LITERATURE REVIEWS
Overview of ferroelectric and relaxor ferroelectric properties
Perovskites and tungsten bronze exhibit exceptional piezoelectric and ferroelectric properties, with perovskite-structured relaxor materials being the focus of extensive research A significant advantage of perovskite structures is the ability to substitute various cations at both the A and B sites without significantly altering the overall structure, allowing for a complete solid solution across a range of compositions Compared to other structures, perovskites demonstrate considerable anisotropy in their piezoelectric properties and can easily undergo phase transitions The mineral perovskite, represented by the formula ABO3, features an orthorhombic structure where A-site cations have valences ranging from +1 to +3, while B-site cations possess valences of +3, +4, or +5 In this arrangement, B-site ions are located at the body center, A-site cations occupy cubic corner positions, and oxygen atoms are positioned at the face centers, forming octahedra around the B-site This structure is characterized by BO6 octahedra that share corners in three dimensions, resulting in a symmetric configuration where A cations are coordinated by twelve oxygen atoms and B cations by six.
To get a stabilized structure there is a size constraints like charge neutrality constraints The size constraint is described by the tolerance factor t For the perovskite structure,
In the ideal perovskite structure, the A-site cation radius (in 12 coordination) and the B-site cation radius (in 6 coordination) must yield a tolerance factor (t) ranging from 0.95 to 1.04 for cubic symmetry, while larger values are required for distorted perovskite systems.
Figure 1.1 (a) Cubic perovskite unit cell ABO 3 , (b) Perovskite lattice structure BO 6
Ferroelectricity, first discovered by Valasek in 1921 in Rochelle single crystals, has since garnered significant interest in the development of new ferroelectric materials These materials are characterized by a permanent dipole moment and exhibit spontaneous polarization along one or more polar axes below the Curie temperature (T c) Like pyroelectric materials, ferroelectrics can have their polarization direction reversed by an external electric field The unique arrangement of cations and anions within ferroelectric materials generates dipole moments in each unit cell, allowing for the measurement of polarization through surface current A key characteristic of ferroelectric materials is their hysteresis behavior in the polarization versus electric field relationship, where remnant polarization (P r) persists even after the electric field is removed At the Curie temperature, ferroelectric materials transition to a paraelectric phase, behaving as standard dielectrics without hysteresis Further details on hysteresis will be discussed in the following section.
1.1.2.1 Phase Transitions in Ferroelectric Materials
Ferroelectric phase transitions can be categorized into two types: order-disorder and displacive In order-disorder ferroelectrics, each unit cell contains a dipole moment that points in random directions at high temperatures As the temperature decreases, these dipoles align in an orderly fashion within a domain, resulting in a coherent direction This transition is typically observed in hydrogen-bonded ferroelectric materials Conversely, displacive transitions involve a phenomenon known as polarization catastrophe, where the displacement of ions from their equilibrium positions leads to a stronger force from local electric fields than the elastic-restoring forces This results in a permanent dipole moment due to the asymmetric shift in ion positions, as seen in ionic crystals like barium titanate (BTO).
Ferroelectric materials experience phase transitions, which can be classified as either first order or second order A key feature of the second order phase transition is the gradual decrease of spontaneous polarization (P s) as the temperature rises, ultimately reaching zero at the transition point.
The transition in triglycine sulfate occurs at a critical temperature (T_c) and is classified as a second-order transition, while barium titanate experiences a first-order transition characterized by a sudden drop in polarization (P_s) to zero at T_c These first and second-order transitions are illustrated in Figure 1.2.
Figure 1.2 Polarization as a function of temperature in (a) first and (b) second order phase transition [18]
Spontaneous polarization arises from the alignment of dipoles within a dielectric material, driven by internal processes rather than external influences This phenomenon occurs through various atomic mechanisms, contributing to the overall polarization The total polarization (P_total) can be expressed mathematically to encapsulate these interactions.
