Doctorat De L'université De Toulouse

Ana María

Hernández López

Professeur Jacques Noudem

Sánchez Félix

De Jésus

Bernard Durand

Paul Sabatier

Encadrant Zarel

Valdez Nava

Sophie Guillemet-Fritsch

Juan Antonio

Aguilar Garib

Zarel Valdez Nava Y Bernard

Ana De Jesús

Bolarín María

Miró

Víctor Román Nava Quintero

Julio Pérez

THÈSE THÈSE En vue de l'obtention du

all of you have left in me a mark.

Thanks for having opened me the doors and for trust in me to face this important challenge, guiding me with such patience and caring all these years. Thank you very much for giving so much of you to my education, for your time and availability and, most of all, for supporting and encouraging me to keep growing and giving the best of me always. I'll keep the best memories of the long discussions and the advantage of listen and having different points of view,

success and wellness. Thanks also for the constant effort so that this cotutelle had the bases to be built and finished.

To Jorge Luis MENCHACA ARREDONDO my most sincere and immense gratitude, five years ago I found a great teacher and friend on my way. Thank you for believing in me, for opening doors to huge opportunities and encouraging me to be always braver. Thank you so much for having ventured to support me in this life project.

I was fortunate to work in CIRIMAT and LAPLACE laboratories at the University of Toulouse III -Paul Sabatier. In them I could experiment, learn, advance and share with people whose experience contributed to my training. My thanks to all those who work in them, as well as to my fellow doctoral students and postdoctoral students who made my stays in this university more enjoyable and with whom I was able to discuss and share ideas on multiple occasions. Special thanks to Jean-Jacques DEMAI, Marie-Claire BARTHELEMY, Benjamin DUPLOYER and Sorin DINCULESCU for their technical support in carrying out my experiments. With great appreciation I also thank Ly, Nahum, Abdé, Romain, Precious, Simo, Guillaume, Cédric, Cyril, Mateusz and Trong for their company, for the shared coffees with such interesting talks, for their support in difficult times and for the laughs.

Thanks also to my teachers at the CICFIM for contributing with their knowledge to my training.

A deep gratitude to those who gave me their friendship and support during these years in Monterrey: Monica, Roberto, Liz, Juan, Maricela, Armando, Jeane, Marco, Fernando, Oswaldo, David and Abraham, I am fortunate to have so much love from your part, thank you for so many beautiful moments, for your hugs and smiles.

Amanda, thank you for having entered with such joy in my life and allowing yourself to be part of yours, thanks for so much love and that energy that illuminates more than you imagine. I'll always remember your words accompanied by a great and warm smile.

Codorniz, thank you for welcoming me into your home and sharing that special family with me, for the hugs and comforting words, for so many laughs, for being unconditional and not leave me alone.

To all those who despite the distance have always been with me, Papitas, Pardito, Diani, Flaquito, Cesitar, Carlitos, Lau, David, Felix, Karencita, Jenn, thank you for this great friendship that has seen us grow and make our dreams become a reality, all of you are always in my heart. Thanks also to Carlitos Franco, Wilmer, Ale, Daniel and John for accompanying me in different ways with their friendship and support on this path. I will always thank the life that during these years has given me the great gift of enlarging my family. For their immense and unconditional support, the strength they give me, so much love and joy, to help me make my dreams come true and allow me to be part of their lives: Gaby, Jime, Santi, Roberto, Pepe, Guille and MariaJo, deserve my infinite thanks for allowing me to write these words today, I owe you a great part of this achievement.

In my beloved Colombia you will always find an immense part of who I am, of my heart: my beautiful family. How to thank for so much love? To my grandmother, my aunts and uncles, my cousins, my nephews, Yaneth and Yas: it is you who appear daily in my thoughts, thank you for enlightening my life with your existence, thank you for supporting me and always believing in my. Thank you for giving so much of you for my happiness, for encouraging me to always dream big and to receive me with open arms every time and no matter what. I love you immensely.

To the love of my life, who does not allow a single day to pass without me having a reason to fall in love more and being even happier. My life with you is the light in my eyes, my dreams at your side only become bigger and the world for me is better since you and I are walking hand in hand. It is for you Rho and for everything that awaits us, always together.

To those who have given their all to make my wings bigger and bigger: my parents. Thank you for supporting my decisions and giving me strength when I doubt them. Thank you for always being by my side and believing enough in me to make sense of all these years away from you. Thank you for showing me your love in so many ways, for taking care of me and taking care of my little dog angels that I miss so much. I always carry them with me, every step I have taken and I will give, has your legacy. (Richerson,2005). ....................................................... 23 Figure 1.2. Transmission electron micrographs of core-shell structures in doped BT ceramics. (A) TEM bright field image of a X7R-type BaTiO 3 ceramics by Grogger, Hofer, Warbichler, Feltz, & Ottlinger, (1998). (B) TEM of a typical core-shell grain in a BT specimen doped with yttrium and magnesium by Kim et al., (2008). .............................................................................................................................................................. 25 Figure 1.3. (a) Glassy second phase at triple-grain junction with selected area diffraction patterns of BaTiO 3 grain inset (BF image), (b) high-resolution image of BaTiO 3 -glass interface showing an amorphous nature, and (c) energy-dispersive X-ray spectroscopy spectra for triple junction and BaTiO 3 grain (Bo) (TEM) (Wu et al., 2007). ......................................................................................................................................................... 26 Figure 1.4. Basic structure of a multilayer ceramic capacitor. ....................................................................... 36 Figure 1.5. MLCCs production process. Adapted from Basics of Ceramic Chip Capacitors by Johanson Dielectrics. 2008. ............................................................................................................................................. 38 Figure 2.1. X7R MLCC .................................................................................................................................... 49 (B) Plate with protective resistors in parallel to connect the samples that are inside (C) a metallic cell placed over a heating plate which temperature is monitored with (D) a multimeter reading the measurements of a thermocouple (K type). ..................................................................................................................................... 52 ..................................................................................................................... 54 . XRD patterns of BaTiO 3 starting powders. JCPDS: 89-1428. ...................................................... 60 Figure 2.9. SEM images of (a) BT-A and (b) BT-B powders. Particles size: andwith 2.5 and5 wt% of Y 2 O 3 ). ..................................................................................................................... 64 Groups A and B during HALT experiment at standard conditions (400 V,140 °C). ............................................................................................................................................................ 72 Group A, (b) Group B, and (c) Group C during HALT performed with 400 V and different temperatures. .................................................................... 74 Figure 3.3. Comparison of the TTF and current evolution for MLCCs from Groups A and B when tested under HALT standard conditions (400 V,140 °C). .......................................................................................... 76 ................................................................................. 78 Figure 3.6. Correlation of the time-to-failure for the failures of each group of MLCCs. HALT conditions: 600 V and temperature indicated on the plots. (a) Group A, (b) Group B and (c) Group C. .................................. 79 Figure 3.7. Comparison of the TTF for MLCCs from (a) Group A, (b) Group B, and (c) Group C. HALT conditions: 600 V,temperature indicated on the plots. .................................................................................... 80 Figure 3.8. Weibull plot for Group A. HALT conditions: (a) 400 V, 140 -230 °C and (b) 600 V, 140 -220 °C. .................................................................................................................................................................... 86 HALT conditions: (a) 400 V, 110 -225 °C and (b) 600 V,. Changes in the scale parameter of Group B as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section. ......... 90 Figure 3.12. Weibull plot for Group C. HALT conditions: (a) 400 V, 20 -90 °C and (b) 600 V, 20 -80 °C. 92 Group B, and (c) Group C according the electrical and thermal stress. Solid lines represent the best fits given by equation (3). ..................................................................................................................................................... 99 Figure 4.1. SEM images of BaTiO 3 undoped raw powders and the respectively 5 wt% Y 2 O 3 -doped and thermally treated powders. (a) (b) (c) .2. Variation of 2θ according the c/a ratio value, based on the cubic lattice 3.996 Å, for the planes (002). .............................................................................................................................................................. 113 Figure 4.3. X-ray diffraction patterns of raw BaTiO 3 powders. JCPDS: 89-1428. ....................................... 114 Figure 4.4. X-ray diffraction patterns of thermally treated (1350 °C) undoped BaTiO 3 and Y 2 O 3 -doped BaTiO 3 (2.5, 5.0 and 20.0 wt%) powders. Powders issued from (a) BT-A and (b) .5. Enlargement in the zone around 45° for X-ray diffraction patterns of thermally treated (1350 °C) undoped BaTiO 3 and Y 2 O 3 -doped BaTiO 3 (2.5, 5.0 and 20.0 wt%) powders. ................................................ 117 .9. SEM images from (a) .10. Mean size distribution of (a) .11. X-ray diffraction patterns of undoped BaTiO 3 and 2.5 and 5.0 wt% Y 2 O 3 -doped BaTiO 3 ceramics. Ceramics formed from (a) BT-A and (b) sintered in air. ..................................................... 122 ................................................................................................................................. 125 Figure 4.14. SEM images from BT-A ceramics sintered in reducing atmosphere. (a) (b) and (c) . Size distribution of BT-A ceramics sintered in reducing atmosphere. (a) (b) and (c) . XRD patterns of BT-A powder and ceramics sintered in reducing atmosphere and re-oxidized. Lateral enlargements of zone around 45° are presented for doped samples. ................................................. 131 ................................................................................................................................. 134 Figure 4.19. SEM images from BT-B ceramics sintered in reducing atmosphere. (a) (b) and (c) .20. Mean size distribution of BT-B ceramics sintered in reducing atmosphere. (a) (b) and (c) . XRD patterns of BT-B powder and ceramics sintered in reducing atmosphere and re-oxidized. Lateral enlargements of zone around 45° are presented. ............................................................................... 139 (b) .24. Size distribution of BT-C ceramics sintered in reducing atmosphere. (a) and (b) . XRD patterns of BT-C powder and ceramics sintered in reducing atmosphere and re-oxidized. Lateral enlargements of zone around 45° are presented. ............................................................................... 144 ........................................................................................................................................ 146 Table Index Table 1.1. Effective ionic radii of various elements (Park et al, 2009;Tsur et al, 2001a). ............................. (Kahn, 1981;Kishi Mizuno, & Chazono, 2003). ................... Table 2.1. HALT parameters for the three groups of MLCCs. ......................................................................... Table 2.2. Chemical composition of BaTiO 3 powders. .................................................................................... ......................................................... Table 3.1. TTF when HALT is performed using different voltages and the same temperature. ....................... . Weibull parameters for . Weibull parameters for MLCCs -Group C. .................................................................................... ............................................................................................. Table 3.6. Voltage stress constant (n). ........................................................................................................... air, two temperature steps: 1310 °C then 1150 °C 15 h. ................................................................................ .............................................................. Table 4.11. Density of BT-C ceramics sintered in reducing atmosphere at 1310 °C. .................................... Table 4.12. Summary of secondary phases detected in ceramics sintered in reducing atmosphere and °C. ..................................................................................................................................................................

Figure 3.2. Resistance evolution of individual MLCCs from (a)

Table 3.2. Weibull parameters for

General Introduction

Nowadays, the electronic devices are part of our lives: computers, telephones, electrical appliances are some examples. Currently the presence of electronic components is increasing more and more in industries such as the automobile and aeronautics, as well as in in the devices or processes that require automation. One of the principal components of these devices is the capacitor, which main function is the energy storage. There are multiple types of capacitors, one of the most used are the multilayer ceramic capacitors (MLCCs). The MLCCs offer essential advantages due to their low cost, one of the reasons of its predominance in the electronics market. According to the application there are different kinds of MLCCs to choose, regarding principally the capacitance they offer but also the dielectric material and its performance under different conditions, such as the temperature.

The characteristics of the MLCCs are going to be determined by extrinsic and intrinsic parameters; i.e., the nature, characteristics, synthesis and treatment of the dielectric material and the production process of the capacitors. These factors can influence on the final reliability of the capacitors and hence of the devices. For this reason, it is highly important to develop ceramic materials suitable for the different markets. One of the principal strategies to obtain reliable capacitors is to focus in the tailoring of the dielectric ceramic by modifying the material composition.

Barium titanate (BaTiO 3 ) has been the most used material as the base for the dielectric of the MLCCs due to properties such as its large permittivity. To enhance its electrical properties, it needs to be modified through the inclusion of several additives and dopants in the base formulation for the dielectric. The perovskite structure of the BaTiO 3 has the ability to host these dopants, which according to different conditions will occupy the A or B sites in the lattice. The occupation of the dopants within the cell structure will determine the initial electrical properties, and it is assumed that it will also determine the reliability (lifetime) of the final product. The formulation of barium titanate powders includes as dopants rare-earth elements (REE). Among them, the Y 2 O 3 is the most common for the fabrication of multilayer ceramic capacitors with base-metal electrodes (BME-MLCCs) because it has a lower cost than Ho 2 O 3 , Er 2 O 3 and Dy 2 O 3 and provides similar properties.

Also, cations such as Mn 2+ , Mg 2+ and Ca 2+ , that can contribute to the global distribution of the electronic defects generated when the doping ions are introduced into the lattice and during the capacitors fabrication process. In addition to these dopants, additives are added aiming to modify the production conditions, like the SiO 2 used to lower sintering temperatures. The final properties will result from the interactions that barium titanate, dopants and additives can have among each other under the specific sintering conditions. The complexity of the system is increased when given some conditions, secondary phases are formed. In previous works, these secondary phases, This thesis manuscript is divided in four chapters.

The first chapter is a bibliographic introduction in order to situate this work in the current context. It presents the general properties of the BaTiO 3 , and how they can be enhanced by the use of dopants such as the Y 2 O 3 in formulations that are used for its application as the dielectric material of multilayer ceramic capacitors.

The Chapter 2 describes the different experimental methods as well as the characterization techniques used in this work.

In the Chapter 3 is presented the electrical characterization of multilayer ceramic capacitors (MLCCs) using accelerated life tests (HALT) to determine the mean time to failure (MTTF) of each group of samples and perform Weibull statistical analyses that can be used in conjunction with the Arrhenius model to obtain the activation energy (E a ) value related to the failure of the capacitors under determined conditions.

In the Chapter 4 is presented the Y 2 O 3 -doping of two types of BaTiO 3 powders (one reagent grade and the other two commercially formulated) and the preparation of ceramics issued from those powders under different sintering conditions. The influence of the dopant and the presence of secondary phases over the structural and microstructural BaTiO 3 properties are described in this chapter.

Chapter 1

Introduction

Barium titanate (BaTiO 3 ) has attracted the attention for decades both, in the fundamental research field as in industry for device applications. This is a noteworthy ferroelectric material because it has a high ferroelectric activity, dielectric constant and spontaneous polarization (Li, Xu, Chu, Fu, & Hao, 2009) and presents a high resistivity (10 10 -10 12 Ω cm) (Belous, V'yunov, Glinchuk, Laguta, & Makovez, 2008). For the above mentioned, barium titanate has a great potential for technological applications in the electronics industry. In fact, due to its high dielectric constant, low dielectric loss and superior performance at high frequency, one of its most common applications is as the dielectric material for ceramic capacitors (Wang, Chen, Gui, & Li, 2016). Among these BT-based ceramic capacitors, the multilayer ceramic capacitors (MLCCs) are widely used in military, automotive and telecommunication applications in which the devices are subjected to meaningful changes in temperature, voltages and frequencies (Wang et al, 2001). Nonetheless, when the BaTiO 3 is pure exhibits a great change in dielectric constant near the Curie temperature (Tc) which renders the ceramic material unsuitable for capacitor applications. For this reason, the capacitor BTbased formulations must be chemically modified to meet the required capacitance-temperature characteristics (X. H. Wang et al, 2001;J. Wang et al, 2016;T. Wang, 2009).

Ceramics

Ceramics are the first material that the humanity has produced by transformation of raw materials.

The word is derived from Greek keramikos, which means argil, "especially potter's clay". Ceramics own their distinctive qualities due to the composition of the raw materials as well as the way they are processed. They are divided in two types of materials: traditional and technical ceramics. The first group (alumino-silicate) is generally produced from natural raw materials (clay, feldspar, kaolin, quartz) and they are generally implemented by casting (slip). The latter (metal-metalloid associations) are obtained by sintering or by electrofusion (the oxides are poured directly into a mold) (Fantozzi, Niepce, & Bonnefont, 2013). Actually, the second group has inspired the definition of the term "ceramics", as expressed by M. Barsoum & M. W. Barsoum (2002): "solid compounds that are formed by the application of heat, and sometimes heat plus pressure, comprising at least two elements provided one of them is a non-metal or a nonmetallic element solid. The other element(s) may be a metal(s) or another nonmetallic elemental solid(s)". This thesis work is focused on BaTiO 3 ceramics. These ceramics belong to the technical ceramics classification of the electronics that are semiconductors (thermistors, resistors).

BaTiO 3 -Structural characteristics

Barium titanate (BaTiO 3 ) is a ceramic material that has been widely studied due to its excellent dielectric, ferroelectric and piezoelectric properties (Nikulin, 1988;He et al., 2013). It presents a stoichiometric cubic perovskite of ABO 3 -type (A = alkaline-earth element and B = transition metal) containing sties with cubic environments of oxygen while B-sites are in an octahedral environment with corner-linked octahedral, as shown in Fig. 1.1. Below the Curie temperature (Tc) the BaTiO 3 is non-centrosymmetric, and can present a crystal distortion (Valdez-Nava et al, 2010).

Barium titanate has five crystalline forms: hexagonal, cubic, tetragonal, orthorhombic and rhombohedral, occurring at various phase transition temperatures: 1432 °C, 130 °C, 5 °C and -90 °C, respectively. The most stable phase at room temperature is the tetragonal phase; this is the most used form because of its excellent ferroelectric, piezoelectric and thermoelectric properties (Li et al, 2009). Tetragonal lattice (below Curie temperature, 120°C). (Richerson,2005).

Role of the dopants on the electrical properties of BaTiO 3

The crystal structure of this oxide belongs to the perovskite type, as shown in Fig. 1.1. This structure allows it to present a high dielectric constant. Pure BT exhibits a great change in dielectric constant near Curie temperature (Tc) 120°C (X. H. Wang et al, 2001). As a ferroelectric material, BT has a temperature point known as the Curie temperature (Tc), above which it becomes substantially non-electric, i.e. dielectric (Nikulin, 1988). If the material is above Tc (and up to 1400°C) it is centrosymmetric and paraelectric. Although barium titanate presents great electrical properties, it cannot be used in its pure form as a dielectric material.

Many efforts have been done in order to enhance barium titanate electrical properties for its different applications. One of the most common and effective methods has been to design the formulation including several additives and dopants. The difference between additives and dopants is not defined with exactitude for this field of study. However, it is usually considered that the additives contribute to the improvement of the production process while the dopants are supposed to have a direct impact over the final properties of the material, i.e. the dielectric properties. In this work this is the considered differentiation.

Cations such as Mn 2+ , Ca 2+ and Mg 2+ are added as dopants that can partially compensate the electrons and holes that the system might have due to the presence of oxygen vacancies (Yoon et al., 2007;Yoon, Kang, Kwon, & Hur, 2010).

Manganese can perform a double role; it can compensate the oxygen vacancies as an acceptor being incorporated at the Ti 4+ sites, but it can act as well as an additive inhibiting an excessive grain growth. It can take different valences (Mn 2+ , Mn 3+ or even Mn 4+ ) during the post-sintering process, being considered as an unstable acceptor-type dopant (Paunovic, Mitic, Marjanovic, & Kocic, 2016) but helps the material to keep a high insulation resistance while accepting electrons to form a lower oxidation state (Lee, Tseng, & Hennings, 2001).

Calcium is added to contribute as well to limit the oxygen vacancies concentration which improves the reliability, and can dissolve in the BT lattice participating in the core-shell formation (Yoon et al., 2010). The mechanism by which calcium exerts these effects has been argued along decades, which is related to things like the final application of the Ca-doped BT materials and the different ways that Ca 2+ can be added. However, it has been reported that the occupation site of Ca 2+ is critical for it can exert the effect of increase the resistance degradation (Fang, & Shuei, 1999;Han, Appleby, & Smyth, 1987;[START_REF] Völtzke | Ca-containing additives in PTC-BaTiO3 ceramics: effects on the microstructural evolution[END_REF]Zhu, Zhang, & Chen, 2013).

The introduction of dopants that can be donors or acceptors also modifies the structure of barium titanate and can contribute to the creation of chemical inhomogeneity like core-shell structure (T.

Wang, X.H. Wang, Wen, & Li, 2009;Kim et al, 2008;Armstrong, & Buchanan, 1990). Magnesium has been reported as a key cation in the formation of the core-shell structure and the inhibition of grain grown since it remains at the grain boundaries while the RE ions dissolve in the BT lattice (Huang et al., 2015;Kim et al., 2008).

The core-shell structure consists of pure ferroelectric BT (tetragonal structure) in a core that is surrounded by a shell of BT containing dopants and additives (mixture of tetragonal and cubic phases) with paraelectric behavior, as shown in the Fig. 1.2. (Kim et al, 2008). Hennings and Rosenstein (1984) reported the formation mechanism of this structure. They were able to show that the cores are the same phases as the shells, since the paraelectric shells grew epitaxially on the ferroelectric cores. Considering the core-shell structures are not thermodynamically stable, its formation will be affected both by the sintering temperature and the donor-acceptor ratio (T. Wang et al, 2009). Grogger, Hofer, Warbichler, Feltz, & Ottlinger, (1998).

(B) TEM of a typical core-shell grain in a BT specimen doped with yttrium and magnesium by Kim et al. (2008).

The microstructure of the ceramics resulting from the elaboration process will have an influence on the dielectric properties. For instance, the milling process can cause defects on the particles' surface and activate the diffusion of the additives into the grains. It has been reported that as the milling time increases, the shell region gets thicker and the core region gets smaller, leading to a high chemical homogeneity at the core-shell interface increases (Wang et al., 2009).

The formulation of barium titanate for its use in ceramic capacitors also includes sintering aids like SiO 2 . It is one of the most common because it has been reported to participate in the formation of a liquid phase that helps to reduce the sintering temperature and to a more uniform dispersion of the dopants. SiO 2 has the ability to form a liquid phase from the ternary system BaO-TiO 2 -SiO 2 , diminishing the eutectic point from 1320°C to near 1260°C (Felgner, Müller, Langhammer, & Abicht, 2001;Liu & Roseman, 1999;Ösküz, Torman, S. Sen, & U. Sen, 2016). This ternary eutectic point is well known and corresponds to the BaTiO 3 -Ba 6 Ti 17 O 40 system at approximately 1330 °C (Felgner et al., 2001). When SiO 2 is present, this temperature decreases to about 1280 °C -1260 °C. This is the reason why SiO 2 is considered as a suitable additive to produce ceramics with high density while lowering the sintering temperature, and it may even induce an improvement in the dielectric properties of BT (Öskus et al., 2016;Wu et al., 2007). Cheng (1989) also reported that the presence of SiO 2 and TiO 2 , leaded to the formation of a liquid-phase former that enhanced the ionic diffusion, resulting in a uniform microstructure. This liquid phase also purified the grain interior, increasing the grain conductivity. He also evidenced that the SiO 2 and TiO 2 are located at the grain boundaries influencing only the microstructure, not the electrical properties. The liquid phase has been evidenced in studies such as the one conducted by Wu et al. (2007) and (c) energy-dispersive X-ray spectroscopy spectra for triple junction and BaTiO 3 grain (Bo) (TEM) (Wu et al., 2007).

Despite the advantages of using sintering additives, the interactions that can take place between them and the BT matrix, can turn the structural and electrical nature modifications of the doped material into undesired ways. Chemical defects and even secondary phases, such as Ba 2 TiSi 2 O 8 and Ca 2 Y 8 Si 6 O 26 have been reported in formulated BT-based X7R MLCCs (Wu et al., 2007). Those phases could lead to the deterioration of the electrical properties that are supposed to be enhanced by the additives and dopants presence (Liu & Roseman, 1999;Öskus et al., 2016). Yan et al. (2016) reported that when adding 0.5 wt% of SiO 2 to BaTiO 3 , no second phase was detected and it showed homogeneous microstructure with small grains. However, with further increase of SiO 2 addition to 1 and 2 wt%, Ba 2 TiSi 2 O 8 secondary phase was detected and the dielectric constant of those ceramics at the Tc decreased gradually.

