayer, after each drying of the layers, the next layer is printed and dried again.

Other types of drying (or curing) can be led depending on the nature and thickness of the layer. When considering thick layers (>100 µm) the drying has to be progressive in order to avoid cracks and bubbles within the layers. During this progressive drying a ramp of 1.2 °C/min is chosen and controlled by a Heratherm (Thermo Scientific) oven. Control of the thickness should be done either after the drying step, or after firing.

Partial conclusion

From the above sections, thick-film technology appears to be cheap and straightforward. The flexibility and accessibility of this technology result from the possibility to print different shapes and thicknesses, with a stack of layers of different nature.The prototyping of this technology with the integration of the conditioning electronics on the same substrate offers a major advantage. However, several issues can appear due to the multicomponent nature of the pastes and the fired films, and the presence of the substrate on which the layers are bounded (except for freestanding layers for MEMS applications). A deep understanding of the physico-chemical reactions occurring during the transformation of the deposited layers into the functional component is necessary to optimize the properties of the final component.

Sintering

The densification step is one of the key steps in the process. In a first stage, the densification of the screen-printed deposited materials has been carried out by a conventional sintering approach, in order to validate the screen-printing fabrication process as a route to MEMS production for energy harvesting applications. Then, we have implemented the Spark Plasma Sintering (SPS) technique into the fabrication process for further improvement of densification, and therefore optimization of overall properties.

Conventional sintering method and its application into the screen-printing fabrication process will be first described. The Spark plasma sintering (SPS) technique will be then introduced.

Definition of sintering

Sintering is defined as a thermal treatment for bonding particles into a coherent, predominantly solid structure via mass transport events that often occur at atomic scale [23]. This consolidation leads to higher strength and lowers the surface energy by reducing surface area through the formation of interparticles bonds.

Types of sintering

From a technical point of view, free sintering (conventional sintering) which is carried out without any mechanical stress (heating under air or controlled atmosphere) can be distinguished from constrained sintering performed in the vast majority of cases with the simultaneous action of heat and external pressure, and more often used for materials hard to densify. Different types of sintering can be mentioned:

 Solid state diffusion sintering: Consolidation is made in the absence of any liquid phase and includes single phase, mixed powders and mixed phases sintering in the solid state.

 Liquid Phase sintering: Consolidation is favored by a low amount of liquid phase that accelerates mass transport rates and densification. The liquid can result from melting of one component or formation of an eutectic and allows an efficient rearrangement of particles. The capillary force allows rapid compaction without the need of pressure.

 Constrained sintering: Consolidation with the help of pressure (Hot Pressing (HP), Hot Isostatic Pressing (HIP)), or assisted by microwave (microwave sintering) or Electric Current Activated/Assisted Sintering (ECAS)

We will focus in the next section on solid state sintering that represents the main concern of this study:free sintering by conventional method and then Spark Plasma Sintering (SPS). Table II-6: Changes observed during the three stages of solid state sintering (X = neck size, D = particle diameter, ΔL = length variation, L0 = initial length, S = specific area, S0 = initial specific area ) [25].

Principle

Stages of sintering

Parameter

Initial Stage

This stage is initiated at particle contact points by weak Van der Waals cohesive forces. Contact pressure is often estimated at 1 MPa [25]. The particle rearrangement takes place and the geometry of the contacts evolves with sintering. The neck growth is accompanied by interparticle shrinkage. At the end of the initial stage, the initial surface energy is reduced by almost 50 %, the ratio X/D is less than 0.33, the relative density of the material varies between 60 and 66 % and the reduction of the specific surface area less than 50 %.

Intermediate Stage

It is the main part of the densification process during which different phenomena govern the evolution of the microstructure. Important geometric changes in the pore shape occur, leading to an interconnected pore structure made of cylindrical pores along three grains edges (Figure . The densification often observed towards the end of the intermediate stage, is due to the mobility of the grain boundaries in the compact densifying and consisting of an essential area of solid-solid interfaces. At the end of this stage, the system is described as a stack of polyhedral grains linked by their faces and the relative density reached is about 92%.

Final Stage

Final stage occurs when most of the pores shrink. The porous network left in the previous stage becomes geometrically unstable, as the density increases the pores spheroidize and are no longer connected. At this stage, the closed porosity is difficult to remove, densification is slowed down and accompanied by grain growth.

Constrained sintering under pressure

The application of pressure during the sintering of a compact allows improving the rate of densification at the same temperature, compared to free sintering (without pressure application). The applied pressure also influences the rearrangement stage (particles sliding) and allows to eliminate agglomerates, particularly for nanometric powders.

The applied pressure increases the contact between particles providing additional energy W that is quantitatively estimated with Eq. (2.5).

𝑊 = 𝑃𝛽 (Eq. 2.5)

Where W is the energy supplied by the pressure, P is the applied pressure and 𝛽 the volume of a mole of particle.

The use of pressure during sintering is an efficient approach to improve densification while minimizing grain growth [26][27].

Conventional sintering method

Conventional sintering is most commonly used for its simplicity of implementation. Heat treatment is carried out at temperature below the melting temperature of the main components of the material, allowing the formation of bonds between particles through diffusion of matter [28]. In addition to its simple implementation, this technology is the least limited in terms of shape and size of materials that can be sintered. However, it is a high energy consumption process since densification relies on the diffusion mechanisms activated at high temperatures.

Conventional sintering is carried out in electric furnaces, some with the potential to reach 3000 °C while controlling the sintering atmosphere. Heat is transmitted to the sample by convection and radiation mechanisms, so temperature gradients may exist between the surface and the sample volume [29][30].

Shaping (case of ceramics)

Powder blending

Ceramic powders usually incorporate additives as sintering aids to decrease high sintering temperatures and to inhibit grain growth. The mixing also includes a lubricant/binder (e.g. stearic acid, zinc stearate, organic) which have several functions:

 Powder flows more easily.  Die friction is reduced, so more uniform product density is achieved, part is ejected without cracking and die life is increased.

This process is carried out in the same way as described in section 1.4.4 "Powder milling", of this chapter.

Compaction

The powder is pressed into a shaped mold/die at high pressure: e.g. 350-800 MPa for steels, 70-275 MPa for aluminum and 100-150 MPa for alumina molds. Presses need capacities (maximum force) up to hundreds of tons force (several MN) to achieve these pressures. The press capacity usually limits the size of the part that can be formed. The compact, called the 'green compact', remains fragile and must be handled carefully.

For ceramic materials, the linear dimensions of the green compact will be 15-20 % greater than those of the sintered body due to the porosity (up to 50 %). For metals, the powder particles themselves deform during compaction and the green compact has a similar density to the final product (up to 95 % of bulk metal); there is little or no shrinkage during sintering [31]. This compaction step can be carried out using different methods (uniaxial or isostatic pressure). For the screen-printed samples isostatic pressing beforehand conventional sintering step is necessary in order to improve densification and adhesion between layers [32].

Pressing

Uniaxial pressing (case of ceramics)

Uniaxial pressing involves the compaction of powder into a rigid die by applying pressure in a single axial direction through a rigid punch or piston. The presses are usually mechanical or hydraulic.

In the framework of this thesis, the ceramic discs are shaped using a manual hydraulic press (Specac press KBR) located at IMS laboratory, with a gradual application of a load of 2.5 tons for a 13 mm diameter steel die.

Isostatic pressing (case of printed thick films)

Isostatic pressing is used to compact the printed samples placed in a flexible plastic bag. This sealed container (sealed after vaccum) is the mold for the sample, fluid pressure is exerted over the entire outside surface of the container. The pressure exerted by the fluid during isostatic pressing manufacture, provides uniform compaction of the sample. Isostatic pressing is commonly used over conventional metallurgical techniques to produce large quantities, have high thickness to diameter ratios, or for superior material properties. Isostatic pressing tends to have long cycle times and is preferred for short production runs. This manufacturing process consists of two main categories, cold isostatic pressing and hot isostatic pressing.

In the framework of this thesis, the pressing of the different layers of the printed structures, are carried out at the EXXELIA TEMEX society (Pessac, France) using an isostatic pressure of 40 MPa at 65 °C during 4 min.

Sintering of screen-printed thickfilms by conventional method

The dried and pressed screen-printed layers are then sintered. The duration of a classical conventional sintering cycle in an oxidizing (air) or neutral (nitrogen) atmosphere is approximately 60 minutes with a 10-15 minutes step at temperature between 850 °C and 950 °C depending on the inks. Different events occur during the heat treatment (Figure II-17):

 From ambient temperature to 500 °C: decomposition of binders of high molecular weight (debinding). Oxygen supply is required at this stage, as well as elimination of combustion or decomposition products.

 From 500 °C to 800 °C, softening of the particles of the vitreous binder is carried out and sintering process begins.

 From 750 °C up to the sintering temperature, the vitreous binder becomes liquid and wets the particles. The grains are getting closer, the sintering becomes faster and the contact between the glass and the substrate starts to reach adhesion.

 At the sintering temperature, densification continues as the chemical and mechanical interactions between the substrate and the layer are favored by the presence of vitreous binders or oxides.

 During cooling, the glass phase gradually solidifies and seals the layers on the substrate. The layer generally brings mechanical constraints to the substrate. These are applied to the layer-substrate interface. After the heat treatment, the thick layers show residual porosity due in part to the voids left after the removal of the organic binder (Figure II-18) [6]. In some specific cases, a significant level of porosity can be desired, for example in the case of some ferroelectric layers when vibrations in the thickness mode (k 33 , d 33… ) are targeted [33][34] or gas sensors [35], but it is often inadequate for several applications [36][37], in particular when good mechanical properties are required. For example, in the case of conductive inks (Figure , the lack of compactness contributes to the increase in the resistivity of thick layers compared to that of bulk materials. In general depending on the ink nature, several solutions can be considered to control the compactness of the screen-printed deposits.

 The most common solution is the introduction of a glass phase in more or less high concentration. It softens at the sintering temperature, wets the grains, brings them closer together, and fills the intergranular zones. As a result, the deposit is obtained with low porosity.

In the case of dielectric inks, the glass phase must be added in limited quantities, otherwise the dielectric constant will drop significantly. This glass phase can be for example a lead borosilicate with a low melting point (ternary system Bi 2 O 3 -SiO 2 -PbO melting at 500 °C) or a glass that recrystallizes on cooling (ternary system Al 2 O 3 -SiO 2 -BaO). In the case of resistive inks, the glass phase allows to limit the porosity but also to modify the electrical resistance of the layer. In this case, the most commonly used glass phase is lead borosilicate.

In addition to reduce the porosity of the layer, the glass phase also promotes adhesion of the deposit onto the substrate. For example, placed on ceramic substrates, the glass phase is present at the interface between the ceramic and the deposit. On cooling, the glass phase solidifies and ensures adhesion of the deposit to the substrate. Good compatibility between the coefficients of thermal expansion of the glass and the substrate is necessary.

 When the presence of a glass phase is problematic (for example, in the case of conductive inks), a low level of porosity can be achieved by increasing sintering temperature (850 < T (°C) < 950) close to the melting temperature of the metals (T m (Ag)=961 °C, T m (Au)=1063 °C, T m (Cu) =1083 °C, …). However, a small quantity of glass phase (2 to 10 % in volume of lead borosilicate) or of reactive binder (3 % in volume of CdO, CuO or Al 2 O 3 ) does not significantly affect the properties of the layer.

 When the active components of the ink have a very high melting temperature (1250 °C-1400 °C), which is the case for most oxides, the limitation of the sintering temperature below 1000 °C is not enough to ensure proper sintering of the thick layers. In this case, it is possible to add a mineral phase compatible with the active material whose role is to cause intergranular melting via an eutectic composition. This phenomenon of dissolutionprecipitation by formation of a transient liquid phase at a temperature close to the sintering temperature accelerates and improves the densification of the material and consequently reduces the porosity.

Furnace set-up for conventional sintering

Spark Plasma Sintering (SPS)

ECAS (Electric Current Activated/Assisted Sintering) technology has many variants such as the Pulsed Electric Current Sintering (PECS), the Plasma Assisted Sintering (PAS), the Pulse Discharge Sintering (PDS), and the Flash Sintering (FS). Spark Plasma Sintering (SPS) is a nonconventional sintering technique that belongs to this ECAS group and to the techniques called FAST (Field Assisted Sintering Technique). It consists on the simultaneous application of a uniaxial pressure and an electrical current. This technique differs from others in its specific method of heating the sample. Heating is carried out by passing a pulsed electric current of high intensity and low voltage through the electrodes of the press, the punches, the matrix (in graphite or WC-Co) and sometimes through the sample if conductive. When the sample is an insulator, the current only passes through the mold [40], this current allows the temperature to rise by Joule effect heating.

The most appealing features of SPS lies on the high heating rates, allowing to achieve high densification in fast thermal cycles. As a consequence, this technique has been the most widely used technology among ECAS technologies in recent years.

For this process, the powder is loaded in a die (typically graphite) whose inner wall has been previously covered with a graphite foil (papyex) (Figure II-21) used to prevent possible reactions between the matrix and the material, but also to facilitate the release of the sample from the mold. A graphite foil disc is also placed between the powder and the pistons. The matrix is placed between the graphite spacers that will be used to drive and concentrate the current from the electrodes, as well as to transmit the pressure applied to the sample. The current flow allows the temperature to rise by Joule effect. This current gets through punches, and can also pass totally or partially through the powder according to the electric conductivity of the material to sinter [40] . The matrix tranfers the heat produced by conduction towards the core of the sample. For conventional sintering methods, such as natural sintering and resistive hot pressing, the heating of the furnace resistances allows the temperature rise, the heat created is transferred by convection/radiation leading to longer heating times in contrast with SPS.

In the majority of cases, this assembly (matrix + punches) is in graphite so that sintering temperatures can reach more than 2000 °C, but the pressure is limited to 100 MPa. However, it is possible to use other materials such as steel or ultra-hard carbide systems. In this case, the temperature is limited to 900 °C (100MPa), and the applied pressure can reach 900 MPa (100°C) for a tungsten carbide system. SPS sintering process is usually done with primary vacuum, using controlled atmospheres (neutral, nitrogen, argon). The experimental parameters that have a strong influence on the densification in SPS are mainly the temperature, the applied pressure, and the heating and cooling rates. During a SPS cycle, the temperature can be measured by an optical pyrometer (at the surface of the die, or the top piston from above) and by a thermocouple placed at the closest to the sample. The comparison of these two methods of measurement can lead to a difference of several tens of degrees [41].

The applied force is in between 3 kN and 50 kN (considering SYNTEX SPS-515S) and is converted to a pressure considering the diameter of the mold. Throughout the SPS cycle, a sensor records the displacement of the set-up between the electrodes along the compaction axis, allowing to observe the dilatation/contraction effects which can be useful for reproducibility process behavior when considering samples of same nature.

The heating rates can reach several hundred degrees per minute which represents a significant advantage of SPS technology compared to more conventional methods, where the heating speed is limited to a maximum of a few tens of degrees per minute. Cooling is done by natural or controlled ramp.

The SPS is recognized as a very efficient technology to sinter a wide range of materials, whether they are electrical/thermal conductors or insulators [42]- [44]. It can be used to consolidate functional, new or unusual materials, nanomaterials, and multi-materials [45]- [47]. SPS allows to sinter materials at lower temperature and shorter time than conventional or hot pressing techniques. This represents a significant advantage for materials hard to sinter by conventional techniques, for nanostructured materials as well as for controlling interfaces in multi-materials.

This technique is generally used without the use of sintering aids. Some examples of materials sintered by SPS are:

 Metals: nanocrystalline iron [48], aluminum powder [41], iron molybdenum alloy [49], Mo-Si-Mo Multi-Layer Metal Assembly [50], formation of a new phase (Cu x V 2 O 5 ) by direct interaction of metallic copper with vanadium oxide V 2 O 5 [51]. [54], YAG [54], MgO [54], ZrO 2 [55], ZnO [56]), superconducting YBaCuO [57], non-oxides (sintering of translucent AlN [58] , SiC [59], cubic BN [60]), cermets (TiB 2 + Cu, ZrB 2 + Cu [61])

 Ceramics: oxides (Al 2 O 3 -γ [52], Al 2 O 3 -α [53], Y 2 O 3
 Composites: several ceramic-metal, ceramic-intermetallic, ceramic-ceramic composites have been sintered by SPS, such as WC-Co [62], alumina-TiC-Ni [63], TiB 2 -SiC [64], Si 3 N 4 /SiC [65], Si 3 N 4 /BN [66], CuTiZrNiSnSi alloy from a mixture of amorphous powders and copper powder. Cu particles provide ductility to the final product [67].

 Polymers: polyethylene, polypropylene and polyimide [68].

SPS Machine

The SPS equipment used during this thesis work is a SYNTEX Dr. Sinter lab. 515-S (Figure . This equipment located in the ICMCB laboratory allows to reach a temperature of ~2500 °C with a maximum heating rate of 500 °C/min. It provides the option to monitor the temperature by a thermocouple (25 °C -900 °C ) and optical pyrometer (600 °C -3000 °C) control. The uniaxial press has a maximum load of 50 kN.

In the framework of this thesis, only the thermocouple is used, under a vacuum atmosphere with a primary vacuum (6-10 Pa)) with a pulsed direct current (12-2 On/Off). For ceramic pellets and multilayer structures, graphite molds of 10 mm and 30 mm have been respectively used.

Partial conclusion

Some advantages and limitations of SPS can be underlined:

Benefits: The trend towards lower energy consumption while keeping optimum reliability requires an optimization of the sintering stage decreasing the sintering temperature, limiting the number of thermal treatments and controlling the chemistry according to the sintering environment. Such an optimization is mandatory in particular when processing complex devices such as integrated printed thick-films, for which the co-sintering/assembly with metals remains challenging. In this context, the use of advanced sintering process such as Spark Plasma Sintering appears as a relevant approach given its specificities: fast kinetics, lower sintering temperatures and short sintering cycles. This chapter focuses on the characterization techniques used to control each step of the fabrication process and to probe the performances of the obtained materials.



Chapter Experimental Methods

Physico-chemical characterizations 1.Particle size distributions

The measurement of the size and statistical size distribution of the particles is carried out using laser diffraction spectroscopy. This method is used to estimate the particle size of wet or dry particles. Wet process is carried out using the powder dispersed in a medium (water, alcohol, etc.). Ultrasound can be used for better dispersion. For dry process, the powder is fed directly into the empty vessel. The principle of measurement involves the diffraction of laser radiation by suspended particles (Mie theory) [1]. The particles are approximated as spheres, homogeneous and isotropic and of a given refractive index. Laser granulometry is therefore precise in the case of spherical powders.

For this study, particle size distributions of the raw powders are evaluated at ICMCB using laser diffraction spectroscopy Malvern Mastersizer 2000 from wet dispersions after ultrasound (1 minute in water). According to the supplier, this device can analyze the particle size distribution over a wide range of particle sizes: from 0.02µm to 2000µm with an accuracy of 0.1 % for a monomodal powder.

Density measurement

The experimental density 𝜌 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 of the disk shaped ceramic samples is determined by geometric method measuring dimensions and volume. From the evaluation of the mass 𝑚, thickness 𝑙, and radius 𝑟 of the sample, the following expression is used ( The relative density (𝑑 𝑟 ) of the sample is deduced subsequently from the ratio of the experimental and the theoretical densities.

𝑑 𝑟 = 𝜌 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝜌 𝑡ℎ𝑒𝑜𝑟𝑖𝑐𝑎𝑙 * 100 % (Eq. 3.2)
With the measurement errors l=±0.15 mm, r= ±0.13 mm, and m= ±0.01 mg an incertitude of ∆𝑑 𝑟 = 0.141 g/cm 3 for 𝑑 𝑟 is found out. In order to have a more precise determination of the relative density, complementary methods can be used: helium pycnometry, Archimede's method or mercury porosimetry.

In this work, analysis of SEM images is used to estimate the level of porosity (paragraph 1.1.5) and then to confront the results with the experimental density (𝜌 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 ) obtained by geometric method.

Layer thickness measurement

A tencor profilometer (Model KLA-Tencor alpha step IQ available at IMS) is used to evaluate thicknesses of the dried or fired printed layers. This operation is necessary during the screenprinter settings, or to characterize the final energy harvester volume. Thanks to a scan of a diamond stylus, this equipment is able to measure step height, roughness and waviness on sample surfaces. Figure III-2 shows an example of the thickness profile that can be obtained.

X-ray diffraction

X-ray diffraction analysis (XRD) is used to qualitatively characterize the phase(s) present in the sample (powder or ceramic). XRD can also give other structural features such as lattice parameters, crystallite size, etc. An X-ray beam of defined wavelength irradiates the sample to be analyzed. If this one is crystallized, the atoms arranged periodically cause the incident X-rays to diffract (Figure III-4). This phenomenon occurs at certain angles, characteristic of the observed crystalline phase. The directions in which interference is constructive, called diffraction peaks, can be determined by Eq. 3.3, known as Bragg's law [3].

2𝑑 sin 𝜃 = 𝑛 • 𝜆 (Eq. 3.3)
Where 𝑑 is the interreticular distance, θ the deviation of the half angle between the incident beam and the direction of the detector, 𝑛 the reflection order and λ the wavelength of the incident X-rays.

Scanning electron microscopy (SEM) 1.5.1 Principle and equipment

Scanning electron microscopy (SEM) is used to observe sample microstructure (grain size and their morphology, porosity) and local chemical analysis using an EDS detector (Energy Dispersive Spectroscopy). The principle is based on the interaction between an electron beam and the sample irradiated. This interaction produces secondary and backscattered electrons.

Electrons are used for imaging; the secondary electrons give topological (surface) information while backscattered electrons provide information on chemical composition. Backscattered electron images in the SEM display compositional contrast that results from different atomic number elements and their distribution [5]. Energy Dispersive Spectroscopy (EDS) allows to identify particular elements and their relative proportions (atomic percentage).

A scanning electron microscope consists essentially of an electron gun fitted with a tungsten filament cathode, whose function is to produce a fine electron beam on the sample, a sample stage to control sample position, and detectors to capture and analyze the radiation emitted by the sample. In addition, the apparatus needs to be equipped with a vacuum pump system (Figure III-5) [6]. The scanning electron microscopes used in this work are the JEOL, JSM-6100 for ceramic samples (IMS Laboratory) and ZEISS EVO50 for specific observation of the interfaces of the printed structures (Placamat -UMS 3626, Université Bordeaux). Both SEM are equipped with an EDS (Energy Dispersive Spectroscopy) detector that enables qualitative/quantitative analyses and element mapping.

Samples preparation

Prior to SEM observations, ceramic samples are coated with ultrathin layer gold deposited on the sample by low-vacuum sputter deposition.

SEM observations are performed on fractured sections for ceramic samples. For printed multilayer structures, sections are prepared using cross polished (Ilion+ II 697) technique at a low energy (5keV), in order to obtain a proper cross-section surface. Samples are prepared at PLACAMAT Platform at ICMCB laboratory.

Images analysis

Evaluation of the porosity from SEM images is carried out by counting observable holes of the microsection plane image and then by calculating their cumulative area. The process is done using the program ImageJ. The ratio of the surface of holes on the total observed surface allows an estimation of the percentage of porosity in the solid [7].

Average grain size is directly measured during images acquisitions using different tools provided by the SEM interface program considering approximately a hundred grains.

Thermal analyses

Thermogravimetric analysis (TGA)

Thermogravimetric analysis or thermal gravimetric analysis (TGA) determines the mass of a sample over time as the temperature changes. This measurement provides information on phase transitions, adsorption, desorption, as well as thermal decomposition, and solid-gas reactions (e.g. oxidation or reduction) [8].

The used equipment is a Thermobalance SDT Q 600 TA Instrument available at ICMCB. TGA analysis of samples is carried out on a small amount of powder (~ 500 µg) under argon atmosphere. The temperature range is 25-680°C and the ramp is 2°C/min.

Dilatometry

Measurements of thermal coefficient of expansion (TCE) allows to better understand thermomechanical interactions between the material's constituents of the multilayer thick films structure occurring during sintering. This analysis accurately measures the dimensional changes of a sample as a function of temperature without applying force. This allows to characterize the linear coefficient of expansion α 𝐿 (°C -1 ) by the following expression:

α 𝐿 = ∆𝐿 𝐿 0 1 ∆𝑇 = 𝑓(𝑇) (Eq. 3.4)
With ∆𝐿 the length increase, 𝐿 0 the initial length and, 𝑇 the sample temperature.

Measurements are carried out with a dilatometry analyzer (DIL Netzsch 402 ED available at ICMCB) using disc samples of 3mm thickness and 6mm diameter with an accurary of ∆𝐿 𝐿 0 ⁄ of 0.002%.

Dielectric and electromechanical characterizations

Sample preparation

In order to access the dielectric and electromechanical properties of the ceramic materials, conductive electrodes have to be deposited on the two parallel faces of the ceramic. For printed multilayer structures, gold electrodes are printed within the thick film process (see chapter 4).

For bulk ceramics, after sintering, both sides are polished using abrasive paper or a fine-grained diamond grinding wheel. Gold electrodes of around 100 nm are then deposited by sputtering onto the ceramic surfaces (tape scotch is placed at the side borders of the pellets in order to avoid short circuit between surfaces). Two silver wires (diameter 0.1mm) are finally attached to the center of each electrode using silver epoxy ink (ESL1901S (see Annex 1 chapter 2)) further dried at 120°C during 1h.