E.q 1.2 where P e , P i , P o and P sc correspond to electronic, ionic, orientational and space charge polarization respectively [19]
Electronic polarization (Pe) refers to the distortion or movement of electron clouds within atoms or molecules caused by an external electric field This process involves the displacement of the outer electron clouds relative to the positively charged atomic cores, leading to a shift from their original symmetrical distribution.
Atomic or ionic polarization (P i) occurs in an ionic lattice when positive ions are displaced toward an applied electric field, while negative ions move in the opposite direction This movement creates an overall dipole moment for the entire structure.
Orientational polarization (P o) occurs when molecules with permanent dipole moments align due to asymmetric charge distribution, resulting in dipole polarization.
Space charge polarization (Psc) occurs when high electric fields lead to significant carrier injection in materials with a dense concentration of charge carriers This results in the migration of charge carriers, creating space charges at interfaces or grain boundaries, which plays a crucial role in the overall polarization of the material.
The polarization is not constant rather it will vary concerning the measuring frequency [19] The variation of polarization for the frequency is given in Figure 1.3
Figure 1.3 Frequency dependence of polarization [19]
Ferroelectric materials exhibit polarization behavior characterized by a closed curve known as the hysteresis loop, which sets them apart from standard dielectric materials The hysteresis loop is crucial for identifying ferroelectrics, and its rectangular shape is essential for the functionality of memory cells Additionally, the relationship between the electric field and polarization in these materials is linear.
E.q 1.3 where and are the vacuum dielectric permittivity (8.854 × 10 -12 F/m) and susceptibility of the material, respectively A typical ferroelectric hysteresis loop is shown in Figure 1.4
As the strength of the electric field (E) increases, the polarization of the material rapidly rises as domains with varying polarization directions align with the field This alignment continues until saturation is achieved, where all domains are oriented in the same direction At this saturation point, the material consists of a single domain, and the extrapolated linear segment on the polarization axis indicates the saturation polarization (P s).
As the strength of the electric field decreases, polarization diminishes but does not completely return to zero, resulting in a phenomenon known as remnant polarization (P r) When the field reaches zero, some domains remain aligned, indicating that a coercive field (E c) is necessary to eliminate the remnant polarization or reduce it back to zero Additionally, applying a stronger negative field will lead to dipole alignment in that direction, allowing the cycle of polarization to be completed by reversing the field direction.
Ferroelectric materials consist of small regions called domains, which exhibit uniform polarization These domains often have varying orientations, leading to a complex arrangement within the material In a single domain, all dipoles are aligned in the same direction, which can be reversed by applying an external electric field The overall polarization in a specific direction depends on the balance of oppositely aligned domains; if they are equally represented, the net polarization is zero Domain walls separate these regions, and changes in temperature or external electric fields can alter the dipole moment, resulting in the movement of domain walls, nucleation, and the formation of new domains.
Principles for High Energy-Storage in Dielectric Capacitors
Basic knowledge on dielectric capacitor 1.2.1
A capacitor typically consists of two conductor plates separated by dielectric materials, commonly arranged in a parallel-plate configuration Its primary function in electronic devices is to store electric energy, which is quantified by capacitance The capacitance is determined solely by the physical dimensions of the conductors and the permittivity of the dielectric materials, remaining unaffected by the potential difference between the plates or the total charge stored For instance, the capacitance of a parallel-plate capacitor filled with specific dielectrics can be approximated using established formulas.
E.q 1.7 where C is the capacitance, A is the area of overlap of the two plates, is the relative permittivity, is the electric constant ( , and d is the distance between the plates Obviously, the capacitance is directly proportional to the overlap area of the conductor plates and the relative permittivity of the dielectrics, while inversely proportional to the separation distance between the plates
When an external voltage V is applied to the conductor plates, electric polarization occurs, leading to the accumulation of equal positive and negative charges on the plates, which is the charging process of the capacitor This process concludes when the electrical potential from the accumulated charge Q matches the external voltage V, establishing the relationship Q/V = C, where C represents the capacitance of the capacitor Additionally, external bias can alter the relative permittivity of the dielectrics, resulting in variations in capacitance, which is then defined in terms of incremental changes.