Finally, rare-earth oxides are added as well as dopants and they can interact, due to their donor or acceptor ionic behavior, creating chemical defects and activating compensation mechanisms. The doping of BT with rare-earth ions (e.g. Y 3+ , Dy 3+ , Ho 3+ ) improves its dielectric performance. For this reason, the researches in materials science and electronics engineering to improve the dielectric properties of the BaTiO 3 as a dielectric base material and modify it directing the objectives towards the market necessities, has highly increased the last decades. Gong, Wang, Zhang, & Li (2016) reported an increase of the reliability of co-doped BaTiO 3 -based MLCCs when using Ho 3+ and Dy 3+ . These dopants present a synergistic effect exhibiting a better insulation degradation behavior compared with the doped samples containing just one of the two. Similar results have been reported for donor-and acceptor-cosubstituted BT, which have shown a better insulation resistance and life stability. The most common of these systems is BaTiO 3 -MgO-R 2 O 3 , with R = La 3+ , Gd 3+ , Dy 3+ , Ho 3+ , Er 3+ , Y 3+ , Yb 3+ (Kuo, Wang & Tsai, 2006). The doping behaviors of R = Ho 3+ , Dy 3+ and Y 3+ have been reported by authors like Makovek, Samardžija, & Drofenik, (2004). They observed that these ions have similar solubility in BaTiO 3 lattice and their incorporation into it is mainly dependent of the starting composition of the powders. The Ba-or Ti-richness of the powder affects the measure in which the RE ions are going to be incorporated in each site. Park et al, (2009) compared the doping behaviors of these RE ions in BaTiO 3 -MgO-R 2 O 3 systems, obtaining the densest ceramics with the Dy 3+ ions, which exhibited the better shell formation as well due to a higher solubility compared to the Y 3+ and Ho 3+ ions. However, Y-and Ho-doped ceramics showed a most stable microstructure at high temperature. The similarities in the doping behavior of these particular three ions can be due to its similar ionic radius. Some of the BT dopants with their respective ionic radii according the coordination site they can occupy are shown in the Table 1.1.

The ionic radius determines the occupation site in the BT lattice of the RE dopants. Larger RE ions such as La 3+ and Sm 3+ are predominantly donor dopants, occupying the A-site. Smaller ions like the Yb 3+ are acceptor dopants; they occupy the B-site. The ions with intermediate ionic size (Dy 3+ , Ho 3+ , Er 3+ , Y 3+ ) can be placed both in A-and B-sites, presenting both donor and acceptor dopant behavior (Kuo et al, 2006;Park et al, 2009;Tsur, Hitomi, Scrymgeour, & Randall, 2001a). (Park et al, 2009;Tsur et al, 2001a). One of the most common observations with the RE-doped BT systems is the change of the crystalline structure due to the insertion of RE ions into the BT lattice, either in A-or B-sites. The presence of dopants can lead to a transformation from a well-defined tetragonal phase to a mixture of tetragonal phases or even a new structural phase. In the literature this change of phase is usually described as a mixture of tetragonal and cubic phases and denominated as a "pseudo-cubic" phase.

Ion

As previously mentioned, the additives and sintering conditions affect the microstructure as well.

For instance, the diffusion of oxygen atoms through the grain boundaries into the grains, to annihilate oxygen vacancies, can be faster during the cooling step. As a result, barium vacancies remain at the grain boundaries and form high-resistance regions. This increases the ceramics resistivity (Cheng, 1989). Besides the dielectric properties, the ferroelectric characteristics can also be modified. Shifts in transition temperatures or the broadening of the ε-T curve (diffuseness of the ferroelectric transition) can be some of the effects of dopants. Depending on the nature of the incorporated dopant in the BT lattice, it can go from classical ferroelectric to diffuse ferroelectric or even relaxor (Petrović, Bobić, Ramoška, Banys, & Stojanović, 2011). Also, the electrical behavior can be altered by the dopant concentration, which can lead to a dielectric or semi-conductivity behavior (Urek, Drofenik, & Makovec, 2000).

Two of the most principal applications for barium titanate are the positive temperature coefficient resistors (PTCRs) and the multilayer ceramic capacitors (MLCCs). The formulation for both of them is tailored with the incorporation RE cations to control conductivity and electrical degradation, respectively (Tsur, Dunbar & Randall, 2001b). The trivalent RE cations are of particular interest thanks to its amphoteric behavior. These substitutions cause a charge imbalance in the system that can be compensated either ionically under oxidizing conditions or electronically under reducing conditions (Fu, Mi, Wessel, & Tietz 2008;Makovek et al., 2004). Compensation mechanisms have been proposed (J. Zhi, Chen, Y. Zhi, Vilarinho, & Baptista, 1999;Jeong, Lee, & Han, 2005; Paredes-Olguín, Lira-Hernández, Gómez-Yañez, & Espino-Cortés, 2013) as illustrated below using the Kröger-Vink notation, when the dopant is Y 2 O 3 :

• When Ba 2+ is substituted:

! ! ! ! !" !"#$! ! → 2! !" . + 2!′ (1) 3! ! ! ! !" !"#$! ! → 6! !" • + ! !" !!!! + ! !" !!
(2)

• When Ti 4+ is substituted:

! ! ! ! !" !"#$! ! → 2! !" ! + 2ℎ • (3) ! ! ! ! !" !"#$! ! → 2! !" ! + ! ! •• (4)
All mechanisms (1) to (4) might be active at the same time. However, the sintering parameters (temperature and ! ! ! ) will lead to the predominance of one of them. The dominant mechanism will determine the electrical properties of the doped sample, such as its resistivity. A decrease in the resistivity can be due to the presence of charge carriers, as in mechanisms (1) and (3). If (1) is the prevailing mechanism, ceramic will behave as an n-type semiconductor. Mechanism (3) will lead to a p-type behavior. On the other hand, if mechanism (4) is leading, the ceramic can be an oxygen conductor. On the basis of thermodynamic analyses, the mechanisms (3) and (4) are more probable to occur (Zhi et al., 1999;Paredes-Olguín et al., 2013). However, in Y-doping cases, it has been observed that if the concentration is less than 1 %, mechanism (1) is prevalent (Paredes-Olguín et al., 2013). The behavior as donor or acceptor of these RE cations will be also affected by the A/B

ratio. An excess of BaO or TiO 2 will influence the probability of A-or B-site occupation. In the presence of an BaO excess, Y 3+ acts as an acceptor, while it behaves like a donor if there is an TiO 2 excess (Makovek et al., 2004). Y 2 O 3 is a common BT-dopant and the most suitable rare-earth oxide for the MLCCs production because it offers the electrical properties enhancement advantages as the Ho 2 O 3 , Er 2 O 3 and Dy 2 O 3 at lower costs (Zhang et al., 2016).

Known as the "magic ions", Dy 3+ , Ho 3+ and Y 3+ , are categorized as helpful for the lifetime of the MLCCs (Tsur et al., 2001a,b) for this reason, the amphoteric RE cations have been the most used for this type of applications. Since the optimization of industrial processes is crucial it is a determining factor as well at the moment to set the sintering parameters. Indeed, low sintering temperatures are preferred by industries for economic reasons.

In this work the Y 2 O 3 was chosen as dopant because of its wide use in the dielectric formulations for ceramic capacitors. The thermodynamic and kinetic factors that might influence its occupation site as well as the electrical properties of the ceramics will be discussed below.

Role of Y 2 O 3

The formulation of BaTiO 3 (BT) materials, used in the manufacturing of the MLCCs, must be tailored to control the electrical properties, especially at high temperature and under high electric field (Ashburn & Skamser, 2008;Yoon, Park, Hong & Sinn, 2007). For this purpose, several additives and dopants are added to BaTiO 3 . One of the most used dopants is the Y 2 O 3 , which is added with the aim to generate compensation mechanisms that contribute to improving the reliability of the capacitors.

The Y 3+ has an ionic radius of 0.107 nm, it is intermediate between that of the Ba 2+ ion (0.161 nm)

and the Ti 4+ ion (0.06 nm). Therefore Y 3+ can occupy either Ba 2+ or Ti 4+ cation site in the BT lattice (Wang et al., 2014;Tsur et al., 2001a). This allows Y 3+ to behave as acceptor or donor according to the position in the lattice. The inclusion of the Y 3+ ion in the BT structure depends on kinetic and thermodynamic factors (Makovec et al., 2004). It is reported that the formation energy of Kovalenko, & Makovec, 2005). The partial pressure of oxygen and sintering temperature will also induce the formation of Ba 2+ or Ti 4+ vacancies, leading Y 3+ to occupy either both or one of the sites (Belous et al., 2005;Paredes-Olguín et al., 2013). This will be influenced also by the Ba/Ti ratio, the dopant concentration and its solubility. Yttrium cations have different solubility in Ba-and in Ti-sites. Zhi et al. (1999) indicated a solubility of Y 3+ at the Ba-site of about 1.5 at% when sintered in air at 1440 -1470°C, while it reaches 4 at% when sintered under reducing conditions (V'yunov, Kovalenko, Belous, & Belyakov, 2005). For the Ti-sites instead, the solubility is higher, approximately 12.2 at% at 1515°C when sintering in air. Wang et al. (2014) reported that the introduction of Y 3+ in the BT lattice, can lead to structural changes, as the phase transformation from tetragonal to cubic.

! !" • + ! !" !! is 7.23 eV whereas it is only 4.35 eV to form a ! !" • + ! !" !!!! defect (Belous, V'yunov,
The amount of yttrium ions can be spent in different processes occurring in the system during the processing of the ceramic materials. Belous et al. (2008) studied yttrium-doped BT, identifying in which processes is expended the dopant. It is known that the raw materials may contain impurities.

In this case paramagnetic impurities were identified as able to occupy Ti-sites. Thus, some part of the Y 3+ can participate in an exchange of them. Yttrium also influences the charge compensation mechanisms. And as a collateral effect, it has been found it can participate in the formation of precipitates such as Ba 6 Ti 17 O 40 and Y 2 Ti 2 O 7 . These secondary phases have been usually found when the solid solubility of the dopant in the BT is surpassed.

With the appropriate amount of dopants, the structural, optical and electrical properties of a BTdoped system can be improved (Hernández Lara et al., 2017). On the other hand, there are numerous reports where the formation of secondary phases has been observed when doping BT with rare-earth elements (REE) (Belous et al., 2008;Yoon et al., 2007;Zhang et al., 2016). The formation of these precipitates depends on different factors, i.e. the sintering conditions and the dopant concentration (M. T. Buscaglia, Viviani, M. Buscaglia, Bottino, & Nanni, 2002). These secondary phases are usually formed when the amount of dopant is above of its solubility limit in the BT-lattice. This excess of dopant can lead to its interaction with other free ions present in the system, like Ti 4+ . Then, if the conditions are appropriate, a precipitate will be formed. Some of the secondary phases that have been observed are Ba 2 TiSi 2 O 8 (Wu, Wang, McCauley, Chu, & Lu, 2007), Ba 6 Ti 17 O 40 (Belous et al., 2008), Y 2 TiO 5 (Yoon et al., 2007), and one of the most common when doping with RE oxides (Dy 2 O 3 , Er 2 O 3 , Y 2 O 3 and Ho 2 O 3 ), is the pyrochlore-type phase, R 2 Ti 2 O 7 (Jeong et al., 2005). Among the pyrochlores, Er 2 Ti 2 O 7 (Buscaglia et al., 2002), Gd 2 Ti 2 O 7 (Hernández Lara et al., 2017), Ho 2 Ti 2 O 7 (Makovec et al., 2004) and Y 2 Ti 2 O 7 (Yoon et al., 2007;Zhang et al., 2016) have been reported. Y 2 Ti 2 O 7 is suspected to be detrimental to the reliability of BT-based MLCCs (Yoon et al., 2007;Zhang et al., 2016).

The effect of the presence of these secondary phases over the BaTiO 3 structural and dielectric properties is of high interest for industrial applications. Several authors have reported a detrimental effect of Y 2 Ti 2 O 7 on BT dielectric performance (Wu et al., 2007;Yoon et al., 2007;Zhang et al., 2016). The yttrium pyrochlore (Y 2 Ti 2 O 7 ) has a highly conductive nature and is suspected to be related with the resistance degradation of the material through the acceleration of oxygen vacancies electromigration (Zhang et al., 2016). The investigation of the formation parameters and possible effects of this phase is of high interest in the academic and industrial field since Y 2 O 3 is a one of the most frequent dopants used in the MLCCs production.

Sintering atmosphere influence over dopant occupancy in BT-doped ceramics

One of the most important parameters to obtain a BT material with the appropriate properties for its application as ceramic dielectric is the oxygen partial pressure (! ! ! ) during sintering treatment.

! ! ! affects the incorporation of dopants into the BT-lattice (Buscaglia et al., 2002;Tsur et al., 2001b). The site occupancy of dopants in BT-lattice is restrained by the valence of the ion, its size, the A/B ratio (i.e. the activity of Ti in the system) and by the oxygen vacancies concentration. It has been observed that the ! ! ! influences the charge compensation mechanisms (ionically or electronically) dictating a change in the A/B ratio in the perovskite lattice, which can lead to the formation of precipitates. Furthermore, the changes induced by the ! ! ! significantly affects the electrical behavior (Fu et al., 2008).

Either a reducing or an oxidizing sintering atmosphere can be used for the production of BT-doped ceramics. However, taking into account the cost reduction at industry level due to the use of nickel for the inner electrodes instead of the expensive noble metals previously employed, (palladium or silver palladium alloys), one of the factors that forces the use of reducing atmospheres is to protect Ni-electrodes from oxidation. Thus, the process must to be carried out in reducing atmospheres, such as CO/CO 2 or N 2 /H 2 , being the latter the most used (Albertsen, Hennings, & Steigelmann, 1998;Hagenbeck & Waser, 1998;Okino et al., 1994). Meanwhile, in the research field, either reducing or oxidizing atmospheres have been utilized.

The control of ! ! ! employed during the sintering of BT-doped ceramics can even contribute to the formation of Ti 3+ ions, assuming the substitution of Y 3+ for Ba 2+ in the BT-lattice. Tien & Carlson (1963) performed some experiments to determine the relation between the degree of oxidation and the resistivity-temperature characteristics of Y-doped polycrystalline BT. They found that the oxygen partial pressure increases the slope of temperature-resistivity curves above Tc and the resistivity at room temperature. This behavior is related to the amount of Ti 3+ present in the system.

Under equilibrium conditions, the relation between ! ! ! and Ti 3+ concentration is described by: 2Ti 4+ + O 2-⇌ 2Ti 3+ + ½ O 2 . Previous reaction is overlapped by the Y 3+ dopant, its level and the prevailing equilibrium conditions will then determine the concentration of Ti 3+ . Following the expression for

the equilibrium constant ! = (!" !! ) ! ! ! ! !/! (!" !! ) ! (! !! )
, [Ti 3+ ] is constant at a given temperature and equilibrium conditions as determined by dopant amount and the prevailing ! ! ! . If the ! ! ! is constant as the temperature is decreasing, then the equilibrium constant will be decreasing which as well will dictate an increase of Ti 3+ concentration, and this will influence the electrical behavior of the material (Tien & Carlson, 1963). Tsur et al. (2001aTsur et al. ( , 2001b) ) investigated the site occupancy of rare earth ions in the BT-lattice according to the atmosphere conditions. They found that when BT is fired at low ! ! ! and high temperatures, dopants such as Er, Y, Ho and Dy are amphoteric (Tsur et al., 2001a). They also observed that samples fired in air present larger cell volumes than the ones sintered in reduced atmospheres. The latter is due to the lower presence of oxygen vacancies in air sintered samples, thus site occupancy is directed towards more B-site occupancy (Tsur et al., 2001b).

Multilayer ceramic capacitors (MLCCs)

In the past decades, the electronic devices design has gone toward the miniaturization and reduction of power consumption. This trend requires high reliability for the electronic components (Shimada, Utsumi, Yonezawa, & Takamizawa, 1981). Among the most important electronic items are the Multilayer Ceramic Capacitors (MLCCs) (Fig. 1.4). MLCCs were developed in the 1960s and its use increased in the 1980s (Pan & Randall, 2010). These pieces are used in strongly growing markets (Acosta, Zang, Jo & Rödel, 2012), making up approximately 30% of the total components in a typical hybrid circuit module (Futureelectronics.com. (n.d.)). They present an economical volumetric efficiency for capacitance and high reliability. MLCCs are characterized by a high dielectric constant (K) and thinner dielectric layers (Jain, Fung, Hsiao, & Chan, 2010). MLCCs can be broadly divided, depending on the application, into two types: for temperature compensation and for high-dielectric constant. MLCCs for high-dielectric constant use barium titanate as the dielectric component. Among this type of capacitors, the X7R is the most stable, covering a broad spectrum of applications. X7R formulations are called "temperature stable" ceramics, which allows apply them widely in miniaturization of electronic components (Li, Zhang, Zhou, Chen, & Wang, 2007). NPO). Class II is known as Stable capacitors, the most common among them are X7R, X5R and Y5V. Finally, class III: Z5U, known as the General Purpose capacitors (Ashburn, & Skamser, 2008;Pan & Randall, 2010;Standard, E.I.A., 2002). The specifications of classes I and II are shown in Table 1.2. They can be classified by its rated voltage, tolerance, type of dielectric, capacitance, packaging type and case size. The most common values for capacitance are 10 nF, 100 nF and 1 µF.

The rated voltage (RV) can be between 4 V and 10 kV, and the most common capacitors have a RV of 16, 25, 50 or 100 V (Futureelectronics.com. (n.d.)). The EIA specification for X7R MLCCs is a temperature variation of capacitance (ΔC/C) within ± 15 % from -55 °C to 125 °C. (Li et al., 2007;Park et al., 2009).

Table 1.2. Types of MLCCs and specifications (Kahn, 1981;Kishi Mizuno, & Chazono, 2003). voltage and exhibit as little as 30% of their nameplate value at 90 % of their voltage range (Pan & Randall, 2010).

EIA

The capacitor technology has changed according to the industrial and commercial demands. Since many of MLCCs applications are manipulated at extreme operational conditions, like high temperatures (beyond 200 °C), the capacitors must be processed out under high degree requirements to ensure a high-yield, large-scale, low-cost production process (Kahn, 1981). MLCCs with X7Rformulation based on BaTiO 3 dielectric material, are usually produced under a sintering process with a temperature between 1200 °C and 1300 °C and low ! ! ! of about 10 -9 -10 -11 atm. This is followed by a re-oxidation step at 800° -1000°C in ! ! ! between 10 -6 -10 -8 atm. (Wu et al., 2007).

This last step contributes as well to the attempt to diminish the contribution of oxygen vacancies (Pan & Randall, 2010). A whole general view of the industrial production process of these capacitors is shown in the Fig. 1.5.

The characteristics of each MLCC type challenge a highest quality for its production. Each step during this process must be carefully supervised, taking care of some key factors that will critically influence the lifetime and resistance degradation of the capacitors. Some of the considerations to take into account, as it has been explained, are the characteristics of the starting BT powder and the features of the final formulation to be applied, i.e. optimization of additives and dopants. There are as well some aspects related particularly to the process, as the coating of the dielectric material and the control of atmospheric conditions during thermal processing. As long as the production steps are under control, the process will be robust ensuring a high-quality product (Ashburn & Skamser, 2008). Nevertheless, even though research in the last decades has allowed to the industries the optimization of the production process, exhibiting a great improvement in the technology of the electronic field, some failures are still observed in some cases.

Two failure modes have been identified in Base-Metal-Electrode (BME) Multilayer Ceramic Capacitors (MLCCs): catastrophic and slow degradation. Catastrophic failures are mainly due to present processing defects (extrinsic defects), such as voids, cracks and delaminations. These are characterized by a time-accelerating increase in leakage current. On the other hand, the slow degradation failures are related with the electromigration of oxygen vacancies, which are considered intrinsic defects, and are characterized by a near-linear increase in leakage current against stress time (Liu, 2015).

These failure modes can be distinguished using a 2-parameter Weibull plot. The early (catastrophic)

failures can be distinguished by a slope parameter of β >1. This β value indicates that these are not infant mortalities (Liu & Sampson, 2012).

Early failures have been related to the decrease of the dielectric thickness, being triggered by external electrical overstress. This has represented a problem to control a high reliability with the miniaturization of MLCCs. The breakdown leakage current that characterize an early failure is an avalanche-like type (Liu & Sampson, 2012). Since, as mentioned before, these failures are related to extrinsic defects, i.e. minor construction defects introduced during fabrication of the capacitors, the production control and quality requirements are a crucial factor to obtain a reliable final product.

It has been reported that insulation resistance (IR) degradation of BT-based BME-MLCCs might be related with three probable aspects: the dielectric layer, the BT grain boundaries, and the internal electrode interfaces between Ni-BaTiO 3 (Liu, 2015).

Chapter 2

Introduction

In this chapter we present the different analytic techniques used for the characterization of samples as well as the experimental set-up performed throughout this work. To start the characterization of multilayer ceramic capacitors will be presented and then the preparation and characterization of the Y 2 O 3 -doped BaTiO 3 powders and ceramics.

Electrical characterization of multilayer ceramic capacitors

Multilayer ceramic capacitors (MLCCs) samples description

Multilayer ceramic capacitors (MLCCs) of the X7R type (Fig. 2.1) were provided by KEMET de México. In this work we counted with three different groups of samples, denominated: A, B, and C.

The differences of these groups of MLCCs lie in the composition of the formulated barium titanate powder used as dielectric ceramic material of each one.

Electrical characterization tests

Multilayer ceramic capacitor samples were subjected to life tests to accomplish their characterization with the determination of life parameters.

High Accelerated Life Test (HALT) protocol for individual I-V measurements

To set up the right conditions to perform adequately a HALT in house, it was necessary to know the behavior of the three groups of capacitors. In this way, measurements of resistance degradation during time, under a fixed high voltage value and different temperatures to cover a broad range that could provide the information required, were performed.

First, an individual sample was tested on probe station (Signatone model S-1060R QuieTemp DC) thermally regulated (hot chuck system 1 °C resolution and can operate at temperatures up to 300 °C). In this case, the contacts with the sample are ensured with needle micromanipulators. A source meter unit (SMU 2410, Keithley, Cleveland, OH, USA) (source voltage from 5 µV to 1100 V; measure voltage from 1 µV to 1100 V) was used to apply the voltage and measure the current and time during the test. This experimental set up is shown in Fig. 2.2.

First, a HALT was performed under industrial standard conditions: 400 V and 140 °C for 24 h. A fast rise in the current, which means a decrease in the resistivity to be near zero, indicated the moment when the dielectric breakdown of the capacitor occurred. In this work, the test was stopped when 24 h had passed without failure or at the moment that a breakdown was observed.

Additionally, HALT were conducted under the same voltage value but using different temperatures to observe the behavior at higher and lower than 140 °C values.

High Accelerated Life Test (HALT) protocol

Three groups of MLCCs of the X7R type were tested under a high accelerated life test (HALT).

Measurements of time-to-failure (TTF) of each group of samples were performed under a given set of stress conditions (Table 2.1). The HALT protocol combined two values of voltages and for each one a broad range of temperatures. In this way, it was possible to determine an activation energy linked to the failures for each group of stresses.

For each test, at least 12 pieces of capacitors were subjected to electrical and thermal stress; both parameters (voltage and temperature) were kept constant during the experiment. When it was observed that the ensemble or majority of samples had failed, the test was stopped and data of the evolution of the current with the time were taken to determine the time-to-failure (TTF) of the samples for each combined stress conditions.

In-house device for HALT measurements with multiple samples

With the purpose of testing multiple samples while controlling the experimental conditions, a second setup was developed and built in-house (Fig. The setting up of the samples for the test performance includes the details shown in Fig. 2.4. To maintain the voltage after a capacitor failed, the protective resistors (MS176-5 µΩ, Caddock Electronics Inc.) were joined (Fig. 2.4.a) and considering the total current that the dc supply could deliver (1 mA), the system had a maximum capacity of 20 samples. To connect the samples (Fig. The capacitors are connected in parallel to a voltage source. If they are working right, the current will not pass through them; otherwise they will become conductive leading to a decrease of the resistance, reflected in a current rising. The data acquired from each HALT experiment was followed in real time with the software, being possible to know the current value in function of the time. Thus, it was possible to know when one or more samples simultaneously, had suffered a breakdown each time the current value increased. This can be seen in the Fig. 2.6, where each step is a rise of the current corresponding to an electrical broken sample. The value of that increment depends on the imposed voltage as well as the resistance value of the protective resistors. This value is constant per failed sample. In the example taken for the Fig. 2.6, under the experimental conditions shown for Fig. 2.6.A, it is 0.6 mA because the applied voltage was 600 V; while in the second case shown in Fig. 2.6.B it is 0.4 mA because the applied voltage was 400 V. When more than one sample fails at the same time, the step will correspond to the mentioned rising of current value multiplied by the number of failed samples. An example of this case is shown enclosed in a green box in the Fig. 2.6.A, the failures 6 and 7 occurred simultaneously, thus that step is equivalent to 1.2 mA and the time to failure was considered two times at the moment to analyze the data. In the plots presented in Fig. 2.6, each failure is signaled with an "F" letter and a number, also the initial and final current values are presented. These values, as explained, are determined based on the failed samples. To assure the circuit was correctly functioning, a short circuit connection was always incorporated to the system, so it was observable that the current was flowing through it and this is why the initial value of the current is not zero.