Dielectric measurements

Basics

The response of a material subjected to alternative field with variable frequency generally depends on the frequency of the field. The permittivity, deduced from capacitance measurements, is a complex function of the (angular) pulsation ω of the applied field that decomposes into real and imaginary parts as follow:

𝜀(𝜔) = 𝜀 0 (𝜀 𝑟 ′ (𝜔) -𝑖𝜀 𝑟 ′′ (𝜔)) (Eq. 3.5)
With 𝜀 0 ~8.85 × 10 -12 F/m the permittivity of free space (vacuum).

𝜀 𝑟 ′ characterizes the ability to store charges in the dielectric and the imaginary part 𝜀 𝑟 ′′ , is the contribution of energy dissipation. Dielectric losses are usually expressed by the loss angle 𝛿:

tan 𝛿 = 𝜀 𝑟 ′′ 𝜀 𝑟 ′ (Eq. 3.7)
An ideal capacitor would have high relative permittivity 𝜀 𝑟 ′ and negligible dielectric losses. In a parallel plate capacitor, the dielectric material separates two conductive metal electrode plates. The capacitance is a function of the distance between plates, the surface of electrodes, and the relative permittivity.

𝐶 = 𝜀 0 𝜀 𝑟 ′ ( 𝑆 𝑡 ) (Eq. 3.8)
With S the electrodes surface of the capacitor and t its thickness.

Considering ferroelectric materials, the thermal evolution of the relative permittivity 𝜀 𝑟 ′ (or dielectric constant) presents a divergence inferred by a maximum of the dielectric constant at the Curie Temperature (T C ) which corresponds to the transition temperature between the ferroelectric (T<T C ) and paraelectric (non-ferroelectric) phases (T> T C ) [9]. An illustration is given for BaTiO 3 in Figure III-6.

Set-up

Dielectric measurements are carried out at ICMCB on disc samples. The sample is placed inside a tubular furnace, suspended near a thermocouple for temperature regulation, and between two electrically insulated cylindrical copper electrodes. These are connected to an impedance bridge LCR meter HP4194A, which allows to measure the capacitance and dielectric loss of the sample as a function of temperature and frequency (Figure III-7). Measurements are performed under vacuum with a frequency sweep from 100 Hz to 1 MHz, a number of points between 200-1000, under low excitation level of 1V. Thanks to a resistor located within the furnace, heating is carried out from room temperature until 350 °C (623 °K). The HP4194A analyzer and the Eurotherm temperature control are driven with a LabVIEW program developed at ICMCB laboratory.

Relative permittivity constant and dielectric loss values can be obtained at room temperature and at 1kHz (as usually reported in literature [10]) or as a function of temperature (25°C -350°C) and frequency (100Hz-1MHz)

Electromechanical characterizations

Polarization

The polarization step is necessary for piezoelectric ceramics to exhibit piezoelectric properties. It consists of submitting the sample to a continuous high voltage. The spontaneous polarization in ferroelectric polycrystalline ceramics is random and a polarization process (also called "poling process") is necessary to obtain a macroscopically piezoelectric ceramic. During this process, the domains within the grains reorient in the direction of the applied electric field. A remanent polarization is thus achieved within the material after the removal of the electric field. The polarization of the samples is made in an AET Technologies chamber furnace available at IMS (Figure III-8). The samples are placed inside an isolated platform. Electric contacts are provided by two conductive silver wires (diameter 0.1mm) glued on one side to the center of each electrodes. On the other side, they are connected to two metal rods that deliver the connection with the power supply.

After vacuuming, introduce of nitrogen into the chamber is carry out for ensuring a controlled dried polarization atmosphere, the system is brought to a temperature slightly below the Curie temperature T C . Then, the voltage is applied across the sample (power supply AET Technologies 1.6kV-1.5mA) and held during 10 minutes. Throughout this period, the current should not exceed 10µA in order to avoid breakdown of the dielectric material. The sample is subsequently cooled (10 °C/min) while maintaining the electric field. Finally, the electric field is cut off, and the sample is short-circuited for evacuating residual charges located at the surface.

Vibration modes

When excited by an alternating electric field the piezoelectric sample deforms at the field's frequency. When the frequency becomes close to a specific vibration mode of the sample, impedance (or admittance) submits high variations and minimum and maximum of the impedance can be respectively identified to the resonance and anti-resonance frequencies (Figure III-9). For complex shapes of sample, resonant modes are interfering and are hence difficult to identify. Therefore particular sample shapes are usually chosen to favor a welldefined resonance mode and to ease the understanding of the acoustic wave propagation (Table III-1).

As already mentioned in the state of the art chapter, 33 or 31 modes are usually promoted for energy harvesting piezoelectric applications.

In the framework of this thesis, the 31 mode will be chosen for energy harvesting application using resonant cantilevers. Also, for disks sintered by SPS, the planar mode will be considered. Based on the proposed equivalent circuit for a piezoelectric resonator, for a sinusoidal excitation of angular frequency , the behavior of the conductance G and the susceptance B can be determined as a function of 𝜔. Indeed, the complex admittance Y (inverse of the impedance Z) can be described as follow:

𝑌 = 𝐺 + 𝑗𝐵 = 1 𝑅 0 + 𝑗𝐶 0 𝜔 + 1 𝑅 𝑚 + 𝑗𝐿 𝑚 𝜔 + 1 𝑗𝐶 𝑚 𝜔 = 1 𝑅 0 + 𝑗𝐶 0 𝜔 + 𝑅 𝑚 -𝑗 (𝐿 𝑚 𝜔 - 1 𝐶 𝑚 𝜔 ) 𝑅 𝑚 2 + (𝐿 𝑚 𝜔 - 1 𝐶 𝑚 𝜔 ) 2 (Eq. 3.9) If 𝑎 = 𝐿 𝑚 𝜔 - 1 𝐶 𝑚 𝜔
, then:

𝑌 = 1 𝑅 0 + 𝑅 𝑚 𝑅 𝑚 2 + 𝑎 2 + 𝑗 (𝐶 0 𝜔 - 𝑎 𝑅 𝑚 2 + 𝑎 2 ) (Eq. 3.10)
The conductance G and the susceptance B are respectively real and imaginary parts of the admittance Y. As a result, they can be identified from Eq. 3.10:

𝐺 = 1 𝑅 0 + 𝑅 𝑚 𝑅 𝑚 2 + 𝑎 2 (Eq. 3.11) 𝐵 = 𝐶 0 𝜔 - 𝑎 𝑅 𝑚 2 + 𝑎 2 (Eq. 3.12)
Figure III-11 illustrates an example of G and B curves as a function of frequency for a resonance mode of a piezoelectric material, from which the R m , C m and L m can be extracted. These two curves can be in depth studied (maximum, minimum, limits when 𝜔 tends to zero or infinity (Annex 1). By assuming R 0 to be infinite and by using G(𝜔) and B(𝜔) curves, the component values of the motional branch of the equivalent circuit can be then deduced with the following relationships:

𝑅 𝑚 = 1 𝐺

Electromechanical properties calculations

Calculations of electromechanical coefficients such as electromechanical coupling coefficients factors (k) and piezoelectric coefficients (d) are done in accordance to the IEEE standard model [13]. In practice, resonant modes have to be identified and characteristic frequencies have to be measured.

Characteristic frequencies

The highlighting of the admittance circle B(G) is sufficient to prove that the material is piezoelectric and characteristic frequencies can be identified in this circle for a particular resonance (Figure .

 𝑓 𝑢 and 𝑓 𝑛 defined at 𝐺 =  𝑓 𝑟 and 𝑓 𝑎 , the resonance and anti-resonance frequencies defined respectively at maximum and minimum impedance Y  𝑓 𝑝 and 𝑓 𝑠 , the parallel and series resonance frequencies defined at the maximum resistance and maximum conductance respectively.

IEEE Standard [13] identifies these six frequencies which are often merged, when the quality factor 𝑄 𝑚 is higher than 50: 𝑓 𝑢 𝑓 𝑠 𝑓 𝑟 and 𝑓 𝑎  𝑓 𝑝 𝑓 𝑛 .

Figure III-12: Characteristic frequencies that can be identified in the admittance circle for a particular resonance. The deviation between cercle and axes represents R0 and the capacitance C0 of the dielectric part of the equivalent circuit.

Mechanical Quality factor 𝑸 𝒎

The mechanical quality factor 𝑄 𝑚 represents the mechanical losses of a piezoelectric material. It is expressed as a function of the characteristic frequencies of the resonance peak of G and can be hence deduced from the elements of the equivalent circuit R m , C m and L m . For a given f r , high quality factor Q m will clearly be related to the curve shape (high and narrow peak) (Figure .

𝑄 𝑚 = 𝑓 𝑟 𝑓 𝑛-𝑓 𝑢 = 1 𝑅 𝑚 √ 𝐿 𝑚 𝐶 𝑚 (Eq. 3.14)

Electromechanical coupling coefficient k

The electromechanical coupling squared coefficient k 2 is defined as the ratio of the mechanical energy accumulated in response to an electrical input or vice versa. For a disk where the planar vibration mode is promoted, electromechanical coefficients 𝑘 𝑝 and 𝑘 31 can be calculated thanks to the measured frequencies f r and f a according to the equations: The value of 2.51 comes from the Bessel function [14]. Another parameter, 𝑘 𝑒𝑓𝑓 , is frequently used to express the effective electromechanical coupling coefficient of an arbitrary resonator, either at fundamental resonance or at any overtone. It is expressed as follows:

𝑘 31 2 =
𝑘 𝑒𝑓𝑓 2 = 𝑓 𝑎 2 -𝑓 𝑟 2 𝑓 𝑟 2 (Eq. 3.17)
In this work, k p , k 31 and k eff will be the coefficients taken into account.

Elastic compliance s

The elastic matrix for a cylindrical poled ceramic is:

S11 S12 S13 0 0 0 S12 S11 S13 0 0 0 S13 S13 S33 0 0 0 0 0 0 S44 0 0 0 0 0 0 S44 0 0 0 0 0 0 2( S11 -S12 )
Elastic compliance is the ratio of a material's change in dimensions (strain) in relation to an externally applied load (stress). For a piezoelectric material, the compliance depends on whether the strain is parallel or perpendicular to the poling axis and on the electrical boundary conditions. For instance, for 31 mode of a disk, 𝑠 11 𝐸 elastic constant is calculated at a constant electric field E from the following equation:

𝑠 11 𝐸 = 1 4𝜌𝑓 𝑟 2 𝐷 2 (Eq. 3.18)
Where 𝜌 is the density of the material and D is the diameter of the disk ceramic; Young's modulus can be also deduced using the inverse of the 𝑠 11 𝐸 expression (Eq. 3.18).

Piezoelectric constants d

The piezoelectric charge coefficient d describes the ratio of electric charge generated per unit area to an applied force (C/N or m/V). Taking into account the dielectric matrix presented in chapter 1, and using the planar vibration mode of a disk, from which k 31 is calculated (previous paragraph), the piezoelectric constant is calculated with the following expression:

𝑑 31 = 𝑘 31 √𝜀 ′ 𝑠 11 𝐸 (Eq. 3.19)
Where 𝜀 ′ represents the dielectric permittivity measured far from the resonance frequency, usually measured at 1kHz or 2𝑓 𝑟 . It should be noted that the piezoelectric coefficient calculated above is only valid at frequencies far from resonance and doesn't consider any non-linear behavior of the ceramic. It may also vary with the degree of polarization of the ceramic.

Figure of merit FoM

Even if the electromechanical coupling coefficient indicating the energy conversion ability is a good criteria to choose the piezoelectric material, the Figure of Merit (FoM) [14]- [17] should be taken into account to further compare different materials for energy harvesting applications. This FOM applicable for piezoelectric materials, but not for devices, is defined as the electrical energy density divided by the mechanical deformations in dielectric materials.

𝐹𝑜𝑀 = 𝑑 2 𝐸 2 𝜀 ′ (Eq. 3.20)
Where 𝐸 the Young's modulus, d the piezoelectric constant, and 𝜀 ′ the dielectric constant.

CONCLUSION 158

Introduction

The objective we are seeking is to fabricate and characterize a screen-printed low-frequency piezoelectric energy harvester that can be used in autonomous systems. In this case, the MEMS structure must vibrate with a target resonance frequency value below 100 Hz.

For this purpose, in this chapter, after general considerations on EH design, the selection of the EH structure including the choice of materials and geometry is justified. Then, fabrication process is optimized. In a second step, in-depth investigation of the PZT based EH is carried out, focusing on interfaces, microstructure and electromechanical properties relationships. For this purpose, ceramic samples (printed or bulk disks) are also prepared in order to better understand the phenomena occurring at the interfaces, or to ease the dielectric and electromechanical characterizations. Finally, a simple cantilever EH is tested under mechanical vibrations whereas the selected EH with a complex geometry is tested as a piezoelectromagnetic energy harvester, by integrating a magnet on its extremity.

EH design considerations 1.Resonance frequency and strain of a rectangular micro-cantilever

The piezoelectric energy harvester converts mechanical into electric energy more efficiently when the applied vibration frequency is closer to the resonance frequency of the device. A few percent of mismatched frequency with resonance results in a dramatic decrease of output power. Therefore, adjusting the resonant frequency of the device to the external vibration source is essential in order to ensure a good energy conversion efficiency [1]. Also, for a mechanical structure integrating a piezoelectric material and a seismic at its end, harvesting the maximum of ambient energy implies maximizing the strain on the top surface of the structure. In the case of a simple shaped rectangle micro-beam, analytical expressions of the resonance frequency 𝑓 𝑟 and of the strain ε along the length x of the micro-beam can be expressed as following [2][3]:

𝑓 𝑟 = 1 2𝜋 √ 𝑘 𝑚 𝑒𝑓𝑓 + 𝑀 𝑒𝑓𝑓 (Eq. 4.1) ε Rectangle (𝑥) = 6F Ebh 2 (L-𝑥) (Eq. 4.2)
With k = 3EI/L 3 and 𝐼 = 𝑏ℎ 3 114 Chapter 4: Multilayer EH fabrication And where k is the stiffness of the micro-beam, I the micro-beam's second moment of area , m eff its effective mass for the first flexural resonant mode, M eff the effective mass of the seismic mass (ponctual mass at the free-end of the micro-beam equivalent to the effect of the seismic mass). F is the equivalent inertial force at the free-end of the micro-beam due to the vibration of the support, E is the Young's modulus of the micro-beam with L its length, h its thickness and b the width.

Finally, the resonance frequency can be simplified, by assuming that the seismic mass is much heavier than the micro-beam:

𝑓 𝑟 = 1 2𝜋 √ 𝑘 𝑚 𝑒𝑓𝑓 + 𝑀 𝑒𝑓𝑓 ~1 2𝜋 √ 𝑘 𝑀 𝑒𝑓𝑓 (Eq. 4.3)
For a simple shaped rectangular micro-beam, according to equations 4.1 and 4.3, different solutions can be proposed in order to match the ambient vibration frequencies (< 100 Hz) with the resonance frequency of the EH structure. The natural frequency of energy harvester is usually adjusted by increasing the weight of the seismic mass. However, the use of big seismic masses severely affects the structural integrity and durability of the harvesters. Another option is to decrease the stiffness of the resonator. This can be done by optimizing the cantilever's geometry (ie. increase of length and decrease of width and thickness) or by decreasing the Young's Modulus (ie. using flexible materials). However, in MEMS applications the area of the harvester has to be under 10cm 2 . This area restriction would typically result in a resonance frequency much higher than 100 Hz. Therefore, the method for reducing the spring constant of the energy harvester through the use of specific geometries requires to fit the maximum allowed area, and as result the use of flexible materials is an interesting alternative solution. Also, according to equation 4.2, the reduction of the micro-beam resonator stiffness will be beneficial to increase the generated strain during vibration and hence the harvested power. The two next paragraphs detail solutions found in the literature to reduce the resonant frequency with complex geometry, and to improve generated strain with adapted materials.

Complex geometry

To overcome the MEMS size limitations and maintain a low resonant frequency, a long cantilever can be for instance folded into a spiral one, as seen in ) is another solution that again reduces the natural frequency by increasing the effective length, while maintaining high power [5]. This zig-zag can be modeled as a few straight beams, with rectangular cross sections, placed next to each other on the main plane. Each beam is connected to its neighbor beams at its ends. If the beam comprises a piezoelectric layer, strain occurs in the piezoelectric layer when the beams deflect out of the plane, which generates electrical energy. This zig-zag geometry can outperform 1D cantilever beams in terms of power density and low resonance frequency for a given surface area. However, the fundamental bending mode shape of the zig-zag still includes torsion as in the spiral geometry. As the number of beam elements increases, the torsion related to natural frequencies decreases faster than the bending modes. Other solutions are found in the literature to reduce the effect of torsion in spiral or zig-zag configurations. Berdy

Materials for the passive substrate

Because of their lower Young modulus, flexible substrates enable considerable reduction of the resonance frequency and offer enhanced toughness compared with brittle Si-based cantilevers. Moreover, the piezoelectric response on flexible substrates is higher because of increased strain (equation 1.2). Therefore, researchers try nowadays to exploit the piezoelectric effect with various flexible substrates, such as metal based (aluminum, copper, brass, stainless steel foils), textile fabric, common paper and flexible plastic [9]- [11]. Flexible electronics have advantages such as low-cost synthesis of material, and easy manufacture of thin film devices by printing technologies or vacuum evaporation/sublimation, or large surfaces can be obtained [12]. Furthermore, for printing process, it can be extended to "smart materials and systems" with new ink-based functional materials such as electroactive polymers for example. Among flexible substrates, thin polymeric foils are extremely attractive because they are lightweight and inexpensive making it possible to target high-volume and low-cost commercial products. Nevertheless, the processing of these materials being usually carried out at temperatures below 180-190 °C makes them attractive for organic technology based on lowtemperature printing or evaporation techniques [12], but not for inorganic materials.

Polyethylene terephthalate (PET) and polyethylene naphthalate (PEN) constitute the two main flexible substrates used today in the development of flexible electronics. They provide good resistance to solvents and a discrete tolerance to temperature. Also their intrinsic transparency makes them suitable as substrates for transparent electronics [13][14].

In contrast, metal-based substrates are attractive for piezoelectric vibration energy harvesting MEMS, especially metallic foils, due to their low stiffness and high fracture strength, both necessary to withstand mechanical deformations and to increase the reliability. Moreover, the large Thermal Expansion Coefficient (TEC) of metals such as copper, nickel, or stainless steel (as compared with that of PZT) produces compressive stress in plane during cooling down from the crystallization temperature to the Curie temperature, which can be used to reduce the permittivity and enhance the FoM for energy harvesting. Indeed, the total stress of a thin film material mechanically constrained to a substrate includes three contributions : intrinsic stress (deposition parameters), extrinsic stress (dimensional changes occurring during crystallization or phase transition), and thermal stress [15][16]. The contribution of thermal stress, in particular during cooling, is significant in thick films. It arises from the thermal expansion mismatch between the substrate and the material. The direct correlation between the thermal stress/strain and the volume fractions of c-and a-domains in a tetragonal film is well documented [15]. According to the type of stress (tensile or compressive), specific domain states (a-or c-) are favored (Figure IV-2). As a result, tuning the difference of TEC between the film and the substrate allows to control the domain state at Tc. The resulting domain structure affects film properties such as dielectric constant and remanent polarization [16]- [19]. In the literature, for EH applications, piezoelectric ceramics (already polarized) can be bonded on the metallic substrates or thin/thick films can be deposited on the metallic substrate prior to their polarization. For instance, Berdy et al. developed the meandering EH. The meandering piezoelectric energy harvester is a commercial bimorph type with thick ceramic (270µm) on brass (0.13-mm) and thin nickel electrodes. The shaping is done using a femtosecond pulsed laser (Figure IV-3). In case of piezoelectric ceramics, when complex geometries are chosen, laser micromachining can be done. Polishing can also be led to reduce the ceramic thickness and hence improve the flexibility.

Summary of energy harvesting specifications

The summary of the energy harvester specifications is depicted in Figure IV-6. The use of screenprinting thick film technology to deposit the active piezoelectric film on a metallic substrate (already shaped) followed by a post-polarization step is attractive. Indeed, it represents a low cost and easy shaping process, piezoelectric films are thick enough and passive substrate is flexible (provided it is thin enough). Finally, when using bulk ceramics bonded on the metallic substrate, there is no need of additional mechanical steps usually required to achieve the expected geometry (laser micromachining or mechanical polishing). This mechanical step could induce stresses in the piezoelectric material and lead to a modification of the piezoelectric properties.

Methodology

Figure IV-7 shows the basic scheme of the multilayer structure considered as the "elementary brick" of the study. It consists of a piezoelectric layer screen-printed on the top of a metallic substrate and sandwiched between two electrodes. Nevertheless, keeping in mind the final goal to optimize the process and the properties of the EH with a complex geometry, our approach is also to consider three types of PZT based samples: a bulk ceramic, a screen-printed disk, and a simple multilayer cantilever (Table IV-1). Indeed, according to the sample shape and constituting elements, microstructural, dielectric, electromechanical characterizations and energy harvesting tests are more or less suitable and will be performed accordingly. Through such complementary investigations, we aim a better understanding of the impact of PZT microstructure and interfaces (electrodes/active layer/substrate) on the electromechanical performances of the multilayer energy harvester. The next paragraphs give details on the nature of each constituent of the multilayer.

Electrodes

A gold and terpineol-based ink ESL8836 from ESL (ElectroScience, www.electroscience.com, Annex 2) is used for the modified zig-zag structure, the cantilever and the printed disk.

Electrodes should be very thin compared to the PZT layer. This kind of conductive film is specially designed to achieve thin and dense films on ceramic substrates (<9µm). Moreover, the fact that it is well suited for automatic thermosonic wire-bonding is interesting for the electrodes connections needed for the next steps of polarization and electromechanical tests. Note that, as in most of the thick film pastes, a glass frit is present in the composition to promote densification and adhesion on the substrate (Table IV-3). Previous thesis work showed good compatibility between gold paste and PZT pastes after sintering. This is the reason why once again we selected this type of conductor.

Substrate

Since the target resonance frequency is relatively low, a substrate material with a low Young's modulus has to be selected to reduce the stiffness of the EH. The substrate should also be compatible with all the fabrication steps of the process, especially the firing of the printed layers, typically between 850°C-950°C. As mentioned in chapter 3, silicon wafers, or alumina substrates classically used in thick film technology have too high Young's modulus. Therefore, metallic substrates are preferred. Different metallic substrates used as passive substrates for EH can be found in the literature [15][25]- [28]. Among them, stainless steel (SS) is selected because of its high melting temperature (Table IV

Design of the complex geometry

This section shows how modeling has allowed to select the specific zig-zag geometry briefly introduced in Table IV-1. This specific geometry has been designed and optimized for piezoelectromagnetic application. The objective is to maximize the power density while maintaining a fundamental frequency in the range of 60 Hz to match the resonance frequency of the North American power grid. A permanent magnet is used in the design as a tip mass to harvest energy from the electromagnetic field of the current-carrying wire and to help tune the natural frequency of the system to the desired frequency.

For the optimization of the geometry, the energy harvester is modelled using the 3D FEA software COMSOL Multiphysics and its associated MEMS module. The material properties (stainless steel and PZT) used for these simulations are presented in Tables IV-6 and IV-7. Note that the properties of the Au electrode are not taken into account, considering that its thickness is lower than that of the PZT and will not affect the overall performances. ) which excludes the extra space near the clamp that is used for fine-tuning the resonant frequency. The 0.254 mm thick stainless steel substrate supports the 75 µm thick strips of PZT on each beam. A fixed-end boundary condition is imposed by clamping one end of the central beam. The remainder of the structure is unrestricted and a neodymium magnetic proof mass is attached to the opposite end. This kind of magnet is selected due to its strong magnetic flux density and availability in a variety of sizes. The properties of this magnetic tip mass used for the simulation are given in Table IV-8. This proposed geometry results in higher energy harvesting efficiency: bending modes are dominant during harvesting and torsional mode effects in the clamped beam are reduced. The proposed geometry also minimizes the area of strain nodes, which subsequently results in a greater harvestable area. With an eigenfrequency analysis performed using the Solid Mechanics physics in COMSOL, the natural frequency and mode shapes can be obtained. The obtained strain contour and the corresponding displacements are shown in Figure IV-12. Each beam experiences either tension (red color) or compression (blue color) along its entire length during cyclic motion. This is a critical but interesting characteristic, as any strain node within the length of the beam would require segmented electrodes to avoid charge cancellation. Additionally, an alternating strain pattern across adjacent beams is observed, and as output voltage depends on it, continuous electrode across the entire structure cannot be used before polarization. Consequently, the PZT need to be placed along the length of each beam with discontinuities at each beam end to avoid strain nodes. The particular configuration of the electrodes developed to avoid voltage cancellation will be detailed in the next paragraph (screens and polarization). 3 Fabrication process: cantilever and complex EH structure 3.1 Screen fabrication

Screen characteristics

The determination of the screen's characteristics (mesh count and emulsion thickness) is guided by the search of a compromise between definition and layer thickness. The electrodes must be thin (few microns after firing) and well defined while the PZT must be thicker (40-80µm after firing) to ensure good properties, but no too much to avoid high thermal stresses. The selected screens and their characteristics are described in Table IV

Layer mask and photolithography patterning

The software CleWin5 is used to design the electrodes and the piezoelectric layer in accordance with the substrate geometry defined in section 2.3. Short-circuits are avoided using a gap of 200 µm between the electrodes layers. The layers design ( Table IV-10) is converted separately into a suitable photo-plotter format, and then translated into a patterned thick-film screen using a UV photo sensible polymer film (chapter 3, section 1.2.2).