Figure 1.10 The diagram of charge separation in parallel-plate capacitor under the function of electric field [30]
During charging, external bias facilitates the movement of charges between conductor plates, indicating that work is performed while electric energy is simultaneously stored in the dielectrics The stored energy, denoted as W, can be calculated using a specific formula.
Measuring methods of energy-storage density for dielectric
In research, the energy-storage density (U), representing the energy stored per unit volume of a dielectric, is commonly utilized for comparison purposes Typically, U values can be determined through two primary methods: the static method and the dynamic method.
Figure 1.11 illustrates a static method for measuring energy-storage density Initially, the sample capacitor is charged using an external bias, allowing electric energy to accumulate in the dielectric Subsequently, the capacitor is connected to a load resistor (R) through MOSFET switching, completing the circuit This process results in the discharge of a portion of the stored energy, generating a transient current within the closed circuit The discharged energy can be calculated using the I(t) - t curve with a specific formula.
The energy density (U) can be calculated by dividing the work done (W) by the volume of the capacitor, as represented in equation E.q 1.10, where R denotes the load resistance and t indicates the discharge time It is important to highlight that the U value obtained in this manner reflects the recoverable energy-storage density, as a portion of the stored energy is inevitably lost during the charging and discharging processes.
Figure 1.11 The diagram of measurement circuit for the energy-storage density [30]
The energy-storage density can be derived from the formula (1.9) using the dynamic method It is established that the charge density (Q/A) on a capacitor's conductor plate is equivalent to the electrical displacement D in the dielectrics Therefore, by integrating this relationship with formula (1.9), the energy-storage density U can be accurately represented.
In the context of dielectrics with high permittivity, the relationship between the external applied electrical field (E), defined as V/d, and the electrical displacement (D) closely approximates the electrical polarization (P) Consequently, formula (1.11) can be reformulated to reflect this similarity.
The U value of dielectrics can be easily calculated through numerical integration of the area between the polarization and the electric field-polarization (P - E) loops, as indicated in formula (1.9) As depicted in Figure 1.12 (a), the polarization reaches its maximum (P max) as the electric field increases from zero to its peak (E max), resulting in stored electrical energy (U store) represented by the green and red areas During the discharge phase, as the electric field decreases from E max to zero, the recoverable electrical energy density is illustrated.
The release of U reco, indicated by the green area in the figure, signifies that some of the stored energy, represented by the red area within the loops, is depleted during the depolarization process due to hysteresis loss Consequently, the energy-storage efficiency can be defined based on these findings.
Figure 1.12 (Color online) The typical dependence of (a) polarization and (b) permittivity on electric field of ferroelectrics in the first quarter [30]
Since the permittivity is defined as dP/dE, as shown in Figure 1.12 (b), the formula (1.9) can be expressed as:
For the linear dielectric materials, whose permittivity is independent of the external applied field, the formula (1.11) could be simply expressed as follows:
The energy-storage density of linear dielectric materials is directly proportional to both the relative permittivity of the dielectrics and the square of the operating field It is important to highlight that the U value derived from dynamic measurements typically exceeds that obtained from static measurements.
Potential dielectrics for high energy-storage application 1.2.3
To design effective dielectric materials with high recoverable energy-storage density and minimal energy loss, three key criteria must be met: a high electric breakdown field, large saturated polarization, and low remnant polarization Figure 1.13 illustrates the P-E loops and energy-storage characteristics of four dielectric types: (a) linear dielectrics with constant permittivity, such as Al2O3 and glass; (b) ferroelectrics exhibiting spontaneous polarization, like BaTiO3 and PbTiO3; (c) relaxor ferroelectrics with nanosized domains, including (Pb,La)(Zr,Ti)O3 and (Ba,La)(Zr,Ti)O3; and (d) anti-ferroelectrics characterized by zero net remnant polarization, exemplified by PbZrO3.