Powders characterization

The barium titanate powders used as the dielectric in the production of the Group B and C MLCCs are the same that were utilized in this work for the fabrication of the ceramics described subsequently in this chapter. These ceramics will be denominated as BT-B and BT-C, respectively.

It is important to remark that BT-A powder was not used in any case to fabricate MLCCs, as well as that the base-powder of the MLCCs -Group A, was not used for this part of the work.

X-Ray Diffraction

The determination of the crystalline structure and phase were achieved using non-destructive analytical X-ray diffraction (XRD) analyses. This method is based on constructive interference of monochromatic X-rays and a crystalline sample. The X-rays are generated by a cathode ray tube;

then they are passed through three basic steps: filtered to produce a monochromatic radiation, concentrated by collimation, and directed toward the sample. The interaction given between the sample and the incident rays produces constructive interference (and a diffractive ray) when conditions satisfy Bragg´s Law (H. [START_REF] Bragg | The reflection of X-rays by crystals[END_REF]:

!" = 2! sin ! (5)
Where ! is the wavelength of the electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample, d is the distance between different plane of atoms in the crystal lattice, and θ is the angle of diffraction. The X-rays are then detected, processed and counted, generating a diffraction pattern that can be considered as a "fingerprint" of the material. It provides information about the crystalline phase(s) present in the sample.

In this work, X-ray analyses were performed using a Bruker D4 Endeavor diffractometer shown in

Induced coupled plasma atomic emission spectroscopy

This analytical technique was used for the determination of the chemical elements composition of the different starting powders. The inductively coupled plasma atomic emission spectroscopy (ICP-AES) is a technique that exploits the fact that excited electrons emit energy at a given wavelength as they return to ground state. The fundamental characteristic of this process is that each element emits energy at specific wavelengths peculiar to its chemical character. Although each element emits energy at multiple wavelengths, in the ICP-AES technique it is most common to select a single wavelength (or a very few) for a given element. The intensity of the energy emitted at the chosen wavelength is proportional to the amount (concentration) of that element in the analyzed sample (Thomson, 2012). With the determined wavelengths that are emitted by the sample and by determining their intensities, the analyst can quantify the elemental composition of the given sample relative to a reference standard. The ICP-AES analyses for this work were executed by Marion Technologies.

Scanning electron microscopy

The SEM analyses were performed using a scanning electron microscope JEOL JSM-6510LV. The electron bombardment was carried out to an acceleration voltage from 0.5 kV to 30 kV. The images were obtained at 20 kV.

The samples, either powders or ceramics, were fixed over the sample holder using a graphene adhesive, and then covered with a thin layer of silver. The surface and grain morphologies were observed by this technique. Frequency counts of particles and grain sizes were performed by the analysis of several SEM micrographies with the Image J software. Gaussian distribution was applied to determine the mean size and standard deviation of the samples.

Manufacture and characterization of ceramics

Raw materials description

Two types of barium titanate (BT) powders were used for doping them with Y 2 O 3 . In the first place a reagent-grade BT (Ferro Electronic Materials INC) without additives. Then, two BT powders commercially formulated for its application as the dielectric ceramic material of X7R MLCCs. The composition of the three BT powders is shown in Table 2.2, it was determined by an inductively coupled plasma atomic emission spectroscopy (ICP-AES) analysis (performed at Marion Technologies). From these analyses it is worth to highlight the fact that the formulated powders already contain 1.05 wt% of Y 2 O 3 , which is one of the most common additives for BT dielectric ceramic powder and the one chosen in this work for the doping experiments. 60 The powders were also analyzed by X-ray diffraction obtaining the diffraction patterns shown in Fig. 2.8. Even though the three powders have a tetragonal structure (JCPDS: 89-1428), the definition of the peaks is better for the BT-B and BT-C powders, that correspond to the commercially formulated for its industrial application. This is due to the presence of the additives, whose interaction with the BT matrix enhances the intensity between the peaks, as seen for the (002) and ( 200) planes (Kim et al., 2008). present similar particles morphology and their sizes are in a close range.

Powders doping procedure

Barium titanate (BT) powders (composition shown in Table 2.1) were mixed with the appropriate amount of Y 2 O 3 to achieve the corresponding doping concentrations presented in Table 2.2. The raw materials were mixed by traditional solid-state reaction. Powders were ball-milled in a polyurethane mill bottle with yttrium-stabilized zirconia balls, using ethanol as the grinding media for 4 h. Doped powders were dried and 1 wt% of polyvinyl butyral (PVB) was added as binder.

Finally, this mixture was grinded and sieved obtaining the desired powder.

0 1.0 1.5 2.0 2.5 5.0 20.0 BT-A* BT-A_0 BT-A_1 BT-A_1.5 BT-A_2 BT-A_2.5 BT-A_5 BT-A_20 BT-B** ------ BT-B_1 BT-B_1.5 BT-B_2 BT-B_2.5 BT-B_5 BT-B_20 BT-C** ------ BT-C_1 BT-C_1.5 BT-C_2 ------ ------ ------ *:
BT reagent grade (pure). **: BT commercially formulated.

Green ceramics manufacturing

Ceramics were obtained from the powders previously prepared. The powders were compacted with a manual hydraulic press (Specac) using uniaxial pressure to compact the powders in a pressing die as shown in Fig. 2.10. Cylindrical pellets (diameter: 8 mm, thickness: 1.7 mm) were produced applying a uniaxial pressure of 300 MPa for 30 s. The mass and dimensions of each compact disk were measured before and after the sintering to determine the density value. The density values of the ceramics are reported based on the theoretical density of 6.02 g/cm 3 , reported of the barium titanate.

Ceramics sintering

The term sintering refers to the thermal treatment that allows the bonding of particles into a more consistent solid structure. The two principal phenomena included in sintering process are the reduction of the porosity (densification) and the grain growth. This happens by mechanisms of mass transport that often occurs on the atomic scale. From the thermodynamic point of view the sintering is driven by a reduction of the surface energy [START_REF] Coble | Sintering crystalline solids. I. Intermediate and final state diffusion models[END_REF][START_REF] German | Sintering: from empirical observations to scientific principles[END_REF].

In this work, different sintering programs were used for the conducted experiments. One sintering program was performed using a laboratory chamber furnace with fiber insulation (model LF, Nabertherm). Pellets were placed over a platinum cover inside an alumina container. The thermal cycle was a two-steps program: samples were first heated to a higher temperature aiming to promote an intermediate densification, then the temperature was reduced, and a lower temperature value was held to complete the densification. This strategy has been reported to present advantages such as a uniform pore microstructure while controlling grain growth and enhancing densification [START_REF] Chen | Sintering dense nanocrystalline ceramics without final-stage grain growth[END_REF][START_REF] Polotai | A novel approach to sintering nanocrystalline barium titanate ceramics[END_REF]; X. [START_REF] Wang | Two-Step Sintering of Ceramics with Constant Grain-Size, II: BaTiO3 and Ni-Cu-Zn Ferrite[END_REF]).

The thermal program followed for the production of undoped and doped BT ceramics under air is shown in the Fig. 2.11. The thermal cycle was carried out from room temperature until 1350 °C (no holding time) with a heating rate of 10 °C/min, then a cooling rate of 30 °C/min was applied till reach a sintering temperature of 1150 °C that was held for 15 h; finally, a cooling rate of 150 °C/h was used in the final stage. This two-step sintering program was used to obtain undoped and 2.5 and 5 wt % Y 2 O 3 -doped ceramics issued from BT-A and BT-B powders. On the other hand, it was also performed a sintering process carried out at a company (KEMET de México). This sintering process was used aiming to mimic the industrial production conditions for the X7R-MLCCs. The thermal program and conditions are shown in Fig. 2.12; samples are fired in a kiln with reducing atmosphere and a temperature of 1310 °C hold for 3 h, then samples are taken out and passed to a kiln for a post-sintering treatment with an oxidizing atmosphere (used to restore the characteristics of the dielectric). In this case, due to the nature of the process, two set of samples were derived from each lot of processed ceramics. Each group was divided taking the half of the ceramics just after the firing under reducing atmosphere and the rest of them were passed through the re-oxidizing step.

Thermal treatment of powders

Aiming to observe the behavior of the samples as powders, the doped ones with the higher Y 2 O 3 content were subjected to a thermal program in air. BT-A and BT-B powders undoped and Y 2 O 3doped with 2.5, 5 and 20 wt%, were thermally treated in air under 1310 °C for 3h. This process was performed in a laboratory chamber furnace using the program observed in Fig 2 .13. Although BaTiO 3 presents electromagnetic properties that make it suitable as base material for the formulation of the dielectric material for MLCCs (Tsur, Dunbar, & Randall, 2001;Wang et al., 2014), it is not by itself adapted for applications since it must follow an industrial process (shaping and sintering) along with intrinsic properties that show a large variation with temperature. (D. [START_REF] Yoon | Processing of barium titanate tapes with different binders for MLCC applications-Part I: Optimization using design of experiments[END_REF]J. Yoon et al., 2009).

Capacitors must maintain their properties within a certain tolerance in a wide range of temperatures during its lifetime. Doping remains the strategy to adapt the dielectric properties of the dielectric layer to the target application, especially for broad temperature use under high electric fields. (Ashburn, & Skamser, 2008;[START_REF] Paunović | The effects of additive on microstructure and electrical properties of BaTiO 3 ceramics[END_REF].

Since reliability is a critical parameter in design of electronics, components manufacturers keep track of it through different parameters. Assessment of the reliability can be very accurate trough periodic analysis of products on service and by accounting for failed products, but it is not predictive and takes a long time. Therefore, other methods need to be used to reduce the evaluation time to have an indication of the reliability prior the commercial release of the components.

Accelerated test conditions have to be designed to get the most accurate prediction possible of the lifetime of capacitors in service conditions. The most common tests for reliability of MLCCs are the insulation resistance and combined stress measurements, also known as highly accelerated lifetime test (HALT). [START_REF] Paulsen | Highly accelerated lifetesting (HALT) of kemet Base-Metal-Electrode (BME) ceramic chip capacitors[END_REF][START_REF] Vassilious | Understanding accelerated life-testing analysis[END_REF].

Electrical systems such as capacitors may be tested using two types of tests; either constant stress test or progressive stress test can be performed. In the first type, a number of specimens are taken to their breakdown under defined stress conditions, and then the times to failure are measured; in the second type, breakdown voltages may be measured. At the moment of performing the electrical test, whatever the type, for the given conditions each tested sample will produce a different result, so the total of obtained data can be analyzed by a statistical distribution. [START_REF] Chauvet | Breakdown statistics as a tool to investigate electrical aging[END_REF].

Different statistical distribution models could be applied in the data analysis from these tests, including the Weibull, Gumbel and lognormal. The Weibull distribution is widely used in this field, and is the one used in this work, in which a two-parameter Weibull analysis is performed. [START_REF] Chauvet | Breakdown statistics as a tool to investigate electrical aging[END_REF][START_REF] Diaham | Dielectric breakdown of polyimide films: Area, thickness and temperature dependence[END_REF].

When tailoring the properties of MLCCs, besides the initial electrical parameters, it is of great interest to analyze and seek the correlations between basic structural and chemical formulation to the reliability (time-to-failure) of capacitors. Very few studies in the literature address this, understandably because producing MLCC for reliability testing requires at least pilot size facilities to produce many samples with a reproducible process to minimize the influence of other parameters than the one being tested.

Moreover, the aim of the test is over a fixed kind of capacitors since dielectric is formulated to the best possible performance. Hence, conclusions regarding the effect of the doping over the reliability of the MLCC are rather speculative.

Given the numerous and complex interactions between the additives and dopants during and after the sintering process, a simpler approach needs to be undertaken. In this work we determine the time-to-failure of BaTiO 3 -based X7R MLCC capacitors containing 1.05 %wt yttrium in their formulation.

High Accelerated Life Tests

The traditional way to evaluate the reliability of MLCCs is performing an accelerated test under a representative number of samples subjected to determined conditions of temperature and voltage with the aim to determine the time to failure using a statistical model. Also, it is possible to determine the failure modes [START_REF] Liu | Reliability evaluation of base-metal-electrode multilayer ceramic capacitors for potential space applications[END_REF]. At industrial level this kind of tests are performed under fixed values of temperature and voltage, however they can be carried out using different values covering a broad range of stresses, with the aim to know if the failure mechanism changes depending on the value of those [START_REF] Scarpulla | Thin MLCC (multi-layer ceramic capacitor) reliability evaluation using an accelerated ramp voltage test[END_REF].

High Accelerated Life Tests (HALT) have been widely used to evaluate the reliability of electronic devices such as multilayer ceramic capacitors. The principal result of these kinds of tests is the determination of the time-to-failure (TTF) of the MLCCs when they are subjected to life stress conditions much higher than the normal using-level conditions (ambient temperature and rated voltage). The expected or average TTF is known as the mean time to failure (MTTF) which can be taken as a reliability indicator. The high-raised stress conditions are normally high voltages and temperatures that cause an electrical and thermal stress which would be not caused at normal conditions since these devices have a very long expected life [START_REF] Liu | Highly accelerated life stress testing (HALST) of base-metal electrode multilayer ceramic capacitors[END_REF]. To evidence the moment when a breakdown occurs, the HALT follows the leakage current or insulation resistance of the MLCCs under the defined stress parameters (J. [START_REF] Yoon | Analysis the reliability of multilayer ceramic capacitor with inner Ni electrode under highly accelerated life test conditions[END_REF]. The collection of TTF data from HALTs allows using it for the estimation of an activation energy associated to the electrical degradation mechanism(s) that causes the breakdown [START_REF] Paulsen | Highly accelerated lifetesting (HALT) of kemet Base-Metal-Electrode (BME) ceramic chip capacitors[END_REF].

The HALT methodology normally begins by causing the failure of the electronic components, MLCCs in this case, under different combinations of electric and thermal stress. Then a failure distribution can be fitted, and the quantification of the time-to-failure is done. Having this data is then possible to determine the value of the activation energy (E a ) and get an insight of the information about the failure mechanism of the tested samples. As previously mentioned, the objective of preforming a HALT is to obtain the TTF, this value can also be used to predict median life under normal conditions of use. However, it must be used carefully and considering there are different factors beside the stress conditions that can highly influence the median life of an electronic component like ceramic capacitors.

In this study, failure data are fit to a Weibull distribution and the statistic t 63.2 is chosen as the characteristic time life of the samples. The Weibull parameters are determined and then used in conjunction with an Arrhenius model to find the activation energy related with the failure under determined conditions of the tested groups of MLCCs.

High Accelerated Life Test (HALT) -standard conditions

High accelerated life tests are widely used in the industries that produce ceramic capacitors in order to assure the reliability of its products. The conditions of the HALT are mostly determined by the protocols that have been developed for the different applications capacitors can have. In this way, capacitors can be tested for long periods under different combinations of temperatures and voltages.

The testing voltage is given by n times the rated voltage (nVr), which is basically a voltage beyond which the capacitor will be operating under unusual conditions. Thus, it was intended to perform a HALT using industrial testing parameters in-house. The main objective of this first experiment was to examine if it is possible to take the results as a criterion to discriminate among the MLCCs groups. The HALT conditions that we will denominate as standard will be a testing period of 24 h applying 140 °C and 8*Vr = 400 V. Thus, resistance evolution was observed during the time lapse of 24 h or until a breakdown was evidenced by a conspicuous decrease of the resistance [START_REF] Paulsen | Highly accelerated lifetesting (HALT) of kemet Base-Metal-Electrode (BME) ceramic chip capacitors[END_REF]. Samples from three groups (A, B, and C) of MLCCs X7R-type were subjected to the HALT standard conditions (400 V and 140 °C) while following the current evolution under these conditions.

As to the groups A and B, the behaviors of their samples under the standard HALT conditions (400 V and 140 °C) are shown in the Fig. 3.1. In this figure is possible to observe the current evolution of these groups of MLCCs, each one of the "steps" correspond to an increase in the current given by the breakdown of a capacitor, i.e. each step is a failure.

As seen in this figure, the first remarkable observation is the clear shorter time in which the samples from Group B fail. The Group A showed to be affected to a lesser extent by the high voltage and temperature compared to the Group B. While the Group A did not show evidence of breakdown before 24 h, the samples from the Group B failed before this period.

Testing the samples in this way allowed us to observe the clear differences among the three groups with respect to their response when submitted to these stress conditions. The first group that showed a clearly different behavior when standard HALT conditions where applied was the Group C. It was not possible to perform the HALT at standard conditions for Group C samples since they suffered a breakdown immediately when tested at this voltage (400 V) and a temperature above 90 °C, so there is no gathering data for this group under the HALT standard parameters. However, HALT tests for this group were performed using the same electrical stress conditions but lower temperature ranges. They are certainly affected in a higher or less extension by the voltage and temperature imposed. Under these conditions, the MLCC pieces from the Group A are considered a more reliable material, bearing in mind that they did not fail at extreme conditions before 24 h. The Group B is more affected by these stress conditions, presenting higher resistance degradation over the time. Finally, the Group C is the most damaged when subjected to this test since its breakdown was instantaneous under these conditions. From this starting point it was possible to expect that the different behavior among the groups was observed as well at different HALT combination of conditions. To confirm this, the next step was to broad the range of thermal stress.

Impact of temperature on breakdown of MLCCs

For a first attempt, the experiment was carried out testing one sample at time in a Signatone S-1160 probe station. The thermal stress was provided by a hot chuck system and the electrical parameters were controlled and followed by a Keithley's 2410 Source Measure Unit (SMU).

Performing high accelerated life tests in the probe station (one sample per test) allowed to follow the current and resistance evolution of the three groups of samples, when tested at 400 V and different temperatures.

A general overview of the resistance behavior of the three groups, when HALT was performed at 400 V and different temperatures, is shown in the Fig. 3.2. For the three cases, the resistance was rather stable during the beginning of the test and then it started to decrease until a rapid step down that was the signal for a breakdown of the sample.

As is possible to observe in Fig. 3.2, there is a distinct difference in the range of time that the failures of the MLCCs are produced. Even for groups A and B that were tested under the same temperatures, the longer times to failure were seen for Group A (Fig. 3.2.a). Despite the TTF for MLCCs from Group B (Fig. 3.2.b) are in the middle of the ones from Groups A and C, the values are closer to the first. In fact, Group A and B show more similitudes with regard to its behavior under higher stress values; i.e. these groups are possible to test under temperatures above of 100 °C while Group C is not. Regarding the Group C (Fig. 3.2.c) this set of samples was the most affected by the high temperature. The first evidence is that as previously said, the range of testing temperatures had to be set to a maximum of 80 °C so the failure was not immediate and then the data showed that Group C presents the shorter times to failure of the three groups.

Since the voltage was the same in all the cases (400 V), the effect of the temperature over the resistance degradation is clear; when the thermal stress is higher the time-to-failure is shorter. This is a common effect for the three groups; however, we remind that each group of MLCCs is affected to a greater or lesser extent by the thermal stress. Thus, these experiments allow not only differentiate and even classify the MLCCs groups by their time-to-failure (TTF) but also provide a clear clue of how the thermal stress causes an important effect over the resistance degradation of the samples. Knowing this and considering the tests reproducibility and time to perform them, the next step was to perform the HALT testing multiple samples at once under the same stress conditions. In this way, the performance of a statistical analysis of the TTF will be achieved and a characteristic life time will for each group will be obtained, which will also lead us to obtain an activation energy related with the failure of each sample.

Determination of Time to Failure (TTF) and Mean Time to Failure (MTTF)

The Mean Time to Failure (MTTF) is a value that provides the average life time expected for nonrepairable items such as the MLCCs.

To continue with the characterization of the three groups of MLCCs, high accelerated life tests were from then performed in an in-house device that allows testing multiple samples at the same time while controlling the voltage and temperature (Section 2.3.2.4). Aiming to gather enough data to the subsequently statistical analyses, 12 samples of each group were tested under HALT.

Breakdown was assumed to have occurred when an abrupt increase in the current of about 0.4 mA (when testing at 400 V) was detected. The failure times were determined by these increments in current indicating a short circuit. This increase in current is well described in the literature, and often related to the breakdown of the layer of dielectric [START_REF] Teverovsky | Breakdown voltages in ceramic capacitors with cracks[END_REF].

The MLCCs groups have very distinct behaviors according the HALT conditions, with the breakdown times ranging from seconds (Group C) to tenths of hours (Group A). The times to failure of samples from Groups A and B when tested under standard HALT conditions are shown in the Fig. 3.3. Samples Group A last longer than the ones from Group B, having a range of TTF from approximately 22 to 30 hours, while the Group B has a TTF range from about 3 to 4 hours. Despite the early failures, both groups of samples fail with a low dispersion that allows performing HALTs with multiple samples tested at the same time, obtaining accurate data. However, as observed in the parallel plot of the TTF for each detected failure, is possible to say that the Group A under these conditions presented less dispersion, being the majority of the failures around the same value of time. From these figures (Fig. 3.4.) is also observed that the dispersion of TTF decrease at higher values of temperature. This could be related with the failure mechanism and the way it is thermally activated. At low temperatures it is more difficult to overpass the activation energy necessary to start the breakdown phenomenon.

However, these results only provided an insight about the way that thermal stress affects the samples reliability. Considering this, another voltage value was applied while using a thermal stress of about the same range of temperatures, so the effect of electrical stress could also be analyzed. In this way, HALTs were performed with an electric stress of 600 V and the results of the times-tofailure can be seen in the Fig. 3.6. Again, it can be seen the effect of the thermal stress over the TTF As seen, the drop in the TTF values can be considered as significant, decreasing in several hours for the case of Group A and Group B and some minutes for the Group C. About the dispersion of the TTF results it is as well low, as seen in the time ranges in Fig. 3.7.

Until this point, it can be suspected that there is an interaction among the two stress variables. In further sections it will be analyzed considering the statistical analyses performed to the obtained results from HALT experiments.

The Weibull distribution

In this study, times to failure are fit to a Weibull distribution and the statistic t 63.2 has been chosen as the characteristic life of the samples.

The cumulative density function for the two-parameter Weibull distribution is represented by the following expression:

! ! = 1 -! !( !!! ! ) ! (1)
Where F(x) is the cumulative probability of failure, is the scale parameter that represents the time or voltage for which the failure probability is 63.2%. The units of are the same of the measured times or voltages. The shape parameter is a measure of the range of the failure times or voltages, and, the larger its value, the smaller is the range of measured data. The location (or threshold)

parameter is frequently set as zero (it implies a threshold voltage in a progressive test or a threshold time to breakdown in a constant stress one) [START_REF] Abernethy | The new Weibull handbook fifth edition, reliability and statistical analysis for predicting life, safety, supportability, risk, cost and warranty claims[END_REF][START_REF] Chauvet | Breakdown statistics as a tool to investigate electrical aging[END_REF][START_REF] Diaham | Dielectric breakdown of polyimide films: Area, thickness and temperature dependence[END_REF].

Data sets can be complete or censored; the second group corresponds to those sample sets in which not all of them present breakdown. Both the first or second type of data sets, they must be ranked, and a good approximation can be given by the median rank equation known as Bernard's approximation [START_REF] Ross | Comparing linear regression and maximum likelihood methods to estimate Weibull distributions on limited data sets: systematic and random errors[END_REF]:

! !, ! = !!!.!! !!!.!" (2)
Where i represents the rank of a failed sample and n the total number of tested samples.

For plotting the Weibull distribution law, the cumulative density function (cdf) (1) must be transformed as follows:

!" 1 -! ! = !" ! !( ! ! ) ! (3) !" 1 -! ! = - ! ! ! (4) !" -!" 1 -! ! = ! !" ! ! (5) !" !" ! !!!(!) = ! !" ! -! !" ! (6)
The equation 6 represents the linear way to plot the Weibull cdf, having as the terms:

! = !" !" 1 1 -!(!) ; ! = !" ! ; ! = -! !" ! ; ! = !
From where is possible to obtain the values of and .

With the aim to know the value, is possible to manipulate the Weibull cdf equation so this value can be read from the x-axis time scale, it can be expressed mathematically as = x, substituting this into the Weibull function, we get:

! ! = 1 -! ! ! ! = 1 -! !! = 0.632
The characteristic life has as unique feature that it occurs at the F(x) = 63.2% regardless of the Weibull distribution, i.e. the value.

In the present work, the Weibull parameters have been determined applying a graphical and an analytical procedure, the median rank (MR) and the least squares method (LSM), which in fact is related with the first one and is also known as the rank regression method (RRM) because the estimation of the parameters by using it is dependent upon regressing some form of logarithm and rank transformations of the data according to the rank position [START_REF] Nwobi | A comparison of methods for the estimation of Weibull distribution parameters[END_REF][START_REF] Ross | Comparing linear regression and maximum likelihood methods to estimate Weibull distributions on limited data sets: systematic and random errors[END_REF].