PZT paste

Paste Formulation

PZT paste is fabricated at the IMS laboratory. It is based on the mineral part and a commercial organic vehicle ESLV400 (alcohol-ester type solvent with an ethylcellulose binder (see Annex 3). The mineral part is a mixture of PbZr x Ti

Paste preparation

To improve the efficiency of the sintering aid, the size of the powders constituting the sintering aid are first homogenized. A milling step is hence carried out and afterwards, the grain sizes of CuO, Li 2 CO 3 and Bi 2 O 3 powders are 5µm ±0.03, 19µm ±0.11 and 6µm ±0.03 respectively (results presented in Annex 4). In previous works [22] , the described mixture PZT +3%wt LBCu paste is used to print the PZT layers. PZT, Li 2 CO 3 , Bi 2 O 3 and CuO are weighed and mixed with the turbula in a container with 8 agate balls and 40 ml of ethanol for 12 hours. After drying at 120°C, during 7h, the organic binder ESLV400 and the powder are mixed in a mortar. The paste is then processed in the three-cylinder mixer for 20 minutes to homogenize the mixture (see chapter 3). The proportion of the organic binder is critical to achieve the good rheological properties of the paste and as a result a good definition of the layer. On one hand, a fluid ink (higher quantity of organic binder) lead to a better smoothing after printing ie. marks left by the screen meshs disappear. On the other hand, a more viscous ink allows a better hold and definition of the pattern, but mesh traces can still be visible. Of course, in both cases, pseudo-plastic and thixotropic behaviors should be kept (see chapter 2). Moreover, if the paste has too high organic phase content, it can lead to the apparition of cracks and bubbles due to a rapid evaporation of the solvent during the drying step. Therefore, three different proportions have been tested (Table IV

Layers deposition

Once the alignment settings between the screen and the substrate are performed, the bottom gold electrode is first printed and dried for 20 minutes at 120°C. Next, the PZT layer and top gold

Sintering

After printing, the stack of the printed layers is first isostatically pressed 5 min at 40 MPa and fired at 65°C in order to improve the PZT densification [30]. The thermal profile used has already been optimized in previous work at IMS Laboratory [22], leading to efficient densification of the PZT +3wt% LBCu at 900°C. Higher sintering temperature than 900°C results in composition inhomogeneity reflecting significant loss of PbO. The corresponding density and electromechanical properties are altered as shown in many studies reported in literature for non-stoichiometric PZT [34][35].

The temperature profile shown in

Polarization

Once fired, electrical connections for polarization and electrical characterizations are performed.

Simple cantilever

For the simple cantilever structure, Ag wires of diameter 100µm are glued on the top and bottom Au electrodes with Ag epoxy paste as detailed in chapter 3. For the modified zig-zag structure, the strain-matched polarization technique is used as Berdy et al. [6]. This implies more complicated electrodes connections as detailed in the next paragraph.

Strain matched polarization technique (SME) for the zig-zag geometry

During vibration, each adjacent beam has opposite strain as shown by COMSOL simulation of the strain (paragraph 2.3, Figure , and positive strain produces negative charges and vice versa. Thus, to match the strain plots and to avoid voltage cancellation across the harvester, a strain matched-electrode polarization is done where each beam of the EH is polarized such that the adjacent beam has the opposite polarization direction (Figure . By using this approach, after the polarization, the top electrodes of all the beams are connected together for the EH test, and all the beams have the same voltage polarity . . Heating effect is added to improve the bonding (T= 80°C). After this wire bonding (two wires are connected in parallel to improve the reliability), each beam is polarized in opposite directions (as in bimorph configurations according to their tension or compression under vibration). This polarization step is carried out using two independent power suppliers according to the protocol described chapter 3, section 3.3.1. An electric field of 50kV/cm is applied for negative and positive beams during 10 min at 280°C.

Fabrication of printed disks and ceramics

To better understand the different key parameters of the fabrication process that could impact the performances of the EH structure, ceramics and free-standing printed PZT disks are also studied. The study of ceramics allows to investigate the influence of the LBCu sintering aid on the densification of the active PZT material, while the free-standing PZT printed disks with the same PZT formulation (PZT + 3%wt LBCu, + organic binder), allow to analyze the active SS substrate effect.

Printed disks

Screen-printed disks are made using the same Au and PZT+LBCu inks described in section 3.2.1. Once printed, the electroded PZT layers must be completely released from the substrate. This is achieved thanks to a sacrificial layer process classically used in MEMS process. The role of this sacrificial layer is to support the active layers during the densification process, without affecting the sintering process and with the minimum interactions with the active layers. The sacrificial layer needs to be first deposited on a ceramic substrate prior to the Au, PZT and Au layers stacking (Figure . This sacrificial polyester based layer ESL 244T (further information in Annex 5) is removed during the sintering process leading to free-standing piezoelectric disks ready for polarization process and for electromechanical characterizations [36]. Here, the circular shape of electroded printed PZT layers is aimed to further conduct piezoelectric characterizations on a simple disk, according to IEEE standards [34]. The screen selected for the deposition of gold electrodes is the same as the one used for the cantilevers fabrication (325 meshs, 15 µm emulsion). A 150µm thick metallic stencil is used to achieve thick printed PZT layers in one step. The screen for the sacrificial layer is a 70µm screen mesh with 50µm thick photosensitive film. The firing cycle and the polarization step are carried out using respectively the sintering profile described paragraph 3.4. and the polarization protocol detailed in chapter 3. With a maximum applied voltage of 0.35kV.

Ceramics

The PZT powder is prepared using the same paste formula as for the screen-printing process (PZT + 3%wt LBCu ) adding 15 wt % ESLV400 organic binder to the powder mix, followed by a drying step at 120°C during 8h. The green pellets (13mm diameter) are uniaxally pressed with a pressure of 18.5± 2 MPa, and then sintered following the firing cycle detailed in the section 3.4. Afterwards, Au electrodes (100nm) are sputtered on the ceramic disk surfaces for polarization and electromechanical characterizations (following the protocol explained in chapter 3). A maximum electric field of 8 kV/cm is applied.

Characterizations

Microstructural analysis

The microstructures of PZT corresponding to the ceramic, the printed disk and the simple cantilever are compared (Figure . As previously mentioned, the PZT is mixed with similar content and nature of organic binder and sintering aid (3%wt LBCu) whatever the design. The firing profile remains the same for all the three structures. Highly densified ceramic is obtained at 900°C (relative density 97 %) confirming efficient densification at such low temperature thanks to the use of the LBCu sintering aid. SEM images of the fracture surface confirm a low level of apparent porosity and reveal a mean grain size of about 3μm with a narrow grain size distribution (Figure IV-24 (a)). The relative density is lower for printed structures (Figure IV-24 (b, c)). An estimated apparent porosity of 8% and 20% is evaluated, for printed disks and cantilevers respectively. The grain size distribution is broader and it is difficult to estimate precisely the average grain size considering the melted aspect of the grains or agglomerates. In the co-fired structures, the sintering shrinkage mismatch between the electrodes and the active PZT layer must be considered. Differences in shrinkage behavior can generate stresses and defects and lead to constrained sintering compared to free sintering [35][37]. Retardation of PZT sintering kinetics can thus be expected. In cantilevers, mechanical clamping from the substrate is an additional parameter to consider. Furthermore, the specific preparation for SEM observation of cantilevers can explain the melted aspect of PZT grains (

Study of interfaces within the multilayer cantilever

When considering EH cantilevers structures, thermal stresses take place during firing cycle due to the difference of thermal expansion coefficients (CET) between the different materials constituting the structure. Hsuen et al. have proposed a mathematical solution to evaluate the thermal stress in multilayered films on substrates. For this purpose, the system's total strain is decomposed into a uniform bending component [38]. The cross-section of our multilayered system is shown in Figure IV-27, where the film layers of individual thicknesses (𝑡 1𝐴𝑢 , 𝑡 𝑃𝑍𝑇 , 𝑡 2𝐴𝑢 ) are bonded sequentially to the stainless steel (SS) substrate (thickness t s ). The coordinate system is defined in such a way that the interface between the bottom Au layer (noted 1Au) and the SS substrate is located at z = 0, with 𝑧 = ℎ 𝑛 𝑙𝑎𝑦𝑒𝑟 . Given the conditions: (1) The multilayer structure is subjected to a temperature change (∆𝑇), with residual thermal stresses (σ) (eq. 4.4 and eq. 4.5), (2) the substrate's thickness is much more higher than the one of the active layer (𝑡 𝑠 ≫ 𝑡 𝑃𝑍𝑇 ), (3) the layers arrangement is asymmetrical and, (4) only the PZT and SS CET mismatch is considered to contribute to final bending (Au layer effect is overlooked). The curvature 1 𝑟 ⁄ of the structure can be then evaluated using Eq. 4.6.

Figure IV-27: Cross section of multilayer structure with coordinate system used in the analysis [38].

𝜎 𝑠 = 𝐸 𝑠 ′ (3𝑧 + 2𝑡 𝑠 )
3𝑟 (for -𝑡 𝑠 ≤ 𝑧 ≤ 0 ) (Eq. 4.4)

𝜎 𝑃𝑍𝑇 = 𝐸 𝑠 ′ 𝑡 𝑠 2
6𝑡 𝑃𝑍𝑇 𝑟 (for 𝑡 𝑠 ≫ 𝑡 𝑃𝑍𝑇 ) (Eq. 4.5)

1 𝑟 = 6𝐸 𝑃𝑍𝑇 ′ 𝑡 𝑃𝑍𝑇 (𝛼 𝑃𝑍𝑇 -𝛼 𝑠 )∆𝑇 𝐸 𝑠 ′ 𝑡 𝑠 2 = ∑ 1 𝑟 𝑖 (with 𝑟 𝑖 = PZT or S) (Eq. 4.6)
Where 𝜎 𝑠 and 𝜎 𝑃𝑍𝑇 are the thermal stresses in the substrate and PZT layer, respectively. 𝐸 ′ = 𝐸 (1 -𝑣 ⁄ ) is the biaxial modulus with 𝐸 the Young's Modulus and 𝑣 is the Poisson's ratio of SS substrate or PZT layer individually. 𝛼 𝑃𝑍𝑇 𝑎𝑛𝑑 𝛼 𝑠 are the thermal expansion coefficients of the substrate and PZT layer, respectively. 1/r is the physical representation of the component curvature upcoming from the mismatch between the substrate and the active layer. Using the properties reported in Table IV-14, the estimated curvature of the multilayer structure is calculated for different PZT thicknesses, considering a ∆𝑇 = 100°𝐶. For a PZT thickness of 100µm, an absolute value of 2.69 mm for the theoretical maximum curvature is obtained with a concave facing up structure whereas the experimental curvature is 3.5 mm (Figure IV-28). Experimental curvature is evaluated at the highest curvature point containing the PZT active layer of the structure. To validate the trend predicted by the analysis, several cantilevers with different PZT thicknesses have been fabricated (35, 55, 60, 70, 80, 100 µm). The maximum deviation between the experimental and calculated values reaches 29% for a PZT thickness of 100 µm (Figure IV-28), this high percentage of error can be explained considering that at higher 𝑡 𝑃𝑍𝑇 (80-100 µm) the condition of the analytical solution 𝑡 𝑠 ≫ 𝑡 𝑃𝑍𝑇 is no longer valid. Decreasing PZT thickness leads indeed to both lower curvature values and a better agreement between experimental and calculated data. Thermal stresses can thus be significantly reduced by adjusting the PZT thickness. The interface layer still ensures cohesion between the electrode and the substrate without the presence of Kirkendall porosity that could be more detrimental [16]. However, such diffusion process at the electrode/substrate interface creates a passive layer whose mechanical properties would impact more globally the properties of the device and has to be accurately controlled.

Dielectric characterizations

Dielectric measurements at different temperatures and frequencies are first carried out on PZT ceramics in order to determine the Curie temperature (Tc) (Figure . The Curie temperature, determined at the maximum of capacitance, occurs at 330°C as expected for the PZ26 [39]. Considering measurements performed 24 hours after poling at 0.5kV/mm, a relative permittivity of 1200 and dielectric losses lower than 0.14% are measured at room temperature for 1 kHz. The permittivity value is slightly lower than the one reported for commercial PZT (Pz26 from ferroperm) ceramic (' 1300 -sintering at 1200°C). Nevertheless, the differences between the two ceramics in terms of grain size and poling conditions (2-8kV/mm for the commercial ceramic) can explain this difference in permittivity values. Dispersion of the permittivity at low frequencies near Tc is observed but there is no signature of conduction mechanisms activated at high temperature (T>400°C). However, the increase of tan from 380°C reflects the existence of residual space charges. Capacitance measurements are also carried out for the printed disk. Relative permittivity close to 600 and dielectric losses ∽2.5% at room temperature and 1 kHz are obtained. Such lower permittivity values compared to PZT ceramics can be partly explained by the lower relative density in the printed disk but cannot be rigorously compared because the applied poling electric field is not the same. However, the level of porosity is also a parameter that determines the maximum value of the field applied during poling.

Electromechanical characterizations

Admittance measurements are performed for ceramics, printed disk and simple cantilever structures. Results for simple cantilever EH harvesting are showed in Figure IV-32. By using the resonant frequency f r and anti-resonant frequency f a , effective electromechanical coupling factor k eff = 11% is found, as well as a mechanical quality factor of Q m =301. Values of k eff of 26% and 28% approximatively are obtained for printed disk and ceramic pellets, respectively (Graphics in Annex 6). In general, better properties for ceramic pellets are expected due to higher densification. Nevertheless k eff of printed disk is found to be similar demonstrating the efficiency of the process with the sacrificial layer and LBCu sintering aid. Furthermore the polarization conditions of the ceramic pellets with an applied field depending on the thickness of the sample are probably not optimized, which could disrupt the complete exploitation of the ceramic pellet performance [41].

Correlating the printing structures, the lower k eff value obtained for the cantilever clearly shows the effect of the passive metallic substrate. Furthermore, a good value of piezoelectric coefficient d 31 of 95 pC/N is estimated for printed disks (values are calculated as explained in chapter 3 section 3.3.4). Cantilever piezoelectric coefficients have a contribution from d 31 depending on substrate properties, which cannot be equivalent with the standard IEEE model [34]. It is worth to know that these measurements have been carried out without any clamping of the PZT layer on the substrate. Nevertheless, the simple conductance measurement is relevant as it is directly related to the piezoelectric response of the structure.

Table IV-15 reports the material characteristics and summarizes the dielectric and piezoelectric properties of the PZT based EH structures compared with ceramics and printed free structures (printed disk). A systematic comparison with the commercial ceramic from Ferroperm is also included as well as two examples of PZT layers deposited on metallic substrate found in literature. As expected, the bulk ceramics present the highest dielectric permittivity due to higher density. Compared to the commercial one (sintering at 1200-1300°C), the ceramic sintered in the present work at 900°C presents slightly lower permittivity values but they remain in the same range of the commercial ones despite a significantly lower sintering temperature. Lower dielectric properties are also obtained for printed PZT in comparison with ceramics due to lower densification as discussed in section 5.1. Dielectric losses are also increased in printed layers (by a factor 10).

Electromechanical coupling and piezoelectric coefficients k 31 , k eff , and d 31 , are deduced using the standard IEEE model [40]. Ceramics samples show the highest values approaching those of the commercial sample, comforting the role of LBCu to enhance densification at low temperature [22].

Free-standing printed disks with printed electrodes exhibit also very good piezoelectric and electromechanical coefficients. For these printed disks, the lower level of densification (compared to ceramic pellets) combined with higher thickness of printed electrodes, and poorer interface quality (compared to sputtered electrodes) [42] impact the global dielectric and piezoelectric performances. Nevertheless, similar piezoelectric properties are observed as those of the ceramic pellets also sintered with LBCu. Again, as already mentioned, the polarization conditions probably affect the piezoelectric properties.

For EH cantilever structures, lower electromechanical coupling and piezoelectric coefficients are obtained, as confirmed by finite element simulation analysis for the modified zig-zag cantilever [29]. Overall lower properties are expected for cantilever multilayer structure due to the presence of the passive metallic substrate supporting the active PZT layers. The substrate induces mechanical clamping stresses that limit the active material densification. Lou-Moeller et al. [29] also confirmed the limitations of the properties of printed PZT (PZ26) thick film when bounded on silicon and alumina substrates. They showed that sintering aids, inherent porosity and mechanical clamping from the substrate, are the three main contributions leading to lower properties values. Furthermore, referring to literature where very dense thin films are also deposited by aerosol on a cantilever SS substrate [43], electromechanical coupling factor k eff of around 10 are also obtained (Table IV-15). In our case, even if our printed PZT layers present more porosity than the aerosol PZT layers, their higher thickness help to improve the electromechanical coefficient of the multilayer cantilever. More dense and thicker PZT layers clearly improve the performances of the EH as shown in Table IV-15 through the results reported by Colin et al on thinned bulk PZT glued on both sides of a SS cantilever [26]. With such a bimorph configuration and even with a glue interface between the SS substrate and the PZT, an increase of coupling coefficient is obtained thanks to the optimized properties of the thinned bulk ceramic. It is necessary to take into account that electrical properties will also depends on polarization step, therefore a rigorous comparison can only be made under same pooling conditions. Here, the tested cantilever is a simple cantilever (dimensions 10x2x0.250mm) with a 50 µm PZT screen-printed on it. It is worth noting that these dimensions have not been optimized for the application (middle branch of the modified zig-zag geometry).

Model for piezoelectric vibration energy harvester

Thanks to the coupling between vibrations and electrical energy through the piezoelectric element, most of piezoelectric vibration energy harvesters (PVEH) based on a linear mechanical oscillator excited around one of its resonance frequencies can be modeled by the simple PVEH model presented Figure IV-33 [44]. This basic linear model is based on electromechanical transduction. The electrical and mechanical equations of equilibrium provide an accurate and reliable representation of the PVEH behavior around its resonance frequency. Even if it does not describe all types of configurations, its study is a prerequisite for more complex modelling (multiple resonance modes, non-linearity due to ferroelectric hysteresis, mechanical non linearities). In this model, the piezoelectric element is characterized by its electromechanical force coefficient α [NV -1 ], its clamped capacity (at no strain) C P [μF] as well as its leak resistance R P [Ω] (or conductance A P =1/R P [S]). M [kg] is the equivalent dynamic mass, D [Nm -1 s] is the damping coefficient due to mechanical losses, and K[Nm -1 ] represents the stiffness of the system (if the piezoelectric element is short-circuited). An external force applied to the system F[N] (due to external vibration for instance) induces x [m] the relative displacement between the mass and the housing. V [V] and I [A] are respectively the voltage at the ends of the piezoelectric element and the generated electrical current, if an electric load is connected. The equilibrium equations of this electromechanical system are therefore:

𝐼 = 𝛼𝑥̇-𝐶 𝑝 𝑉 ̇-𝐴 𝑝 𝑉 ̇ (Eq. 4.7)
𝑀𝑥̈+ 𝐾𝑥 + 𝐷𝑥̇+ 𝛼𝑉 = 𝐹 (Eq. 4.8)

Then, for the characterization of the PVEH, four parameters are usually used. They are the natural pulsation ω 0 [rad. s-1 ] when the piezoelectric element is short-circuited, as well as three dimensionless parameters: the squared electromechanical coupling coefficient k 2 , the mechanical quality factor Q M and the resistive loss coefficient ξ E . These parameters have the followed expressions:

𝜔 0 = √ 𝐾 𝑀
(Eq. 4.9)

𝑘 2 = 𝛼 2 𝐾𝐶 𝑃 + 𝛼 2
(Eq. 4.10)

𝑄 𝑀 = √𝐾𝑀 𝐷 (Eq. 4.11)
ξ 𝐸 = 1 2𝑅 𝑃 𝐶 𝑃 𝜔 0 (Eq. 4.12)

In the majority of applications, R P is very large compared to (C p ω 0 ) -1 and ξ E can be neglected. Q M corresponds to mechanical losses. k 2 corresponds, in quasi-static mode, to the efficiency of the electromechanical conversion between electrical and mechanical energy. For an open circuit system submitted to a static force it represents the ratio between the generated electrostatic energy and the total energy in the system. If the PVEH is excited by a sinusoidal ambient acceleration, and if it is connected to an electrical load modeled by the complex admittance 𝑌 𝐿 = 𝐴 𝐿 + 𝑗𝐵 , the electrical network is shown Figure IV-34. In the frequency domain, the corresponding piezoelectric voltage V is then given (Eq. V being the RMS value of the piezoelectric voltage

Results

Linear electromechanical model

Before the measurement of the harvested power, the electromechanical parameters of the linear model presented in the previous paragraph are determined using the equivalent circuit shown Without tip mass, the resonant frequency is shown to be 130Hz and so, further tests under vibrations are led without any tip mass glued on the tip. The rather weak electromechanical squared k 2 can be related to huge difference between the PZT and the stainless steel substrate volumes. The calculated merit factor 𝑘 2 𝑄 𝑚 = 0.133 is here too low to achieve maximum harvested power, as shown in [45] (20 times lower than the reference value of π).

Tests under vibrations

The cantilever is driven under vibration on the shaker with accelerations varying from 0.2g to 0.5g. The voltage is then measured across a resistive load of 2.7MΩ, value close to the optimal theoretical value (𝑅 𝑜𝑝𝑡 = 1 𝐶 0 •2𝜋•𝑓 0 = 2.64 M which corresponds to the value of the impedance modulus at resonance frequency). A voltmeter with an internal resistance of 100M is used. With this resistive load, a maximum power of 1.3µW is produced by the harvester at 0.5 g amplitude with a natural frequency of 129.3Hz (Figure .

A decrease in resonance frequency is noticed with increasing acceleration and the shape of the peak becomes asymmetric. This classic behavior is attributed to the nonlinear response of PZT under stress due to Young's Modulus and quality factor decreases [46][47]. Indeed, reduction of quality factor is due to increase in mechanical losses with the amplitude of vibration (mainly air friction). On the other hand, the resonance frequency decreases because the Young's Modulus reduces the spring constant (so-called "softening effect"). The harvested power is lower than those reported in the literature (Table IV -17). However, the substrate thickness and properties, the mass tip, the type of cantilever (i.e. unimorph or bimorph) and better piezoelectric properties represent several degrees of freedom to improve the performances.

Piezoelectromagnetic energy harvester (hybrid application)

These experiments have been led at University of Waterloo, Canada, Department of Mechanical and Mechatronics Engineering (Egon Fernandes supervised by Pr Armaghan Sahelian). This collaborative project has been conducted thanks to the UW-UB fund (2015-2017).

Principle and experimental set-up

The working principle of the piezoelectromagnetic screen-printed energy harvester is shown Figure IV-39. A permanent magnet is attached to its tip. If the harvester is mounted above an ACcarrying electrical wire, the coupling between the magnet and the alternating magnetic field produced by the wire creates a sinusoidal electromagnetic force. This force excites the cantilever and as a result the piezoelectric material is deformed. Charges are generated across the electrodes due to the direct piezoelectric effect, and, if the harvester is connected to an electrical load, a voltage is generated. The amplitude of the output power is maximized if the frequency of the AC current (ie. the frequency of the electromagnetic force) matches the harvester's resonance frequency.

Results

First experiments measuring tip displacement and open-circuit for the EH show a good agreement between COMSOL model and measurement (Figure IV-41). Also, with magnet tip mass and fine tuning of the harvester clamping, the experimental resonant frequency is 60.3Hz (only 0.1Hz error with the modeled value), value compatible with the North American power grid.

Then, the energy harvester is tested with increasing resistive loads from 10 kΩ to 1 MΩ and the generated power is calculated from the square of the measured root mean square (RMS) voltage 𝑉 𝑅𝑀𝑆 across the load resistance 𝑅 using:

𝑃 = (𝑉 𝑅𝑀𝑆 ) 2 𝑅 (Eq. 4.15)
The measured and simulated power are shown in Figure IV-42 and are again in excellent agreement. No noticeable shift in resonant frequency is seen across the load sweeps. Further tests show that the optimal load range is between 1 MΩ and 2 MΩ, with small variation (less than 5%) in power production. The 1MΩ value is then selected for the following tests. Finally, with the 1MΩ load resistor, the power outputs are measured using different distances to the wires (6.5, 9.5 and 12.5mm), and various electric current values (from 1 to 7 A). Too small distance or high current values are avoided for possible detrimental effect on the structure during vibration. The obtained curves (Figure show that, as expected, the overall power output grows significantly as the distance between the magnet and wire are minimized. This is due to the fact that the force on the magnet is inversely proportional to the square of the distance and the power output is proportional to the square of the force [29]. Again, because of changes in both Young's Modulus and quality factor for higher current (ie. larger force) nonlinear effects appear and result in a lower experimental power than expected [50]. The results have been compared to previous works found in the literature. For this purpose, the normalized power density of the piezoelectromagnetic energy (in μW/(T*A*mm 3 )) is calculated for a fair comparison. The overall power output is indeed dependent of the distance magnetwire, the remanence of the magnet and the current in the wire. This normalized harvested power density is calculated by considering the effective volume as the sum of the volume of all beams and the magnet. The results gathered in Table IV-18 show that the printed EH developed during this work gives a normalized power density more than 2 times higher compared to Paprony et al. [51] and Olzevsky et al. [52] works (2.9 and 2.2 times increase respectively). This validates the proposed modified zig-zag geometry combined with the advantages of the screenprinting thick film technology. The results are even comparable to the bulk PZT units [50], [53] whereas it is known that bulk PZT has a higher electromechanical coupling . Finally, the energy harvester has a good potential compared to larger scale units [50][53].