The diagram in Figure 1.13 illustrates the hysteresis and energy storage density characteristics for various materials, including linear dielectrics, ferroelectrics, relaxor ferroelectrics, and anti-ferroelectrics In this representation, the green area in the first quadrant signifies the recoverable energy density (U reco), while the red area indicates the energy loss (U loss) associated with these materials.
Linear dielectrics, while offering higher breakdown fields and lower energy losses, are not ideal for high energy-storage applications due to their lower polarization values In contrast, ferroelectrics exhibit larger saturated polarization and moderate electric-field endurance; however, their higher remnant polarization results in reduced recoverable energy-storage density and efficiency Relaxor ferroelectrics and anti-ferroelectrics are more favorable for high energy storage applications because they feature larger saturated polarization, smaller remnant polarization, and moderate breakdown fields Additionally, advancements in manufacturing processes, such as glass-crystallization techniques and composite technologies, have revealed that glass-ceramic and polymer-based ferroelectrics can effectively combine the high breakdown fields of linear dielectrics with the larger polarization of ferroelectrics, making them promising candidates for energy storage solutions.
Overview of barium titanate-based materials
In recent years, extensive research has focused on lead-free BaTiO3-based ceramics due to their environmentally friendly properties and potential applications These ceramics exhibit composition-dependent relaxor behavior, which is influenced by the types and rates of ion substitutions Notably, when the composition deviates significantly from the base BaTiO3 and involves heterovalent ion substitutions at the 6-coordination number crystallographic site, the relaxor behavior becomes more pronounced.
Barium titanate (BaTiO3 or BTO) is a pioneering ceramic material extensively researched for its remarkable dielectric, ferroelectric, and piezoelectric properties Its high dielectric constant is attributed to its unique perovskite crystal structure, making BaTiO3 a significant subject of study in material science.
Figure 1.14 Schematic of the perovskite structure of BaTiO 3 (a) Cubic lattice (above Curie temperature, 120 o C), (b) Tetragonal lattice (below Curie temperature, 120 o C)
In the structure of BaTiO3, each barium ion is surrounded by 12 oxygen ions, forming a face-centered cubic lattice, while titanium atoms occupy larger octahedral interstitial positions surrounded by six oxygen ions Due to the significant size difference, titanium ions are too small to remain stable in these positions, leading to off-center minimum-energy configurations directed towards the surrounding oxygen ions The +4 charge of each titanium ion contributes to a high degree of polarization When an electric field is applied, the titanium ions shift from random to aligned positions, resulting in increased bulk polarization and a high dielectric constant.
Barium titanate (BaTiO3) exists in three crystalline forms: cubic, tetragonal, and hexagonal, with the tetragonal polymorph being the most utilized due to its superior ferroelectric, piezoelectric, and thermoelectric properties The crystal structure and polarization characteristics of BaTiO3 are significantly influenced by temperature Above 120°C, BaTiO3 adopts a cubic structure with random polarization, as the Ti4+ ion resides at the center of an octahedron formed by oxygen ions In this state, high thermal vibrations lead to random orientations of the titanium ions, resulting in no retained polarization or ferroelectric behavior upon the removal of an electric field However, as the temperature drops below the Curie temperature of 120°C, BaTiO3 undergoes a displacive transformation to a tetragonal structure, characterized by a change in unit cell dimensions and an off-center displacement of the Ti4+ ion towards one of the oxygen ions, generating a spontaneous dipole When an electric field is applied in opposition to this dipole, the Ti4+ ion shifts to an equivalent off-center position, inducing a reversal of polarization, hysteresis in the electric field versus polarization curve, and the emergence of ferroelectricity.