The reliability of different samples of multilayer ceramic capacitors (MLCCs) was studied by the performing of highly accelerated life tests (HALT). Regarding fit the results to a statistical model, a number of mean time to failure (MTTF) data under various levels of electric (V) and thermal (T) stress were collected [START_REF] Liu | Highly accelerated life stress testing (HALST) of base-metal electrode multilayer ceramic capacitors[END_REF].

As previously described, data was collected from HALT at different values of temperature and two voltage values, 400 V and 600 V. It is worth to emphasize that choosing to perform the HALT using distinct voltages and thermal values that covered really low and high temperatures had the goal to observe the behavior of the insulation resistance in a wide window of imposed stresses. This was thought on the basis that it has been reported that the failure modes are related with the slope of the Weibull fitting [START_REF] Abernethy | The new Weibull handbook fifth edition, reliability and statistical analysis for predicting life, safety, supportability, risk, cost and warranty claims[END_REF]Liu & Sampson, 2012), but this parameter can be quite different depending on the range of stress levels in which the HALT is being carried out (Härtler, 1986). This could lead to an inaccurate prediction of the life-time from the TTF obtained data. In fact, there are other factors that can influence the prediction of the life time, such as the fact that to induce the dielectric breakdown under the nature of the HALT, is necessary to apply stress values that might introduce different failure mechanisms, different to the ones that could be present under normal conditions of use. Also, since more than one failure mode could be present, the statistical model used for the data analyses, must be capable to show those mechanisms [START_REF] Liu | Highly accelerated life stress testing (HALST) of base-metal electrode multilayer ceramic capacitors[END_REF].

Weibull analysis -Group A

The Fig. Thus, it could be said not only that life distribution under different thermal stress values obey the Weibull distribution but also, the failure mechanism(s) of the MLCCs -Group A appear to be the same up to a 200 °C [START_REF] Wang | Reliability evaluation method for oil-paper insulation in power transformers[END_REF]. A change in the behavior of the failures when thermal stress is higher than 200 °C is related with a new failure mechanism. Also, the observation of this behavior supports the choice of studying a wide range of temperatures while keeping the electrical stress constant. Our results until now show that when HALT is performed at low thermal stresses the dispersion and the distribution of the failures is not the same that at high temperatures.

From the linear equation of each plot shown in Fig. 3.8 were determined the parameters and , that are associated to the characteristic life and may provide a clue of physics of failure,

respectively. The values of the scale parameter and the shape parameter for each temperature and voltage are presented in the Table 3.2. For both electrical stress values, the characteristic life decreases as the temperature increases, this behavior was also observed when testing the samples in the probe station. In the case of the value, it is constantly reduced until the temperature is 200

°C, from there it does not present a clear pattern. The changes of according the testing temperatures are shown in Fig. 3.9. In the figure is possible to see that not all the points could be fitted under a same distribution as the selected ones are delimited by the dashed lines in Fig. 3.9.

With respect to the observed influence of the electrical effect, it is noticeable that it decreases the median life of the capacitors as well, so it confirms that both stresses affect significantly the insulation resistance of the samples. Taking into account that the values obtained for T > 200 °C are not congruent with the expected response to the imposed thermal stress, only values below this limit were considered for further determination of the activation energy for the failure, considering that another mode of failure could be involved up to this limit.

On the other hand, the values of the shape parameter ( ) determined for the data gathered using 400 V and temperatures below 200 °C are all higher than 2 and beyond that temperature they tend to be lower than 2. For the 600 V case, the values are above 2 for all the temperatures. However, this parameter does not present a tendency in function of the temperature as can be seen in Table 3.1. It has been reported that when 1.0 < < 4.0 it implies failure due an early wear out, while if > 4.0 it implies a rapid wear out (Liu & Sampson, 2012;[START_REF] Abernethy | The new Weibull handbook fifth edition, reliability and statistical analysis for predicting life, safety, supportability, risk, cost and warranty claims[END_REF].

Weibull analysis -Group B

The times-to-failure of MLCCs from the Group B stressed at 400 and 600 V were determined and analyzed using the Weibull distribution. The results are shown in Fig. 3.10, in both cases of electrical stress it was found a similar behavior of data in the tested temperatures in terms of the applied fit. This leads to say that these samples fail under the same failure mode. Also, in Fig. 3.10.a is seen that when the HALT is performed at 400V and over 200 °C, the data obtained at 210

°C and 225 °C is almost overlapped with the data at 200 °C. In fact, as seen in Table 3.3, the values for these three test temperatures (200 °, 210 ° and 225 °C) are the same.

The changes of the scale parameter are shown in Table 3.3 and more clearly in the Fig. 3.11, from there is possible to observe that it decreases as the temperature increases. Regarding the shape parameter, in this case the values are all higher than 2 and they do not present a tendency according the temperature.

The observed in the Fig. 3.10 as well as the data shown in Table 3.3, show that the life of MLCCs -Group B is affected both, by higher values of thermal and electrical stress. The characteristic life With the performance of high accelerated life tests at different temperatures and voltages it was possible to differentiate the groups according to its insulation resistance. According to the statistical analyses of the obtained data, the Group A has the higher mean life time, then the Group B and last, the Group C.

The three groups of MLCCs samples were designed based on a typical X7R composition with 1.05 % of Y 2 O 3 . However, the composition of their dielectric material, i.e. the amount of dopants in each one, is not exactly the same. This might be reflected in the behavior of the samples when they are tested under a HALT, as the results analyzed by the Weibull distribution have shown.

The following step to continue with the characterization of the samples through its characteristic life is to determine the activation energy (E a ) related to the failures. The estimation of the E a will be based on the collected accelerated-tests data and applying the Arrhenius-Weibull model. Once the parameters of the life-stress have been determined using the Weibull distribution as the life distribution as in our case, it is possible to utilize the Arrhenius model to find the E a value.

It is worth to remind that the activation energy that will be determined for each group of MLCCs does not represent a single particular failure mode since a combination of failure modes can be given according the tests conditions and other parameters inherent to the nature of the dielectric material such as its composition or even the production process of the ceramic capacitors [START_REF] Groebel | Determination and interpretation of activation energy using accelerated-test data[END_REF].

Regarding the parameters determined by the Weibull analyses, all the shape (slope) parameters were higher than 1. This indicates that the failures cannot be reversed by a regular thermal process (burn-in) as if they were infant mortalities.

Arrhenius model applied to the analysis of combined stress (V, T) effect over MLCCs life.

HALT uses the simultaneous application of an electric and thermal stress while measuring the time to failure (TTF) for the MLCCs. These two combined factors can induce a shorter time to failure that provides information about the expected life under service conditions. In the case of the temperature, as for other thermally activated processes, failure seems to follow an Arrhenius-type behavior (Eq. 1), with the failure frequency (inverse of time to failure) increasing with an increase in temperature [START_REF] Groebel | Determination and interpretation of activation energy using accelerated-test data[END_REF][START_REF] Hartler | Parameter estimation for the Arrhenius model[END_REF]Liu, 2015).

1 ! = !! !! ! /!" (1)
t: time to failure (TTF) (s); E a : activation energy for the thermally activated process (eV);

k: Boltzmann's constant (8.62 × 10 -5 eV/K);

T: absolute temperature (K);

A: pre-exponential factor (s -1 ).

The TTF due to thermal activation at a given temperature can be calculated from the data at different temperatures if the activation energy is known from Eq. 1, as a set of two time-temperature conditions (Eq. 2).

! ! ! ! = ! ! ! ! ( ! ! ! ! ! ! ! ) (2)
where t 1 = TTF, at T 1 and V 1 , (s); and t 2 = TTF, at T 2 and V 2 , (s).

In Eq. 2, both the activation energy and the pre-exponential factors in Eq. 1 are constant. Regarding factor A, it represents the minimum TTF, which is consistent with the fact that these processes do not take place instantaneously, even at a very high temperature.

Since the electric field affects the time to failure of the capacitors, an empirical equation in which the pre-exponential factor that is still constant is modified by the applied voltage, has been proposed (Eq. 3) (Ashburn, 2013).

! ! ! ! = ! ! ! ! ! ! ! ! ! ( ! ! ! ! ! ! ! )
(3) t 1 = TTF, at T 1 and V 1 , (s); t 2 = TTF, at T 2 and V 2 , (s);

V 1 and V 2 = test voltages under conditions (V); n = voltage stress exponent;

E a = activation energy for dielectric wear out (eV); k = Boltzmann's constant (8.62 × 10 -5 eV/K);

T 1 and T 2 = absolute test temperature (K).

These factors are well-described in the literature (Ashburn, 2013) and the expected coefficient of the voltage stress exponent (n) is in the range of 1.5-7.1 (Ashburn, 2013;[START_REF] Maher | Electric Field Effects on the Insulation Resistance and Reliability of Various Types of BaTiO3 based X7R MLCC's at Elevated Temperatures[END_REF][START_REF] Randall | Lifetime modeling of sub 2 micron dielectric thickness BME MLCC[END_REF]. This great variation in n is an indicator of the uncertainty related to the effect of the voltage. It also highlights the importance of determining any correlations of the basic structural and chemical formulation with the reliability (TTF) of capacitors.

Very few studies in the literature addressing this were found, which is understandable because producing MLCCs for reliability testing requires at least pilot size facilities to produce many samples with a reproducible process in order to minimize the influence of other parameters than the one being tested.

The Arrhenius model was developed originally to define the rates of chemical reaction according to the temperature it is carried out. However, it has also been applied in accelerated life testing because it helps to stablish a relationship between the reliability and the thermal (i.e. temperature) stress imposed during these tests. Commonly in the industry this model is applied with the assumption of fixed parameters that are related to defined values of failure mechanisms such as electromigration of corrosion. In the literature activation energy values can be found related to a precise type of material, electronic component or failure mode, and this is precisely what can represent an issue when using them to determine the characteristic life of a different system. The activation energy can provide clues about how the life of a product is affected by its service conditions. This means that the activation energy can vary even from one product batch to another.

Also, it can be different according to the present failure modes and which one can be prevalent. [START_REF] Groebel | Determination and interpretation of activation energy using accelerated-test data[END_REF][START_REF] Hartler | Parameter estimation for the Arrhenius model[END_REF] In this work we chose to estimate the E a based on the results of performed tests to get more accurate information regarding the effect of the imposed stresses in this study and the correlation of the same.

As we plotted the data according to Eq. 1, the activation energies can be estimated if we only consider the data below 200 °C for the Group A and Group B (Fig. 3.9 and Fig. 3.11) samples and below 70 °C for the Group C (Fig. 3.9) samples. Eq. 1 shows the relationship of the frequency of failure (mean time to failure; MTTF), as shown below in Eq. 4, which can be transformed into Eq. 5

to obtain the activation energies related to the failures of the three types of MLCCs. The E a values were determined by applying the Arrhenius model to the life time of the capacitors (Fig. 3.14).

1 ! = !! !! ! /!" = !""# (4) ln !""# = ln ! - ! ! !" ( 5
)
where MTTF is the mean time to failure (s -1 ).

The value of the E a can be taken as a measure of the effect that the imposed thermal stress over the capacitor has on its life. Since the pre-exponential factor in this equation includes both the electrical stress and the thermal contributions (Eq. 3), a large activation energy value will imply a large effect of the imposed temperature on the capacitor life.

Applying the Arrhenius model, the plots shown in Fig. 3.14 were obtained. Then a linear fitting according equation (3) was adapted and the values of the activation energy were determined and are presented in Table 3.5. The activation energies are reported in Table 3.5. Those values are calculated by assuming that the voltage and thermal effects are a single combined factor and thus, the activation energy was calculated following the Arrhenius expression.

The activation energy values found when HALT was performed using 400 V show that the thermal effect is higher for the MLCCs from Group C, then for Group B and last the Group A. This confirms what we have previously stated, the life of MLCCs -Group A will change slowly as the temperature changes, i.e., it has better insulation resistance than the other samples. Regarding the E a found when 600 V were applied, is possible to say that the values are different compared to the ones at 400 V for Groups B and C, while the E a of the Group A is not significantly different when electric stress is higher. This can indicate that lives of Groups B and C are more affected when voltage is higher than life of Group A, so their failure mechanism(s) can be activated faster when the electrical stress is as well increased. Also, the E a values for the three groups at 600 V are rather similar. These results can indicate that the electrical stress affects in a lesser extension the life of the tested capacitors than the thermal stress does it. The numeric values of the activation energies should be related to the failure mechanism of the dielectric breakdown under stress conditions. It has been reported in general that the activation energy value of 1.9 eV was associated with an avalanche breakdown mode; while this can be in a range of 1.25-1.42 eV for the thermal activated failure [START_REF] Nomura | Multilayer ceramic capacitors-recent trends[END_REF]Rawal, & Chan, 1984). Other authors have suggested that for a thermal breakdown in MLCCs, the E a will fall within the range of 1-2 eV (Liu & Sampson, 2012). Furthermore, the values in a range from 1.3 -1.5 eV have been described as being related to a dielectric wear out in BaTiO 3 -based dielectric capacitors (Yoon, Lee, & Lee, 2009).

Considering this and the results described in this work, such as the E a values presented in Table 3.5, it could be confirmed that the failures were highly influenced by a thermal activated breakdown process. It is worth to remind that electronic components may have multiple failure modes and one of them tends to prevail over the others, and the found results in this kind of works can be pointing out to it; i.e., to the one with the lower activation energy. For this reason, we consider it is better not to take the reported E a values since it should be determined for the conditions of the experimental life test instead of simply associate one by default. Nevertheless, it is possible to use the value of the activation energy to know and describe how large it is the effect that the imposed stress is causing over the time-life of capacitors. In this work it could be seen that the capacitors (when HALT is conducted at 400 V) have different E a , giving us a clue about which one is most affected by the thermal stress.

Even if the activation energy ranges overlap, this does not contribute to defining the exact failure mechanism. Among the possible mechanisms that may explain the obtained values, Chazono et al. (Chazono, & Kishi, 2001) proposed that the oxygen vacancies migrate under the influence of the high electrical field that is applied during the HALT testing. [START_REF] Yoon | Analysis the reliability of multilayer ceramic capacitor with inner Ni electrode under highly accelerated life test conditions[END_REF] suggested that as the vacancies are accumulated at the electrode interface, a Fowler-Nordheim (tunneling) conduction mechanism can be induced, which favors the breakdown of the dielectric layer due to the local increase in the conductivity. The activation energies within the range of 1-2 eV fall reasonably within the range of the E a required for the mobility of oxygen vacancies (Chan, Sharma, & Smyth, 1981;Han, Appleby, & Smyth, 1987). In the present study, higher doping with calcium had a significant impact on the time to failure of the Group C samples.

A rough estimation of n for Group A composition, which only considered the test conducted at the same temperature, so that the relationship excludes the thermal part between 400 V and 600 V,

gives the average value reported in Table 3.6 (n (T 1 = T 2 )). To calculate this parameter with all the temperatures and the two voltages by means of the objective function (Eq. 6), the obtained values of n are shown in Table 3.6 (n (all conditions)). Although all values in Table 3.6 seem to be consistent with other reports (Rawal & Chan, 1984), the most accurate is n (all conditions) because it predicts the failure time under more conditions.

!" = -ln ! ! ! ! + ! ln ! ! ! ! + !" ! ( 1 ! ! - 1 ! ! ) (6)
Is important to mention that with the results find in this work we cannot specifically talk about the reliability of the tested MLCCs, however we could consider them as reliable under certain use conditions. At an industrial level is rather the same way, since they are defined reliable within the determined use conditions by the producer. Also, the performance of this type of electronic components is highly related to its base-material composition itself. Considering this, we think that the differences found about the behavior of the capacitors that lead us to say that some groups are more affected by the high stress levels can be analyzed as well from a chemical compositional point of view of its dielectric material. Since it has been reported that the decrease in the insulation resistance of ceramic capacitors can be due to the formation of secondary phases such as the Y 2 Ti 2 O 7 in the BaTiO 3 dielectric layers (Zhang et al, 2016), we continued this work with the systematic analyses of two of the base-powders use for the fabrication of the MLCCs from Group B and Group C, considering the fact that they seem to be the less reliable. In the next part of this Chapter we are going to develop a study based on the doping of BaTiO 3 powders with Y 2 O 3 . The aim of this study will be to drive the system in an isolated way (not in the form of capacitors but prepared as ceramics) to the formation of secondary phases and by the performance of structural and microstructural analyses determine if the BaTiO 3 structure can be affected by its presence, and maybe understand how this can change its electrical properties.

Chapter 4: Y 2 O 3 -Doping of BaTiO 3

Introduction

In the tailoring of BaTiO 3 as the base dielectric material for MLCCs fabrication, it is important to define the relations between the structure, microstructure and electrical properties. There are reports of secondary phases due to the presence of other elements, such as the dopants, which addition is intended to improve the electrical properties of the material. Among the reported phases are the pyrochlores, Y 2 Ti 2 O 7 related to Y 2 O 3 , that as side effect are supposed to be the cause of long term failure mechanisms of MLCCs under nominal operation (Zhang et al., 2016).

This research is aimed to find the secondary phases in this material and to perform an evaluation of the reliability of MLCCs that use BaTiO 3 based material that might contain those phases. All the conditions to which the ceramic is exposed during its preparation, from the raw material to the last thermal treatment, must be well known as well as the output from those steps. For that reason, it is necessary to perform powders and ceramic characterization by techniques such as Induced Coupled Plasma (ICP) spectroscopy, X-Ray Diffraction analyses and SEM, to know the chemical composition, structure and phase composition, porosity and grain size, respectively.

The formulation used in this application must be designed to control the electromagnetic properties of the layer, especially at high temperature and under high electric field (Ashburn & Skamser, 2008;Yoon, Park, Hong, & Sinn, 2007) so that several additives and dopants are added to BaTiO 3 . They include cations such as Mn 2+ , Mg 2+ and Ca 2+ , which can partially compensate the electrons and holes in the system due to the presence of oxygen vacancies (Yoon et al., 2007;Yoon, Kang, Kwon, & Hur, 2010). They also include sintering aids, such as SiO 2 , which reduce the sintering temperature. Indeed, it has been reported that SiO 2 leads to the formation of a liquid phase from the ternary system BaO-TiO 2 -SiO 2 , diminishing the eutectic point from 1320 °C to near 1260 °C (Liu & Roseman, 1999;[START_REF] Koschek | On the Electronic Structure and the Local Distribution of the Second Phase Ba 6 Ti 17 O 40 in BaTiO 3 Ceramics[END_REF]; Ösküs, Torman, S. Sen, & U. Sen, 2016). Rare-earth elements (Dy 3+ , Ho 3+ , Sm 3+ , La 3+ , Yb 3+ or Y 3+ ) have been used as well; they substitute Ba and Ti sites in the BaTiO 3 structure (Zhang et al., 2016;Wang et al., 2014a). However, in particular Dy 3+ , Ho 3+ and Y 3+ , have shown an amphoteric behavior (occupying A-or B-site) which claims to be helpful for the lifetime of the MLCCs (Tsur, Dunbar, & Randall, 2001). Y 2 O 3 is commonly employed as dopant in the commercial formulation of powder for industrial fabrication of MLCCs because it results in similar properties than adding Ho 2 O 3 , Er 2 O 3 or Dy 2 O 3 , and it is less expensive (Zhang et al., 2016). Dopants also take part in the formation of a so-called "core-shell" structure that is claimed to contribute to the temperature stability of the dielectric properties (Kim et al., 2008;Park et al., 2009;Wang et al. 2014;Zhang et al., 2016). Y 3+ ionic radius (0.107 nm) is intermediate between that of the Ba 2+ ion (0.161 nm) and the Ti 4+ ion (0.06 nm). Therefore Y 3+ can occupy either Ba 2+ or Ti 4+ cation site in the BaTiO 3 lattice (Tsur et al., 2001;Wang et al., 2014) and can behave as acceptor or donor according to the position in the lattice. The energy required to form a Ti 4+ vacancy in the BaTiO 3 lattice is 7.56 eV whereas it is only 5.94 eV to form a Ba 2+ vacancy (Belous, V'yunov, Kovalenko, & Makovec, 2005;Makovec, Samardžija, & Drofenik, 2004; Paredes-Olguín, Lira-Hernández, Gómez-Yañez & Espino-Cortes, 2013). The partial pressure of oxygen and sintering temperature will also induce the formation of Ba 2+ or Ti 4+ vacancies, leading Y 3+ to occupy either one or both (Belous et al., 2005;Paredes-Olguín et al., 2013). This will be influenced also by the Ba/Ti ratio, the dopant concentration and its solubility, which varies according to Y 3+ occupying either the Ba-or the Ti-site. Zhi et al. (1999) indicated a solubility of Y 3+ at the Ba-site of about 1.5 at% when sintering in air at 1440 -1470 °C, while it reaches 4 at% when sintering under reducing conditions (V'yunov, Kovalenko, Belous, & Belyakov, 2005). For the Ti-sites instead, the solubility is higher, i.e. around 12.2 at% at 1515°C when sintering in air. Wang et al. (2014a) reported that the introduction of Y 3+ in the BaTiO 3 lattice can lead to structural changes going from tetragonal to a so-called pseudocubic phase transformation. Also, it has been observed that the solid solubility of the dopant in the BaTiO 3 is surpassed, when secondary phases are formed as precipitates. In the case of Y 3+ , Belous et al. (2008) reported the formation of the

BaTiO 3 raw powders

The chemical composition of the BaTiO 3 powders used as raw materials was determined by ICP analyses and is shown in Table 4.1. As previously mentioned, the powders that are formulated for an industrial application contain dopants and additives. In Table 4.2 is presented a brief summary of the function that these components should exert in the formulation of the BaTiO 3 powders as dielectric base of ceramic capacitors.

110

Compound Function

SiO 2 Sintering aid that contributes to a better densification. Can contribute to the creation of a liquid phase, reducing the sintering temperature.

Mg 2+

Involved in the core-shell creation. Can replace Ti 4+ -sites, inhibiting the grain growth.

Ca 2+ Can substitute A-or B-sites causing beneficial changes at a structural and electrical level. Contributes to enhance the reliability.

Mn 2+ Added to keep high insulation resistance. It can also inhibit the grain growth.

Rare Earth Elements (REE)

Particularly the amphoteric such as Dy 3+ , Ho 3+ and Y 3+ (the one used in this study) have demonstrated to improve the MLCCs insulation resistance. Also involved in the core-shell creation.

The denomination of the different samples, according to the starting powder and the final concentration of Y 2 O 3 , is shown in the Table 4.3.

Composition

BaTiO 3 powders thermal treatment and characterization

With the aim to observe any structural change induced by high level of doping, the powders BT-A_2.5, BT-A_5, BT-A_20, BT-B_2.5, BT-B_5, and BT-B_20 were thermally treated (TT) at 1310°C in air for 3 h. This thermal treatment replicates the sintering temperature conditions in which multilayer ceramic capacitors are produced at industry level. In this case the powders are denominated BT-X_YTT, where "X" indicates the raw BaTiO 3 powder, "Y" the Y 2 O 3 wt%, and "TT" thermally treated.

• Particles morphology and size SEM images of the undoped BaTiO 3 powders, BT-A_0 and BT-B_1, are shown in Fig. 4.1.a and Fig. 4.1.c respectively. Both powders present particles with a coarse-faceted morphology. Two particle sizes are observed, a range of 0.48 µm and 1.25 µm for the BT-A_0, and of 0.46 µm and 0.81 µm for the BT-B_1. The mean size value of the particles from BT-B_1 is roughly lower than the one of the BT-A_0 particles. This slight difference is probably related to the treatment given to the formulated powder to fulfill the particle size required for its use in the MLCCs production process.

After thermal treatment at high temperature, the SEM images of Y 2 O 3 -doped powders , show more rounded and defined particles, compared to the non-thermally treated, non-doped powders (Fig. 4.1.a and Fig. 4.1.c,respectively). The mean grain size is similar for the two powders, respectively 0.58 µm and 0.53 µm. Some aggregates are observed, probably due to a beginning of sintering. •

Structure and phase composition

The way that the BaTiO 3 structure can be affected by an added dopant can be reflected in the c/a ratio, which changes from cubic structure (c/a = 1) to higher values when the crystal lattice is modified for reasons like the presence of other ions. This change in the c/a ratio is reflected directly in the diffraction pattern. For BaTiO 3 with a cubic crystalline phase, sharp peaks in a 2θ value around 31.6° and 45.3° corresponding to the ( 110) and ( 200) planes respectively, are observed.