Conclusion

In this chapter, screen-printing and co-firing of PZT layers in sandwich between Au electrodes all deposited on stainless steel substrate (301 SS) have been successfully fabricated, with simple cantilever shape or complex modified zig-zag geometry. Their microstructural characteristics and functional properties have been investigated and compared to those of PZT based ceramics and printed disk. The densification has been achieved at 900°C with the use of the LBCu sintering aid. Lower densification is shown for the cantilever structures with the SS passive substrate and can be due to the mechanical clamping from the SS substrate that generates constrained sintering. Even if the overall piezoelectric properties are reduced, properties are comparable to those of the literature, confirming the good potentiality of such devices for EH MEMS applications. Compared to bulk ceramics, the main limiting features are the interfaces and the bending issues. The microstructural analysis of the interfaces in the cantilever has highlighted the formation of an interphase layer between the substrate and the bottom gold electrode after sintering. This interface is considered as a passive layer that ensures cohesion between the electrode and the substrate but that could limit the dynamics of the structure under performance. Bending arising from TEC differences between the different materials constituting the cantilever structures has been shown to be dependent on the thickness of the active piezoelectric material. Both modeling and experimental approaches have confirmed the possibility to reduce thermal stresses by decreasing the PZT layer thickness. This insight will be further exploited in chapter 5.

Both simple and modified zig-zag cantilevers have been finally tested for EH application. For the simple cantilever, the maximum power of 1.3µW measured with a shaker is too low for the implementation of the EH in a MPPT circuit (MPPT : Maximum Power Point Tracking) whose own consumption is at least 10 µW [55]. It is worth noting that this simple cantilever has not been optimized for this application, being simply the central part of the modified zig-zag structure. In addition to material properties (active or passive layers), thicknesses optimization, tip mass use and bimorph cantilever structure type are some possible routes for performances improvement.

Additionally, in the case of the piezo-electromagnetic modified zig-zag energy harvester, within the collaboration with the University of Waterloo, Department of Electrical Engineering (Zongxian Yang and Sid Zarabi supervised by Associate Professor Lan Wei and Pr David Wairn) a dynamic power conditioning module circuit has been developed. This circuit is adapted to the tens of microwatts provided by the modified zig-zag EH. Again, as for the MPPT circuit, the system is completely powered by the EH. Even with a low input power, encouraging results were displayed with this dynamic power management, which was able to work with the electrical characteristics of the fabricated printed modified zig-zag energy harvester. This flexible system could achieve a read-transmit duty cycle depending on the characteristics of different EHs and intensity of current passing through the wire being monitored (Figure IV-44).

Introduction

PZT based energy harvester is a complex multi-material structure whose fabrication raises multiple issues related to (i) the control of the chemistry and microstructure (non-stoichiometry and volatility of elements, grain size) and (ii) the control of interfaces (interdiffusion, thermal expansion mismatch between ceramic and metals leading to delamination and bending). These features strongly affect properties such as electrical breakdown strength, electrical conductivity, piezoelectric strain and ferroelectric switching. Thanks to various sintering aids such as Li 2 CO 3 Bi 2 O 3 CuO (LBCu) [1], LiBiO 2 + CuO [2][3] or Li 2 CO 3 + PbO [4] the sintering temperature of thick films and PZT based ceramics was efficiently lowered (~900 °C) compared to conventionally sintered commercial PZT ceramics (T>1200 °C). However, the chemistry remains hardly controlled and the densification not always optimized. Indeed, conventional sintering performed at high temperature and during long duration can generate PZT composition fluctuations. In particular, the loss of PbO is a major drawback leading to change in chemistry and degradation of electrical properties.

Over the last few decades, electric current activated/assisted sintering (ECAS) methods, such as spark plasma sintering (SPS), have been considered as high-efficient techniques for the densification of ceramics [5]- [8]. In this context, the use of advanced sintering process such as Spark Plasma Sintering appears as a relevant approach given its specificities: fast kinetics, lower temperatures and short sintering times. Optimization of the sintering while decreasing sintering temperature and limiting the number of thermal treatments is consistent with the trend towards lower energy consumption while maintaining optimum reliability. Such an optimization is particularly critical when processing complex devices such as printed PZT thick films integrated in MEMS, for which the co-sintering with metals remains challenging.

After a survey of the literature focused on piezoelectric ceramics sintered by SPS, a first part of this chapter is devoted to SPS investigations performed using the same commercial PZT powder as for conventional process (section 2). Optimization of the sintering conditions, microstructural and electrical investigations of the PZT ceramics obtained by SPS are presented. In particular, our strategy to use a protective powder layer to target one-step sintering is highlighted. The impact of sintering aid addition is addressed. Then, the SPS ceramics performances are compared with conventional PZT ceramics and screen-printed thick films. The second part of this chapter is devoted to the transfer and further optimization of SPS conditions towards the co-sintering of the printed PZT based EH multilayer structure.

State of the art on SPS sintering 1.Piezoelectric ceramics

A review of literature shows that sintering of PZT and related solid solutions by SPS are performed under low oxygen partial pressure at temperatures that usually remain higher than 900 °C (Table V-1)). The various reported studies underline the influence of composition, additives (La 2 O 3 , PbO excess, etc…) and microstructure (grain size effect) on the electrical and optical properties of PZT ceramics obtained by SPS [3], [7], [9]- [23]. The SPS route was also recently investigated for the sintering of lead-free piezoceramics, in particular for (K,Na)NbO 3 (KNN). KNN shares with PZT the tendency for volatility of the A-site cations in the perovskite ABO 3 structure and is a challenging lead-free ceramic that could be of real interest for some applications where PZT dominates [24], [25].

Three remarks arise from this brief survey of literature:

i)

The efficiency of SPS compared to conventional sintering can hardly be properly evaluated as the dielectric and piezoelectric properties are not systematically reported and when provided they relate to different initial compositions and various microstructures in terms of grain size. However, it is worth noting that most of the studies use SPS at lower or similar temperatures as the ones used for conventional sintering of screen-printed thick films. The dwell time (~5') is also drastically reduced compared to conventional approaches for which several hours are required to achieve high density.

ii) Sintering aids are only rarely used whereas in conventional sintering they are required to reduce the sintering temperature, in particular to limit the loss of PbO.

iii) A post-annealing is most of the time performed at temperatures similar or even higher than the sintering temperature and under air in order to eliminate oxygen vacancies and recover insulating properties. The control of oxygen vacancies is critical as they may play an important role in the fatigue process under electric field [26]. This post-sintering thermal treatment, performed in the range 700 -1100 °C, is a key step to control charged defects and, more generally defect chemistry [27]. In particular, space charge accumulation at the grain boundaries can significantly alter the polarization process (reorientation of domains) and contribute to the conductivity and dielectric losses. Such post-sintering annealing represents also a drawback because it weighs on the global thermal budget limiting thus the gain of energy efficiency provided by fast sintering at low temperature.

In this context, we focus on the investigation of SPS with as a main goal to avoid the post sintering annealing step. Our objective is also to reduce the sintering temperature without using sintering aids. Our strategy is built on the use of a protective powder layer directly deposited on the top of the PZT bed powder. The use of insulating disks or thermal buffers during SPS was already reported in literature. These thermal and electrical barriers allow to reduce the heat conduction and to control current distribution across punch/die/powder assembly (limited current leakage). They can be located either directly at the contact of the powder or between the rams and punches [28]. Alumina powders were also used to prevent ferroelectric ceramics from chemical reduction during SPS sintering [29] and to prevent the pistons from deforming copper spiral extremities in SPS co-sintering of transformers for power electronics [30]. No reaction occurs between the alumina and the powder to sinter.

In the context of this thesis, considering our goal to optimize the SPS sintering not only for PZT ceramics but also for the multilayer (Au/PZT/Au/stainless steel), our specifications for the protective layer must meet multiple criteria:

 To protect PZT from the chemical reduction without hindering densification.  To be inert at the selected sintering temperature in order not to interact chemically with PZT but also with the metallic electrode in the case of the multilayer.  To be removed easily by polishing or etching without altering the material in contact.

We have first selected the strontium carbonate SrCO 3 which meets all expectations, and has also proved to be very effective as a sacrificial layer in the fabrication of the released screen-printed PZT, metals or vitro-ceramic thick films [31] [32]. Another carbonate has been also tested showing promising results. Sintering conditions are first optimized using the raw powder PZT (PZ26 from Ferroperm, www. meggittferroperm. com) without sintering aid or protective layer. Then, the efficiency of the protective layer during SPS to avoid post-annealing step is tested. SPS experiments are finally performed starting from the same formulation used for the conventional approach by adding to the raw powder 3wt% of LBCu sintering aid (Chapter 4).

2.1

Sintering of PZT without sintering aid

Sintering temperature optimization

Spark plasma sintering is performed using an SPS apparatus Syntex Inc., SPS-515S (section 2. 2 Chapter 2). PZT powder without sintering aid is loaded in a cylindrical graphite die with an inner diameter of 10 mm and heated under low oxygen partial pressure. The temperature is raised at 50 °C/min and kept at a constant value in between 800 and 875 °C for 5 min. A maximum pressure of 100 MPa is applied along the Z-axis of the graphite die during the whole sintering process. Note that these values of sintering time and pressure have been selected after investigations performed also with a pressure of 50 MPa and dwell time of 30 minutes for which lower density values have been obtained. Afterwards, the samples are annealed in air at 800 °C for 10 h in order to remove surface carbon contamination and to limit oxygen vacancies caused by the reducing conditions.

Structural and microstructural characterizations of PZT ceramics obtained by SPS a) XRD investigations

As described in Chapter 4, the initial commercial powder PZ26 (PbZr x Ti 1-x O 3 with 0.44<x<0.53) exhibits a perovskite type structure with a coexistence of tetragonal and rhombohedral phases at room temperature. Room temperature XRD patterns of the SPS ceramics are indexed in the tetragonal and rhombohedral symmetries (Figure V-1 (a)). Extra peaks attributed to pyrochlore phase occur when the sintering temperature is below 875 °C. The diffraction peak at 44.5° observed in the patterns of both the initial powder and the powder sintered at 800 °C corresponds to the rhombohedral singlet (200). This peak is slightly shifted towards lower angle when increasing sintering temperature (Figure V-1 (b)). A better crystallinity is also observed for the ceramic sintered at temperature higher than 850 °C with in particular a pronounced splitting of tetragonal (002)/(200) peaks for a sintering temperature of 875 °C. The other rhombohedral reflections located at 22° (100) and 55. 4° (112) are also shifted towards lower angles (21.5 and 55° respectively) for the patterns corresponding to 850 and 875 °C. Although the global composition of the powder does not change when the sintering temperature increases, the recorded XRD patterns reveal a change in phase structure. Wagner et al. already reported such a transition from rhombohedral to tetragonal structure induced by increasing the sintering temperature in the relaxor-ferroelectric system PNN-PZT [34]. In this paper, an increase of the tetragonal content from 45 to 82% is reported when grain size increases from 0. 5 to 3.7 μm. This effect, ascribed to grain growth, was correlated to stress relaxation. A higher content of tetragonal phase evidenced by the ratio I(002)/I(200) was also reported in PZT-PMnN sintered by SPS compared to conventional sintering [14]. A surface effect due to the pressure applied during SPS cannot be discarded to explain the changes observed on the XRD patterns. However, extreme caution should be taken when interpreting changes in the (002)/(200) ratio intensity or broadening, as polishing or grinding steps also result in significant modifications [35][36] [37]. This is well illustrated when comparing the XRD patterns of the ceramic after SPS (sintering 850°C), after polishing at the heart, and after complete grinding (powder) ( ). An increase of the sintering temperature of only 50 °C (i. e. 850 °C) allows a significant improvement in densification, with a relative density reaching 94 %. Open porosities are nevertheless observed and the grain size increases from the range 500 nm-1 m to 1-2 m. Quite homogeneous microstructure is revealed with no evidence of differential sintering caused by the presence of agglomerates in the initial powder. Note that the grinding of the powder before SPS has been also studied and has been shown to have no effect on the improvement of sintering. The 100MPa pressure applied during sintering is thus appropriate for an efficient break-up of agglomerates in the first stage of sintering. The optimal density is finally obtained at a sintering temperature of 875 °C with 98% of relative density. Larger average grain size in the range ~2-4 m is observed

(Figure V-3 (c)).
Referring to the work of Wagner et al [34], when the sintering temperature increases up to 875 °C a change in phase structure is observed by XRD, and a change in grain size from 0.5 μm to about 4 μm is generated.

It is worth noting that SPS allows to efficiently densify PZT at temperature lower than 900 °C without any additives. Density and microstructure of the SPS ceramics are comparable to those of conventionally sintered commercial ceramics at 1200 °C (www. meggittferroperm. com).

Referring to the SPS studies reported in Table V-1, although the sintering temperature of 875 °C is slightly lower, density remains comparable. On the conductance graphic, the resonance frequencies are different because of different diameters of the disks. The highest conductance peak and mechanical quality factor are observed for the Au electrodes deposited on a polished surface, whereas the sputtering of Au on a rough surface lead to deteriorated piezoelectric properties. This result is mainly attributed to the highest applied field during the polarization. Polarization with the rough electrodes can presents discontinuities and as a result the applied field could not be as high as required for a good alignment of the dipoles. The polished surface improves the interface and as a result, higher field can be applied.

A polished sample with screen-printed Ag-epoxy is also compared. The properties are improved compared to the sample with Au on a non-polished surface, but it is nevertheless not as good as for the sputtered Au. This is attributed to the quality of the electrical interface with the epoxy. Au Electrodes deposited on a polished surface of the SPS ceramic are then selected prior to electrical measurements. , where higher diameter of B(G) circle for 875 °C is observed, supporting a better electromechanical response for this temperature. The effective coupling factor k eff is evaluated close to 36%, whereas it hardly reaches 20% for the ceramic sintered at 850 °C. Such results confirm that maximum density is beneficial for piezoelectric properties. In case of free-standing thick film disk fabricated by conventional process, the value of k eff is lower (26.5%), mainly due to porosity and electrode effects [38]. The optimum sintering temperature regarding densification and properties corresponds to 875 °C and is thus selected for further SPS experiments.

2.1.2

Approach towards one-step sintering of PZT by SPS

Protective layer strategy

As mentioned in the previous section, ceramics obtained by SPS need to be annealed in air at 800 °C for 10 h, in order to remove surface carbon contamination and to limit oxygen vacancies caused by the reducing sintering conditions. Here we focus upon an affordable solution for onestep sintering of PZT by SPS using a protective layer. As drawn schematically on Figure V-9, a bed of protective powder is introduced into the system in between the PZT powder and two pieces of graphite foils. The strategy relies on the use of carbonates whose decomposition temperature depends on the nature of the alkaline cation (Table V-3). Strontium carbonate SrCO 3 already used at IMS as sacrificial layer for printed MEMS is first selected since its decomposition temperature is well above the optimized SPS sintering temperature (i. e. 875 °C). In addition, the decomposition temperature of SrCO 3 in SrO can be further increased in controlled firing atmosphere (firing under CO 2 ) [32] . Here, SrCO 3 is used for the first time to prevent chemical reduction of the active piezoelectric material during SPS under low oxygen partial pressure. Tests performed using BaCO 3 which have a higher decomposition temperature than SrCO 3 are also performed. The removal of this protective layer after SPS is ensured by either polishing or chemical etching in diluted phosphoric acid prior to microstructural and electrical characterizations.

Electrical characterizations a) Dielectric characterizations

In order to prove the efficiency of the protective layer against reduction, electrical measurements have been led directly after sintering and etching of SrCO 3 . Dielectric characterizations performed as a function of temperature and in the frequency range 100 Hz -100 kHz are shown on Figure V-11. The Curie temperature (Tc) corresponding to the maximum of permittivity is located at 330 °C as expected for the PZ26 composition (www. meggittferroperm.com). The room temperature permittivity reaches 1500, a value higher than the one reported for this commercial powder ( 1300 -sintering at 1200 °C) and much higher than the one reported by Wu et al. ( <500, sintering at 900 °C with an annealing 1h at 1100 °C).

A slight frequency dispersion of the permittivity can be observed in the vicinity of the Curie temperature but there is no signature of conductivity (increase in permittivity) at high temperature (T>400 °C). The permittivity at Tc and at 1 kHz reaches a value as high as 19800 reflecting the high quality of the ceramic. The room temperature dielectric loss (tan) is lower than 1% and remains stable as a function of temperature up to 350 °C (insert Figure V-11). The observed increase of tan from 380 °C at the lowest frequencies (<1 kHz) nevertheless reflects the existence of residual space charges. However, the obtained dielectric characteristics, comparable or even better than those of commercial ceramics, attest to the quality of the grain boundaries and confirm the efficient role of the protective layer. In such conditions, SPS without subsequent annealing allows to obtain in one-step high quality piezoelectric ceramics exhibiting effective properties.

b) Electromechanical characterizations

An additional proof that the annealing is not required here, is the effective polarization of the ceramic directly after SPS. The polarization process failed when PZT is densified without a protective layer due to the charges and associated leakage current, making the annealing prior polarization process mandatory in this case. When using the SrCO 3 protective layer, Au electroded PZT ceramics can be directly polarized before electromechanical characterization. In order to anticipate the transfer towards spark plasma sintering of EH multilayers, which will necessarily require adaptation of sintering conditions due to the reactivity between the different layers (carbonate and PZT, PZT and gold electrodes), other carbonates such as BaCO 3 have been tested. Ceramics are performed using same SPS conditions as for SrCO 3 (875 °C -5 min -100 MPa). The density of the obtained ceramics is close to 97.8%, a value similar to the one obtained with SrCO 3 . Electromechanical measurements performed directly after SPS without annealing step are shown in Figure V-14. Results are compared to those obtained with SrCO 3 as a protective layer. Slightly lower but comparable k eff is observed for samples with BaCO 3 protective layer, with a value of 38%, whereas for SrCO 3 k eff =40%. The room temperature dielectric permittivity at 1 kHz for PZT sintered with BaCO 3 reaches 950 , a value lower than the one obtained using SrCO 3 . Relative densities are similar whatever the nature of protective layer, a microstructural effect can be discarded to explain such a difference. Higher electric field can be applied to PZT sintered with BaCO 3 compared to PZT sintered with SrCO 3 , this could explain the lower permittivity values when using BaCO 3 . This could also reflect that BaCO 3 acts as a more efficient thermal barrier against diffusion and chemical reduction with as a result a lower level of charged defects within the PZT. However, if the room temperature dielectric losses at 1 kHz remain below 1%, losses start to increase at lower temperature (from 150 °C instead of 350 °C in the case of SrCO 3 ). Other effects such as electrodes effects should be thus considered.

Influence of sintering aid

For sake of comparison with conventional sintering of PZT and in order to study the densification of PZT based EH multilayer by SPS, specific investigations focused on the role of sintering aid on both densification, microstructure and electrical properties have been conducted. Spark plasma sintering is performed using the PZT powder mixed with 3wt% of LBCu loaded in a cylindrical graphite die with an inner diameter of 10 mm and heated under low oxygen partial pressure. The same SPS conditions (100 MPa, 50 °C/min, 5 min. ) as for PZT without LBCu are considered. According to the sintering temperature, here between 700 and 875 °C, the samples are annealed in air either at 650 °C (for sintering at 700 °C and 800 °C) or 800 °C (for sintering temperature 875 °C) for 10 h. It is observed that whatever the sintering temperature, ceramics display very high densification with a density close to the theoretical one. The addition of sintering aid clearly allows for a decrease of sintering temperature while keeping high density value. When using LBCu, the onset of densification by SPS is estimated close to 500 °C. The densification is favored by the melting of additives leading to a liquid phase and promoting particles rearrangement. One point is to rule if liquid phase sintering aids either enter in the PZT lattice or remain as a second phase at the grain boundaries [39]. Both microstructural (EDS analysis) and structural investigations are required. The work reported by X. X. Wang [3] on PZT + LBCu ceramics obtained by conventional sintering highlights that the addition of LBCu enhances both densification and grain growth and confirms the presence of additives at the grain boundaries by XPS analysis. However, structural analysis is not provided.

Summary

In order to evaluate the potentiality of SPS to sinter PZT ceramics without sintering aid and in one-step (without post annealing), the microstructural and electromechanical properties of the screen-printed thick film, the commercial PZ26 ceramic and the SPS ceramics are compared (Table V-5). These results show that for the SPS ceramic despite a lower sintering temperature, 875 °C instead of 900 °C (screen-printed thick films ) and 1200 °C (commercial ceramics), and the absence of additives, the electromechanical coupling factor reaches a good value of 40%. Nevertheless, such a value is still lower than that corresponding to the commercial ceramic (50%) possibly because of non-optimized polarization conditions. The comparison clearly highlights and demonstrates the potential of the SPS process for an efficient densification in one step thanks to the use of a carbonate protective layer (SrCO 3 and BaCO 3 ). It was also shown that the sintering temperature can be lowered (700 °C) using sintering aid (3 %LBCu). However, even if the density remains high, the electromechanical properties are deteriorated. Work is in progress to correlate the chemical homogeneity (arising from the introduction of LBCu) to the lower electromechanical performance observed.

Transfer towards multilayer printed structures

The EH structure considered in this part is the cantilever made of a PZT layer in sandwich between two Au electrodes printed on a stainless substrate (SS/Au/PZT/Au) (Figure V-18). Multilayers are fabricated using the same screen-printed based process detailed in chapter 4, letting out the densification that includes a pressure step and conventional sintering at 900 °C during 2h. The main challenge in aiming at the transfer towards SPS sintering of multilayers lies in the control of interfaces. The reduction of the number of steps in the EH fabrication process by targeting one-step SPS sintering is also an ambitious objective.

Interfaces in multilayers by SPS: Metal/Ceramic interfaces

SPS is widely used for the assembly of materials and is recognized as an efficient sintering process for co-sintering or bonding. The control of chemistry and defects at interfaces is a key issue. If temperature and pressure contribute to mass transport enhancement, the influence of current through electromigration or defects concentration and mobility has also to be considered [40]. The current and/or temperature effects on the formation of interphases were mainly studied for multilayers intermetallic systems [41][42]. The studies reported in literature dealing with ceramic/metal or metal/polymer multilayers assemblies concern to a large extent Functionnaly Graded Materials (FGM) [43]. Composites made of biocompatible ceramic and metal (Al 2 O 3 /Ti) were investigated by SPS in order to optimize the mechanical properties [44]. It was shown through bending tests that fracture occurs within a reaction layer formed at the interface. Hardness and bending strength of the alumina-titanium composites were compared to those of FGM samples [45]. The reactivity of titatium with alumina and the presence of microcracks for SPS sintered Al 2 O 3 /Ti functionally graded materials were also reported by Madec C. et al 2018 [46]. Focusing on materials designed by SPS for electronic devices applied to energy harvesting, only few studies were reported. Issindou et al [47][47] worked on simple SPS magnetostrictive ceramics optimized by SPS, but no multilayers were studied. Cu/PZT functionally graded materials were fabricated by SPS targeting actuators applications [48]. The impact of copper particles addition into PZT matrix on the dielectric properties and the electrical conductivity was investigated. Piezoelectric properties were not reported. In the case of multilayers stacking, monolithic transformers for power applications were co-sintered by Spark Plasma Sintering [30]. The reported transformer is made of two spiral copper coils, a dielectric layer and a spinel ferrite magnetic circuit. The advantages of SPS lies here on the reduced sintering temperature that allows to co-sinter copper with the ferrite powder and on the possibility to obtain a monolithic structure that eases the heat transfer from the coils. Deformation and leakage inductance issues were identified and were solved by adapting dimensions and sintering conditions (sintering aid). However the argon atmosphere during SPS was revealed as detrimental regarding to the ferrite resistivity. This study illustrates well several issues that must be tackled when using SPS to co-sinter complex structures.

The overall approach envisaged for the optimization of EH cantilever sintering and the methodology are explained in the next section. The different steps that constitute this approach are critically discussed. Finally, some perspectives of improvement are proposed.

Approach

The SPS sintering conditions optimized for PZT ceramics and discussed in the previous section of this chapter cannot be fully transposed towards the sintering of the multilayer EH structure, due to:

 The shaping of the multilayer structure is done before sintering, while ceramics are shaped from their powder form into pellets during SPS sintering through an applied uniaxial pressure. Shaping of the multilayer structure is made by screen-printing. Therefore pressure parameter cannot be transposed from ceramic to multilayer.

 As previously discussed, the presence of the substrate and the printed electrodes brings to the structure additional stresses. This additional contribution is thus to be considered during the densification step. By consequence, even if the obtained SPS ceramics are highly densified (~98%), similar level of densification cannot be expected for multilayer structure. Nonetheless, higher densification than conventional one is aimed (relative densification >82%)

The approach dedicated to the sintering of the multilayer structure by SPS includes:

 A focus on the critical parameters related to multiple interfaces: bending, delamination, interdiffusion  Optimization of the SPS set-up configuration  Optimization of other key parameters of the assembly: nature of protective layer, specificities of each material of the multilayer structure in terms of nature and thickness.

For this, several experiments are performed, starting from the results obtained for SPS sintering of PZT ceramics and conventional sintering of multilayer structures. The first assumptions are:

 When considering the multiple interfaces within the multilayer (top Au/PZT/bottom Au/SS), the optimal sintering temperature defined for ceramics (875 °C for pure PZT ) should be slightly decreased in order to prevent interfaces related issues (in particular interdiffusion from the glass frit contained in the gold paste). However, it must be maintained sufficiently high to guarantee satisfactory densification.

 A uniaxial pressure as high as the one used for ceramics (50-100MPa) cannot be applied to the multilayer structure; this one can lead to complete damage of the sample. Therefore a minimum uniaxial pressure is used, the pressure equivalent to the SPS contact force (3kN).