When the symmetry of the system is not cubic anymore, it causes that certain planes can appear on the diffraction pattern. Thus, in some zones where just one peak was observed, are now spotted two or more depending on the crystalline arraignment. In the case of a tetragonal phase, the planes ( 101) and ( 110) will be seen, as well as the ( 002) and ( 200) around the same 2θ values previously mentioned. We calculated a theoretical change of the 2-theta value for the (002) plane as a function of the possible c/a ratio is shown in the Fig. 4.2. A change in the c/a ratio is more notorious for ( 002) and ( 200) planes since the distance between their peaks is higher than the one of (101) (110) peaks. In fact, as long as c/a value increases, the distance among their peaks is intensified; i.e. at higher values of c/a the tetragonality is more evident. Also, the intensity ratio between ( 002) and ( 200) peaks, when the BaTiO 3 is in a tetragonal phase, is 1:2. However if there is a gradient in the composition of the matrix, it is possible to have the presence of various c/a ratios, which leads to a different appearance of the peaks. They can look less intense, broaden and even like if they were joining. For these reasons, in this work we will discuss how the structural phase of the BaTiO 3 is affected by the presence of the added Y 2 O 3 , following principally the observable changes in the peaks around 45°.

To remind the structural phase of the BaTiO 3 starting powders, the corresponding diffractograms are shown in Fig. 4.3. The three powders present a distinct splitting of ( 002) and ( 200) planes around 45°, related to a tetragonal phase identified by the JCPDS: 89-1428. These results are going to be the base over which the structural analysis of the samples is going to be developed. 45° look different with respect to the BT-B_1, being like joined. This might be related to an inhomogeneous distribution of the dopant in the BT matrix, which will lead to the presence of different c/a ratios in the samples; i.e. a mixture of tetragonal structures. Contrary to the BT-A samples, the Y 2 O 3 phase is detected only for the BT-B_20 powder. Moreover, in the diffraction pattern of this sample, three additional peaks are detected between 2θ ≈ 29.5 -30°. They correspond to a secondary phase identified as Ba 6 Ti 17 O 40 . This orthotitanate has been reported previously in different works such as the ones by [START_REF] Lu | Core-Shell Structures in ZrO 2 -Modified BaTiO 3 Ceramic[END_REF], Belous et al. (2008), andParedes-Olguín et al. (2013). Since the BT-B matrix contains additives and dopants, it can be expected that they interact not only with the BaTiO 3 but also among them, and if an excess of ions is produced as a consequence, then some precipitates can get formed. In this case, it can be said that the incorporation of Y 3+ atoms in the BaTiO 3 lattice leaded to a segregation of Ti 4+ , being possible a a reaction between BaTiO 3 and TiO 2 producing the Ti-rich phase [START_REF] Yuan | The effect of doping process on microstructure and dielectric properties of BaTiO 3 -based X7R materials[END_REF]. Thus, the interaction between the doped matrix and the additives, under our experimental conditions, leaded to the precipitation of Ba 6 Ti 17 O 40 .

BaTiO 3 ceramics characterization

The sintering of ceramics (powder compacted at 300 MPa) was carried out both, in air and reducing atmosphere following two different thermal cycles: 1) In air, two temperature steps: 1310 °C then 1150 °C for 15 h. The ceramics sintered using this program are BT-A (A_0, A_2.5, A_5) and BT-B (B_1, B_2.5, B_5).

2) In reducing atmosphere (pO 2 ≈ 10 -8 -10 -11 atm, N 2 , H 2 O, H 2 ): 1310 °C for 3 h (this sintering process was carried out in industrial conditions (KEMET de México), simulating the production conditions of the MLCCs). The ceramics sintered using this program are BT-A (A_0, A_1.5, A_2, A_2.5, A_5, A_20), BT-B (B_1, B_1.5, B_2, B_2.5, B_5, B_20), and BT-C (C_1, C_1.5, C_2).

BaTiO 3 ceramics sintered in air • Density

The density values of the BT-A and BT-B ceramics obtained under these sintering conditions are summarized in Table 4.4. It is possible to see that the high-level of Y 2 O 3 affected the densification decreasing it with respect to the undoped samples. Nevertheless, as observed in Fig. 4.6, the density for BT-A undoped ceramic is higher than the one of the ceramics doped with 2.5 and 5 wt% Y 2 O 3 , although for these was quite equal. For the BT-B ceramics, the density values are different among them, being as well lower when the content of Y 2 O 3 increases. Even when the densification for both cases (BT-A and BT-B) is lower according to the Y 2 O 3 content, the ceramics formed from the BT-B powder present higher density values. This difference can be due to the additives present in the BT-B powder formulation, since one of the purposes for include them into the formulation is to improve the densification of the ceramic material. 4.4), which could be caused by the high amount of Y 2 O 3 . Despite this fact, the grains present a homogeneous appearance. About the grain size, the difference among both ceramics is minimum, thus the doping level did not affect it. • Structure and phase composition patterns are in agreeing with a BaTiO 3 perovskite and do not show secondary phases. However, it can be seen the peaks corresponding to the ( 002) and ( 200) planes have changed according the dopant level. This can be a reflection of a chemically inhomogeneous composition of the ceramics.

This results in the presence of various c/a ratios, which in turn affects the intensity and form of the peaks as well as the splitting of them.

Comparing the XRD patterns of doped ceramics (BT-A_2.5, BT-A_5, BT-B_2.5, and BT-B_5) it is possible to see that the influence of the Y 3+ over the BaTiO 3 structure is greater in the case of the BT-B ceramics. If the peak splitting at 45° -which evidences a tetragonal phase -of both groups of ceramics is compared then it is possible to see that the ones from the BT-B doped ceramics look more joined, being almost like if there was just one broaden peak. It can be considered that the dopant effect on these samples lattices is stronger. This behavior points out the strong interaction between additives and dopants present in the BT-B, which was also reflected in the density values as well as on the microstructure of these ceramics.

123

A summary of the observations for the thermally treated powders and sintered ceramics in air is shown in Table 4.5. x: no secondary phases were detected. N.S.: not sintered under these conditions.

BaTiO 3 ceramics sintered in reducing atmosphere

Ceramics from BT-A, BT-B and BT-C powders were sintered at 1310 °C during 3h, in a reducing atmosphere, and then underwent a re-oxidizing process. The ceramics sintered under this protocol were BT-A (A_0, A_1.5, A_2, A_2.5, A_5, A_20), BT-B (B_1, B_1.5, B_2, B_2.5, B_5, B_20), and BT-C (C_1, C_1.5, C_2).

With the purpose to detect differences among sintering steps (sintering in reducing atmosphere and re-oxidizing under a weekly oxidizing atmosphere), ceramics from each group were separated to perform analyses to both conditions, denominating them as "sint" and "reox" respectively. SEM analyses of some of the ceramics were also performed. In order to follow the dopant behavior into the BT-lattice, and detect any structural change during the different treatments, the main tool used in this work is the X-Ray Diffraction analysis.

BaTiO 3 ceramics issued from BT-A powders with Y 2 O 3 content from 0 to 20

wt%.

• Density

The effect of the dopant level was also observed under these sintering conditions. In the Table 4.6 are given the density values of BT-A ceramics, as well as in the Fig. 4.12. The densification for doped ceramics is lower and the values do not change significantly among the doped ceramics.

With these ceramics, the effect of the Y 2 O 3 content over their densification is noticeable, finding values between 60 -75 % for the doped ceramics. Regarding the possible differences between the density of the ceramics with same dopant level sintered in air and the ones sintered in a reducing atmosphere, in Fig. 4.13 is shown a comparison of the values. For the ceramics BT-A_0, BT-A_2.5, and BT-A_5 sintered under reducing atmosphere the density is higher than the one obtained when sintered in air. The density of the undoped ceramics is about the same under both sintering processes. Meanwhile, the BT-A_2.5 and BT-A_2.5 ceramics sintered in reducing conditions are 7% and 10% denser than the ones sintered in air. results from the Y 3+ ions incorporation into the BT lattice (Kim et al., 2008;Wang et al., 2014a;[START_REF] Wang | Microstructure and dielectric properties of BaTiO 3 ceramic doped with yttrium, magnesium, gallium and silicon for AC capacitor application[END_REF]. However, the incorporation of dopants results in a non-homogeneous distribution of these in the BT matrix during the sintering process. With the obtained patterns it is not possible to discriminate the c/a ratios corresponding to the range of 2θ that lead to the broadening of the peaks. Despite the changes in the lattice, the position of the BT planes was not shifted.

Moreover, in Fig. Finally, the XRD analyses of the BT-A_20 ceramics (Fig. 4.16.g) revealed the presence of secondary phases as well. Nonetheless, there are some differences among the BT-A_20_sint and BT-A_20_reox patterns. In the BT-A_20_sint diffraction pattern, peaks corresponding to Y 2 TiO 5 and Y 2 Ti 2 O 7 are observed. On the other hand, the BT-A_20_reox presents the Y 2 Ti 2 O 7 along with Y 2 O 3 . The differences found between the reduced and re-oxidized ceramics with respect to their secondary phases can be due to the formation of some Ti 4+ to Ti 3+ during the sintering and with the post-sintering annealing process it is reverted, leaving less available to form secondary phases.

Also, the lattice distortion and the formation of additional phases are related with the incorporation of Y 3+ ions into the BT-lattice. Since the Y 3+ ion has an intermediate size between Ba 2+ and Ti 4+ ions, it can occupy either A-or B-site in the BT crystal structure. In principle, Y 3+ will replace first Ba 2+ sites, but then if the activity increases on this site, it also replaces Ti 4+ ions, which could have contributed to the formation of Ti-rich precipitates. Another factor that could lead to the formation of these secondary phases is that the solubility limit of Y 2 O 3 in BT has been reached. A summary of the principal observations from the XRD analyses performed on BT-A ceramics sintered in reducing conditions is presented in Table 4.7. x: no secondary phases were detected.

BaTiO 3 ceramics issued from BT-B powders with Y 2 O 3 content from 1 to 20

wt%.

• Density

The density of the ceramics produced from the BT-B formulated powder, is shown in the Table 4.8.

The density increases slightly when BT-B ceramics are doped with 1.5 and 2 wt% of Y 2 O 3 , then from 2.5 up to 20 wt% it decreases rapidly. The variation of density with Y 2 O 3 content is plotted in Fig. 4.18, where it is seen that the density is clearly lower when Y 2 O 3 level is higher than 2 wt%.

The density values of BT-B ceramics (Table 4.8) are about 20% higher than the ones from the BT-A ceramics (Table 4.6). This was expected since the BT-B contains sintering additives that contribute to the improvement of the densification. In this case, the BT-B contains SiO 2 (0.30 wt%), which has been reported to contribute to the improvement of the densification process (Liu, & Roseman, 1999;Wu, Wang, McCauley, Chu, & Lu, 2007). A contrast between the density results obtained for the ceramics BT-B_1, BT-B_2.5, and BT-B_5 sintered under reducing atmosphere (Table 4.8) and the ones sintered in air (Table 4.6) is presented in the Fig. 4.18. This figure shows that the density of the ceramics sintered under the different atmospheres is different. For the BT-B_1 ceramics, the one sintered in air has higher density, but for the ceramics above this dopant level, the ones sintered in reducing conditions present higher densities. The BT-B_1 fired in air is 6 % denser than the BT-B_1 fired in reducing atmosphere.

While BT-B_2.5 and BT-B_5 sintered in air are about 3 % and 10 % respectively less dense than those sintered in reducing atmosphere. The value for BT-B_1.5_sint is 0.43 µm, 0.42 µm for BT-B_2_sint, and 0.41 µm for the BT-B_5_sint (Fig. 4.20). Thus, the grain size does not significantly change with the increase of Y 2 O 3 content. Indeed, the morphology of the grains is similar between the three samples, i.e., the three of them present agglomerations of spherical grains and also some grains with a more angular-bordered form (Fig. 4.19).

Despite the differences in the density values of these three ceramics, the SEM images show that they have a similar morphology and surface. Finally, for the BT-B_5 and BT-B_20 ceramics, the Ba 6 Ti 17 O 40 phase was identified (Fig. 4.18.e and Fig. 4.18.f). Also, in the BT-B_20 ceramics, peaks corresponding to the Y 2 O 3 phase are observed.

The precipitation of these different phases with respect to the Y 2 O 3 concentration in the samples can be given by the interaction among the BT-B matrix and the additives and dopants it contains; i.e., the Y 2 O 3 added to reach the specified doping concentrations.

In the case of the BT-B ceramics, it must be reminded that the raw powder contains a high content of Mg 2+ (0.29 %), while the BT-A being reagent grade is considered practically Mg-free. The formulated powder BT-C has a ratio of Mg 2+ of 0.0062 %. Since the Mg 2+ can substitute Ti 4+ -sites in the BT lattice (Wang et al., 2014a) it leads to the Ba-sites replacement by Y 3+ until the saturation in these sites is reached. Then the subsequent Y 3+ added will enter into the Ti 4+ -sites. The free Ti 4+

in the system will increase the possibility of secondary phases rich in Ti 4+ formation.

The BT-A and BT-B 20 wt% Y 2 O 3 -doped ceramics present different secondary phases. In BT-A_20

XRD patterns Y 2 Ti 2 O 7 and Y 2 TiO 5 are observed (Fig. 4.16.g), while in the ones from BT-B_20 ceramics the Ba 6 Ti 17 O 40 and Y 2 O 3 secondary phases were detected (Fig. 4.20.f). However, is seen that the higher the Y 3+ dopant level, the higher is the possibility of Ti-rich phases formation.

The raw powder composition must be taken into account at the time of discuss these differences.

Since chemical composition of the powders is different, the interactions of the Y 2 O 3 dopant are not the same with both BT matrixes. As aforesaid, the BT-B additives play a role on the final structural and microstructural ceramics properties. x: no secondary phases were detected.

BaTiO 3 ceramics issued from BT-C powders with Y 2 O 3 content: 1 to 2 wt%.

• Density

These ceramics discussed in this section are formed from another formulated powder. The composition of BT-C is different from the BT-B (Table 4.1). The main differences attending to the interests of next discussions are on the amount of Ca, Si, and Mg present in these powders, which are higher in the BT-B. A reminder of the concentration of these components in the formulated powders is presented in Table 4.10. The density values of BT-C ceramics are presented in the Table 4.11 and Fig. 4.22. The densification for these ceramics is above 90%. Although the marginally difference in the density, it was equal for BT-C_1.5 and BT-C_2, and lower for BT-C_1.

Comparing the density values of the BT-C and BT-B ceramics with the same Y 2 O 3 concentration (BT-B_1, BT-B_1.5, and BT-B_2), is possible to see that they are quite similar, being the ones of BT-B ceramics just about 1 % lower. This means that despite the difference in the SiO 2 content (being the double for the BT-B powder) the densification was not improved or diminished by it.

This leads to consider that is not just the SiO 2 which exerts an effect over the densification of BTdoped ceramics, but also the rest of additives present in the BT-formulated powders composition. •

Structure and phase composition

In the BT-C case, the doping concentrations are 1, 1.5 and 2 wt% Y 2 O 3 . The BT-C_1 ceramics (Fig. The pyrochlore Y 2 Ti 2 O 7 is detected in BT-C_1.5 and BT-B_2 ceramics. This secondary phase is also observed in the X-ray diffraction patterns of the ceramics issued from BT-B powders with same dopant concentrations. Also, it is worth to mention that apparently the presence of the Y 2 Ti 2 O 7 phase improves the densification (Fig. 4.17 and Fig. 4.22) probably because it has a lower melting point (1580 °C) than BaTiO 3 (1625 °C). Finally, a comparison of the characteristics of the different ceramics issued from BT-A, BT-B and BT-C powders and sintered in reducing atmosphere is presented. The density value of each group of ceramics is reported in Fig. 4.25 according to the dopant level. The BT-A_0 ceramic exhibited the highest density being close to the value for BT-B and BT-C ceramics with dopant level from 1 to 2 wt%. In fact, the density of this group of doped ceramics is roughly different, as can be observed in this figure . Regarding the ceramics issued from BT-A with the same dopant level, the density of them compared to the one of the BT-B and BT-C ceramics is considerably different, being 20 and 30 % respectively lower. Additionally, the density of BT-B ceramics with dopant level between 2.5 and 20 wt% is again higher than the one for the BT-A ceramics with the same Y 2 O 3 concentration.

However, there is a divergence in the behavior of the density as a function of the [Y 2 O 3 ] between BT-A and BT-B ceramics. First, the density of BT-A_1.5 and BT-A_2 is quite equal. Beyond this dopant concentration, it slightly increases and is practically the same for BT-A_2.5, BT-A_5, and BT-A_20. Otherwise, even when the BT-B_1.5 and BT-B_2 have fairly the same density, as in the BT-A case, the behavior of it beyond this dopant level is opposite to the observed in the BT-A ceramics. For these ceramics (BT-B_2.5, BT-B_5, and BT-B_20) the density values decrease when the concentration of Y 2 O 3 increases (although the density is rather the same for the three). Not with standing, it was determined that the densification was below 95% in all cases.

Moreover, the density of ceramics issued from the same powders but sintered under different atmosphere is also different. The ceramics sintered under reducing atmosphere present higher values than the ones fired in air. The atmosphere plays a role in densification mechanism. In fact, when samples are sintered in air, more oxygen vacancies are created which derive in larger volumes and therefore lower densities. The crystalline structure for all the ceramics obtained in this work is tetragonal. Nonetheless, the tetragonality of the BT is certainly decreased by the incorporation of Y 3+ ions. As a matter of fact, the increment of its concentration causes stronger modifications on the lattice parameters. In the same way, the introduction of the Y 3+ in the BT lattice promoted the formation of secondary phases.

Indeed, the high levels of doping used in this work were set with the intention to drive the system to it. Y 3+ replaces Ba 2+ and Ti 4+ sites and when the solubility limit in both sites is surpassed, secondary phases can be produced. Of course, the incorporation of Y 3+ is also markedly affected by the processing conditions and the composition of the raw BT. As seen in this work, the sintering atmosphere played a role in the formation of secondary phases. While in the ceramics fired in air, only the Y 2 O 3 is detected besides the BaTiO 3 phase. In the ceramics sintered under reducing conditions various phases besides those were identified. A recall of the phase composition for reduced ceramics is given in Table 4.12. The differences in the degree of secondary phases formation regarding the firing atmosphere are related with the higher degree of substitution of the RE ions when a reducing atmosphere is used. These conditions promote the formation of oxygen vacancies increasing the diffusion of the ions into the system, and leaving as well Ba 2+ and Ti 4+ ions free to react among them and with the excess of dopant, forming Ti-rich phases as the ones detected in this work. Therefore, even when no liquid phase was present during the sintering process, the surface diffusion of the ions contributed highly with the precipitation of additional phases. Also, we consider that the interaction of the additives with the BT-matrix and the sintering conditions favored the surface diffusion for above the volume diffusion because not significantly changes in the grain size of the samples were observed.

Regarding the composition of the raw BT powders, the interaction of the rest of the additives and dopants can influence the results too. The A-and B-sites can be replaced not only by the amphoteric Y 3+ ion but also by ions such as Ca 2+ and Mg 2+ , and their interactions will also affect the preference of a site by a specific atom. Their incorporation will also drive to an excess of ions such as the Ti 4+

in the system, so the formation of secondary phases will be promoted also by the presence of the metal elements. In fact, the compositional design of the formulated powders used in this work included Mg 2+ and Ca 2+ . The Mg 2+ has been reported to inhibit the grain growth because it tends to segregate at the grain boundaries, improving the coalescence during sintering. Also, when it acts together with RE ions contributes to the formation of the "core-shell" structure which is highly desired to accomplish the MLCC specifications (Huang et al., 2015;[START_REF] Wang | Microstructure and dielectric properties of BaTiO 3 ceramic doped with yttrium, magnesium, gallium and silicon for AC capacitor application[END_REF]. This will also require a careful control of the MgO/R 2 O 3 ratio and the firing parameters (Kishi et al., 2003).

In the same way, the Ca 2+ is used to improve the MLCC reliability by limiting the concentration of oxygen vacancies (Yoon et al., 2010). x: no secondary phases were discerned to the extent of the XRD detection limit.

Zhi, J., Chen, A., Zhi, Y., Vilarinho, P. M., & Baptista, J. L. (1999). Incorporation of yttrium in barium titanate ceramics. Journal of the American Ceramic Society, 82(5), 1345-1348.

temperatures range of 100 -200 °C when tested at 400 and 600 V. Meanwhile, the Group C present this behavior but in a much lower range of 20 -90 °C. This was reflected thorough the analyses of the time-to-failure (TTF) data using the Weibull distribution, since the plots obtained for these conditions presented a similar behavior. Then, it was possible to determine the activation energy (E a ) value for each set of testing conditions and it was found that at 400 V the Group A has the lower value of E a (1.06 0.08 eV) which indicates and confirms that the applied stress has lower effect over this Group compared with the Group B (E a = 1.25 0.05 eV) and the Group C (E a = 1.45 0.06 eV). Hence, when the electrical stress is 400 V, the Group C is expected to have the life time that will change more rapidly as the temperature changes. On the other hand, when a higher voltage was applied (600 V) even though the TTF observed were lower compared to the ones obtained at 400 V, the activation energy determined was not significantly different for the three groups. However, the values were found to be lower than for the testing conditions at 400 V in the cases of the Group B (E a = 1.09 0.02 eV) and the Group C (E a = 1.08 0.02 eV). The Group A a similar activation energy despite the higher electrical stress (E a = 1.01 0.09 eV), which once again can be an indication of its higher stability compared to the other two groups. Even though the failure mechanisms were not determined, with the determined values for the activation energy related to them is possible to say that since they are above the same for the three groups of samples, this could imply that despite their compositional differences and the way they are affected by the high values of stress, they fail under the same mechanism(s).

In general, the electrical characterization of MLCCs samples was possible, associating an E a value to the breakdowns and observing the influence of high stress values over the reliability of the samples. This part of the work also allowed us to set-up an in-house device that was completely developed at the LAPLACE laboratory and can be used for the performance of high accelerated life tests over MLCCs in an accurate way to obtain information about its expected life time to use it and relate it with the failure modes and the reliability of the samples. Also, bearing in mind that the this part, were the same that have been applied in the manufacturing of MLCCs pieces corresponding to the Groups B and C characterized in the first part. Thus, powders and ceramics with different Y 2 O 3 concentrations were prepared and subsequently thermally treated or sintered, respectively. Heat treatment of powders was conducted on air, while sintering of ceramics was carried out both, in air and reducing atmosphere. It was evidenced that the crystalline structure of

CHAPITRE 1 : Introduction bibliographique

Le titanate de baryum (BaTiO 3 ou BT) est un matériau ferroélectrique remarquable car il a une activité ferroélectrique élevée, une constante diélectrique et une polarisation spontanée (Li, Xu, Chu, Fu et Hao, 2009) et présente une résistivité élevée (1010-1012 Ω cm) (Belous, V '). yunov, Glinchuk, Laguta et Makovez, 2008). En en raison de sa constante diélectrique élevée, de ses faibles pertes diélectriques et de ses performances supérieures à haute fréquence, l'une de ses applications les plus courantes est le matériau diélectrique pour les condensateurs céramiques (Wang, Chen, Gui et Li, 2016). Parmi ces condensateurs céramiques, les condensateurs céramiques multicouches (MLCC) sont largement utilisés dans les applications militaires, automobiles et de télécommunication dans lesquelles les dispositifs sont soumis à des changements significatifs de température, de tension et de fréquence (Wang et al, 2001). Néanmoins, lorsque BaTiO 3 est pur, il se produit une grande variation de la constante diélectrique à proximité de la température de Curie (Tc), ce qui rend le matériau céramique inadapté aux applications de condensateur. Pour cette raison, les formulations à base de condensateur BT doivent être modifiées chimiquement pour répondre aux caractéristiques de température-capacité requises (X.H. Wang et coll., 2001;J. Wang et coll., 2016;T. Wang, 2009).

Le titanate de baryum

La structure cristalline de cet oxyde appartient au type pérovskite Cette structure lui permet de présenter une constante diélectrique élevée. Le BT pur présente une grande variation de la constante diélectrique près de la température de Curie (Tc) à 120 ° C (X. H. Wang et al, 2001). De nombreux efforts ont été déployés pour améliorer les propriétés électriques du titanate de baryum pour différentes applications. L'une des méthodes les plus courantes et les plus efficaces a consisté à modifier la formulation en insérant plusieurs additifs et dopants. La différence entre les additifs et les dopants n'est pas définie avec exactitude pour ce domaine d'étude. Cependant, on considère habituellement que les additifs contribuent à l'amélioration du processus de production alors que les dopants sont supposés avoir un impact direct sur les propriétés finales du matériau, c'est-à-dire les propriétés diélectriques. Dans ce travail, c'est cette définition que nous avons pris en compte.

Rôle de Y 2 O 3

La formulation de BaTiO 3 (BT) utilisée dans la fabrication des MLCC, doit être adaptée aux propriétés électriques, en particulier à haute température et sous champ électrique élevé (Ashburn & Skamser, 2008;Yoon, Park, Hong & Sinn, 2007). À cette fin, plusieurs additifs et dopants sont ajoutés à BaTiO 3 . L'un des dopants les plus utilisés est Y 2 O 3 , qui est ajouté dans le but de générer des mécanismes de compensation contribuant à améliorer la fiabilité des condensateurs.

Y 2 O 3 a un rayon ionique de 0,107 nm, il est intermédiaire entre celui de l'ion Ba 2 + (0,161 nm) et l'ion Ti 4 + (0,06 nm). Par conséquent, Y 3 + peut occuper le site cationique de Ba 2 + ou Ti 4 + dans le réseau BT (Wang et al., 2014;Tsur et al., 2001a). Cela permet à Y 3 + de se comporter comme accepteur ou donneur en fonction de la position dans le réseau. L'inclusion de l'ion Y3+ dans la structure BT dépend de facteurs cinétiques et thermodynamiques (Makovec et al., 2004). La pression partielle d'oxygène et la température de frittage induiront également la formation de lacunes Ba 2 + ou Ti 4 + , conduisant Y 3 + à occuper l'un ou l'autre des sites (Belous et al., 2005;Paredes-Olguín et al., 2013). Ceci sera également influencé par le rapport Ba / Ti, la concentration en dopant et sa solubilité. Les cations yttrium ont une solubilité différente dans les sites Ba et Ti. Zhi et al., (1999) ont indiqué une solubilité de Y 3 + au site Ba d'environ 1,5 at% lorsqu'ils étaient frittés sous air à 1440 -1470 ° C, alors qu'ils atteignaient 4% en cas de frittage dans des conditions réductrices (V'yunov, Kovalenko, Belous et Belyakov, 2005). Pour les sites Ti, la solubilité est plus élevée, environ 12,2% à 1515 ° C lors du frittage dans l'air. Wang et al. (2014) ont rapporté que l'introduction de Y 3 + dans le réseau BT peut entraîner des changements de structure, tels que la transformation de phase quadratique -cubique. Belous et al. (2008) (Hernández Lara et al., 2017). D'autre part, il existe de nombreux travaux où la formation de phases secondaires a été observée lors du dopage de BT avec des terres rares (REE) (Belous et al., 2008;Yoon et al., 2007;Zhang et al., 2016). ). La formation de ces précipités dépend de différents facteurs, à savoir les conditions de frittage et la concentration en dopant (M.T. Buscaglia, Viviani, M. Buscaglia, Bottino et Nanni, 2002). Ces phases secondaires sont généralement formées lorsque la quantité de dopant est supérieure à sa limite de solubilité dans le réseau BT. Cet excès de dopant peut entraîner son interaction avec d'autres ions libres présents dans le système, comme Ti 4 + . Ensuite, si les conditions sont appropriées, un précipité se forme. Certaines des phases secondaires observées sont Ba 2 TiSi 2 O 8 (Wu, Wang, McCauley, Chu et Lu, 2007), Ba 6 Ti 17 O 40 (Belous et al., 2008), Y 2 TiO 5 (Yoon et al., 2007) (Jeong et al., 2005). Parmi les pyrochlores, Er2Ti2O7 (Buscaglia et al., 2002), Gd 2 Ti 2 O 7 (Hernández Lara et al., 2017), Ho 2 Ti 2 O 7 (Makovec et al., 2004) et Y 2 Ti 2 O 7 (Yoon et al., 2007;Zhang et al., 2016) ) a été reporté. Y 2 Ti 2 O 7 est suspecté de nuire à la fiabilité des MLCC basées sur BT (Yoon et al., 2007;Zhang et al., 2016). L'effet de la présence de ces phases secondaires sur les propriétés structurales et diélectriques de BaTiO 3 présente un grand intérêt pour les applications industrielles. Plusieurs auteurs ont rapporté un effet néfaste de Y 2 Ti 2 O 7 sur les performances diélectriques de BT (Wu et al., 2007;Yoon et al., 2007;Zhang et al., 2016). Le pyrochlore à base d'yttrium (Y 2 Ti 2 O 7 ) est de nature hautement conductrice et est suspecté d'être lié à la dégradation de résistance du matériau par l'accélération de l'électromigration des lacunes d'oxygène (Zhang et al., 2016). L'étude des paramètres de formation et des effets possibles de cette phase présente un grand intérêt dans le domaine académique et industriel, Y 2 O 3 étant l'un des dopants les plus fréquemment utilisés dans la production des MLCC.

Influence de l'atmosphère de frittage sur la répartition des dopants dans les céramiques dopées au BT

L'un des paramètres les plus importants pour obtenir un matériau BT ayant les propriétés appropriées pour son application en tant que diélectrique est la pression partielle d'oxygène (PO 2 ) pendant le traitement de frittage. PO 2 affecte l'incorporation de dopants dans le réseau BT (Buscaglia et al., 2002;Tsur et al., 2001b). L'occupation de site des dopants dans le réseau BT est limitée par la valence de l'ion, sa taille, le rapport A / B (c'est-à-dire l'activité de Ti dans le système) et par la concentration en lacunes d'oxygène. Il a été observé que PO 2 influence les mécanismes de compensation de charge (ioniquement ou électroniquement), imposant une modification du rapport A / B dans le réseau pérovskite, ce qui peut entraîner la formation de précipités. De plus, les changements induits par le PO 2 affectent significativement le comportement électrique (Fu et al., 2008).

Condensateurs céramiques multicouches (MLCC)

Au cours des dernières décennies, la conception des appareils électroniques a été axée sur la miniaturisation et la réduction de la consommation d'énergie. Cette tendance nécessite une grande fiabilité pour les composants électroniques (Shimada, Utsumi, Yonezawa et Takamizawa, 1981). Les condensateurs céramiques multicouches (MLCC) figurent parmi les éléments électroniques les plus importants (Fig. 1). Ils présentent un rendement volumétrique économique pour la capacité et une grande fiabilité. Les MLCC sont caractérisées par une constante diélectrique élevée (K) et des couches diélectriques plus fines (Jain, Fung, Hsiao et Chan, 2010). Selon l'application, les MLCC peuvent être divisés en deux types: pour la compensation de température et pour la constante diélectrique élevée.

Les MLCC pour une constante diélectrique élevée utilisent le titanate de baryum comme composant diélectrique. Parmi ce type de condensateurs, le X7R est le plus stable, couvrant un large spectre d'applications. (Liu, 2015). Ces modes de défaillance peuvent être distingués à l'aide d'un tracé de Weibull à 2 paramètres. Les défaillances précoces (catastrophiques) peuvent être distinguées par un paramètre de pente de β> 1.

Cette valeur de β indique qu'il ne s'agit pas de mortalités infantiles (Liu et Sampson, 2012).

Les défaillances précoces ont été liées à la diminution de l'épaisseur du diélectrique, provoquée par une contrainte électrique externe. Cela a représenté un problème pour contrôler une haute fiabilité avec la miniaturisation des MLCC. Le courant de fuite en cas de panne qui caractérise une défaillance précoce est de type avalanche (Liu et Sampson, 2012). Comme mentionné précédemment, ces défaillances sont liées à des défauts extrinsèques, à savoir des défauts de construction mineurs introduits pendant la fabrication des condensateurs, le contrôle de la production et les exigences de qualité sont un facteur crucial pour obtenir un produit final fiable. Il a été rapporté que la dégradation de la résistance d'isolement des BME-MLCC à base de BT pourrait être liée à trois aspects probables: la couche diélectrique, les joints de grains BT et les interfaces d'électrodes internes entre Ni-BaTiO 3 (Liu, 2015).

Introduction

Les condensateurs doivent conserver leurs propriétés dans une certaine tolérance dans une large gamme de températures au cours de leur vie. Le dopage reste la stratégie adéquate pour adapter les propriétés diélectriques de la couche diélectrique à l'application cible, en particulier pour une utilisation en température élevée dans des champs électriques élevés. (Ashburn et Skamser, 2008;[START_REF] Paunović | The effects of additive on microstructure and electrical properties of BaTiO 3 ceramics[END_REF]. Étant donné que la fiabilité est un paramètre essentiel dans la conception de l'électronique, les fabricants de composants en tiennent compte à travers différents paramètres. L'évaluation de la fiabilité peut être très précise à travers l'analyse périodique des produits en service et en tenant compte des produits défaillants, mais elle n'est pas prédictive et prend beaucoup de temps.

Résultats et discussion

La capacité à température ambiante (Fig. 3.1) pour trois compositions est très similaire, autour de 0,1 µF en dessous de 104 Hz avec des pertes diélectriques similaires. La classification X7R spécifie que les valeurs de capacité doivent se situer dans une plage de 15% lorsque le condensateur est exposé à une variation de température entre -55 ° C et +125 ° C. La figure 3.2 montre l'impact de la température dans les valeurs de capacité à 1 kHz.

Figure 3.1. Variation de la capacité et des pertes diélectriques des trois types de MLCC en fonction de la fréquence Les valeurs numériques des énergies d'activation doivent être liées au mécanisme de défaillance de la rupture diélectrique dans les conditions de contrainte. Néanmoins, il existe peu d'informations dans la littérature disponible pour établir cette corrélation. Des valeurs d'énergie d'activation de 1,9 eV ont été associées à un mode de claquage par avalanche (Liu, 2012); pour une défaillance activée par la chaleur, elle peut être comprise entre 1,25 et 1,42 eV [START_REF] Nomura | [END_REF]) (Rowal, 1984). D'autres auteurs proposent qu'une dégradation thermique dans l'Ea de la MLCC soit comprise entre 1 et 2 eV. En outre, des valeurs comprises entre 1,3 et 1,5 eV ont été décrites comme étant liées à l'usure diélectrique de la capacité diélectrique à base de BaTiO 3 (Yoon, 2009). [START_REF] Chazono | DC-electrical degradation of the BT-based material for multilayer ceramic capacitor with Ni internal electrode: impedance analysis and microstructure[END_REF] indiquent que les lacunes en oxygène migrent sous l'influence du champ électrique élevé appliqué lors des essais HALT. [START_REF] Yoon | Analysis the reliability of multilayer ceramic capacitor with inner Ni electrode under highly accelerated life test conditions[END_REF] ont suggéré que lorsque les lacunes étaient accumulées à l'interface de l'électrode, un mécanisme de conduction de Frowler Nordhem (tunneling) pourrait être induit et favoriser la dégradation de la couche diélectrique en raison de l'augmentation locale de la conductivité. Les énergies d'activation dans la gamme de 1-2 eV se situent raisonnablement dans l'intervalle de Ea requis pour les mobilités de lacunes d'oxygène (Chan, 1981) (Han, 1987). Dans cette étude, un dopage plus élevé avec du calcium a eu un impact significatif sur le délai d'échec des échantillons MLCC-2, à tel point qu'il n'était plus possible de réaliser le test à des tensions élevées. Le calcium a été signalé comme élément dopant accepteur dans BaTiO 3 . Bien que cela puisse d'une part augmenter la résistivité globale de la céramique (Han, 1987) x: no secondary phases were detected. BT-A_20 and BT-B_20 ceramics were not sintered under these conditions. A 400 V, le groupe A a la valeur la plus faible de Ea (1,06 ± 0,08 eV). le stress a un effet plus faible sur ce groupe que le groupe B (Ea = 1,25 ± 0,05 eV) et le groupe C (Ea = 1,45 ± 0,06 eV). Par conséquent, lorsque la contrainte électrique est de 400 V, le groupe C devrait avoir la durée de vie qui changera plus rapidement si la température évolue. En revanche, lorsqu'une tension plus élevée a été appliquée (600 V), même si les TTF observés étaient inférieurs à ceux obtenus à 400 V, l'énergie d'activation déterminée n'était pas significativement différente pour les trois groupes. Cependant, les valeurs étaient inférieures à celles des tests à 400 V dans le groupe B (Ea = 1,09 ± 0,02 eV) et dans le groupe C (Ea = 1,08 ± 0,02 eV). Le groupe A possède une énergie d'activation similaire malgré le stress électrique plus élevé (Ea = 1,01 ± 0,09 eV), ce qui peut encore une fois être une indication de sa plus grande stabilité par rapport aux deux autres groupes. Même si les mécanismes de défaillance n'ont pas été déterminés, avec les valeurs déterminées pour l'énergie d'activation qui leur est associée, il est possible de dire qu'étant au-dessus des trois groupes d'échantillons, cela pourrait impliquer que malgré leurs différences de composition et leur sont affectés par les valeurs élevées de stress, c'est le même mécanisme qui conduit à leur dégradation. Cette partie du travail a pu être réalisée grâce à un dispositif entièrement développé par le laboratoire LAPLACE et pouvant être utilisé pour effectuer des tests de vie accélérés sur des MLCC de manière précise afin d'obtenir des informations sur sa durée de vie prévue. De plus, sachant que les principales différences entre ces groupes de condensateurs sont la composition du matériau diélectrique, à savoir la quantité d'additifs et de dopants, ces résultats ont fourni des informations confirmant que les échantillons auront des propriétés différentes en fonction de la composition de la formulation de céramique diélectrique. L'étape suivante de l'étude a consisté à évaluer la possibilité de formation de phases secondaires due à la présence de Y 2 O 3 en tant que dopant. Comme ce n'est pas le seul dopant trouvé dans la formulation diélectrique MLCC, le rôle de Y 2 O 3 en tant que dopant a été évalué dans des poudres BT pure et deux poudres BT formulées industriellement dans le but d'étudier les interactions possibles entre les différents dopants. Des poudres et des

Figure 1 . 1 .

 11 Figure 1.1. Scheme of the BaTiO 3 perovskite structure. A) Cubic lattice (above Curie temperature, 120°C). B) Tetragonal lattice (below Curie temperature, 120°C).(Richerson,2005). ....................................................... 23

Figure 2 .

 2 Figure 2.2. (A) Experimental set-up: (1) probe station Signatone S-1160; (2) heating chuck, Signatone model S-1060R; (3) sourcemeter unit Keithley 2410. (B) Enlarged view of the MLCC under test. ........................... 51

Figure 2 . 4 .Figure 2 . 5 .

 2425 Figure 2.4. (a) Plate with the protective resistors (1) connected in series with each sample; (b) View of an MLCC (1) inside the glass capillary (2) together with a spring (3); (c) View of the assembled connections (cables + springs) together with the MLCCs in the metallic plate interior canals; (d) Enlarged view of the interior of the cell, where red arrows highlight the samples inside of a glass capillary. ................................. 54

Figure 2 . 6 .

 26 Figure 2.6. Representation of the data acquired in a HALT experiment. (A) Insulation resistance measurements at 600 V and 130 °C. (B) Insulation resistance measurements at 400 V and 170 °C. .............. 56 Figure 2.7.

Figure 2 . 10 .

 210 Figure 2.10. Manual hydraulic press and pressing die during the making of green ceramics........................ 62

Figure 2 . 12 .

 212 Figure 2.12. Representation of the sintering program at industrial level. ....................................................... 65

Figure 3 . 4 .Figure 3 . 5 .

 3435 Figure 3.4. Correlation of the time-to-failure for the failures of each group of MLCCs. HALT conditions: 400 V and temperature indicated on the plots. (a) Group A, (b) Group B and (c) Group C. .................................. 77

Figure 3 . 9 .

 39 Figure 3.9. Changes in the scale parameter of Group A as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section. ......... 88

Figure 3 . 13 .

 313 Figure 3.13. Changes in the scale parameter of Group C as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section. ......... 93

Figure 4 . 6 .Figure 4 . 8 .

 4648 Figure 4.6. Density of the ceramics sintered in air as a function of Y 2 O 3 concentration. .............................. 119 Figure 4.7. SEM images from (a) BT-A_2.5 and (b) BT-A_5 ceramics sintered in air. Scale bar: 1µm. ...... 120 Figure 4.8. Size distribution of (a) BT-A_2.5 and (b)

Figure 4 . 12 .

 412 Figure 4.12. Density of BT-A ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content. ... 125

Figure 4 . 17 .

 417 Figure 4.17. Density of BT-B ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content. ... 133

Figure 4 .

 4 Figure 4.22. Density of BT-C ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content. .. 141

Figure 4 . 26 .

 426 Figure 4.26. Density values of ceramics sintered in reducing atmosphere at 1310 °C as a function of Y 2 O 3 in the starting powder. ........................................................................................................................................ 146

  particularly those related to Y 2 O 3 doping, are believed to be responsible for the long-term failure mechanisms of MLCC's under nominal operation. This thesis work has the objective to analyze the role of Y 2 O 3 as BaTiO 3 dopant and its possible contribution to the formation of secondary phases. The achievement of this objective involves two experimental blocks. First, the electrical characterization of MLCCs with Y 2 O 3 -doped BaTiO 3 as dielectric by the performance of high accelerated life tests (HALT) that lead to obtain life indicators. Secondly, the development of a doping study that includes the preparation of powders and ceramics under different sintering conditions using Y 2 O 3 as dopant and two kinds of BaTiO 3 powders (one pure and two formulated for industrial applications).

Figure 1 . 1 .

 11 Figure 1.1. Scheme of the BaTiO 3 perovskite structure. A) Cubic lattice (above Curie temperature, 120°C). B)

Figure 1 . 2 .

 12 Figure 1.2. Transmission electron micrographs of core-shell structures in doped BT ceramics. (A) TEM bright field image of a X7R-type BaTiO 3 ceramics byGrogger, Hofer, Warbichler, Feltz, & Ottlinger, (1998).

  through TEM analyses as shown in Fig. 1.3.

Figure 1

 1 Figure 1.3. (a) Glassy second phase at triple-grain junction with selected area diffraction patterns of BaTiO 3 grain inset (BF image), (b) high-resolution image of BaTiO 3 -glass interface showing an amorphous nature,

Figure 1 . 4 .

 14 Figure 1.4. Basic structure of a multilayer ceramic capacitor.

Figure 1 . 5 .

 15 Figure 1.5. MLCCs production process. Adapted from Basics of Ceramic Chip Capacitors by Johanson Dielectrics. 2008.

Figure

  Figure 2.1. X7R MLCC

Figure 2

 2 Figure 2.2. (A) Experimental set-up: (1) probe station Signatone S-1160; (2) heating chuck, Signatone model S-1060R; (3) sourcemeter unit Keithley 2410. (B) Enlarged view of the MLCC under test.

  2.3). A voltage source (1 kV-10 mA) (MPS1P10/24, Spellman, Hauppauge, NY, USA) (Fig. 2.3A) was connected to a parallel array (Fig. 2.3B) of capacitors placed inside a thermally stabilized hotplate (Fig. 2.3C), and the temperature was measured with a thermocouple and kept at a uniform value (Fig. 2.3D).

Figure 2 . 3 .

 23 Figure 2.3. System for perform HALT over multiple samples at once. (A) HV power supplier (1 kV -10 mA). (B) Plate with protective resistors in parallel to connect the samples that are inside (C) a metallic cell placed over a heating plate which temperature is monitored with (D) a multimeter reading the measurements of a thermocouple (K type).

2. 4

 4 .b-1) and avoid welding, they were placed inside a capillary glass (Fig.2.4.b-2) and pressed with a spring test probe (RS Pro 1.27mm Pitch Spring Test Probe with Point Tip) (Fig.2.4.b-3), which ensured both the electrical contact and the mechanical support of the sample. The glass tubes with the samples and springs were placed inside an aluminum block to maintain thermal homogeneity (Fig.2.4.c-d). The aluminum block also served as the electrical ground. The heating plate temperature was fixed and measured with a thermocouple (K-type), which was inserted inside a glass tube in the aluminum block. The temperature was always kept below 280 °C, which takes into account the melting temperature (296-300 °C) of the solder material used to assemble the springs with the connecting cables. When the set-up was ready (Fig.2.5) and the desired temperature reached, the electrical stress was applied.

Figure 2 . 4 .

 24 Figure 2.4. (a) Plate with the protective resistors (1) connected in series with each sample; (b) View of an MLCC (1) inside the glass capillary (2) together with a spring (3); (c) View of the assembled connections (cables + springs) together with the MLCCs in the metallic plate interior canals; (d) Enlarged view of the interior of the cell, where red arrows highlight the samples inside of a glass capillary.

Figure 2 . 5 .

 25 Figure 2.5. Upper view of the set-up. a. Metallic cell closed (with the samples inside) above the heating plate. b. Plate with protective resistors.

Figure 2 . 6 .

 26 Figure 2.6. Representation of the data acquired in a HALT experiment. (A) Insulation resistance measurements at 600 V and 130 °C. (B) Insulation resistance measurements at 400 V and 170 °C.

Fig. 2

 2 Fig. 2.7. Powders and ceramics were deposited on a circular sample holder in poly-(methyl

Figure 2

 2 Figure 2.7. X-ray Diffractometer Bruker D4 Endeavor.

Figure 2

 2 Figure 2.8. XRD patterns of BaTiO 3 starting powders. JCPDS: 89-1428.

Figure 2 . 9 .

 29 Figure 2.9. SEM images of (a) BT-A and (b) BT-B powders. Particles size: BT-A: 0.48 -1.25 µm; BT-B: 0.46 -0.81 µm. Scale bar: 5 µm.

Figure 2 .

 2 Figure 2.10. Manual hydraulic press and pressing die during the making of green ceramics.

Figure 2 .

 2 Figure 2.11. Sintering program A: Two-steps sintering program in air. (BT-A and BT-B ceramics undoped and with 2.5 and 5 wt% of Y 2 O 3 ).

Figure 2 .

 2 Figure 2.12. Representation of the sintering program at industrial level.

Figure 2 .

 2 Figure 2.13. Thermal program for powders treated in air.

Figure 3 . 1 .

 31 Figure 3.1. Current evolution of Groups A and B during HALT experiment at standard conditions (400 V, 140 °C).

Figure 3 . 2 .

 32 Figure 3.2. Resistance evolution of individual MLCCs from (a) Group A, (b) Group B, and (c) Group C during HALT performed with 400 V and different temperatures.

Figure 3 . 3 .

 33 Figure 3.3. Comparison of the TTF and current evolution for MLCCs from Groups A and B when tested under HALT standard conditions (400 V, 140 °C).

Figure 3 . 4 .

 34 Figure 3.4. Correlation of the time-to-failure for the failures of each group of MLCCs. HALT conditions: 400 V and temperature indicated on the plots. (a) Group A, (b) Group B and (c) Group C.

Figure 3 . 5 .

 35 Figure 3.5. Comparison of the TTF for MLCCs from (a) Group A, (b) Group B, and (c) Group C. HALT conditions: 400 V, temperature indicated on the plots.

Figure 3 . 7 .

 37 Figure 3.7. Comparison of the TTF for MLCCs from (a) Group A, (b) Group B, and (c) Group C. HALT conditions: 600 V, temperature indicated on the plots.

  3.8.a and Fig. 3.8.b show the life data points of MLCCs of the Group A, at 400 V and 600 V, respectively. Data was statistically analyzed and fitted according a Weibull distribution.As seen in figures 3.18.a and 3.18.b the data fit properly with a Weibull distribution, showing an analogous behavior between the different temperatures; i.e. straight lines are obtained at different temperatures and are approximately parallel between them. Nevertheless, a different behavior of the distribution is observed for temperatures higher than 200 °C.

Figure 3 . 8 .

 38 Figure 3.8. Weibull plot for Group A. HALT conditions: (a) 400 V, 140 -230 °C and (b) 600 V, 140 -220 °C.

Figure 3 . 9 .

 39 Figure 3.9. Changes in the scale parameter of Group A as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section.

Figure 3 . 11 .

 311 Figure 3.11. Changes in the scale parameter of Group B as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section.

Figure 3 . 13 .

 313 Figure 3.13. Changes in the scale parameter of Group C as a function of the HALT temperature. The temperatures delimited by the dashed lines were considered for the Arrhenius plot in the next section.

Figure 3 . 14 .

 314 Figure 3.14. Characteristic life according the Arrhenius model for MLCCs from (a) Group A, (b) Group B, and (c) Group C according the electrical and thermal stress. Solid lines represent the best fits given by equation (3).

Ba 6

 6 Ti 17 O 40 and Y 2 Ti 2 O 7 as secondary phases. The pyrochlore phase Y 2 Ti 2 O 7 was evidenced byYoon et al. (2007) andZhang et al. (2016) and they suspected that these phases are detrimental to the reliability of BaTiO 3 -based MLCCs.In this work, the role of Y 2 O 3 was evaluated on two kinds of raw materials. The first one is pure BaTiO 3 while the second material is a commercial formulation designed for MLCCs of X7R type (-55 °C and 125 °C, 15% tolerance) which among other elements, already contains 1.05 wt% of Y 2 O 3 .Powders and ceramics with different Y 3+ doping concentrations (1 up to 20 wt%), as Y 2 O 3 , were prepared and subsequently thermally treated or sintered, respectively. The aim was to investigate the structural changes of BaTiO 3 induced by the doping with Y 2 O 3 and to promote the formation of secondary phases.

  reagent grade (pure). **: BT commercially formulated.