Delamination and bending are the critical parameters encountered. Transient thermal gradients can induce stress gradients through the multilayer resulting in delamination issues. The most challenging aspect here identified is to avoid the delamination between the active piezoelectric layer and the electrodes (bottom and/or top electrodes). This is mandatory to guaranty not only a viable process but also to ensure the polarization of the multilayer and the reproducibility of the process. Sintering parameters as well as the features of the complete assembly such as the nature and thicknesses of multilayer structure constituents and protective layer are to be optimized. A total of 150 experiments have been carried out during this experimental approach, in order to validate the strategic lines used for improved densification of the multilayer by SPS. They are explained through illustrations in the next section.

Optimization of SPS set-up configuration

Besides the sintering temperature, the pressure is another determining parameter. For screenprinted films, an isostatic pressure of 40MPa (5 min at 65 °C) is applied prior sintering; this favors PZT densification and allows to reach a relative density of ∽80 %. For SPS ceramics densification, samples are compacted by uniaxial pressing during sintering using standard molds (Figure V-20) that allows a homogeneous distribution of both heat and pressure on the sample. In the case of PZT ceramic, the applied pressure of 100 MPa during SPS enhances the densification. High-applied pressure could potentially damage the stack, thus lower but uniform pressure need to be ensured. Taking into account these considerations and considering the geometry of the multilayer, the standard mold based configuration is not suitable. Modification of the SPS tooling set-up through the design of specific mold is a strategy already reported in literature to adapt the process to specific materials and to target widespread applications. Many examples can be mentioned, among them adapted tools for Functionally Graded Materials [49], porous ceramics [50][51], and, nanostructured materials with specific high pressure dies [52]. Tooling optimization is also mandatory to control radial thermal gradients that can generate microstructural non uniformities in sintered specimens, and which tend to become more critical in case of scale-up or when aiming complex shapes ( to samples with complex shapes (from [53]).

In the framework of this thesis, several configurations (punches + carbon elements) have been developed and tested to obtain optimal conditions regarding the incorporation of the multilayer (including the protective layer) and the uniformity of the applied pressure. A total of 10 set-ups have been tested. The main steps towards their optimization are explained.

Starting configuration (Configuration 0)

Starting from simplified configuration made of only the two non-hollowed punches (flat surfaces) of 30 mm∅ (configuration 0), three strategies are considered: modification of the internal set-up by adapting graphite foils (configurations 1 and 2), modification of the graphite punches (configurations 3 and 4) and finally a combination of graphite foils and punches modifications (configuration 5). This is illustrated in

Configuration 1

In the configuration 1, the sample is placed in between the punches and graphite foils (

Configuration 2

In configuration 2, instead of a circular perforated graphite foil, a rectangular shaped matching the area of the multilayer stack is cut within the graphite foil to incorporate the protective layer (

Configuration 3

For configuration 3, graphite punches modification is experimented. The bottom graphite punch is perforated in a circular shape with 1 mm depth. The protective powder is then introduced in it and the sample is placed face-down on top of it (Figure V-25(a)). Samples seem to not be destroyed right after sintering process, but once the protective layer is chemically removed, the active PZT layer shows to be peel-off.

Configuration 4

Configuration 4 corresponds also to a punch modification, but here a notch corresponding exactly to the rectangular shape of the multilayer is cut in the punch ( The whole set of tests show that changing the heating rate or adding a debinding step does not provide improvement. Concerning the cooling rate that can affect the driving force for delamination due to constraints, the different attempts do not show any significant differences.

Optimization of sintering conditions for the multilayer EH structure

No significant improvement obtained either by increasing the sintering time from 5 to 30 minutes. Therefore, sintering conditions are settled on a heating rate of 50 °C/min without debinding step, a sintering time of 5 minutes and natural cooling.

The selected sintering temperature of 850 °C is slightly lower than that optimized for PZT ceramics by SPS (without LBCu) for two reasons: to limit interdiffusion problems as already explained and also because the position of the thermocouple in the configuration 5 used is closer to the sample than when a conventional mold is used.

The form and the nature of protective layer appears as critical parameters that can compromise the integrity of the multilayer after SPS due either to the interaction with PZT or due to the removal process by acid attack. This aspect constitutes one of the strategic lines of optimization and is discussed in detail in the next section.

Even if the optimization of the set-up configuration is essential, this aspect alone is far from sufficient to reach optimized densification of the multilayers. The various tests have clearly shown that the weakest part of the assembly is the interfaces between the PZT and the electrodes (bottom and/or top electrodes) leading to delamination issues. Interdiffusion between the different layers is also a critical parameter highly dependent on the sintering temperature. The close link between temperature, mechanical constraints and chemical reactivity, all related to the nature and thickness of the different components, leads us to explore different ways to further improve the process by SPS through a better control of interfaces. These strategic lines are described in the next section. For each one, a summary of the most relevant experiments is given. Note that each experiment is repeated at least three times in order to confirm its reproducibility. They are all performed with the set-up configuration 5.

Strategic lines focused on interface issues

5. 1. Role of sintering aid: PZT + LBCu as active layer

Experiments with the same multilayers structure as for conventional approach are carried out (SS/Au/PZT+3%wtLBCu/Au), in order to have a system as close as possible to the structure already fabricated in chapter 4 and to test the benefit of the sintering aid LBCu in terms of reduction in sintering temperature. Several samples are densified within a range of sintering temperatures between 700 °C and 800 °C. As previously mentioned (section 2.2), PZT+LBCu ceramics sintered by SPS show high densification within this range of temperature. However, gold electrodes ink are recommended to be fired in the range 850-930 °C with an optimal firing at 850 °C (recommended by the supplier). Considering SPS and ink specifications, a compromise is to settle the sintering temperature at 775 °C. After SPS, the microstructure of the fracture reveals different features (Figure V-28):

 There is an adhesion between the top gold electrode and the PZT layer but the interface is not continuous and some air gaps are clearly visible (Figure V-28 (a)). The presence of LBCu in the active PZT layer seems to improve the adherence between the substrate, the bottom gold electrode and the PZT. Nevertheless, because of different constraint distribution within the active layer, this seems to cause a weakening of the interface between the PZT and the top electrode  The PZT layer exhibits a quite homogeneous microstructure in terms of grain size with no evidence of specific grain growth due to the presence of the sintering aid. A gradient of density is observed with in particular the region located close to the electrode interface that seems to be denser. This can be due to a more constrained sintering near the interface ( The observed discontinuities between gold electrode and PZT and the non-homogeneous distribution of the LBCu (presence of Cu-rich grains) can be detrimental for piezoelectric properties. The weight percentage of sintering aid used (3wt%) has not been optimized for conventional sintering so it is possible that such a value is excessive for SPS resulting in additive segregation detrimental for piezoelectric response. However, Cu segregation is also observed for printed disks conventionally sintered at 900 °C [54]. As shown in literature, the use of lower content of sintering aid (<1-2 wt.%) leads to PZT grain growth whereas an excessive content of additives inhibits grain growth due to impurities segregation [55]. In addition, the existence of an eutectic with a melting point at 690 °C for the system Cu 2 O -PbO [39] could lead to a deviation from PZT stoichiometry if additional PbO is not initially added.

In light of these results, two approaches can be considered to improve the densification and properties of the multilayer, either by decreasing the amount of sintering aid for SPS densification of multilayer or without using LBCu. Considering that PZT ceramics sintered by SPS without sintering aid display excellent properties, the second option has been chosen. The microstructure of a fracture of the PZT within the multilayer is characterized and compared to the one of the screen-printed PZT thick film conventionally sintered (Figure V-29). Very similar microstructures are obtained. Grain size (with wide size distribution) are comparable (~ 1 -4 m) and the level of porosity is in the same range (15-20%) although in the case of SPS, the sintering temperature is slightly lower (850 °C versus 900 °C), and the sintering dwell time significantly shorter (5' instead of 2h). In addition SPS is performed without sintering aid and without preliminary pressure step. Compared to PZT ceramic sintered by SPS, the increase of porosity within the stack can be explained perhaps by a slightly lower sintering temperature but principally by the absence of pressure during SPS sintering of the multilayer. However, even if over all the tests (Table V-6 and additional tests), configuration 5 associated with a sintering temperature of 850 °C appears to be optimal (samples globally appear not damaged), discontinuities (or even delaminations) between the PZT and the top gold electrode can still be observed when the samples are probed at the microscale (Figure V-30). This interface therefore remains a point of fragility. An additional aspect that can affect the quality of the top gold electrode is the use of the protective layer (directly in contact with the top gold electrode) during sintering and its removal after SPS. This contribution in the optimization of the sintered multilayer is discussed in the next section.

Nature of protective layer

An important characteristic of the approach is the use of a protective layer to avoid postreoxidation of the PZT based multilayer. It has been previously proved that high densified ceramics with excellent properties can be obtained without an annealing post-SPS step by using SrCO 3 or BaCO 3 as protective layer. For multilayer structures, the selection of the best form of the protective layer (printed layer or powder bed) and its nature (SrCO 3 or BaCO 3 ) has to be clarified.

As already mentioned, printed protective layer ink is prepared by mixing the powder with the epoxy resin ESL-CV59 as organic binder [32] (Annex 1 (formulation composition)). The advantage is that the epoxy resin is eliminated during sintering (450 °C from TGA analysis) while the remaining mineral part can be removed after SPS by chemical etching with a solution of phosphoric acid (H 3 PO 4 10%vol. ) following the reaction:

Where 𝑀 represents either Sr or Ba. This printed layer (thickness approximatively of 30 µm) is deposited all along the multilayer stack covering the whole area. In contrast, powder bed is directly introduced into the system (modified set-up configuration) ensuring the complete coverage of all the multilayer stack. The ease of removing the protective layer and therefore the quality of the surface of the multilayer depends on its initial form and nature. The following observations can be reported:

 Whatever its nature, protective layer is more difficult to eliminate after sintering when initially printed;

 SrCO 3 is more difficult to remove than BaCO 3 .

Higher reactivity (more intimate contact surface) between the layers of the structures and the carbonate is expected when the carbonate is printed. This effect is observed to be enhanced when LBCu is added to PZT. Contamination is observed on the surface of the sample after chemical attack in particular when using SrCO At this stage, the use of BaCO 3 , possibly because of a higher decomposition temperature (1350 °C) compared to that of SrCO 3 and thus a higher stability in the used SPS conditions , represents the best option to protect the active layer of PZT from chemical reduction and avoid post-thermal treatment (including to remove surface contamination). Note that SEM observations of the interfaces using the same protocol as in chapter 4 (Crosspolishing) proved unsuitable for these still fragile multilayers. Therefore a detailed analysis of the interfaces to probe in particular the interdiffusion zone between the substrate and the bottom gold electrode has not been possible. Optimization of sample preparation for SEM observations should be implemented.

Substrate thickness

Another option to limit interface issues is to adapt the thicknesses of multilayers constituents. As already proved in chapter 4, high thermal stresses during sintering are the cause of bending and delamination problems in the multilayer structure, arising mainly from the mismatch between thermal expansion coefficients. In chapter 4 this thermal stress has been compensated by reducing the PZT thickness (~55µm), but reducing even more this one will directly reduce the performance of the EH. Therefore we choose to modify the substrate thickness not only to limit delamination issues by reducing thermal stresses, but also to target higher deformation during performance of the device. Two different SS301 substrate thicknesses are used: 25µm and 100µm. Samples are fabricated using the same process described in chapter 4 for thick films. The different multilayer structures fabricated are given in Table V-7: As observed in Table V-7, PZT thickness is reduced when using thinnest substrates. Gold electrodes thicknesses are also decreased and are non-symmetric as for the original multilayer structure. Indeed, for these first experiments with thinner SS substrates, the screen-printing process settings, especially the substrate holder thickness and the off-contact distance could not be correctly adapted.

Samples are then sintered using a protective layer of BaCO 3 powder. The chemical removal is made without problem or damage of the samples (Figure V-33). A good adhesion of pure PZT layer is observed whatever the thickness of the substrate. In particular the complete multilayer structure (SS/Au/PZT/Au) seems to be intact for multilayer structure A (SS: 25 µm) ( These damages of the gold top electrode are attributed to the lack of optimizations of the printing settings with reduced SS substrates (substrate holder height not adequate). As a result the squeegee cannot apply homogeneous pressure during printing and deteriorate the humid layer. However, the obtained results are already promising and demonstrate that by reducing the thickness of the substrate, adhesion problems of pure PZT could be solved.

Nature of electrodes

The last strategic line probed concerns the nature of electrodes. Au electrodes present good chemical compatibility with PZT, but Ag or Ag alloys are more favorable at industrial level (reduced cost). Ag has a great conductivity, but is likely to migrate and this can contribute to a failure of electric properties in PZT films. However the presence of Pd, glass or oxides additives [54] can minimize this effect and can act as sintering aids for PZT inducing a rise in densification and electrical properties at low co-firing temperature. A conductive silver-palladium based ink (AgPd) supplied by Exxelia-Temex company (Pessac, France) has been tested as an alternative to gold ink. This ink has a low proportion of Pd present (10 wt.%) (Table V-8). The mineral additive is an oxide (MgTiO 3 ) with low permittivity, used in the manufacture of capacitors by Exxelia-Temex. The ink is printed with the same screen as for gold (325 mesh + 15 µm emulsion). First, a single layer is screen printed for the top and bottom electrodes. The layers are thinner than those printed with gold under the same conditions due to the higher proportion of solvent. A double printing of the two electrodes solves the problem, thickness of around 10 µm each are obtained for multilayer structure using 250µm and 100µm SS substrates.

Electrical tests

Undamaged samples with seemingly good adhesion between layers are further electrically characterized, when it is possible. Basic tests with a multimeter are first led to ensure (i) the absence of short-circuits between top and gold electrodes and (ii) electrical continuity of the top electrode. Then, when these preliminary tests are positive, a voltage is applied for the polarization step. Table V-9 summarizes these results.

In general the most challenging aspect among samples sintered without sintering aid LBCu (samples from 3 to 6) is the degradation of the top electrode mainly when this layer is too thin. On the other hand, samples sintered with LBCu (samples 1 and 2) do not present any damage of the constituent's layers. Nevertheless, electrical test performed on one of this sample shows that it is a bad dielectric (high leakage current impeding the application of a high voltage), whereas a second similar sample, even after a successful polarization step, doesn't show any visible piezoelectric properties. Therefore, the same conclusion that in the case of ceramics densified by SPS can be made, the presence of sintering aid can be critical for the piezoelectric properties of the multilayer containing PZT+LBCu and sintered by SPS.

Conclusion

Spark Plasma Sintering has been successfully used for the densification of PZT ceramics. A relative density as high as 98% has been obtained at a sintering temperature of 875°C without the use of sintering aid. Compared to conventional process, the sintering temperature is thus decreased by 300-400°C while reaching similar density. Furthermore, the post-annealing step usually performed after SPS to ensure re-oxidation of the sample has been avoided thanks to the use of a carbonate protective layer during SPS. Our first goal to efficiently densify PZT in one step while controlling microstructure and chemistry was thus achieved. As a proof, the corresponding overall dielectric and electromechanical properties (a relative permittivity of 1100 at room temperature and a coupling factor k eff of 36%) have been shown to be comparable to commercial PZT ceramics. These results highlight the benefit of SPS as a low time and energy consuming process. The impact of sintering aid addition during SPS has also been addressed. If a further decrease of sintering temperature was proved (98% relative density at 750°C), the poor piezoelectric properties obtained using 3%wt LBCu raise possible chemical homogeneity issues. However, indepth analyses, in particular chemical analysis at the grain boundaries, are necessary to decipher the influence of the LBCu on the microstructure and the related impact on piezoelectric properties.

The second part of this chapter was focused on the transfer and further optimization of SPS conditions towards the co-sintering of the printed PZT based multilayer EH structure.

The challenge was to face the most critical parameters identified in chapter 4, bending and delamination of the different layers. Indeed, the interface metal electrode/active PZT ceramic was shown to withstand high thermo-mechanic stresses that were expected to be enhanced in SPS conditions. The first step of our approach was to adapt the SPS set -up configuration. Both the graphite elements and punches where specifically designed to ensure in particular a uniform application of minimal pressure. Additional lines of optimization were focused on the nature of electrodes, substrate thickness and nature of the protective layer. Even if bending and delamination issues were significantly limited, the integrity of the gold electrode remains critical. The damage of the top electrode led to reduced conductivity and/or short circuits detrimental for piezoelectric properties. The key parameters to solve the problem do not concern only SPS but also the screen-printing process whose optimization could allow to improve the deposition of the electrodes. Finally, the complete approach investigated in this chapter and dedicated to the SPS sintering of EH multilayers is summarized in Figure V-35. This approach, combining both material and processes optimizations, has not only allowed to cope with several issues specific to multilayers but has also demonstrated the potential of Spark Plasma Sintering towards one step elaboration of printed multilayer EH structures.

a resonance frequency of 60Hz has been obtained with an output power of 9 µW (load resistance 1 MΩ). Compared to other piezoelectromagnetic devices in the MEMS-based literature, the normalized power density is significantly improved. Electronics associated with this device has also valorized this microsystem (developed at UW).

Although the performance of the EH has been validated, the identified weak points are the nonoptimal densification of the active layer of PZT (density ≈82%) and the control of interfaces within the multilayer. The limitation of the number of steps in the fabrication is also a concern that is added to the specifications towards the optimization of the whole process.

Thus, in order to be able to achieve all or some of these objectives, the second part of this thesis work was focused on the SPS process. The implementation of SPS has been made in a two-step approach. First, an optimization of the various SPS parameters (temperature, pressure, duration and heating rate) has been carried out for the densification of commercial PZT powders. Optimal SPS conditions have been determined and ceramics with relative density as high as 98% have been obtained at temperatures as low as 875°C, without sintering aid. Compared to conventional sintering of PZT, this represents a decrease of sintering temperature of more than 300°C.In addition, the original use of a protective carbonate layer to prevent the PZT from chemical reduction during sintering has allowed to avoid a post-SPS heat treatment. The electromechanical properties close to those of PZT's commercial ceramics attest to the effectiveness of SPS and the relevance of our approach. Successful one-step SPS sintering with a short cycle represents a significant energy saving.

A further decrease of the SPS sintering temperature has been reached when using LBCu sintering aid but at the expense of piezoelectric performances of the ceramics. Compared to conventional sintering, the fast kinetics of SPS seems to not guaranty the chemical homogeneity required for properties improvement. However in-depth microstructural analyses are required to clearly understand this point.

The second step was dedicated to the most challenging aspect i.e the implementation of SPS for Au/PZT/Au/SS screen-printed multilayer structures. The main locks identified are the porosity of the active PZT layer, interface issues leading to interdiffusion between layers, delamination or curvature of the cantilever. To address these issues, both the design of the SPS set-up and the features (thickness, nature, protective layer) of each material constituting the multilayer have been optimized. Various tests have led to an optimized SPS set-up configuration with specifically designed punches and graphite elements. The selected configuration ensures a uniform application of minimal pressure to avoid damages of the samples. From the material point of view, the most promising optimization lines were shown to be the reduction of the substrate thickness and the use of BaCO 3 instead of SrCO 3 as a protective layer. Once again, the benefit of sintering aid regarding the decrease of sintering temperature (and thus reduced thermal constraints) was shown to be at the expense of the chemical homogeneity of the PZT layer. In particular copper segregation arising from the LBCu sintering aid was evidenced.

Thanks to the different optimizations, it appears that bending and delamination issues can be significantly reduced and robust multilayers can be obtained even after removal of the protective layer. However, the integrity of the gold electrode remains critical. The damage of the top electrode led to reduced conductivity detrimental for piezoelectric polarization. The key parameters to solve the problem do not concern only SPS but also the screen-printing process whose optimization could allow to improve the quality of the top electrode deposit. As a result, dielectric and electromechanical performances would be properly evaluated.

Finally, the complete investigated approach, combining both material and process optimizations, has not only allowed to cope with several issues specific to multilayers but has also demonstrated the potential of Spark Plasma Sintering towards one step elaboration of printed multilayer EH structures. Some perspectives of this thesis work are:

 Optimization of the content of sintering aid (decrease the wt% LBCu) for densification of PZT or PZT based structure by SPS sintering could solve issues related to chemical homogeneity. Thus, the decrease in temperature thanks to the sintering aid would reduce thermal constraints and thus solve some delamination problems.

 Optimization of screen-printing parameters for the deposit of specific thickness of electrodes when using thin stainless substrates. A more robust top electrode would be expected.

 Further optimization of the SPS set-up to implement slighter higher applied pressure on the multilayer to improve adhesion between the layers  The use of bimorph structure to improve power density while equilibrating thermal stresses.

Figure 1 :

 1 Figure 1: Thesis execution synopsis

Figure I- 2 :

 2 Figure I-2: Energy sources available in ambient environment (Photo from of http://techon.nikkeibp.co.jp/Tech-On Japan).

Figure I- 3 :

 3 Figure I-3: (a) Picture of Micro Wind Generator (MWGs) used to power a led unit, output voltage can range from 0.01 to 15V depending on wind spin rate (maximum speed rate 300 rpm) and, (b) dimensions of MGWs structure. The structure weights 10g in total (motor + turbines paddles). (Commercialized by RMD technology, China).

Figure I- 4 :

 4 Figure I-4: (a) Scheme of a thermoelectric generator TEG elementary brick (Image from [6]), and (b) commercial TEG with a output power of 6.21 µW for a temperature increase of 73°K (1MC04-030-15_TEG from PL Engineering Ltd, Russia).

Figure I- 5 :

 5 Figure I-5: (a) Cross-sectional view of the Helmholtz resonator (b) equivalent mechanical model of the Helmholtz resonator (images from [10] ), and (c) scheme of a quarter-wavelength resonator.

Figure I- 6 :

 6 Figure I-6: (a-b) Mechanical energy haversting, using piezoelectric transduction system mounted in shoes for scavenging human movement (c) Power and rectified voltage waveforms from brisk-walking tests. (Images from [12])

Figure I- 7 :

 7 Figure I-7: Positioning of different energy sources at power scale (inspired from [6]).

Figure I- 8 :

 8 Figure I-8: Diagram block of a standard mechanical energy harvesting system.

Figure I- 8

 8 shows a generic model of such a generator, where a cantilever structure with a tip mass is used (Figure I-8 (a)). The vibration source is depicted with a red point. The generic equivalent lumped spring mass system scheme is as well illustrated (Figure I-8 (b)).

Figure I- 9 :

 9 Figure I-9: (a) Cantilever beam with tip mass subjected to a vibration source excited at the base (red point) and, (b) equivalent lumped spring mass system of a vibrating rigid body. (inspired from [16] )

  Figure I-9 (a)), and another with a fixed magnet linked to a moving coil (Figure I-9 (b)). The EMF is described by the rate of change of the magnetic flux:

Figure I- 10 :

 10 Figure I-10: Scheme of electromagnetic generators, with (a) moving and (b) fixed magnet. (Images from [6][23])

Figure I- 12 :

 12 Figure I-12: Scheme of piezoelectric cantilever. (Image inspired from [6])

Figure I- 13 Figure I- 13 :

 1313 Figure I-13 illustrates the piezoelectric effect. In the direct piezoelectric effect, also called generator or sensor effect, pressure generates charges on the surface of the piezoelectric materials. The field produced by the applied mechanical stress can be detected as an electric voltage if the piezoelectric body has electrodes. The sign of the voltage depends on the stress, either compressive or tensile. Mechanical energy is converted into electrical energy when considering the direct piezoelectric effect (Figure I-12 (a)). Conversely, the application of an electric field leads to a deformation of the piezoelectric material. This inverse effect also called actuator effect converts electrical energy into mechanical energy or motion (Figure I-12 (b)).

Figure I- 14 :

 14 Figure I-14: Origin of the piezoelectric effect in the unit cell of a disc of quartz cut with its normal surfaces normal to the axis of non-symmetry.

Figure I- 15 :Figure I- 16 :

 1516 Figure I-15: Polarization principle steps in piezoelectric ceramics.As previously discussed in section 3.2.3, mechanical characteristics are linked to electrical characteristics through basic relationships (Eq. 1.13 and Eq. 1.14) and whatever direct or inverse piezoelectric effects, the proportionality constant is the piezoelectric constant d. High d piezoelectric coefficient is preferred to develop motion or vibration. When written in tensor form, the piezoelectric coefficients transform as a third rank tensor. The matrix of the piezoelectric coefficients is hence revealing the ceramic symmetry. According to the Neumann's principle: the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of this crystal[38]. As an illustration, the matrix of the piezoelectric coefficients in tetragonal crystals (4mm symmetry) is shown in Figure I-15. The "3 direction" is determined as the polarization direction.

Figure I- 17 :

 17 Figure I-17: (a) Piezoelectric material used in the 33-mode and the 31-mode; (b) 31-mode bimorph cantilever in series and parallel connections; and (c) 31-mode and 33-mode unimorph cantilever configuration. (Image from [39])

  3 nanowires[47]-[50].Dahiya et al., presented for instance stretchable piezoelectric nanogenerators for self-powered wearable electronics application, with ZnO nanowires synthetized by hydrothermal method (Figure I-17)[51]. Compared to inorganic piezoelectric materials, piezoelectric polymers, such as PVDF and its copolymer poly (vinylidenefluoride-co-tri-fluoroethylene) (PVDF-TrFE)) are easy for processing and bio-compatible. As a result they are more suitable for flexible energy harvesting. These polymers can be processed in films or in nanofibers. Persano et al., developed for example a large area, flexible, and freestanding piezoelectric textile composed of highly aligned fibers of P(VDF-TrFE)( Figure I-18)[52].