Figure 4 . 1 .

 41 Figure 4.1. SEM images of BaTiO 3 undoped raw powders and the respectively 5 wt% Y 2 O 3 -doped and thermally treated powders. (a) BT-A_0, (b) BT-A_5TT, (c) BT-B_1 (d) BT-B_5TT powders. Scale bar: 1µm

Figure 4 . 2 .

 42 Figure 4.2. Variation of 2θ according the c/a ratio value, based on the cubic lattice 3.996 Å, for the planes (002).

Figure 4

 4 Figure 4.3. X-ray diffraction patterns of raw BaTiO 3 powders. JCPDS: 89-1428.

Figure 4

 4 Figure 4.4. X-ray diffraction patterns of thermally treated (1350 °C) undoped BaTiO 3 and Y 2 O 3 -doped BaTiO 3 (2.5, 5.0 and 20.0 wt%) powders. Powders issued from (a) BT-A and (b) BT-B.

Figure 4 . 5 .

 45 Figure 4.5. Enlargement in the zone around 45° for X-ray diffraction patterns of thermally treated (1350 °C) undoped BaTiO 3 and Y 2 O 3 -doped BaTiO 3 (2.5, 5.0 and 20.0 wt%) powders.

Figure 4 . 6 .

 46 Figure 4.6. Density of the ceramics sintered in air as a function of Y 2 O 3 concentration.

Figure 4 . 9 .

 49 Figure 4.9. SEM images from (a) BT-B_1 and (b) BT-B_5 ceramics sintered in air. Scale bar: 1µm.

Figure 4 . 10 .

 410 Figure 4.10. Mean size distribution of (a) BT-B_1 and (b) BT-B_5 ceramics sintered in air.

Fig. 4 .

 4 Fig. 4.11 shows the X-ray diffraction patterns of the air-sintered ceramics. The patterns from the

Figure 4 .

 4 Figure 4.11. X-ray diffraction patterns of undoped BaTiO 3 and 2.5 and 5.0 wt% Y 2 O 3 -doped BaTiO 3 ceramics. Ceramics formed from (a) BT-A and (b) BT-B, sintered in air.

Figure 4 .

 4 Figure 4.12. Density of BT-A ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content.

Figure 4 .

 4 Figure 4.13. Comparison of the BT-A ceramics density sintered using air or reducing atmosphere as a function of Y 2 O 3 content.

Figure 4 .

 4 Figure 4.14. SEM images from BT-A ceramics sintered in reducing atmosphere. (a) BT-A_5_sint, (b) BT-A_5_reox, and (c) BT-A_20_sint. Scale bar: 1µm.

Figure 4 . 15 .

 415 Figure 4.15. Size distribution of BT-A ceramics sintered in reducing atmosphere. (a) BT-A_5_sint, (b) BT-A_5_reox, and (c) BT-A_20_sint.

  4.16.d an additional peak at 2θ = 30.6° is noticed both, sintered and reoxidized ceramics, which corresponds to the cubic pyrochlore compound Y 2 Ti 2 O 7 (JCPDS: 42-0413). This compound has also been evidenced before by other authors like Belous et al. (2008), Yoon et al. (2007), and Zhang et al. (2016). The diffractograms of the 2.5 wt% Y 2 O 3 -doped BT-A ceramics (Fig 4.16.e.) also reveal the presence of a secondary phase. A peak of weak intensity at 29.5° is detected and identified as the yttrium titanate Y 2 TiO 5 (JCPDS: 40-0795) phase. The BT-A_5 ceramics (Fig 4.16.f.) present peaks that correspond to the phases Y 2 O 3 and Y 2 Ti 2 O 7 .

Figure 4 .

 4 Figure 4.16. XRD patterns of BT-A powder and ceramics sintered in reducing atmosphere and re-oxidized. Lateral enlargements of zone around 45° are presented for doped samples.

Figure 4 . 17 .

 417 Figure 4.17. Density of BT-B ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content.

Figure 4 . 18 .

 418 Figure 4.18. Comparison of the BT-B ceramics density sintered using air or reducing atmosphere as a function of Y 2 O 3 content.

Figure 4 .

 4 Figure 4.19. SEM images from BT-B ceramics sintered in reducing atmosphere. (a) BT-B_1.5_sint, (b) BT-B_2_sint, and (c) BT-B_5_sint. Scale bar: 1 µm.

Figure 4 . 20 .

 420 Figure 4.20. Mean size distribution of BT-B ceramics sintered in reducing atmosphere. (a) BT-B_1.5_sint., (b) and (c)

Figure 4

 4 Figure 4.22. Density of BT-C ceramics sintered in a reducing atmosphere as a function of Y 2 O 3 content.

Figure 4 .

 4 Figure 4.23. SEM images from BT-C ceramics sintered in reducing atmosphere. (a) BT-C_1.5_sint, (b) BT-B_2_sint. Scale bar: 1 µm.

Figure 4 . 24 .

 424 Figure 4.24. Size distribution of BT-C ceramics sintered in reducing atmosphere. (a) BT-C_1.5_sint., and (b) BT-C_2_sint.

  4.25.a) crystallize in the tetragonal phase. No secondary phase or phase transitions are observed. The structure does not vary with the post-sintering conditions. In the case of BT-C_1.5 (Fig. 4.25.b) and BT-C_2 (Fig. 4.25.c) ceramics, the XRD analyses evidence the decrease of the tetragonality. The enlargements of peaks around 45° show how the (002) peak becomes less intense and seem to be joined with the (200).

Figure 4 .

 4 Figure 4.25. XRD patterns of BT-C powder and ceramics sintered in reducing atmosphere and re-oxidized. Lateral enlargements of zone around 45° are presented.

Figure 4 .

 4 Figure 4.26. Density values of ceramics sintered in reducing atmosphere at 1310 °C as a function of Y 2 O 3 in the starting powder.

  BaTiO 3 can be affected by the Y 3+ presence either in powders or ceramics, being more noticeable when Y 3+ doping level increases. Also, under some conditions, the formation of secondary phases was promoted, being identified the Ba 6 Ti 17 O 40 , Y 2 TiO 5 and Y 2 Ti 2 O 7 . These results provide an insight about the behavior of Y 3+ when it is used as BaTiO 3 dopant in high levels. Plus, it the results provide clear evidence that the interactions among additives used in a commercial formulation are quite important and play a role in the final properties and the formation of secondary phases as well.This work evidences that the BT-based formulations for dielectric applications are very sensitive to the most slightly changes in its compositions and this can lead to important changes of the final properties of the material and the reliability of the same. Other perspectives may be considered in order to have a more accurate study to describe the real role of other additives and dopants and especially the interactions they may have in real systems under the conditions used in their different applications. Performing an electrical characterization of the MLCCs samples used in this work aiming to determine its failure mechanism(s) could give interesting information about the properties of the dielectric material.

Figure 1 .

 1 Figure 1. Structure de base d'un condensateur céramique multicouche.

CHAPITRE 2 :

 2 Méthodes expérimentalesDans ce chapitre, nous présentons les différentes techniques analytiques utilisées pour la caractérisation des échantillons ainsi que le montage expérimental effectué tout au long de ce travail. D'abord, la caractérisation des condensateurs céramiques multicouches sera présentée, puis la préparation et la caractérisation des poudres et céramiques BaTiO 3 dopées Y 2 O 3 .2.1. Protocole HALT (High Accelerated Life Test) pour les mesures individuelles I-VPour mettre en place les conditions adéquates pour effectuer correctement un HALT en interne, il était nécessaire de connaître le comportement des trois groupes de condensateurs. De cette manière, des mesures de dégradation de la résistance au cours du temps, sous une valeur de tension élevée fixe et différentes températures pour couvrir une large gamme pouvant fournir les informations requises, ont été effectuées. Les mesures électriques ont été effectuées sur un échantillon à la fois dans une station de sonde Signatone S-1160 à l'aide d'un système de mandrin à chaud de haute précision (modèle Signatone S-1060R QuieTemp DC) (résolution de 1 ° C et pouvant fonctionner jusqu'à 300 ° C) et une source / moniteur CC d'unité de mesure de source (SMU) 2410 Keithley (tension source de 5 µV à 1100 V; mesure de la tension de 1 µV à 1100 V). Cette configuration expérimentale est illustrée sur la Fig.2.1. Pour commencer, une HALT a été réalisée dans des conditions industrielles standard: 400 V et 140 ° C pendant 24 h. Dans ce travail, le test a été arrêté lorsque 24 h se sont écoulés sans défaillance ou au moment où l'échantillon a subi une panne. De plus, les HALT ont été conduits sous la même valeur de tension mais en utilisant des températures différentes pour observer le comportement à des valeurs supérieures et inférieures à 140 ° C.

Figure 2

 2 Figure 2.1. (A) Installation expérimentale: (1) station de sonde S-1160, (2) modèle Signatone S-1060R QuieTemp, (3) SMU Keithley 2410. (B) Vue agrandie de la MLCC testée.

Figure 3 . 2 .

 32 Figure 3.2. Variation de la capacité des trois types de MLCC en fonction de la température (f=1 kHz).

Figure 3

 3 Figure 3.3. Variation de la résistance d'une MLCC-2 à des températures inférieures à 80 ° C et à 400 V.

Figure 3 . 4 .

 34 Figure 3.4. Exemple d'un tracé de Weibull pour les MLCC1 testés dans une large gamme de températures et de différentes contraintes électriques: (a) : 400 V

Figure 3 . 5 .

 35 Figure 3.5. Durée de vie caractéristique selon le modèle d'Arrhenius pour (a) MLCC-1 en fonction du stress électrique et thermique. Discussion sur les énergies d'activation

  Morphologie et taille des particules Les images MEB des poudres BaTiO3 non dopées, BT-A_0 et BT-B_1, sont représentées sur les figures 4.1.a et 4.1.c respectivement. Les deux poudres présentent des particules présentant une morphologie à facettes grossières. Deux tailles de particules sont observées, une plage de 0,48 μm et 1,25 μm pour BT-A_0, et de 0,46 μm et 0,81 μm pour BT-B_1. La valeur de taille moyenne des particules de BT-B_1 est sensiblement inférieure à celle des particules BT-A_0. Cette légère différence est probablement liée au traitement donné à la poudre formulée pour remplir la taille de particule requise pour son utilisation dans le processus de production des MLCC. Après traitement thermique à haute température, les images MEB des poudres dopées à l'Y 2 O 3 BT-A_5TT et BT-B_5TT (Fig. 4.1.b et Fig. 4.1.d) montrent des particules plus arrondies et définies, comparées aux particules non traitées thermiquement, poudres non dopées (Fig. 4.1.a et Fig. 4.1.c, respectivement). La taille moyenne des grains est similaire pour les deux poudres, respectivement 0,58 µm et 0,53 µm. Certains agrégats sont observés, probablement en raison d'un début de frittage.

Figure 4

 4 Figure 4.1. Images MEB de poudres brutes de BaTiO 3 et des poudres dopées à 5% massique de Y 2 O 3 et traitées thermiquement. (a) BT-A_0, (b) BT-A_5TT, (c) BT-B_1 (d) BT-B_5TT. Barre d'échelle: 1 μm

Figure 4 . 2 .

 42 Figure 4.2. Densité des céramiques frittées sous air en fonction de la concentration en Y 2 O 3 .

4. 2

 2 .1.BaTiO 3 frittée sous atmosphère réductrice Dans le souci d'être concis, nous présentons dans le tableau 4.3 l'ensemble des principales observations issues des analyses XRD effectuées sur les céramiques BT-B frittées dans des conditions réductrices Tableau 4.3. Phases secondaires détectées dans les céramiques BT-B frittées sous atmosphère réductrice à 1310 ° C. secondary phases were detected.Enfin, une comparaison des caractéristiques des différentes céramiques issues des poudres BT-A, BT-B et BT-C et frittées en atmosphère réductrice est présentée (figure4.3). La céramique BT-A_0 présente la densité la plus élevée, proche de la valeur pour les céramiques BT-B et BT-C avec un niveau de dopant de 1 à 2% massique. En effet, la densité de ce groupe de céramiques dopées est sensiblement différente. En ce qui concerne les céramiques issues de BT-A avec le même niveau de dopant, leur densité par rapport à celle des céramiques BT-B et BT-C est nettement différente, étant respectivement inférieure de 20 et 30%. De plus, la densité des céramiques BT-B avec un niveau de dopant compris entre 2,5 et 20% massique est de supérieure à celle des céramiques BT-A ayant la même concentration en Y 2 O 3 . Cependant, il existe une divergence dans le comportement de la densité en fonction de la teneur en Y 2 O 3 entre les céramiques BT-A et BT-B. Tout d'abord, la densité de BT-A_1.5 est égale à celle de BT-A_2. Au-delà de cette concentration en dopants, elle augmente légèrement et est pratiquement la même pour BT-A_2.5, BT-A_5 et BT-A_20. Dans le cas contraire, même lorsque le BT-B_1.5 et le BT-B_2 ont une densité similaire, comme dans le cas du BT-A, son comportement au-delà de ce niveau de dopant est opposé à celui observé dans les céramiques BT-A. Pour ces céramiques (BT-B_2.5, BT-B_5 et BT-B_20), les valeurs de densité diminuent lorsque la concentration de Y 2 O 3 augmente (bien que la densité soit plutôt la même pour les trois). De plus, la densité des céramiques issues des mêmes poudres mais frittées sous différentes atmosphères est également différente. Les céramiques frittées sous atmosphère réductrice présentent des valeurs plus élevées que celles cuites dans l'air. L'atmosphère joue un rôle dans le mécanisme de densification. En effet, lorsque les échantillons sont frittés dans l'air, il se crée davantage de lacunes en oxygène qui se traduisent par des volumes plus importants et donc des densités plus faibles.

Figure 4 . 3 .

 43 Figure 4.3. Valeurs de densité des céramiques frittées sous atmosphère réductrice à 1310 ° C en fonction de la teneur en Y 2 O 3 dans la poudre de départ.

Table 1 . 2 .

 12 . Types of MLCCs and specifications

Table 2 . 3 .

 23 . Sample identification of prepared powders doped with Y 2 O 3 .

Table 3 . 5 .

 35 Activation energy values obtained from Arrhenius-Weibull model for MLCCs tested under two different voltages and a range of temperatures.

Table 4 . 1 .

 41 Ba/Ti ratio and chemical composition of BaTiO 3 powders. ..........................................................

Table 4 . 2 .

 42 Additives and dopants on BaTiO 3 dielectric formulation. .............................................................

Table 4 . 3 .

 43 Sample identification of prepared powders doped with Y 2 O 3 . .......................................................

Table 4 . 4 .

 44 Density of the ceramics sintered in air, two temperature steps: 1310 °C then 1150 °C for 15 h. .

Table 4 . 5 .

 45 Secondary phases detected in the different powders and ceramics thermally treated and sintered in

Table 4 .

 4

6. Density of

BT-A ceramics sintered under reducing atmosphere and 1310 °C. .............................

Table 4 . 7 .

 47 Secondary phases detected in BT-A ceramics sintered in reducing atmosphere at 1310 °C. .......

Table 4 . 8 .

 48 Density ofBT-B ceramics sintered in reducing atmosphere at 1310 °C. ......................................

Table 4 . 9 .

 49 Secondary phases detected in BT-B ceramics sintered in reducing atmosphere at 1310 °C. .......

Table 4 .

 4 10. Chemical composition of BaTiO 3 formulated powders.

Table 1 .1. Effective ionic radii of various elements

 1

Ionic radius (Å) B-site (6 coordination) A-site (12 coordination)

	Ba 2+		1.610
	Ti 4+	0.605
	Mg 2+	0.720
	Dy 3+	0.912	1.255
	Ho 3+	0.901	1.234
	Y 3+	0.900	1.234

  Multilayer ceramic capacitors of Classes II and III exhibit aging characteristics. The capacitance of Class II devices typically falls 10 % with applied voltages of 50 to 70 % of the device's maximum working voltage. Class III devices lose capacitance starting at 10 % of the maximum working

	Designation	Class	Temperature range (°C)	ΔC/C (%)	K value up to	BT content (%)	Other dopants	Grain size (µm)
	C0G (NPO)	I	-55 to 125	± 30	100	10-50	TiO 2 , CaTiO 3 , Nd 2 Ti 2 O 7	1
							MgO, MnO,
	X7R	II	-55 to 125	± 15	4000	90-98	Nb 2 O 5 , CoO, Rare-	<1.5
							earth elements
	Z5U	II	10 to 85	+ 22, -56	14000	80-90	CaZrO 3 , BaZrO 3	3-10
	Y5V	II	-30 to 85	+22, -82	18000	80-90	CaZrO 3 , BaZrO 3	3-10

Table 2 .

 2 1. HALT parameters for the three groups of MLCCs.

	MLCCs group	Voltage (V)	Range of temperature (°C)
		400	140 -250
	A
		600	120 -220
		400	110 -225
	B
		600	90 -200
		400	20 -90
	C
		600	20 -80

Table 2 . 2 .

 22 Chemical composition of BaTiO 3 powders.

	Ba	Ti	Y	Ca	Sr	Si	Mn	Mg	Co
	BT_A*
	57.55	19.96	<0.01	0.006	0.04	<0.01 <0.001	0.001 <0.01
	Ba/Ti = 2.88
	BT_B**
	54.67	19.17	1.05	1.34	0.09	0.30	0.05	0.29	0.012
	Ba/Ti = 2.85
	BT_C**
	53.86	18.85	1.05	0.57	0.09	0.17	0.05	0.006 0.017
	Ba/Ti = 2.86
	Values are given in wt%.

*: BT reagent grade (pure). **: BT commercially formulated.

Table 2 . 3 .

 23 Sample identification of prepared powders doped with Y 2 O 3 .

	Composition
	(wt% Y 2 O 3 )→
	Type of powder↓

Table 3 .

 3 1. TTF when HALT is performed using different voltages and the same temperature.

MLCC Group and HALT temperature conditions Range of TTF when tested at 400 V Range of TTF when tested at 600 V

	Group A -140 °C	21 -30 h	3 -5 h
	Group B -140 °C	3 -4 h	0.2 -0.4 h
	Group C -60 °C	5 -13 min	2 -4 min

Table 3 .

 3

	Voltage (V)	Temperature (°C)	(h)		Voltage (V)	Temperature (°C)	(h)
		140	35.67	4.66		120	8.71	3.81
		150	12.72	4,65		140	5.15	3.04
		160	5.62	8.89		150	2.08	2.44
		180	1.87	2.68		165	0.74	2.12
	400	200	0.63	4.02	600	175	0.29	2.96
		210	0.84	1.67		190	0.21	2.69
		220	0.67	2.16		200	0.14	4.25
		230	1.23	1.19		210	0.15	6.05
		250	1.01	0.85		220	0.22	2.28

2. Weibull parameters for MLCCs

-Group A.

Table 3 . 3 .

 33 Weibull parameters for MLCCs -Group B.

	Voltage (V)	Temperature (°C)	(h)	Voltage (V)	Temperature (°C)	(h)
		110	72.2	5.8	90	33.5	2.02
		120	27.0	4.95	110	9.46	3.59
		140	4.07	7.16	125	1.68	4.81
		155	0.87	5.54	130	1.17	3.01
		170	0.23	4.59	135	0.58	3.9
	400			600
		190	0.14	2.1	145	0.31	5.01
		200	0.06	3.11	150	0.25	3.32
		210	0.06	3.06	170	0.07	2.13
		225	0.06	2.01	180	0.03	6.81
					220	0.01	3.08

Table 3 . 4 .

 34 Weibull parameters for MLCCs -Group C.

	Voltage (V)	Temperature (°C)	(h)		Voltage (V)	Temperature (°C)	(h)
		20	154.2	1.20		20	6.11	6.44
		40	3.34	1.26		35	0.75	2.52
		50	1.04	1.63		40	0.38	2.20
	400	65	0.06	5.45	600	50	0.12	2.15
		70	0.04	3.40		60	0.04	4.61
		80	0.05	1.40		70	0.01	3.42
		90	0.03	1.37		80	0.01	1.80

Table 3

 3

	.5. Activation energy values obtained from Arrhenius-Weibull model for MLCCs tested under two
	different voltages and a range of temperatures.
	MLCCs Group	Ea (eV) at 400 V	Ea (eV) at 600 V	ln(A) at 400 V	ln(A) at 600 V	Temperature Range at 400 V	Temperature Range at 600 V
	A	1.06 ± 0.07 1.01 ± 0.09	26.96 ± 2.5	26.52 ± 2.1	140-200 °C	120-200 °C
	B	1.25 ± 0.06 1.09 ± 0.02	33.62 ± 1.3	31.23 ± 0.7	110-200 °C	90-180 °C
	C	1.45 ± 0.05 1.08 ± 0.02	39.90 ± 2.9	38.30 ± 1.8	20-70 °C	20-70 °C

Table 3

 3

	.6. Voltage stress constant (n).
	Group	n (T 1 = T 2 )	n (All Conditions)
	A	5.51	4.46
	B	1.93	5.02
	C	4.95	3.26

Table 4 .

 4 1. Ba/Ti ratio and chemical composition of BaTiO 3 powders.

	Ba	Ti	Y	Ca	Sr	Si	Mn	Mg	Co
	BT_A*
	57.55	19.96	<0.01	0.006	0.04	<0.01 <0.001 0.001 <0.01
	Ba/Ti = 2.88
	BT_B**
	54.67	19.17	1.05	1.34	0.09	0.30	0.05	0.29	0.012
	Ba/Ti = 2.85
	BT_C**
	53.86	18.85	1.05	0.57	0.09	0.17	0.05	0.006 0.017
	Ba/Ti = 2.86
	Values are given in wt%.

*: BT reagent grade (pure). **: BT commercially formulated.

Table 4.2. Additives and dopants on BaTiO 3 dielectric formulation.

Table 4 . 3 .

 43 Sample identification of prepared powders doped with Y 2 O 3 .

Table 4 . 4 .

 44 Density of the ceramics sintered in air, two temperature steps: 1310 °C then 1150 °C for 15 h.

	BaTiO 3 raw material	[Y 2 O 3 ] (wt%) Sample ID	Density (g/cm 3 )
		0	BT-A_0	5.62	0.19
	BT-A (reagent-grade)	2.5	BT-A_2.5	3.66	0.03
		5	BT-A_5	3.67	0.02
		1	BT-B_1	5.79	0.07
	BT-B (commercially formulated)	2.5	BT-B_2.5	4.82	0.03
		5	BT-B_5	4.37	0.02

Table 4

 4

	.5. Secondary phases detected in the different powders and ceramics thermally treated and sintered in
	air, two temperature steps: 1310 °C then 1150 °C 15 h.
	BaTiO 3 raw material	Y 2 O 3 wt% Sample ID	Secondary phase
				Powder (TT)	Ceramic
		0	BT-A_0	x	x
	BT-A	2.5	BT-A_2.5	x	x
	(reagent-grade)	5	BT-A_5	Y 2 O 3	Y 2 O 3
		20	BT-A_20	Y 2 O 3	N.S.
		1	BT-B_1	x	x
	BT-B	2.5	BT-B_2.5	x	x
	(commercially	5	BT-B_5	x	x
	formulated)	20	BT-B_20	Ba 6 Ti 17 O 40 and Y 2 O 3	N.S.

Table 4 .

 4

	BaTiO 3 raw material	[Y 2 O 3 ] (wt%)	Sample ID	Density (g/cm 3 )
		0	BT-A_0	5.70	0.05
		1	BT-A_1	4.51	0.17
		1.5	BT-A_1.5	3.74	0.04
	BT-A (reagent grade)	2	BT-A_2	3.74	0.06
		2.5	BT-A_2.5	4.09	0.09
		5	BT-A_5	4.29	0.05
		20	BT-A_20	4.19	0.06

6. Density of BT-A ceramics sintered under reducing atmosphere and 1310 °C.

Table 4 .

 4 7. Secondary phases detected in BT-A ceramics sintered in reducing atmosphere at 1310 °C.

	BaTiO 3 raw material	Y 2 O 3 wt%	Sample ID	Secondary phases
		0	BT-A_0	x
		1	BT-A_1	x
		1.5	BT-A_1.5	x
	BT-A	2	BT-A_2	Y 2 Ti 2 O 7
	(reagent-grade)	2.5	BT-A_2.5	Y 2 TiO 5
		5	BT-A_5	Y 2 O 3 ; Y 2 Ti 2 O 7
				sint. ceramic: Y 2 O 3; Y 2 Ti 2 O 7;
		20	BT-A_20	Y 2 TiO 5.
				reox. ceramic: Y 2 O 3 ; Y 2 TiO 5.

Table 4 . 8 .

 48 Density of BT-B ceramics sintered in reducing atmosphere at 1310 °C.

Table 4 .

 4 9. Secondary phases detected in BT-B ceramics sintered in reducing atmosphere at 1310 °C.

Table 4 .

 4 10. Chemical composition of BaTiO 3 formulated powders.

		Ba	Ti	Y	Ca	Si	Mg
	BT_B	54.67	19.17	1.05	1.34	0.30	0.29
	BT_C	53.86	18.85	1.05	0.57	0.17	0.006
	Values are given in wt%.

Table 4 .

 4

11. Density of BT-C ceramics sintered in reducing atmosphere at 1310 °C.

Table 4 .

 4 12. Summary of secondary phases detected in ceramics sintered in reducing atmosphere and 1310 °C.

	BaTiO3 raw material	Y2O3 wt%	Sample ID	Secondary phases
		0	BT-A_0	x
		1	BT-A_1	x
		1.5	BT-A_1.5	x
	BT-A	2	BT-A_2	Y2Ti2O7
	(reagent-grade)	2.5	BT-A_2.5	Y2TiO5
		5	BT-A_5	Y2O3; Y2Ti2O7
				sint. ceramic: Y2Ti2O7;
		20	BT-A_20	Y2TiO5. reox. ceramic: Y2O3;
				Y2TiO5.
		1	BT-B_1	x a
		1.5	BT-B_1.5	Y2Ti2O7
	BT-B	2	BT-B_2	Y2Ti2O7
	(commercially
	formulated)	2.5	BT-B_2.5	Y2TiO5
		5	BT-B_5	Ba6Ti17O40
		20	BT-B_20	Y2O3; Ba6Ti17O40
	BT-C	1	BT-C_1	x
	(commercially	1.5	BT-C_1.5	Y2Ti2O7
	formulated)	2	BT-C_2	Y2Ti2O7

  poudres et de céramiques dans différentes conditions de frittage en utilisant Y 2 O 3 comme dopant pour deux types de poudres : une pure et deux formulées pour des applications industrielles. Ce manuscrit de thèse est divisé en quatre chapitres. Le premier chapitre est une introduction bibliographique. Il présente les propriétés générales de BaTiO 3 , et comment elles peuvent être améliorées par l'utilisation de dopants tels que Y 2 O 3 dans les formulations du matériau diélectrique utilisé dans les condensateurs céramiques multicouches. Le chapitre 2 décrit les différentes méthodes expérimentales ainsi que les techniques de caractérisation utilisées dans ce travail. Dans le chapitre 3 nous présentons la caractérisation électrique des condensateurs céramiques multicouches (MLCC) à l'aide d'essais de durée de vie accélérée (HALT) pour déterminer le temps moyen avant défaillance (MTTF) de chaque groupe d'échantillons et effectuer des analyses statistiques de Weibull. Le modèle d'Arrhenius a permis d'obtenir la valeur de l'énergie d'activation (Ea) liée à la défaillance des condensateurs dans des conditions déterminées. Enfin le dopage par Y 2 O 3 de deux types de poudres BaTiO 3 est présenté dans le chapitre 4.

  ont étudié BT dopée à l'yttrium, identifiant les processus dans lesquels le dopant est utilisé. On sait que les matières premières peuvent contenir des impuretés. Dans ce cas, les impuretés paramagnétiques ont été identifiées comme pouvant occuper les sites Ti. Ainsi, une partie des cations Y 3 + peut participer à un échange. L'yttrium influence également les mécanismes de compensation de charge. Et comme effet collatéral, il a été trouvé qu'il peut participer à la formation de précipités tels que Ba 6 Ti 17 O 40 et Y 2 Ti 2 O 7 . Ces phases secondaires ont généralement été trouvées lorsque la solubilité solide du dopant dans le BT est dépassée. Avec la quantité appropriée de dopants, les propriétés structurales, optiques et électriques d'un système dopé au BT peuvent être améliorées

  et l'un des Le plus courant lorsque le dopage avec des oxydes de terres rares (Dy 2 O 3 , Er 2 O 3 , Y 2 O 3 et Ho 2 O 3 ) est la phase de type pyrochlore, R 2 Ti 2 O 7

  massique, puis elles ont été broyées dans un flacon de polyuréthane avec des billes d'oxyde de zirconium . Dans le but d'observer toute modification structurale induite par le dopage, les poudres (x = 2,5 à 20% massique) ont été traitées thermiquement à 1310 ° C sous air pendant 3 heures. Des céramiques ont été préparées avec les poudres contenant 2,5 et 5% massique de Y 2 O 3 . Ensuite, la poudre de poudre a été séchée et 1% massique de polyvinylbutyral (PVB) a été ajouté aux poudres qui ont été mélangées, broyées et tamisées. Enfin, ils ont été compactés par pressage uniaxial, produisant des disques de 8 mm de diamètre. Les céramiques crues ont été frittées à l'air en utilisant un four tubulaire, selon un protocole de frittage en deux étapes qui a atteint 1350 ° C et est ensuite resté à 1150 ° C pendant 15 h. La phase cristalline des poudres et des échantillons frittés a été caractérisée par diffraction des rayons X (XRD, modèle D4 Endeavour, Bruker AXS) dans l'intervalle 2θ 10-80 °. La densité apparente de la céramique a été déterminée à partir de la masse et de la géométrie des échantillons. La morphologie des poudres a été analysée par microscopie électronique à balayage (MEB, JSM-6510LV, JEOL). La taille des particules a été déterminée à partir des micrographies à l'aide du logiciel Image J.

CHAPITRE 3: Caractérisation électrique des MLCC

  Par conséquent, d'autres méthodes doivent être utilisées pour réduire le temps d'évaluation afin d'avoir une indication de la fiabilité avant la commercialisation des composants. Des conditions d'essai accélérées doivent être conçues pour obtenir la prévision la plus précise possible de la durée de vie des condensateurs dans les conditions de service. Les tests de fiabilité les plus courants des MLCC sont la résistance d'isolement et les mesures de contraintes combinées, également appelées tests de durée de vie hautement accélérée (HALT).[START_REF] Paulsen | Highly accelerated lifetesting (HALT) of kemet Base-Metal-Electrode (BME) ceramic chip capacitors[END_REF][START_REF] Vassilious | Understanding accelerated life-testing analysis[END_REF]. Les systèmes électriques tels que les condensateurs peuvent être testés en utilisant deux types de tests; soit un test de stress constant ou un test de stress progressif peut être effectué. Dans le premier type, un certain nombre d'échantillons sont amenés à leur dégradation dans des conditions de contraintes définies, puis les temps d'échec sont mesurés; dans le second type, les tensions de claquage peuvent être mesurées. Au moment d'effectuer le test électrique, quel que soit le type, pour les conditions données, chaque échantillon testé produira un résultat différent, de sorte que le total des données obtenues peut être analysé par une distribution statistique.(Chauvet et Laurent, juin 1992).Différents modèles de distribution statistique pourraient être appliqués à l'analyse des données à partir de ces tests, y compris Weibull, Gumbel et Lognormal. La distribution de Weibull est largement utilisée dans ce domaine et est celle utilisée dans ce travail. En adaptant les propriétés des MLCC, outre les paramètres électriques initiaux, il est très intéressant d'analyser et de rechercher les corrélations entre la formulation structurale et chimique de base et la fiabilité (délai de défaillance) des condensateurs. Très peu d'études dans la littérature abordent cette question, car la production de MLCC pour les tests de fiabilité nécessite au minimum des installations de taille pilote pour produire de nombreux échantillons avec un processus reproductible afin de minimiser l'influence d'autres paramètres que celui testé. En outre, l'objectif du test concerne un type de condensateur fixe, car le diélectrique est formulé de manière optimale. Par conséquent, les conclusions concernant l'effet du dopage sur la fiabilité de la MLCC sont plutôt spéculatives. Compte tenu des interactions nombreuses et complexes entre les additifs et les dopants pendant et après le processus de frittage, une approche plus simple doit être entreprise. Dans ce travail, nous déterminons le délai de défaillance de BT.

  Tableau 3.2. Valeurs d'énergie d'activation obtenues à partir du modèle Arrhenius pour MLCC testées sous deux tensions différentes et dans une plage de températures.

	MLCCs	E a (eV) at 400 V	E a (eV) at 600 V	Temperature range
	MLCC-1	1.06 ±0.07	1.01 ±0.09
	MLCC-2	1.45 ±0.05	1.08 ±0.02
	MLCC-3	1.25 ±0.06	1.09 ±0.02

CHAPITRE 4: Dopage de BaTiO 3 avec Y 2 O 3

  , elle peut également modifier l'équilibre des lacunes en oxygène et les interactions complexes avec d'autres éléments dopants lors du frittage et du recuit. Il est intéressant de noter que malgré les temps d'échec beaucoup plus faibles de la composition de MLCC-2, les énergies d'activation, estimées à une température inférieure, bien qu'elles soient plus grandes, se situent dans la même plage que les deux autres compositions.Dans cette partie, nous avons déterminé l'impact des différences de composition chimique de BaTiO 3 dopé à l'Y 2 O 3 sur la durée de vie des MLCC dans des conditions accélérées. Malgré les petites différences apparentes, la durée de vie de la MLCC peut varier considérablement, se situant aux dixièmes d'heures (36 heures) à moins d'une seconde aux conditions de test de 400 V et de 140 ° C. La variation de la teneur en Ca induit une forte diminution de la durée de vie aux conditions de frittage et de traitement équivalentes. Malgré cela, les énergies d'activation de la défaillance restent dans la même plage de 1,05 à 1,45 eV, ce qui pourrait être lié aux énergies d'activation des lacunes d'oxygène dans BaTiO3. La relation complexe entre la chimie des défauts et les conditions d'élaboration doit donc être étudiée plus avant pour comprendre comment les différentes phases peuvent influencer le délai de défaillance de ces matériaux.Dans optimiser les caractéristiques de BaTiO 3 en tant que matériau diélectrique de base pour la fabrication des MLCC, il est important de définir les relations entre la structure, la microstructure et les propriétés électriques. La présence de phases secondaires, dues à la présence d'autres éléments, tels que les dopants, modifie les propriétés électriques du matériau. Parmi les phases signalées, on peut citer les pyrochlores, Y 2 Ti 2 O 7 , qui sont supposés être à l'origine des mécanismes de défaillance à long terme des opérations de la MLCC sous fonctionnement nominal(Zhang et al., 2016). Ce chapitre vise à trouver les phases secondaires dans ce matériau et à évaluer la fiabilité des MLCC utilisant un matériau à base de BaTiO 3 pouvant contenir ces phases. Toutes les conditions auxquelles la céramique est exposée lors de sa préparation, de la matière première au dernier traitement thermique, doivent être bien connues. Pour cette raison, il est nécessaire d'effectuer des caractérisations de poudres et de céramiques par des techniques telles que la spectroscopie à plasma à couplage induit (ICP), la diffraction des rayons X et le MEB, pour connaître la composition chimique, la structure et la composition des phases, la porosité et la taille des grains. . La composition chimique des poudres BaTiO 3 utilisées comme matières premières a été déterminée par les analyses ICP et est présentée dans le tableau 4.1. Comme mentionné précédemment, les poudres formulées pour une application industrielle contiennent des dopants et des additifs.Traitement thermique et caractérisation des poudres de BaTiO 3 Dans le but d'observer tout changement structurel induit par un fort niveau de dopage, les poudres BT-A_2.5, BT-A_5, BT-A_20, BT-B_2.5, BT-B_5 et BT-B_20 ont été traitées thermiquement (TT ) à 1310 ° C sous air pendant 3 h. Ce traitement thermique reproduit les conditions de température de frittage dans lesquelles des condensateurs céramiques multicouches sont produits au niveau industriel. Dans ce cas, les poudres sont dénommées BT-X_YTT, où "X" indique la poudre BaTiO 3 brute, "Y" Y 2 O 3 % massique et "TT" traité thermiquement.Tableau 4.1. Rapport Ba / Ti et composition chimique des poudres de BaTiO 3 .

	4.1. Poudres de BaTiO 3
	3.3. Conclusions
	Ba	Ti	Y	Ca	Sr	Si	Mn	Mg	Co
	BT_A*
	57.55	19.96	<0.01	0.006	0.04	<0.01 <0.001 0.001 <0.01
	Ba/Ti = 2.88
	BT_B**
	54.67	19.17	1.05	1.34	0.09	0.30	0.05	0.29	115
	Ba/Ti = 2.85
	BT_C**
	53.86	18.85	1.05	0.57	0.09	0.17	0.05	0.006 0.017
	Ba/Ti = 2.86
	Values are given in wt%.

*: BT reagent grade (pure). **: BT commercially formulated.

  Conclusion générale et perspectivesL'objectif de ce travail de thèse était d'analyser le comportement de BaTiO 3 dopé avec Y 2 O 3 . Cette question a été abordée par deux perspectives distinctes mais liées. Les poudres de titanate de baryum (BT) utilisées dans les formulations des matériaux diélectriques des condensateurs céramiques multicouches (MLCC) contiennent différents additifs et dopants pour améliorer ses propriétés électriques. Cependant, les dopants peuvent parfois conduire à la formation de phases secondaires qui sont responsables de la dégradation de la résistance d'isolement des MLCC. L'un des dopants les plus courants et les plus appropriés est Y 2 O 3 , qui est lié aux phases secondaires du type pyrochlore, Y 2 Ti 2 O 7 . De cette manière, une première approche a été faite par la caractérisation électrique des MLCC de type X7R, cette composition étant à base de BaTiO 3 dopé avec 1,05% de Y 2 O 3 . La caractérisation de trois groupes différents (A, B et C) de MLCC a été réalisée au moyen de tests accélérés à haute durée de vie (HALT) qui ont permis de rassembler les données relatives au temps moyen avant défaillance (MTTF). Des analyses statistiques ont été effectuées en utilisant la distribution de Weibull puis en associant les paramètres trouvés au modèle d'Arrhenius pour déterminer l'énergie d'activation liée aux défaillances produites dans des conditions contrôlées. Il a été démontré par le temps de défaillance (TTF) des échantillons soumis à des tests de stress combinés que le groupe A semble être le plus fiable suivi par le groupe B et au moins le groupe C, qui s'est avéré le plus affecté. Des tests combinés à différents niveaux de contraintes thermiques et électriques ont été effectués dans le but de déterminer si la défaillance des échantillons évolue à des niveaux plus élevés. Il a été démontré qu'à des températures plus élevées, la durée de vie attendue des condensateurs est diminuée et qu'une valeur de tension plus élevée produit également cet effet. Pour les groupes A et B, les défaillances semblent liées au même mécanisme dans une plage de températures de 100 à 200 ° C lorsqu'elles sont testées à 400 et 600 V. Le groupe C présente ce comportement mais dans une fourchette beaucoup plus basse de 20 à 90 ° C. La valeur de l'énergie d'activation (Ea)a été déterminée pour chaque condition d'essai.

Figure 3.12. Weibull plot for Group C. HALT conditions: (a) 400 V, 20 -90 °C and (b) 600 V, 20 -80 °C.

ACKNOWLEDGMENTS

This thesis work was developed thanks to the support of the Postgraduate Cooperation Program (PCP-RU2I) Mexico-France, Project 229286, between the National Council of Science and Technology (CONACyT) and the Ministries of Foreign Affairs of Higher Education for the French Republic, with the participation of Kemet de México and Marion Technologies (France). I thank to the CONACyT for having awarded me the doctoral grant (number 516106) and thus promote my postgraduate studies. of Mexico and France to grow at a personal and professional level. I thank to the Universidad Autónoma de Nuevo León and to the Université Toulouse III -Paul Sabatier for the honor of being PhD student in them, as well as for the support for

as it decreases while the temperature increases. However, now is possible to compare the Fig. 3.6 and Fig. 3.4 and see that there is also an effect over the TTF exerted by the electrical stress.

Comparing the TTF observed in Fig. 3.6 and Fig. 3.7 against the ones presented in Fig. 3.4 and Fig. 3.5, at the same temperatures but higher voltage, the breakdown of the samples was achieved in shorter times. Taking by example the HALT at 140 °C at both voltages, for samples of Group A and Group B and HALT performed at 60 °C at both voltages for Group C, the TTF is decreased when the higher voltage is applied as shown in Table 3.1. decreases when either stress is applied at higher values. However, it can be considered that the failure mechanism does not change in the used range of HALT conditions.

Weibull analyses -Group C

MLCCs from Group C have shown to behave different from those of groups A and B, being impossible to test them under exactly same experimental parameters. The temperature range used to test this group of samples was considerably lower than the one utilized for Groups A and B. This fact can lead to the consideration that the dielectric material of the Group C MLCCs is less resistant to the high stress values than the one of A and B samples; i.e., it has a lower insulation resistance.

Despite this fact and also with the aim to confirm these differences, HALT experiments were conducted and TTF at different temperatures using 400 V and 600 V were determined. The Weibull analysis was performed obtaining the plots observed in Fig. 3.12 and the parameters presented in Table 3.4 and Fig. 3.13. TTF was as well affected, decreasing when either temperature or voltage values were augmented. Also, the behavior is fitted with a Weibull model and lines are parallel-like, indicating the failure of the samples occurs under the same mechanism(s). Some deviations from this behavior are observed in the cases of 80 °C and 90 °C (Fig. 3.12.a) and 80 °C when 600V are applied (Fig. 3.12.b), which could mean that similar to the cases of Group A and B, there is a limit of temperature under the one the failure mechanisms are the same and then a change occurs. This is as well reflected in the data shown in Table 3.4 and Fig. 3.13, from where is possible to see that the characteristic life decreases at higher temperatures with some exceptions after the 70 °C in both electrical stress cases. Also, at higher voltage the mean life is lower. The grains have rounded appearance and they are homogeneously distributed. Comparing these ceramics with the ones from BT-A showed in Fig. 4.7, is recognizable that the space among the grains of these BT-B ceramics is lower than the observed in the BT-A micrographs. This is in agreement with higher densification. A summary of the principal observations from the XRD analyses performed on BT-B ceramics sintered in reducing conditions is presented in Table 4.9.

General Conclusion and Perspectives

The objective of this thesis work was to analyze the behavior of BaTiO 3 doped with Y 2 O 3 . This issue was addressed by two distinct yet related perspectives. The barium titanate (BT) powders that are used in formulations for dielectric materials of multilayer ceramic capacitors (MLCCs) contain different additives and dopants to enhance it electrical properties. However, sometimes the dopants can lead to the formation of secondary phases that are believed responsible for the detriment in the insulation resistance of the MLCCs. One of the most common and suitable dopants is the Y 2 O 3 , which is related to secondary phases of the pyrochlore type, Y 2 Ti 2 O 7 .

In this way, a first approach was made by the electrical characterization of MLCCs of the X7R type, which composition is based on BaTiO 3 doped with 1.05 % of Y 2 O 3 . The characterization of three different groups (A, B and C) of MLCCs was performed by means of high life accelerated tests (HALT) that allowed gathering the data related to its mean time to failure (MTTF). Statistical analyses were performed using the Weibull distribution and then associating the found parameters with the Arrhenius model to determine the activation energy related to the failures produced under controlled conditions. The discrimination of the three groups of samples according to its behavior under the stress tests was achieved. It was evidenced by the time-to-failure (TTF) of the samples under combined stress tests that the Group A appears to be the more reliable followed by the Group B and at least the Group C, which was found to be the most affected by the high stress conditions.

Combined tests at different levels of thermal and electrical stress were performed with the aim to determine if the failure of the samples changed at higher levels. It was evidenced that at higher temperatures the expected life of the capacitors is decreased, and a higher value of voltage produces this effect as well. For the Groups A and B, the failures seem to have the same mechanism(s) in a principal differences among these groups of capacitors are given by the composition of its dielectric material i.e., the amount of additives and dopants, these results provided information to confirm that the samples will have different properties (i.e., insulation resistance) according the composition of the dielectric ceramic formulation. For that reason experiments aimed to identify the impact of differences in the chemical composition of Y-doped BaTiO 3 on the lifetime of MLCCs under accelerated conditions, were conducted. Despite the apparent small differences in the chemical composition, the lifetime of the MLCCs can change from tens of hours (36 h) to less than a second at 400 V and 140 °C. The change in the Ca content induces a great drop in the lifetime from equivalent sintering and processing conditions. Despite this, only when thermally evaluated, the activation energies of the failure remain within the same range of 1-1.45 eV, which could be related to the activation energies of oxygen vacancies in BaTiO 3 . Although the thermally activated processes are well-described by the Arrhenius expression, the effect of the electric field is not as simple as the empirical equation claims. It can be suggested from the results that the presence of cations, which was Ca in this case, reduces the activation energy, which thermally reduces the life expectation, but increases the reliability of the MLCC in terms of sensitivity to the electric field. This is reflected not only in the activation energy (E a ) and the voltage sensitivity exponent (n), but also through the pre-exponential factor (A) of the Arrhenius relationship. To further understand the failure mechanism of the MLCCs, the relationship between the microstructure and structural evolution during aging must be established, by observing the compositional evolution and how it is related to the Ca content in the BaTiO 3 , in addition to its role in the formation the secondary phases.

The following step of the study was to evaluate the possibility of the secondary phases' formation due to the presence of Y 2 O 3 as dopant. Since it is not the only dopant found in the MLCCs dielectric formulation, the role of the Y 2 O 3 as dopant was evaluated in a reagent grade BT powders and two industrially formulated BT powders with the aim to see the interactions that can be given in a BT-Y 2 O 3 system and a BT-Y 2 O 3 -additives/dopants system. The formulated starting powders used for

RESUME

Introduction générale

De nos jours, les appareils électroniques font partie de la vie courante : ordinateurs, téléphones, appareils électriques en sont quelques exemples. Actuellement, la présence de composants électroniques augmente de plus en plus dans les industries telles que l'automobile et l'aéronautique. L'un des principaux composants de ces dispositifs est le condensateur, dont la fonction principale est le stockage d'énergie. Il existe plusieurs types de condensateurs, l'un des plus utilisés étant les condensateurs céramiques multicouches (MLCC). Les MLCC offrent des avantages essentiels en raison de leur faible coût, l'une des raisons de sa prédominance sur le marché de l'électronique. Différents types de MLCC existent, en fonction de l'application visée. Les caractéristiques des MLCC vont être déterminées par des paramètres extrinsèques et intrinsèques; c'est-à-dire la nature, les caractéristiques, la synthèse et le traitement du matériau diélectrique et le processus de production des condensateurs. Ces facteurs peuvent influencer la fiabilité finale des condensateurs et donc des dispositifs. Pour cette raison, il est très important de développer des matériaux céramiques adaptés aux différents marchés. L'une des principales stratégies pour obtenir des condensateurs fiables consiste à adapter les caractéristiques du matériau diélectrique en modifiant sa composition. Le titanate de baryum (BaTiO 3 ) est le matériau diélectrique de base des MLCC en raison de ses propriétés, essentiellement sa permittivité élevée. Pour améliorer ses propriétés électriques, il faut le modifier en incluant plusieurs additifs et dopants dans la formulation de base du diélectrique. La structure pérovskite du BaTiO3 a la capacité d'accueillir des dopants qui, selon les différentes conditions, occuperont les sites A ou B du réseau. L'occupation des dopants à l'intérieur de la structure détermine les propriétés électriques initiales, et on suppose également la fiabilité (durée de vie) du produit final. La formulation de poudres de titanate de baryum comprend comme des dopants des terres rares (REE). Parmi ceux-ci, Y 2 O 3 est le plus commun pour la fabrication de condensateurs céramiques multicouches avec des électrodes en métal (BME-MLCC) car il a un coût inférieur à celui de Ho 2 O 3 , Er 2 O 3 et Dy 2 O 3 et offre des propriétés similaires. En outre, des cations tels que Mn 2 + , Mg 2 + et Ca 2 + peuvent contribuer à la distribution globale des défauts électroniques générés lorsque les ions dopants sont introduits dans le réseau et au cours du processus de fabrication des condensateurs. En plus de ces dopants, des additifs sont ajoutés pour modifier les conditions de production, tel que l'oxyde SiO 2 , utilisé pour diminuer les températures de frittage. Les propriétés finales résulteront des interactions du titanate de baryum avec les dopants et les additifs, dans des conditions de frittage spécifiques. La complexité du système augmente lorsque, dans certaines conditions, des phases secondaires sont formées. Dans les travaux précédents, ces phases secondaires, en particulier celles liées au dopage à Y 2 O 3 , seraient responsables des mécanismes de défaillance à long terme lors de l'utilisation des MLCC. Ce travail de thèse a pour objectif d'analyser le rôle du dopant Y 2 O 3 et sa contribution possible à la formation de phases secondaires dans la matrice BaTiO 3 . La réalisation de cet objectif implique deux blocs expérimentaux. Premièrement, la caractérisation électrique des MLCC avec BaTiO 3 dopé à Y 2 O 3 en tant que diélectrique par la réalisation d'essais à vie accélérée élevée (HALT) qui conduisent à obtenir des indicateurs de durée de vie. Deuxièmement, le développement d'une étude de dopage comprenant la préparation de