Figure I- 18 :

 18 Figure I-18: Proof-of-concept for nanogenerators (SNGs = Stretchable Nano-Generators) using ZnO nanowires (NWs) fabricated on: (a) bank cards, (b) free standing PDMS and (c) silicon substrates. The magnified image in each panel shows the as-grown ZnO NWs on respective substrates. (d) The final device structure and (e) SEM image after parylene C and metal deposition on NWs grown on silicon. (Images from [51])

Figure I- 20

 20 shows the process developed by Liu et al.

Figure I- 20 :

 20 Figure I-20: In this process, the Pt/Ti top and bottom electrodes are deposited by DC magnetron sputtering on a SOI wafer and are etched with Ar ions. A Pb(Zr 0.52 ,Ti 0.48 )O 3 film of 2.5µm-thick is deposited in between the electrodes by sol-gel method and a chemical etching is carried out to ensure its microstructuration (mixture of HF, HNO 3 , and HCl). The micro-cantilever structures are finally obtained by RIE/DRIE (Deep Reactive Ions Etching) process of Si or SiO2 (front or backside etching).(Images from[39])

Figure I- 21 :

 21 Figure I-21: (a) Scheme diagram of the fabrication process for a high-efficient, flexible, and large-area PZT thin fi lm-based NanoGenerator (NG) using the Laser Lift Off method (LLO) on flexible PET plastic substrate. (b,c) The cross-sectional SEM images of PZT thin films on a sapphire (b) and a PET substrate (c). (d) A PZT thin film (1.5 cm × 1.5 cm) on a PET substrate being detached from a sapphire substrate after LLO process. The inset shows the PZT thin fi lm on a flexible substrate bent by human fingers. (e) The final flexible PZT thin film NG attached to a glass tube and bent by human fingers (the inset). (Images from [67])

  Figure I-22 (a)), Colin et al measured 3µW at very low frequency (15Hz) and under a 10mg acceleration, demonstrating the efficiency of such piezoelectric energy harvester[71].

Figure I- 22 :

 22 Figure I-22: Examples of bimorph piezoelectric vibration energy harvesters (EH), photograph, microstructure and electrical characterization, (a) thinned bulk PZT assembled on SS substrate [71] , (b) screen-printed PZT EH [4].

  Figure I-21 (b) shows the different harvested powers obtained under acceleration varying from 0.2g to 1.4g. Here, despite an additional high pressure step (100-200MPa) before the sintering (1 hour at 850°C), the screen-printed PZT layers show average apparent porosity of 20%. Denser PZT layers can be deposited on metallic substrate through aerosol technique. For instance Lin et al deposited PZT thick-film directly on a stainlesssteel substrate by aerosol deposition method at room temperature (Figure I-23 (a)) [73] . The obtained PZT thick-film showed excellent adhesion (Figure I-23(b)) and ferroelectric properties. For this EH having a volume of 13 mm 3 , a maximum output power of 200µW (12.658 Vp-p) could be measured with a 1.5g acceleration level and at an excitation frequency of 112.4 Hz (Figure I-22(c)).

Figure I- 23

 23 Figure I-23: (a) Micro-generators structure fabricated through aerosol, (b) SEM photograph of the PZT layer after deposition (sidewall of the PZT layer and cross-sectional view of the cantilever-beam), and (c) Experimental results of the output voltage versus excitation frequency under the open circuit conditions at different accelerations. (Images from [73])

  Figure II-1 shows an example of a hybrid circuit.

Figure II- 1 :

 1 Figure II-1: Hybrid circuit containing conductor tracks, 8 integrated circuits, 2 thick and thin film resistors, and 8 capacitors. The substrate is housed in a 32 pin ceramic package. (Image from [2])

  Figure II-3 summarizes the different steps of the standard thick-film process. For a complete thick-film hybrid circuit, further steps are necessary to report the active or passive components (chips or SMT components) and for the final packaging.

Figure II- 2 :

 2 Figure II-2: Scheme of the screen-printing process principle.

Figure II- 3 :

 3 Figure II-3: Fabrication steps of the standard thick-film technology.

Figure II- 4 :

 4 Figure II-4: (a) Typical mesh scheme of thick-film screens with characteristic parameters (thicknesses of fabric (Ef) and emulsion (Ee), wire diameter (d) and opening of mesh (O)). (b) Picture of a screen after UV patterning with the different constituents, and (c) zoom on the fabric mesh.

Figure II- 5 :

 5 Figure II-5: Photolithographic screen manufacture. (a-c) direct emulsion deposition process (d) screen with deposited negative emulsion film and plastic pattern mask, (e) UV light exposure of the negative emulsion: the UV exposed parts reticle, (f) screen after development: the non-exposed UV parts corresponding to the desired pattern have been dissolved in water.

Figure II- 6 :

 6 Figure II-6: Patterns design with respected circular-shape fiducials (left). Complete assembly for screen fabrication with UV exposure machine Technigraff -Variocop S used at the IMS laboratory (right).

Figure II- 7 :

 7 Figure II-7: Scheme of Newtonian behavior: fluid between two flat and parallel surfaces, one of which is in motion in relation to the other.

Figure II- 8 :

 8 Figure II-8: Variation of the viscosity η of the paste and the speed gradient D during screenprinted deposition.

Figure II- 9

 9 Figure II-9 summarizes the composition of inks for thick-film technology.

Figure II- 9 :

 9 Figure II-9: Constituents of a mineral ink for screen-printing.

  Planetary milling machine (Retsch PM4 at IMS (Figure II-10 (a)) is used for this process stage. The powder is wet in ethanol vehicle and placed in an agate jar (7.5 mm) with agate spheres (10 mm) (Figure II-10 (b)). At each rotation of the platform, the jar rotates around its axis of rotation, but in the opposite direction. The centrifugal and Coriolis forces lead to a rapid acceleration of the milling balls, leading to grinding by friction [19] (Figure II-10(c)).

Figure II- 10 :

 10 Figure II-10: (a) Planetary milling machine used at IMS laboratory (Retsch PM4), (b) agate jar and spheres (b), and (c) principle scheme of planetary milling (Image inspired from [20]).

  T2F at IMS) (Figure. The efficiency in the homogenization comes from rotation, translation, and inversion according to the Schatz geometric theory[21] .

Figure II- 11 :

 11 Figure II-11: Turbula shaker-mixer T2F system used at IMS laboratory.

  A three-roll mill is used (Figure. This equipment is composed of three in lines SiC rolls separated by an adjustable gap. The rolls rotate in opposite directions at different speeds by a factor of 3 relative to each other (Figure II-12 (b)). After each cycle, the ink is scraped off the front roll and the paste is collected and introduced again in the first roll, led for mix, refine, disperse, and homogenize materials fed into it. The roll gaps have to be adjusted, i.e. gradually decreased until the desired dispersion has been obtained. Care should be taken if too much stresses are applied to ductile metal powders present in conductive pastes.

Figure II- 12 :

 12 Figure II-12: Three-roll mill picture (EXAKT 80) used at IMS laboratory (left), and dispersing principle scheme (right) with v3=3v2; v2=9v1 [22].

  Figure II-13 (a)). It allows to measure the shear speed depending on the stress applied. The appropriate quantity of ink is placed between the cone and the parallel plan. Then, thanks to the progressive rotation of the cone a shear stress is produced. The shear speed D is related to angular velocity ω and cone angle α by equation D= ω/ α. Viscosity measurements are carried out by increasing and decreasing the shear speed and deducing the shear stress τ . The curves 𝜂 = 𝑓(𝐷) can then be obtained (Figure II-13 (b)).

Figure II- 13 :

 13 Figure II-13: (a) Scheme of rheometer cone-type system used for viscosity measurements, and (b) characteristic curves 𝜂 = 𝑓(𝐷) that can be obtained (melted chocolate). (Image from [19])

Figure II- 15 :

 15 Figure II-15: DEK Horizon screen-printing machine used at IMS laboratory.

3 :

 3 Examples of screen characteristics and emulsion thickness for different kinds of pastes.

4 :

 4 Impact of the different screen-printing parameters on the printed thickness and resolution. The arrows symbols indicate the increasing (blue arrow) or decreasing of the parameter (black arrow).(Inspired from[5])

  Solid state sintering occurs in three different stages: the initial stage, the intermediate stage and the final stage (Figure II-16). The description of these different stages is based on a model of two spherical particles of the same diameter and of the same nature. Starting from an assembly of particles, the different parameters observed during the different stages are presented in TableII-6. The main parameters that need to be monitored are the neck size ratio (contacts between adjacent particles) defined as X/D, the relative density, the linear shrinkage and the reduction of the surface area S/S 0 (X = neck size, D = particle diameter, ΔL = length variation, L 0 = initial length, S = specific area, S 0 = initial specific area).

Figure II- 16 :

 16 Figure II-16: Graphical representation of the different stages of solid state sintering from a powder compacted with spherical particles of the same size.

Figure II- 17 :

 17 Figure II-17: Different events occurring during conventional sintering cycle of screen-printed layers.

Figure II- 18 :

 18 Figure II-18: Microstructure of a thick-film layer after firing. (Image from [38])

Figure II- 20

 20 Figure II-20 shows the furnace used in the framework of this thesis (AET technologies vertical furnace). The furnace consists of a 16 cm inner diameter ceramic quartz tube vertically positioned, at the top of which a high temperature resistance heating to 1100 °C is located. This system creates a temperature gradient in the tube. A quartz road and a quartz support (sample holder) allow to move the samples into the tube. An engine attached to the base of the quartz rod and a worm gear allows to control the position and speed of movement of the samples. A type K thermocouple allows to supervise the temperature of the samples. Speed variations and the position of the samples in the tube correspond respectively to variations of temperature gradients and temperature values. This system allows to reach heating and cooling ramps of maximum 100 °C/min while maintaining the possibility of long holding time at a fixed temperature. The oven also allows to perform sintering in controlled atmosphere (air or nitrogen).

Figure II- 20 :

 20 Figure II-20: Furnace used for conventional sintering (AET technologies vertical furnace) used at IMS laboratory.

Figure II- 21 :

 21 Figure II-21: Schematic of the SPS sintering process.

Figure II- 22 :

 22 Figure II-22: SPS Doctor Sinter lab. 515-S used at ICMCB Laboratory.

  Figure III-1: Dimensions of the ceramic sample for experimental density evaluation

Figure III- 2 :

 2 Figure III-2: Example of thickness profile (left), and Tencor contact profilometer used at IMS (right) laboratory.

Figure III- 3 :

 3 Figure III-3: Profilometer principle for roughness measurement (Image from [2])

Figure III- 4 :

 4 Figure III-4: Scheme of Bragg's law. According to the 2θ deviation, the phase shift causes constructive (left -) or destructive (right -) interferences. (Image from [4])

Figure III- 5 :

 5 Figure III-5: Schematic of SEM (left) (Image from [6]), and SEM JEOL, JSM-6100 used for observation of ceramics at IMS Laboratory.

Figure III- 6 :

 6 Figure III-6: Evolution of the dielectric permittivity of BaTiO3 as a function of temperature (Image from [8]).

Figure III- 7 :

 7 Figure III-7: Dielectric measurements set-up at ICMCB (left) complete set-up (right) connected sample within the furnace.

Figure III- 8 :

 8 Figure III-8: Pictures of the polarization furnace used at the IMS laboratory.

Figure III- 9 : 3 . 3 . 3

 9333 Figure III-9: Typical impedance curve (in red) with a minimum |𝑍 𝑟 | at the resonance frequency fr and a maximum |𝑍 𝑎 | at the anti-resonance frequency fa. (Image from [11])

Figure III- 10 :

 10 Figure III-10: Electrical equivalent circuit diagram of a piezoelectric resonator near the resonance. C0 and R0 are respectively the capacity and leakage resistance representing the dielectric losses of the sample out of resonance. The branch with subscript m describes the behavior nearby resonance and is defined as the motional branch.

2 (

 2 𝑚𝑎𝑥 , 𝐿 𝑚 = 𝑅 𝑚 2𝜋(𝑓 𝑛 -𝑓 𝑢 ) and 𝐶 𝑚 = 1 4𝜋 2 𝐿 𝑚 𝑓 𝑟 Eq. 3.13) Where 𝑓 𝑢 and 𝑓 𝑛 are measured at 𝐺 = 𝐺 𝑚𝑎𝑥 2 and 𝑓 𝑟 the resonance frequency at G=G max .

Figure III- 11 :

 11 Figure III-11: Conductance G and susceptance B as a function of the frequency. Special points (Gmax, Bmax, Bmin, fn and fu) are represented, allowing extraction of Rm, Cm and Lm. The frequencies fn and fu are defined at 𝐺 = 𝐺 𝑚𝑎𝑥 /2 and correspond to the bandwidth at -3dB or |𝑌| = |𝑌| 𝑚𝑎𝑥 /√2 .

Figure III- 13

 13 Figure III-13 summarizes the procedure used for the determination of the piezoelectric material properties. Capacitance measurements are carried out at 1kHz at room temperature.

Figure III- 13 :

 13 Figure III-13: Scheme of coefficient determination method using IEEE standard (planar vibration mode for a disk) (Inspired from[18]).

  Figure IV-1 (a-left). Here, researches showed that the length of the spiral needs to be at least half a turn to obtain a low frequency. But the fundamental vibration of these long spirals is dominantly torsional, what is therefore not ideal for energy harvesting. A sandwich of two spirals beams (Figure IV-1 (a-right)) is a better option showing a resonance (first mode) vertically and where horizontal and twisting modes are suppressed [4]. A zig-zag geometry (Figure IV-1 (b)

  et al. addressed this problem by using a fixed-fixed configuration instead of a free-fixed one. Two zig-zag beams are connecting at their free end in this meandered geometry (Figure IV-1 (c))[6]. Another cantilever-like configuration without free-ends, called the "elephant", is proposed by Sharpes et al. to reduce torsional effects and enhance pure bending for the fundamental mod (Figure IV-1 (d))[7]. This design is a closed circuit meandering configuration where the two free-ends of the meanders are joined and it produces greater bending in the clamped beam, part showing the highest amount of strain. In this work, higher power is measured compared to the zig-zag configuration, with the piezoelectric layer located on the clamped beam.

Figure IV- 1 :

 1 Figure IV-1: Proposed 2D geometries of energy harvester to reduce resonance frequency of the structure and to improve generated strain, (a) spiral and double spiral connected, (b) zig-zag design with experimental structures in aluminum (length of the beam= 171.4mm), (c) meandering configuration with simulated strain, and (d) elephant drawing, stress analysis and picture of the fabricated EH (steel substrate and PZT). (reproduced from [4], [5], [7], [8])

Figure IV- 2 :

 2 Figure IV-2: llustration of domain structure in the film under (a) tensile stress and (b) compressive stress,in the cases where the stresses are controlled by thermal expansion mismatch (reproduced from[15]).

Figure IV- 3 :

 3 Figure IV-3: Photograph of a laser-machined meandering piezoelectric energy harvester (reproduced from [6])

Figure IV- 4 :

 4 Figure IV-4: (a) Spiral fabricated from a laser micromachined buzzer (PZT/brass). Each spiral is named with different acronyms: M stands for Membrane, S for Simple (1 spire), D for Double (2 spires), H for Hexa (6 spires) and O for Octo (8 spires)), and (b) Normalized amplitude versus frequency (Hz). The resonance frequencies range from 8 Hz to 650 Hz. For each curve, the amplitude is normalized with respect to its maximum value.(reproduced from [20])

Figure IV- 5 :

 5 Figure IV-5: (a) SEM images of PZT layers deposited on Pt/Ti-coated SS mesh substrates ((a) φ15 mesh and (b) φ30 mesh and (b) image of PZT thin films on stainless mesh substrates. (reproduced from [21])

Figure IV- 6 :

 6 Figure IV-6: Summary diagram of EH requirements

Figure IV- 7 :

 7 Figure IV-7: Scheme of the multilayer considered as the "elementary brick" of the EH structure.

Figure IV- 8 :

 8 Figure IV-8: XDR pattern of PZT PZ26 initial powder with diffraction peaks indexed in the rhombohedral and tetragonal symmetries.

Figure IV- 9 :

 9 Figure IV-9: Phase diagram for PZT, with relevant regions labeled (reproduced from [23])

Figure IV- 11 :

 11 Figure IV-11: Dimensioned (mm) schematic of energy harvester substrate (a) optimized geometry (modified zig-zag) and, (b) simple structure corresponding to the middle branch of the modified zig-zag structure used for preliminary experiments and characterizations.

Figure IV- 12 :

 12 Figure IV-12: 3D FEA COMSOL analysis of fundamental mode shape showing (a) Strain. (b) Total displacement (in mm) (isometric view).

  Figure IV-13 shows a resulting screen for the PZT layer after UV patterning. The mask design (as the others) contains four circular guidelines (fiducials) in four corners necessary for the alignment of the PZT layer on the bottom gold layer Table IV-10: Geometries of the different layers of the EH structure (dimensions are in mm).

Figure IV- 13 :

 13 Figure IV-13: (a) Mask with circular guidelines (fiducials) for alignment purpose, (b) photograph of a fabricated screen.

Figure IV- 14 :

 14 Figure IV-14: Viscosity of the ink tested for PZT formulation. Measurements made at 25°C with the Brookfield rheometer (Elorprintec, Pessac).

Figure IV- 15 :

 15 Figure IV-15: Printing tests for two prepared pastes, (a) paste 3 and (b) paste 2. (See Figure IV-14 for the corresponding viscosities. Paste 1 picture is equivalent in deposit quality aspect)

Figure IV- 16 :

 16 Figure IV-16: Stainless steel substrate holder fabricated for the layers deposition on the zig-zag shaped SS substrate.

  electrode are printed successively, with a drying step during 20 min at 120°C between each deposition. A slow drying rate of 1°C/min until 120°C is preferred for PZT layer to avoid bubbles or cracks. A description of these successive steps is illustrated in Figure IV-17. Multiple layers deposition for Au and/or PZT (printing and drying between each deposition) can be done depending if a thicker layer is expected.

Figure IV- 17 :

 17 Figure IV-17: Fabrication steps of the screen-printed EH multi-layer (modified zig-zag and simple cantilever): (a) bottom Au electrode, (b) active PZT layer (c) top Au electrode, (d) cross section of the cantilever (dimensions in mm), (e) modified zig-zag EH with dried PZT layer after printing.



  Figure IV. 18 comprises the following steps: Heating at 40°C/min until 250°C  Heating at 1°C/min between 250°C and 450°C, in order to allow the progressive decomposition of organic binders  Heating at 40°C/min from 450°C until 900°C. Contribution of sintering aid to promote densification (especially melting of the Li 2 CO 3 -Bi 2 O 3 eutectic at around 690°C)  Sintering time: 2 hours at 900°C  Cooling at 40°C/min to about 150°C  Samples are finally let to cool down naturally till room temperature.

Figure IV- 18 :Figure

 18 Figure IV-18: Sintering cycle used for densification of PZT+3%wtLBCu ceramics.

Figure IV- 20 :

 20 Figure IV-20: Left Strain contour plot showing tension (red) and compression (blue) (right) strain matched electrodes.

Figure IV- 21 :

 21 Figure IV-21: (a) Ball-bonding equipment K&S 4524 used at the IMS laboratory and (b) principle.

Figure IV- 22 :

 22 Figure IV-22: Photograph of the fabricated EH with the wire-bonding and scheme of the bonded wires.

Figure IV- 23 :

 23 Figure IV-23: Schematic view of the screen-printed layers for the disks fabrication.

  Figure IV-24 (b)). In comparison, free surfaces in ceramics allow both more efficient debinding and densification providing a faster kinetic pathway for mass transport and leading to enhanced PZT grain growth.

Figure IV- 24 :

 24 Figure IV-24: SEM images of PZT + 3%wt LBCu for (a) fracture section of ceramic, (b) printed cantilever cross polished section and, (c) fracture section of free standing printed disk.

  Figure IV-25 shows the complete energy harvester after firing with two different PZT layer thicknesses (55 and 100 µm). Bending of the structure is observed for the 100μm final thickness (Figure IV-25 (b)) and peeling off of the layer can arise (Figure IV-25 (d)). Indeed, thermal stresses during the firing lead to significant deformation of the structure. This is confirmed by the high difference between the CTE of SS and PZT ceramic highlighted through dilatometry analysis (Figure IV-26). In the high temperature range (500-600 °C), an average of CET values of 16.7 and 4.7 ppm/°C are obtained for SS and PZT, respectively.

Figure IV- 25 :

 25 Figure IV-25: (a) Modified zig-zag cantilever EH structure after firing, (b) with a 100µm thick PZT layer, (c) with a 55 μm thick PZT, (d) peeling off of the layers for 100µm thick layers.

Figure IV- 26 :

 26 Figure IV-26: Thermal expansion coefficient as a function of temperature for SS substrate (a), and PZT ceramic (b).

Figure IV- 28 :

 28 Figure IV-28: Comparison between calculated absolute values using Eq.4.6 and the measured experimental values for the curvature of multilayer structure analysis.

Figure IV- 29 :

 29 Figure IV-29: SEM analysis of (a) Au/PZT/Au/SS, (b) top Au electrode/PZT interface and, (c) interface layer between bottom Au electrode and SS substrate

Figure IV- 30 :

 30 Figure IV-30: Figure 1: Energy Dispersive X-ray (EDS) analysis of SS/Au/PZT multilayer structure: chemical cartography of Au/SS interface layer after sintering.

Figure IV- 31 :

 31 Figure IV-31: Permittivity (a) and tan δ (b) for PZT ceramic at different frequencies and as a function of temperature (23<T(°C) <450).

Figure IV- 32 :

 32 Figure IV-32: Impedance measurements: Conductance (G) and Susceptance (B) of (a) printed disk (b) and printed simple cantilever.

Figure IV- 33 :

 33 Figure IV-33: Scheme of a piezoelectric vibration EH, (a) mechanical model, and (b) electrical model.[44]

  Figure IV-34: (a) Electrical networks showing the PEVH connect to (a) to an electrical load 𝑌 𝐿 (b) to a classical rectifier followed by a resistive load (b) [reproduced from[44]

Figure IV- 35 .

 35 For this electrical network, the governing equations must be the same as for Eq. 4.7 and Eq. 4.8. This is achieved for the values of the electrical resonator {R m = D, C m = K -1 and L m =M}. Here, to get the model, the cantilever is clamped on the shaker ( 2mm is clamped, see Figure IV-36), and the amplitude and the phase of the admittance Y of the piezoelectric resonator are measured around the resonance frequency (Figure IV-37). Using a Matlab fit, the parameters of the model are extracted (TableIV-16).

Figure IV- 35 :

 35 Figure IV-35: PVEH's equivalent electrical network. Electromechanical transduction is modeled by the 𝛼𝑣 voltage source and 𝛼𝑥̇ current source (see Eq. 4.7 and 4.8, Figure IV-33). The mechanical resonance is represented by the electrical resonator {RmCmLm.} [44]

Figure IV- 38 :

 38 Figure IV-38: Output power as a function of frequency for different accelerations, with a resistive load of 2.7 MΩ. (collaboration ISEP/C2N)

  Before the tests, a neodynium magnet (3.175 mm x 3.175 mm x 12.7 mm) is glued on the tip using a thin layer of epoxy adhesive cured for two days (Figure. The piezoelectromagnetic energy harvester is then experimentally tested to validate the results of the FEA model. The experimental test setup is shown Figure IV-40. The unit is mounted above a current carrying wire (10 AWG) using an acrylic base and 1.5 mm thick spacers to control the distance between the magnet and the wire. An LMS SCADAS mobile data acquisition system is used to control the current amplitude and frequency in the wire to perform a frequency sweep analysis using the Sine Control module. A Fluke i400s AC clamp is used to provide the feedback control for the system. The sinusoidal input is amplified through a Modal Shop 2050E09 power amplifier. During excitation, a Polytec OFV-505 laser vibrometer and OFV-5000 controller can measure the tip displacement of the harvester. The output voltage produced by the system is given by the LMS system with input impedance of 10 MΩ using a 10:1 probe. Different resistive loads values are obtained with an Elenco resistor substitution box. The frequency resolution of the data acquisition is 0.01 Hz.

Figure IV- 39

 39 Figure IV-39: (a)Working principle of the piezo-electromagnetic harvester, (b) photograph of the fabricated energy harvester. (Collaboration Waterloo, Canada, reproduced from [29])

Figure IV- 41 :

 41 Figure IV-41: Tip displacement and voltage Frequency Response Function -FRF) ; the wire is at a distance of approximately 12.5mm and carries a 1A current (Collaboration Waterloo, Canada, reproduced from [29])

Figure IV- 44 :

 44 Figure IV-44: Dynamic power conditioning module circuit (a) design architecture, (b) power conditioning module circuit schematic, and (c) Charging/Discharging behavior of the Storage. Here the unit is capable of reading a 60 Hz Alternating Current (AC) sensor signal with a peak voltage in the range of 100 mV to 900 mV with accuracy no less than 91.4%. For carrying currents in the range of 8.4A to 30A, a readtransmit duty cycle from <4min to 18min has been achieved. (Collaboration Waterloo, Canada) (reproduced from [56])

Figure V- 2 )Figure V- 1 :

 21 Figure V-1: (a) XRD patterns of PZT ceramics sintered by SPS at different temperatures (800 °C, 850 °C, and 875 °C) and pattern of started powder (PZ26 from Ferroperm). Sub-indices T and R correspond to tetragonal and rhombohedral respectively. P4mm Bragg positions for Pb(Zr0. 44Ti0. 56)O3 are presented in red below the diffractograms. (b) Zoom of the XRD patterns at 2θ= 42°-48° of PZT ceramics sintered by SPS at different temperature (800 °C, 850 °C, and 875 °C) and pattern of started powder (PZ26 from Ferroperm). Sub-indices T and R correspond to tetragonal and rhombohedral respectively. P4mm Bragg positions for Pb(Zr0. 44ti0. 56)O3 are presented in red below the diffractograms.

Figure V- 2 :

 2 Figure V-2: XRD patterns of the ceramic sintered by SPS at 850°C after polishing and after grinding

Figure V- 4

 4 summarizes the obtained microstructure analysis. The evolution of average grain size and relative density are reported as a function of the sintering temperature and applied pressure. Error bars are estimated from the values obtained on three different samples sintered in similar conditions.

Figure V- 3 :

 3 Figure V-3: SEM images of PZT ceramics densified by SPS at 800 °C (a), 850 °C (b), 875 °C (c), during 5 min under a uniaxial pressure of 100MPa.

Figure V- 4 : 2 . 1 . 1 . 2

 42112 Figure V-4: Variation of grain size and relative density with sintering temperature and applied pressure.

Figure V- 5 :

 5 Figure V-5: Pictures of PZT disks (a) after SPS and post annealing 10 hours at 800 °C (b), after polishing with (c) Au sputtered electrode on the polished face with (d) screen-printed Ag-epoxy electrode on the polished face.

Figure V- 6 :

 6 Figure V-6: Conductance response for different types of electrodes and surface quality.

Figure V- 7 :

 7 Figure V-7: Impedance amplitude and phase measured for ceramics sintered by SPS at 850 and 875 °C.

Figure V- 8 :

 8 Figure V-8: (a) Admittance B(G) circle of PZT ceramics sintered by SPS at different temperatures ( 800, 850 and 875 °C), and (b) zoom close to the graphic axes origin in order to be able to observe the response of the ceramic sintered at 800°C.

Figure V- 9 :

 9 Figure V-9: Scheme of set-up configuration for sintering with a protective layer.

Figure V- 10 :

 10 Figure V-10: SEM image of PZT sintered by SPS using a SrCO3 protective layer.

Figure V- 11 :

 11 Figure V-11: Thermal variation of the permittivity at different frequencies for PZT/SrCO3 sintered by SPS (no reoxidation) -Insert: Dielectric losses as a function of temperature at 1 kHz.

Figure V- 12 :

 12 Figure V-12: Electromechanical measurements for PZT + SrCO3 sintered by SPS (no reoxidation) in contrast with samples with no protective layer and annealing post-treatment (800 °C 10 h) (a) admittance B(G) circle, impedance amplitude (b) and phase (c) for PZT/SrCO3 (no reoxidation) and PZT(after annealing), both sintered by SPS at 875 °C.

Figure V- 13 :

 13 Figure V-13: (a) Experimental and fitted impedance phase angle for the PZT/SrCO3 sample sintered at 875°C with equivalent circuit resulting response. (b) Equivalent circuit considered.

Figure V- 14 :

 14 Figure V-14: (a) Impedance amplitude, and (b) phase for PZT sintered with SrCO3 and BaCO3 protective layer (no reoxidation), both sintered by SPS at 875 °C.

  XRD analysis shows no deviation of the peak positions indicating that the sintering aid does not cause significant modification of the lattice cell parameters (Figure V-15). The most remarkable feature in the XRD patterns of the ceramics sintered with LBCu is the broadening of the tetragonal splitting (002)/(200) (observed also for the others double peaks (001)/(100), (112)/(211) and (103)/(310). However, EDS analysis (Figure V-16) has not provided additional insight to conclude on a possible correlation between chemical inhomogeneity and the observed peak broadening. EDS analysis has not allowed detecting and localizing Cu and Bi possibly due to quantities close to undetectable levels and absence of segregation.

Figure V- 15 :

 15 Figure V-15: XRD patterns for ceramics PZT + 3wt% LBCu sintered par SPS at different temperatures (700, 750 and 875 °C), and for PZT (without LBCu) ceramic by SPS at 875 °C and conventional ceramics sintered at 900 °C.

Figure V- 16 :

 16 Figure V-16: EDX of PZT + 3wt% LBCu ceramics sintered by SPS at 700 °C (very similar results are obtained for 750 °C and 850 °C).

Figure V- 17 :

 17 Figure V-17: Electromechanical response of PZT + 3%LBCu ceramics sintered by SPS (a) Conductance (G) response of samples at 750°C and 875°C (samples at 700°C show little nor comparable response), and (b) comparison with pure PZT ceramics sintered at 850°C and 875°C.

Figure V- 18 :

 18 Figure V-18: Configuration of the multilayer structure (SS/Au/PZT/Au) for SPS sintering.

  Figure V-19 summarizes the general experimental approach used.

Figure V- 19 :

 19 Figure V-19: Summary diagram of experimental approach towards SPS sintering of multilayer structures.

Figure V- 20 :

 20 Figure V-20: Standard set-up configuration for ceramics SPS densification (a), picture of grafite mold and punches(b) and mold during densification (thermal radiation is observed at T°>700 °C (c))

  Figure V-21) [53].

Figure V- 21 :

 21 Figure V-21: Illustrations of SPS optimized tools configuration (a) Schematic view of the gradient die dedicated to FGM (from [49]), and (b) optimized configuration with a sacrificial powder ring dedicatedto samples with complex shapes (from[53]).

  Figure V-22.

Figure V- 22 :

 22 Figure V-22: Flowchart of the different steps towards the optimization of the SPS set-up configurations dedicated to the sintering of multilayer.

  Figure V-23). A 1 mm thick perforated graphite foil (ring-like design) is used to hold in place the protective layer. This configuration is tested either with the sample face-up (Figure V-23(a)) or face-down (Figure V-23(b)). However, all experiments (conducted 3 times) result in samples completely destroyed after sintering (Figure V-23 (c-d)).

Figure V- 23 :

 23 Figure V-23: Scheme of configuration 1 with the powder protective layer incorporated in a ring-like graphite foil, to place the protective layer. (a) sample facing up and (b) sample facing down. (c) Resulting samples (all layers are completely damaged) and (d) picture zoom.

  Figure V-24 (a) and (b)). A more homogeneous distribution of the mechanical stress is thus expected. . Nevertheless, this configuration also results in samples with peel-off of layers (Figure V-24 (c)).

Figure V- 24 :

 24 Figure V-24: Scheme of configuration 2 with protective layer incorporated in a modified rectangular shaped graphite foil, (a) sample facing up and (b) sample facing down configuration. (c) Picture of an example of obtained samples (all layers are completely destroyed).

Figure V- 25 :

 25 Figure V-25: Scheme of configuration 3 with the protective layer introduced in the bottom graphite punch perforated in a circular shape of 1mm depth. (b) Samples right after SPS (layers seemingly well adhered) and (c) layers are peeled-off after chemical removal of protective layer.

  Figure V-26 (a-c)). Nevertheless this configuration does not provide satisfactory results. Layers are peeled off either when the sample is removed after sintering or during chemical attack used to remove the protective layer (Figure V-26 (d).

Figure V- 26 : 3 . 3 . 6 5

 263365 Figure V-26: Scheme of configuration 4 with a rectangular shape notch within the punch of 1mm depth. (b) Set-up right after SPS, (c) peeling-off of layer when moving out the sample and (d) peeling of layers after chemical attack

Figure V- 27 :

 27 Figure V-27: Scheme of configuration 5 using an additional carbon felt element for an extra pressure applied to the sample. (b) Sample after SPS process without any damage and (c) sample after removal of protective later with still a good adhesion maintained between layers.

  Figure V-28 (a-b)).  The distribution of the sintering aid is not homogeneous since several Cu-rich grains are dispersed through the active PZT layer (Figure V-28 (b-c)). Note that Cu segregation has not been observed for PZT + LBCu ceramics sintered by SPS.

Figure V- 28 :

 28 Figure V-28: Microstructure SEM image of PZT + 3%LBCu sintered by SPS at 775 °C. (a) Interface between gold electrode and PZT + 3%wtLBCu, (b) Cu-rich grains and (c) EDX analysis of Cu-rich grains.

Figure V- 29 :

 29 Figure V-29: (a) SEM image of the active PZT layer within the Au/PZT/Au/SS sintered by SPS at 850 °C without sintering aid and, (b) SEM image of screen-printed PZT thick film (900 °C, 2h, sintering aid).

Figure V- 30 :

 30 Figure V-30: SEM image showing discontinuities between PZT and top gold electrode after SPS performed at 850 °C.

3 (

 3 Figure V-31 (a, b)). EDX analysis (Figure V-32 (a)) reveals a carbon-rich surface. Therefore reaction with the organic binder of the ink or the carbon felt is not excluded. One difficulty compared to ceramics sintered by SPS using also SrCO 3 is that no polishing of the multilayer surface (to remove surface contamination) is possible without irreversible damages on the top gold electrode. A thermal post-treatment at 650 °C during 2h is tested to remove contamination, but EDX analysis shows Sr content on the surface of samples (Figure V-32 (b)). This analysis reflects the reactivity of SrCO 3 with the Au electrode (even if SrCO 3 is not expected to decompose below 1100 °C) and is consistent with previous results reporting the presence of strontium in the gold electrode of printed disks sintered with a printed SrCO 3 sacrificial layer[56]. When SrCO 3 protective layer powder is used, surface contamination is lower but whitening is observed on top Au electrode as in previous work[2] (Figure V-31 (d)). When using BaCO 3 protective layer powder, the surface of the sample is not contaminated and the carbonate layer is much more easily removed compared to SrCO 3 (Figure V-31 (e)).

Figure V- 31 :

 31 Figure V-31: Comparison of multilayers after SPS using different form and nature of protective layers. (a) Sample with printed SrCO3 after SPS, (b) after chemical attack with H3PO4 showing the appearance of a dark conductive surface, (c), and after post-annealing treatment at 650 °C during 2h. (d) Powder SrCO3 protective layer form after chemical attack (whitening on top Au electrode). (e) BaCO3 in power form after chemical removal.

Figure V- 32 :

 32 Figure V-32: EDX analysis of samples sintered with printed SrCO3 protective layer, (a) of Au top gold electrode surface after chemical attack and before post-annealing step, showing a carbon-rich surface and (b) on PZT surface layer after post-annealing step at 650 °C during 2h showing evidence of Sr content afterwards.

  Figure V-33 (a)). On the other hand, the multilayer corresponding to structure B (SS: 100 µm), presents more or less damage on the top Au electrode (Figure V-33 (b)). For configuration B' obtained by printing two layers of top Au electrode, damage of the top electrode is still observed (Figure V-33 (c)).

Figure V- 33 :

 33 Figure V-33: Results obtained for samples with lower SS substrate thickness. (a) Structure A (SS: 25 µm), (b) structure B (SS: 100 µm), and (c) structure B': sample with Au top electrode printed twice.

Figure V- 34 :

 34 Figure V-34: Samples obtained after SPS using Ag/Pd electrodes (a) on 250 µm substrate thickness, resulting in destroyed samples, and (b) on 100 µm substrate thickness, resulting in samples with good adhesion

Table I -

 I 2: Advantages and disadvantages of different conversion mechanisms for vibration energy harvesting.

	4	Piezoelectric energy harvesting
	4.1	Basics on piezoelectricity
	4.1.1 Historic and applications
	Transduction type	Advantages	Disadvantages
				 Difficult to integrate with
	Electromagnetic	 No external voltage source  High output current	MEMS fabrication process  Poor performance in micro-scale systems
				 Low output voltages
			 Easy to integrate with	 Low output current
		Electrostatic	MEMS fabrication process	 High output impedance
				 External charged or voltage
				source are often needed
				 Poor coupling for thin films
			 Simple structures	 Limited mechanical
			 No external voltage source	properties
			needed	 High output impedance
		Piezoelectric	 Compatible with MEMS fabrication process	 Charge leakage  Low output current
			 High output voltages	 Depolarization
				 Low coupling for polymers
				 Fragility of ceramic
				piezoelectric layers

Table I -

 I 3: Main properties of a piezoelectric material.

		Properties	Notation	Units	Meaning
					Proportion between the generated
	Piezoelectric charging coefficient	𝑑	𝐶 𝑁 ⁄	electrical charges (in Coulomb) and the force applied to the material (in
					Newton).
					Efficiency of the material for
	Electromechanical coupling coefficient squared	𝑘 2		transduction/conversion of electrical energy into mechanical energy and
					vice versa.
	Dielectric constant (permittivity)	𝜀	𝐹 𝑚 ⁄	Measurement of the charge storage capacity on a material supplied at a given voltage.
	Dielectric dissipation factor	tan𝛿	-	Measurement of the dielectric losses.
					Temperature at which the material
	Curie temperature	𝑇 𝑐	°𝐶	undergoes a structural phase
					transition
	4.4	Energy harvesters based on PZT and metallic substrates

4.4.1 Overview on piezoelectric materials

Inorganic piezoelectric materials have been extensively used in vibration energy harvesting, The most common piezoelectric inorganic materials used are Pb[Zr x Ti 1-x ]O 3 (PZT), ZnO and AlN

[3][39]

Table I -

 I 4: Summary of piezoelectric materials used for energy harvesting applications.

	Materials	Structure	Piezo coefficient	Reference
		ZnO	Nanowires d 33 ∽ 5 -10 pC/N	[48][50]
		BaTiO 3	Thin film	d 33 ∽ 190 pC/N	[53][54]
	Inorganic	AlN	Thin film	d 33 ∽ 5 pC/N	[55]
		PZT	Thin film	d 33 ∽ 250-700 pC/N	[56]
		KNN	Thin film	d 33 ∽ 90 pC/N	[57]
		PVDF	Fabric	d 33 ∽ 20-30 pC/N	[52]
	Polymer
		PET-based	Thin Film	d 33 ∽ 630 pC/N	[58]

Table I -

 I 6: Examples of performances of resonant piezoelectric cantilever type energy harvesters using different technologies

Multilayer / proof mass Deposition piezoelectric layer technology EH volume Frequency/ acceleration (1g= 9.8m/s 2 ) Power References

	Bimorph PZT/100µm
	brass/PZT// Tungsten	PZT-5H Bulk -280µm	1cm 3	120Hz / 0.25g	375µW	[30]
	proof mass 9.15g
	PZTAuIn/10µmSi // Tungsten proof mass 328mg	Thinned bulk PZT 20µm	7x7x0,55 mm 3	154Hz/1.5g	205µW	[63]
	Bimorph
	Ag/PZT/Au/dielectric/110µ mSS/dielectric/Au/PZT/Ag	Screen-printed PZT-5H / 70µm	491mm 3	67Hz/ 0.4g	240µW	[72]
	// Tungsten proof mass 3.1g
	Bimorph/TiPt/PZT/TiPt/PZ T/Au // Tungsten proof mass Si	Screen-printed PZT (PZ26) 20µm	0.64mm 3	242Hz /1g	33.2µW	[4]
	SUS304/Pt/Ti/PZT/Al// not reported	Sol gel PZT thin film 4µm	167.6mm 3	89Hz/1g	15µW	[75]
	Bimorph PZT/ Stainless steel 15µm/PZT // Tungsten proof mass 1.5 g	Thinned bulk PZT 50µm	5 x 40 115µm mm 2 x	16Hz/10mg	3µW	[71]
	Pt/Ti/PZT/SS30µm// Tungsten proof mass 6x4x0,45mm 3 (0.2g)	Aerosol deposition 15µm	13 mm 3	112.4Hz / 1.5g	200µW	[73]
	SS300µm/Pt/Ti/KNN/Pt// SS proof mass 25mg	KNN RF Sputtering 2.2µm PZT RF Sputtering -	7.5 x 5mm 2 x 2.2µm	393Hz/1g 367Hz/ 1g	1.6µW 6.7µW	[76]
	Bimorph PtTi/PZT/PtTi SS60µm/PtTi/PZT/PtTi// Tungsten proof mass 0.46g	Aerosol deposition 10µm	6x8mm 2 x 80µm	120Hz/0,5g	304µW	[77]
	Ni 25µm/ LaNiO 3 /HfO 2 /Ni//PZT /Pt // Brass proof mass 0.4g	PZT RF Sputtering 3µm	0.1155m m 3	72Hz/ 0,5g	60µW	[74]

Content 1 THICK-FILM TECHNOLOGY 52 1.1 INTRODUCTION

	1.1.1 Hybrid thick-film circuit
	1.1.2 Basics of the process
	1.1.3 Evolutions of the screen-printing process
	1.2 SCREENS
	1.2.1 Screen characteristics
	1.2.2 Screen manufacture
	1.3 SUBSTRATES
	1.3.1 Ceramic
	1.3.2 Silicon
	1.3.3 Organic
	1.3.4 Metallic
	1.4 PASTES
	1.4.1 Basics on rheology
	1.4.2 Rheology of a screen-printing paste
	1.4.3 Paste composition
	1.4.4 Paste preparation
	1.5 DEPOSITION
	1.5.1 Squeegee
	1.5.2 Screen-printing machine and critical parameters
	1

.6 DRYING 1.7 PARTIAL CONCLUSION 2 SINTERING 71 2.1 DEFINITION OF SINTERING

  One of the central aspects of this thesis work is the use of thick-film technology for the fabrication of the energy harvester structure. In this chapter, the thick-film technology is presented, detailing the standard different stages and features of the technique. As part of this process, the conventional sintering process is described and the Spark Plasma Sintering technique (SPS), is lastly emphasized. The understanding of each step of the different techniques plays an essential role in the selection of several characteristics of the EH structures (materials, geometries, sintering cycles…). This chapter aims to give a general description of the thick-film technology while highlighting the characteristics considered and selected for this thesis work.

	2.1.1 Types of sintering
	2.2 PRINCIPLE
	2.2.1 Stages of sintering
	2.2.2 Constrained sintering under pressure
	2.3 CONVENTIONAL SINTERING METHOD
	2.3.1 Shaping (case of ceramics)
	2.3.2 Pressing
	2.3.3 Sintering of screen-printed thickfilms by conventional method
	2.3.4 Furnace set-up for conventional sintering
	2.4 SPARK PLASMA SINTERING (SPS)
	2.4.1 SPS Machine
	2.4.2 Partial conclusion

1 Thick-film technology 1.1 Introduction 1.1.1 Hybrid thick-film circuit

Table II -1: Characteristics of stainless steel screens. Screen type (mesh count M) Wire diameter d (µm) Opening of mesh O (µm) Fabric thickness (µm) Tension 0.5% ‡ (N/m) Humid deposit thickness (µm)

 II

	70	65	300	140 ± 3	21-23	185-230
	200	36	90	80 ± 2	20-22	81-97
	325	24	53	52 ± 1.5	13-15	58-71
	400	18	45	40 ± 1	8-10	50-61
	*Data from

DEK society. Thickness of final humid deposit depends on the emulsion thickness and tension.

  Table II-2 summarizes the most important properties of the substrates that can be used in thick-film technology. The next paragraphs give some details on the most relevant substrates.

	Table II-2: Main substrates and properties to be considered when choosing substrates for thick-film
		technology [1][6].
	Properties /Material	Silicon	Alumina	AlN	Polymers	Stainless
			(96%)			steel (SS)
	Dielectric constant (at 1kHz)	11	9.5	8.7	2.6-3.1	--
	Dielectric strength (kV/mm)	10	12	14	9-16	--
	Thermal conductivity (W/m-K)	148	26	160-190	0.2 -0.29	10-34.3
	Thermal coefficient of expansion (CTE) (10 -7 /°C )	2.6	6.3	4.6	10-69	7-21.1
	Young's modulus (GPa)	112-186	300	322	3-5	5-310
	Melting point (°C)	1414	2000	2227	200-270	1230-1700
	Density (g/cm 3 )	2.3	3.8	3.3	1.4	8.1
	Cost	Low	Low	High	Average	Average

Table II -

 II

	Parameter	Value
	Off-contact distance	1 mm for all substrates
		8 kg for bottom electrode
	Squeegee pressure	4 kg for active layer
		6 kg for top electrode
		80 mm/s for bottom electrode
	Squeegee speed	65 mm/s for active layer
		80 mm/s for top electrode
		Electrodes: 15 µm
	Emulsion thickness	Active layer: 50 µm (x 2 for aim thickness < 90
		µm)

5: Parameters of screen-printing process used in this thesis work.

Table IV - 1 :

 IV1 Description of the different materials and corresponding characterizations used in a complementary approach.

		SAMPLE
			Zig-zag	Cantilever	Printed disk	Ceramic
	Layer materials	SS/Au/PZT/Au	SS/Au/PZT/Au	Au/PZT/Au	Au/PZT/Au
	Technology	All layers are screen-printed on SS substrate and co-fired	All layers are screen-printed on SS substrate and co-fired	Multi-layer Au/PZT/Au screen-printed on a sacrificial layer and co-fired	Bulk ceramic (conventional sintering), Sputtered Au after sintering
	Area dimensions	11.5mmx12.7 mm	30mmx2mm	Diameter 8mm	Diameter 1.4mm
	Au thickness	10µm	10µm	10µm	100nm
	PZT thickness	50µm	50µm	100µm	2mm
	Structure (XRD)	No	No	Phase composition	Phase composition
	Microstructure analysis (SEM, EDS)	No	Interfaces, PZT grain size, porosity, Chemical analysis	PZT grain size, porosity, Chemical analysis	PZT grain size, porosity , Chemical analysis
	Dielectric and electro-mechanical characterizations (impedance analyzer + IEEE calculations)	No	Basic electrical model of the EH.	Permittivity Piezoelectric and electromechani-cal coefficients	Permittivity Piezoelectric and electromechani-cal coefficients
	Energy harvesting test (extracted power)	Piezoelectric-magnetic principle	Shaker vibration	No	No
	2.2	Materials constituting the EH structure
	2.2.1 Active material PZT
	Piezoelectric Lead Zirconate Titanate printed (PZT) material is selected for the EH application
	because of its outstanding electromechanical properties compared to other materials chosen for
	this application (see chapter 1, Tables I-4 and I-6). A hard PZT type powder, PZ26 from
	Ferroperm, already studied in the Laboratory for other MEMS fabricated by thick film

technology

[22]

is selected. This powder is used for all the 4 structures studied (Table

IV

-1). The characteristics and properties of this PZT type are given Table IV-2.

Table IV -

 IV 2: Pz26 (Navy I) Hard type PZT properties (From meggitferroperm.com)

	Material property	Symbol	Value
	Density (g/cm 3 )	ρ	7.70
	Mechanical Quality Factor	Qm	>1000
	Relative dielectric permittivity at 1 kHz	ε	1300
	Dielectric dissipation factor at 1 kHz (%)	Tan δ	0.3
	Curie temperature (°C)	TC	>330
	Electromechanical factor (planar mode)	kp	0.56
	Piezoelectric charge coefficient (pC/N)	d33	300
	The exact composition of the commercial PZ26 powder is not provided. The XRD pattern of the
	powder at room temperature displays a perovskite phase without pyrochlore phase. The XRD
	pattern shows that PbZrxTi 1-x O 3 powder has a composition 0.44<x<0.53 near the morphotropic
	phase boundary (MPB) with predominant tetragonal and rhombohedral crystalline structures

. The width of the MPB region depends on the compositional homogeneity and on the sample processing conditions (Figure

IV-9

). A composition belonging in this range is suitable to achieve enhanced piezoelectric properties

[23]

. Concerning the PZT particle size, SEM pictures show that the PZT powder is formed of agglomerates (10 µm) made of micrometer and mainly sub-micrometer particles (Figure

. This is in good agreement with the results provided by granulometry analysis (Annex 1)

Table IV -

 IV

	Compounds	Au	PbO	SiO2	CdO	Al2O3	Bi2O3	CaO
	%mol	84	4.8	4.6	2.7	1.7	1.2	0.9

3: Concentration of the different elements in the commercial ESL8836 gold ink

[24]

.

Table IV -

 IV 4: Properties of metallic substrate materials employed in EH applications (properties generally found in industrial providers) [www.matweb.com and manufactures]

	Material		Density (g/cm 3 )	E (GPa)	Melting temperature (°C)	Expansion coefficient (at <650°C) (µm/m-°C)
	Brass		8.50	97		900-940		19.0
	Copper		8.96	110-128		1084		16.5
	301 Stainless steel	7.88	193		1400 -1420		18.0
	304 Stainless steel	8.00	193		1400-1455		18.7
	316 Stainless steel	8.00	193		1370-1400		17.5
	Table IV-5: Typical concentration of the different elements constituting the SS301 stainless steel
	Compounds	Fe	Cr	Ni	Mn	Si	C	N	P	S
	%mol	70.7-78 16-18	6-8	≤2	≤1	≤0.15	≤0.10	≤0.045 ≤0.030

-4

). Preliminary tests with SS301 and SS316 showing lower CET have been first performed to check the compatibility with the future Au ESL8836 electrode. After the firing at 850°C (temperature recommended by ESL provider), better adhesion and less oxidation are observed with the SS301. SS301 substrate is hence kept as the substrate material of the EH structure (see Table

IV

-5 for SS301 chemical composition).

Table IV -

 IV

	The EH selected geometry is described in Figure IV-11 (a). It is a centrally-supported
	meandering geometry with an overall footprint of 14.7 mm x 12.7 mm (187 mm 2
	Young's modulus	193 GPa
	Density	7.88 g/cm 3
	Poisson's ratio		0.24
	Thickness	0.254 mm
	Table IV-7: Screen-printed PZT parameters determined experimentally at IMS. (collaboration Waterloo,
	Canada, [29]).
	Young's modulus		43 GPa
	Density		5.5 g/cm 3
	Piezoelectric coefficient d 31	-40 pC/N
	Thickness		0.075 mm

6: 301 Stainless steel properties (collaboration Waterloo, Canada,

[29]

).

Table IV -

 IV 8: Neodymium magnet (NdFeB, N42) properties. (collaboration Waterloo, Canada,[29]).

	Young's modulus	160 GPa
	Density	7500 kg/m 3
	Poisson's ratio	0.24
	Dimensions	3.175 mm x 3.175 mm x 12.7 mm
	Weight	0.96 g
	Magnetic remanence	1.32 T

  -9.

	Table IV-9: Selected screens for the printing of the layers on the SS substrate
	Layer	Screen type (mesh	Light-sensitive emulsion	Layer thickness after
		count M) (µm)	thickness (µm)	firing (µm)
	Au electrodes	325	15	8-12
	PZT active layer	200	50 (x2 for thicker layers)	40-80

  1-x O 3 powder (PZ26 Ferroperm) with the ternary system LBCu consisting of a mixture of the powders Li 2 CO 3 , Bi 2 O 3 , CuO (from Sigma Aldrich). The LBCu is an additive used as sintering aid to lower the sintering temperature of PZT. Previous work has already shown a better densification and reproducibility of the PZT based screen-printed thick films when using the PZ26 powder mixed with LBCu[30][31][32]. The complex system LBCu cannot be rigorously considered as a liquid phase sintering. There is an eutectic with a melting point at 690°C for the system Bi 2 O 3 -Li 2 CO 3 , ensuring a liquid phase sintering. The efficiency of LBCu to lower sintering temperature of PZ26 has been fully demonstrated in comparison with other sintering aids such as borosilicate glasses[30][33]. In particular, if only LiBiO 2 is used, the sintering temperature is decreased down to 1000°C but the addition of CuO allows a further decrease down to 800°C[31]. The composition used in this work is given in TableIV-11. Table IV-11: Composition of the mineral part of the PZT ink formulation.

	Powder	%wt
	PZT (PZ26)	97.00
	Li2CO3	0.80
	Bi2O3	1.20
	CuO	1.00

  -12) to determine an optimal proportion mineral/organic phase. The viscosity measurements of the different inks display values less than 50 Pa.s for a shear rate of 100 s-1 (Figure. As expected, pastes 1 and 2 have lower viscosity than paste 3 because of the lower content of organic binder. Although paste 3 viscosity has similar rheological behavior as the two commercial pastes, the quality of the deposited layers is not satisfactory as seen in Figure IV-15, where meshs traces are observed. The probable reason is that the two commercial pastes have been optimized for other applications requiring different rheological behaviors. In contrast, pastes 1 and 2 give both a good quality of deposit. Paste 2 with the ratio PZT powder/organic vehicle ratio (85.7/14.3 %wt.) is then selected, to benefit from its lower vehicle proportion in comparison with paste 1.Table IV-12: Composition of the three tested pastes. The deviations are due to possible errors induced by the weighing procedure.

	Paste	PZT + 3% LBCu (%wt)	ESLV400 (%wt)
	1	85.0 ±0.2	15.0 ±0.2
	2	85.7 ±0.3	14.3 ±0.1
	3	89.9 ±0.2	10.1 ±0.2

Table IV -

 IV 14: Elastic properties, average thermal expansion coefficient (500°C-600°C) and thicknesses of PZT and SS.

	SS Young's Modulus (GPa)	193*
	PZT Young's Modulus (GPa)	40*
	SS Poisson's ratio	0.24*
	PZT Poisson's ratio	0.33**
	α SS (ppm/°C)	16.7
	α PZT (ppm/°C)	4.7
	𝒕 𝑺𝑺 (µm)	250
	𝒕 𝑷𝒁𝑻 (µm)	10-100
		*[29]
		**[39]

Table IV -

 IV 15: Summary of properties for the different PZT equivalent structures. These experiments have been led by Associate Pr. Alexis Bremen (ISEP, LISITE Paris) and Pr Elie Lefeuvre (Université Paris-Saclay, C2N -Palaiseau). Before detailing the experiments, it appears to us useful to give basics on the electromechanical model of the piezoelectric resonator used as EH.

	† Impedance measurements carried out on non-clamped structure
	6	Energy harvesting application
	6.1	Characterization under mechanical vibrations
	Structure/		Ceramic	Printed	Simple	Zig-zag EH	PZ26	Simple	Simple
	Properties		PZT+	disk	cantilever	structure	Ferroperm	cantilever	cantilever
			3%wt	PZT+	(PZT+	Simulated	(ceramic	with thinned	with
			LBCu	3%wt	3%wt	values	pellets	bulk ceramic	aerosol
				LBCu	LBCu	[27]	fired at	PZT/ SS	PZT / SS
					printed on		1200-	15µm/ PZT	[43]
					SS		1300°C)	[26]
	Density g/cm 3	7.6	7.4	6	5.5	7.8	--	--
	Dimensions (mm): Diameter or footprint	ᴓ:11.45	ᴓ:7.74	9.80 x 2	14.70 × 12.70	--	5 x 40	6 x 4
	PZT Thickness	1.92	0.10	0.55	0.55	--	0.10	0.01
	ε'(at 1kHz, 25°C)	1200	600	--	630*	1300	--	--
	Tan δ (at 1kHz)(%)	~0.2	~2.5	--	1.5 *	0.3	--	--
	k31 (%)	28	26	--	--	33	--	--
	keff (%)	28 †	26 †	11 †	15•*	--	23•	10•
	d31 (pC/N)	110 †	95 †	--	40•*	130	--	17•
	--Not Reported.
	* Value used in simulation
	• Impedance measurements carried out on clamped structure

Table IV -

 IV

17:

Comparison with literature results.

Ref.

SS dimension / PZT thickness / Proof mass Power/ frequency/ acceleration Effective volume (without tip mass) (mm 3 ) Normalized Power density µW/ (mm 3 g 2 )

	Zhu, 2011 [48]	110µm/ Screen-printed Tungsten 3.1g PZT-5H 70µm (bimorph)/	240µW/ 67Hz/ 0.4g	162.00	9.2592
	Tsujiura, 2013 [49]	300µm/ PZT RF mass 25mg Sputtering -2.2µm/ Proof	6µW/ 367Hz/ 1g	12.18	0.4930
		30µm/ PZT Aerosol 10µm
	Tang,	(bimorph)/ Tungsten 0.46g.	304µW/ 126Hz/ 0.5g	38.40	31.6667
	2018 [28]	Unimorph	122 µW /111 Hz/ 0.5g	33.60	14.5238
		250µm/ Screen printed
	This work	PZT + LBCu 50µm/ No	1.3µW/ 129.3Hz/ 0.5g	6.00	0.8666
		proof mass

Table IV -

 IV 18: Normalized power density for previous piezoelectromagnetic harvesters and the present work. (Collaboration Waterloo, Canada). (reproduced from [29])

	Ref.	Deposition method	Magnet distance (mm)	Magnetic remanence (T)	Wire current (A)	Power output (µW)	Frequency (Hz)	Normalized Power density µW/ (T*A*mm 3 )
	Paprotny, 2010 [51]	Sputtered AlN	2.5*	1.32	1	2 (simulated)	57*	0.084695
	Olszewsk, 2016 [52]	Sputtered AlN	2*	1.3	2	1.5	42.3	0.111537
	Paprotny,
	2013	Buk PZT	2.5	1.48	20	2700	60	0.329337
	[53]
	Chen,
	2015	Bulk PZT	2	1.4*	2.5	295.3	50	0.263098
	[50]
	He, 2013 [54]	Bulk PMgN-51	4	1.45	10	566	50	2.348645
	This work	Screen-PZT printed	6.5	1.32	7	9	60	0.242502

*Values interpolated from data in the referenced literature.

Table V -

 V 1: Some properties and process conditions of PZT based ceramics densified by SPS

	Material (Grain size)	Sintering temperature (heating rate)	Holding time (min)	Pressure (MPa)	Post thermal treatment	Density (g/cm 3 )	Electrical Properties Reference
	PbZrO3-PbTiO3/	900 °C			1h at 900 °C
	Pb(Zn1/3Nb2/3)O3	(100 °C/min-800 °C +	10	29	In a PbO-rich	7.95	Not reported	[9]
	(Not reported)	33 °C/min -900 °C)			atmosphere
	Pb(Zr0. 53Ti0. 47)O3-1%Nb (Not reported)	1000 °C (100 °C/min)	0, 1, 2, and 4	50	3h at 1000 °C	7.95	Not reported	[10]
	Pb(Zr0. 3Ti0. 7)O3 (Not reported)	900 °C (100 °C/min-800 °C + 33 °C/min -900 °C)	5	29	1h at 1100 °C	7.80	ε<500 (25 °C)	[16]
	Pb(Zr0. 52Ti0. 42Sn0. 02Nb0. 04)O3 (Grain size < 500 nm)	1050 °C (100 °C/min)	5	50	4h at 700 °C under air + 6h at 1000 °C	7.64	d33 ∼350 pC/N (25 °C)	[11]
	Pb(Zr0. 53Ti0. 47)O3-1%Nb2O5 (Grain size 330 nm)	1000 °C (120 °C/min)	1	50	Not reported	Not reported	ε ~920 (25 °C) d33∼180 pC/N	[12]
	PMN-PZT (Grain size 1 m)	980 °C (100 °C/min)	5	50	12h at 850 °C	Not reported	ε ~6000 (25 °C) d33∼400 pC/N	[13]
	PZT-PMnN	900-1000 °C (100 °C/min)	5	50	4h at 700 °C, + 6 h at 1000 °C	7.89	d33∼412 pC/N	[14]
	PZT (SPS + Energy ball milling) (Grain size <300 nm)	750 -900 °C (200 °C/min)	5	48	2h at 700 -850 °C	7.92 -8.3	ε: 700 -1800 (25 °C) d33: 374 -422 pC/N	[15]
	Reference: PZ26 conventional sintering Ferroperm	1200 °C	Not reported Not reported	Not reported	7.7 (Relative density 98%)	ε ~6000 d33∼290 pC/N	[33]

Optimization of the sintering conditions for PZT ceramics

Table V -

 V 2: Summary of polarization conditions and conductance resonance peak characteristics for different type of electrodes.

		Diameter/	Applied Electric field	Maximum of	Mechanical
	Electrode	thickness	during polarization	conductance	quality factor
		(mm)	(kV/mm)	peak G (S)	QM
	Screen-printed Ag-epoxy 10 µm (polished)	10.21/2.86	0.386	6.05E-04	204
	Sputtered Au 100 nm (non-polished)	10.21/2.91	0.233	2.05E-04	95
	Sputtered Au 100 nm (polished)	10.08/2.15	0.465	1.06E-03	657

Table V -

 V 3: Decomposition temperature of principal carbonates. Evaluation of the relative density and SEM images of the ceramic microstructure after removal of SrCO 3 are in agreement with a highly densified ceramic (~98 %) (Figure V-10). The average grain size (2-4 µm) is similar to the one of PZT sintered by SPS without SrCO 3 . As a result, the protective layer does not affect the densification.

	Carbonate	Decomposition temperature (°C) [32]
	MgCO3	350
	CaCO3	850
	SrCO3	1100
	BaCO3	1740
	2.1.2.2 Structural and microstructural characterizations
	XRD patterns at room temperature of the ceramic with and without the use of SrCO 3 are similar
	except the intensity ratio I(002)/I(200) . As already mentioned, mechanical treatments such as
	polishing and etching process affect the surface of the sample and can generate residual stresses.
	As a result, a change in intensity ratio I(002)/I(200) is observed reflecting domain preferential
	orientation modification in the surface layer compared to the bulk [35][36] [37].

Table V -

 V 4: Microstructural features of PZT + 3wt% LBCu sintered by SPS at different temperatures.

	T°C	700°C	750°c	875°C
	Sample
	Density	7.8 (g/cm 3 )	7. 8 (g/cm 3 )	7.8 (g/cm 3 )
	SEM
	(10kx)
	Grain size	~0.6 -1.9 µm	~ 0.7 -1. 8 µm	~ 0.7 -2 µm

Table V -

 V 4 summarizes the results.

Table V -

 V 5: Comparison of the properties of the PZ26 ceramics sintered by different methods

		Temperature Holding time Heating rate	Pressure (MPa)	Annealing	Grain size (µm)	Relative density (%)	keff (%)	ε
	Screen-printed	900 °C
	thick film	2h	40	No	1-4	94	26	600
	(sintering aid)	40 °C/min
		875 °C		Post
	SPS ceramic	5min	100	annealing	2.5-4	97.4	36	1200
		50 °C /min		8h, 800 °C
	SPS ceramic + protective layer (SrCO3)	875 °C 50 °C /min 5 min	100	No	2.5-5	98.2	40	1500
	SPS ceramic + protective layer (BaCO3)	875 °C 50 °C /min 5 min	100	No	-	97.8	38	950
	SPS ceramic + LBCu + SrCO3	700 °C-875 °C 5 min 50 °C /min	100	No	0.6-2	98.0	18 (750°C) 5 (875°C)	1100
	Conventional
	commercial sintering	1200 °C	-	Yes	2-5	98.7	50	1300
	(Ferroperm)

Table V -

 V 6 reports illustrations of the tests performed using the different set-up configurations. These experiments are conducted on the multilayer stack with the following characteristics: SS: 250 µm, Bottom Au: 12 µm, PZT: 55 µm and Top Au: 8 µm. The formulation of inks (Commercial Au, PZT without 3%wt LBCu) described in chapter 4 is used. Concerning the protective layer, SrCO 3 is used with two options: (i) a protective layer of SrCO 3 made of Epoxy CV59 (Annex 1) mixed with SrCO 3 powder, is printed on the top Au electrode without any preliminary firing, debinding or pressure steps. (ii) a bed of SrCO 3 powder is deposited. The selected examples reported in Table V-6 have been performed under vacuum at sintering temperature of 850 °C. Different sintering times, cooling and heating rates are tested.

	Sample (PZT)	Sample Ref	Set-up	Protective layer (SrCO3)	Heating rate (°C/min)	Sintering Time (min)	Cooling rate (°C/min)	Forced applied (kN)	Debinding	Results Delamination Before ca After ca	No delamination
	1	H006	1	Printed	50	5	Natural	3	No
	2	H007	1	Printed	50	5	Natural	3	No
	3	H008	1	Printed	50	5	Natural	3.1	No
	4	H011	1	Powder	50	5	Natural	3.9	No
	5	H020	2	Powder	50	5	Natural	3.9	350°C/ 3min
	6	H022	2	Powder	25	5	Natural	3.9	No
	7	H024	3	Powder	50	5	Natural	3.1	No
	8	H039	3	Powder	50	5	50	3.1	No
	9	H040	3	Powder	25	5	25	3.1	No
	10	H044	4	Powder	25	10	25	3.1	No
	11	H063	3	Power	50	5	40	3.1	200-400 (10 °C/min) 400°C for 10 min
	12	H064	3	Powder	50	5	40	3	200-400 (10 °C/min) 400°C for 10 min
	13	H065	4	Powder	50	5	40	3	200-400 (10 °C/min) 400°C for 10 min
	14	H066	4	Powder	50	5	40	3	200-400 (10 °C/min) 400°C for 10 min
	15	H070	4	Powder	50	5	50	3.1	No
	16	H077	4	Powder	50	30	Natural	3.1	No
	17	H078	5	Powder	50	5	Natural	3.1	No
	 ca: Chemical attack
	 Sintering Temperature for all cases: 850°C

Table V -

 V 6: Summary of first experience for identification of sintering conditions and critical parameters.

	Delamination before ca	Delamination after ca	No delamination

Table V -

 V 7: Multilayer configuration fabricated for experiments with lower substrate thickness

	Multilayer structure/	A	B	B'	Original
	Thicknesses
	PZT (µm)	25	<50	<50	55
	Au thickness (Top/Bottom) (µm)	3/5	6/10	8/10	8/12
	SS substrate (µm)	25	100	100	250

Table V -

 V 8: Composition of AgPd ink from Exxelia-Temex used.

	Metal part	Solvent/ binder	Mineral part

Ag (90 wt.%)/Pd (10 wt.%) Aliphatic solvent + cellulosic binder MgTiO 3 54 wt.% 44 wt.% 2 wt.% However, experiments performed with 250µm substrate thickness do not show improvement in adhesion (Figure V-34). Conversely and as expected, samples with 100µm show good adhesion within the multilayer.

Table V -

 V 9: Summary of successful samples.

	Sample	Nature of PZT and protective layer	Electrode's nature and top thickness	SS substrate's thickness	PZT thickness	Sintering tempe-rature	Short-circuit between top electrodes and bottom	Applied voltage at 280°C, 10min
	1	PZT+ 3%wt LBCu /SrCO3	Au / 8µm ± 2 µm	250µm	55	775 °C	No	Not possible (high leakage current
	2	PZT + 3%wt LBCu /BaCO3	Au /8µm ± 2 µm	250µm	55	775 °C	No	1 kV, 10min, 280 C, under N atmosphere.
	3	PZT /BaCO3	Au / 3µm ± 1 µm	25µm	25	850 °C	Yes	No
	4	PZT /BaCO3	Au /6µm ± 2 µm	100µm	50	850 °C	No	No
	5	PZT /BaCO3	/8µm ± 2 µm Au /(x 2 prints top electrode)	100µm	50	850 °C	No	No
	6	PZT/ BaCO3	AgPd (x 2 prints) /6 µm ± 2 µm	100µm	50	850°C	No	No

Scientific communications

Acknowledgements

Scientific Communications

Journal articles  Maria Isabel Rua-Taborda, Onuma Santawitee, Angkana Phongphut, Bralee Chayasombat, Chanchana Thanachayanont, et al.. Printed PZT Thick Films Implemented for Functionalized Gas Sensors. Key Engineering Materials, Trans Tech Publications, 2018, 777, pp.158-162.  Egon Fernandes, Maria Isabel Rua Taborda, Blake Martin, Sid Zarabi, Hélène Debéda et al. Design, Fabrication, and Testing of a Low Frequency MEMS Piezoelectromagnetic Energy Harvester. Smart Materials and Structures, IOP Publishing, 2018.  Zongxian Yang, Sid Zarabi, Egon Fernandes, Maria Isabel Rua Taborda, Hélène Debéda et al. A Simple Wireless Sensor Node System for Electricity Monitoring Applications: Design, Integration, and Testing with Different Piezoelectric Energy Harvesters. Sensors, MDPI, 2018, Special Issue Low Energy Wireless Sensor Networks: Protocols, Architectures and Solutions, 18(11), 3733.  Book chapter  H. Debéda, M.-I. Rua-Taborda, U.-C. Chung, C. Elissalde, Chapter 10 -One step densification of printed multilayers by SPS: Towards new piezoelectric energy harvester MEMS, Editor(s): Giacomo Cao, Claude Estournès, Javier Garay, Roberto Orrù, Spark Plasma Sintering, Elsevier, 2019.  International conferences  Maria Isabel Rua Taborda, Catherine Elissalde, U-Chan Chung-Seu, Hélène Debéda. Implementation and Optimization of SPS Sintering for a printed Piezoelectric Energy Harvester MEMS. Electroceramics XVI, Jul 2018, Hasselt, Belgium.  Maria Isabel Rua Taborda, Catherine Elissalde, U-Chan Chung-Seu, Hélène Debéda. New densification route of metallic supported printed multilayer for piezoelectric energy harvester; 4th International workshop on Spark Plasma Sintering, May 2018, Cagliari, Italy.  Hélène Debéda, Maria Isabel Rua Taborda, Egon Fernandes, Sid Zarabi, David Nairn et al. Printed MEMS-based self-contained piezoelectric-based monitoring device for smart grids, PowerMEMS 2017, the 17th international conference on micro and nanotechnology for power generation and energy conversion applications, Nov 2017, Kanazawa, Japan.  Sid Zarabi, Egon Fernandes, Maria Isabel Rua Taborda, Armaghan Salehian, Hélène Debéda et al. Design and Development of a Self-contained and Non-Invasive Integrated System for Electricity Monitoring Applications, IEEE 12th International Conference on ASIC (ASICON), Oct 2017, Guiyang, China.  Catherine Elissalde, U-Chan Chung-Seu, Maria Isabel Rua Taborda, Mario Maglione, Graziella Goglio et al. Some strategies to (co)-sinter refractory functional oxides at low temperature by Spark Plasma Sintering.

Annexes

Dielectric ink ESL4924 used for substrate holder fiducials

Chapter

Multilayer EH fabrication Content

The first phase of this work consists in the development of an EH device for autonomous small systems. The different steps of the EH structure fabrication are presented in this chapter, as well as the characterizations and performances.

Chapter Towards SPS sintering route Content

The exploration of new densification route for printed multilayer structure is the focus of this chapter. Our approach based on the use of Spark Plasma Sintering is here presented with all the steps and investigations necessary for the optimization of multilayer sintering. Our approach includes adaptations not only of the material but also of the configuration of the SPS device. This part devoted to SPS investigations has been done in close collaboration with Dr U-Chan CHUNG, research engineer at ICMCB Laboratory (responsible of the Sintering SPS platform).

General conclusion

Energy harvesting offers significant advantages and opportunities for the development of a wide range of smart applications (smart cities, smart homes, smart health, smart agriculture, intelligent transportation, industry, security, marine, etc). Indeed, the increasing use of autonomous electronic devices faces the issue of energy autonomy. Among the possible options, the recovery of vibratory mechanical energy using piezoelectric transducers is one of the most promising alternatives because of the availability of mechanical vibrations and the simplicity of electromechanical piezoelectric conversion.

In this context, this thesis work was dedicated to the study and fabrication of piezoelectric Micro Electro-Mechanical Systems (MEMS), aiming a resonant mechanical energy harvester (frequency<100Hz) for the supply of autonomous systems.

A literature survey of the various types of energy harvester configurations, related piezoelectric materials and fabrication techniques, has highlighted some of the challenging issues relative to the enhancement of the power output and broadening of the working frequency bandwidth. Our approach to address these challenges was based on the optimization of the EH design and the improvement of the active piezoelectric material properties. The fabrication of the piezoelectric MEMS by screen-printing has been described in detail to highlight all the experimental parameters whose optimization is required to target efficient final device. Two different structures, a simple cantilever and a modified zig-zag geometry, have been successfully fabricated by screen-printing and co-firing of multilayers made of Pb(ZrTi)O 3 (PZT) as the active piezoelectric material, sandwiched between two gold electrodes and deposited on a stainless steel (SS) substrate. This confirms the capabilities and the potential of the thick film screen printing technique to design complex geometries. The densification by conventional sintering has been achieved at 900°C with the use of the LBCu sintering aid. Compared to bulk ceramics, the main limiting features of the multilayer EH structures are the interfaces and the bending issues. The SS passive substrate generates constrained sintering that hinders an optimal densification (about 20% of residual porosity).

The bending of the structure arises from high thermal stresses during sintering due to TEC mismatch between the different constituents. Nevertheless, both modeling and experimental approaches have demonstrated and confirmed that decreasing the PZT layer or SS is as an efficient way to reduce these thermal stresses. A suitable substrate/PZT thickness ratio must be carefully selected to ensure low thermal stresses by maintaining a right output power. At the microscale, the microstructural analysis of the interfaces within the cantilever has shown the formation of an interphase layer that ensures the cohesion between the electrode and the substrate but that could also limit the dynamics of the structure. The simple cantilever structure exhibits a maximum power output of 1.3µW (load resistance 2.64 MΩ) at 129 Hz and a normalized power density of 0.86 μW/ g 2 .mm 3 , which is too low for any application implementation. Some perspectives for performance improvement, such as thickness optimization, tip mass use, and bimorph cantilever structure type, are several options for future investigations. The zig-zag geometry developed in collaboration with the University of Waterloo in Canada and dedicated to smart grid technologies has also been tested. It operates on the basis of a coupling between piezoelectric and electromagnetic effects, with the integration of a magnet and the interaction of an electromagnetic field around an alternating current (AC) carrier wire. For a magnet placed at the end of the structure, a current of 7A and a wire-magnet distance of 6.5mm,

Annexes

Annexes Chapter II

Polymer silver condcutor ESL1901 used for screen fiducials Annexes

Annexes Chapter III

Estimation of the values of the equivalent circuit elements

Based on the proposed equivalent circuit for a piezoelectric resonator, the behavior of the conductance G and the susceptance B can be determined as a function of frequency. Indeed, complex admittance Y (inverse of impedance) can be described as following:

, then:

The conductance G and the susceptance B can be then be identified from Eq. 3.12, obtaining:

With 𝜔 = 2𝜋𝑓 and considering the behavior in function of the frequency, G(f) can be described as:

When 𝑓 → +∞ lim(𝑎) = 2𝜋𝐿 𝑚 𝑓 and lim(𝐺

Hence G(f) presents vertical asymptotes at G= 1/𝑅 0 , and a maximum when a=0,t then becomes:

The solution to Eq. A-1.7 results in:

At the resonance frequency G and B take the following values:

In the same way from Eq. 3.14 B(f) can be described as:

When the frequency tends to ∞, B and G values diminish which represents the behavior of a capacitor without piezoelectric effect (Figure III-1-A). Annexes The values of 𝑓 𝑛 , 𝑓 𝑢 and 𝑓 𝑟 can be deduced from experimental measurements of G(f) and B(f) (Figure III-A-2). Annexes

The value of the leakage resistance R 0 is determined using the equation of the admittance circle 𝐵 = 𝑓(𝐺) with the characteristics described previously, subsequently:

Approximate values of B 0 , and R 0 can be inferred from the experimental values points and then refined by the least squares method. For the calculations to be accurate, it is necessary to take the maximum points in frequency around the vicinity of the resonance frequency corresponding to the maximum value of G.