Figure 1.15 Reversal in the direction of spontaneous polarization in BaTiO 3 by reversal of the direction of the applied field [35]
The dielectric properties of BaTiO3 are influenced by grain size and temperature At the Curie point, large-grained BaTiO3 (≥10 μm) exhibits a high dielectric constant due to the formation of multiple domains within a single grain, where the movement of domain walls enhances the dielectric constant In contrast, fine-grained BaTiO3 (~1 μm) forms a single domain per grain, with restricted domain wall movement caused by grain boundaries, resulting in a lower dielectric constant at the Curie point compared to coarse-grained BaTiO3 At room temperature, coarse-grained BaTiO3 ceramics show a dielectric constant ranging from 1500 to 2000, while fine-grained BaTiO3 demonstrates a significantly higher dielectric constant, between 3500 and beyond.
6000 This is because the internal stresses in fine-grained BaTiO 3 are greater than in the coarse-grained material, which leads to a higher permittivity at room temperature [37]
Effects of doping on BaTiO 3 properties
Barium titanate (BaTiO3) is a ceramic material known for its high dielectric properties, making it suitable for piezoelectric applications like ceramic sonar transducers However, its pronounced ferroelectric characteristics and sharp dielectric response near the Curie temperature of approximately 120°C limit its effectiveness in energy storage due to high remnant polarization and poor thermal stability Doping is a recognized method to enhance the electrical properties of electroceramics, as substituting A and/or B cation sites in ABO3 perovskites with appropriate impurity ions can significantly alter their electrical behavior.
Doping barium titanate with isovalent zirconium ions results in the formation of barium zirconium titanate (BZT), represented as Ba(Zr x Ti 1-x )O 3 This modification has been shown to effectively lower the Curie temperature (T c) of the material Additionally, the substitution of titanium ions (Ti 4+) plays a crucial role in this process, given its atomic weight of 47.9 and ionic radius of 0.0605 nm.
Zr 4+ ions, with an atomic weight of 91.2 and an ionic radius of 0.072 nm, significantly enhance the dielectric properties of BaTiO 3 ceramics by reducing leakage current and dielectric loss The introduction of zirconium lowers the Curie temperature (T c) of pure barium titanate, which is originally 120 °C, and influences other phase transitions Isovalent substitution of Ti 4+ with Zr 4+ ions transforms ferroelectric micro-domains into dynamic polar nano-regions, leading to a transition from normal ferroelectric behavior to relaxor behavior as Zr concentration increases BZT ceramics display normal ferroelectric behavior at Zr concentrations below 10 mol.% and relaxor behavior above 20 mol.% The larger ionic radius of Zr 4+ expands the lattice parameters and decreases the ferroelectric-paraelectric phase transition Additionally, Zr 4+ ions are more chemically stable than Ti 4+ ions, reducing conduction from electron hopping and thereby improving BZT properties Notably, Sun et al reported a remarkable energy storage density of 30.4 J/cm 3 and an efficiency of 81.7% in lead-free BaZr 0.2 Ti 0.8 O 3 thin films, demonstrating excellent thermal stability and fatigue endurance Liang et al further highlighted an ultrahigh recoverable energy density of 78.7 J/cm 3 and efficiency of 80.5% in BaZr 0.35 Ti 0.65 O 3 film capacitors, showcasing impressive energy storage capabilities across a wide temperature range.
BaZr 0.2 Ti 0.8 O 3 thin film capacitors exhibit superior energy storage density and efficiency compared to other BaTiO 3-based materials and Pb-based systems Their high dielectric constant, low dielectric loss, and significant tunability highlight their potential in modern electronics However, it is important to note that the dielectric properties of BZT capacitors are influenced by temperature and frequency.
Doping is a widely used technique to enhance the electrical and dielectric properties of barium titanate (BTO) and barium zirconate titanate (BZT) materials Common dopants, including Zn²⁺, Ca²⁺, Sr²⁺, Sm³⁺, and La³⁺, can effectively replace the A sites in the ABO₃ perovskite structure, serving as electron acceptors to improve these materials' performance.
Liu et al indicated that the crystal structures, surface morphology, and dielectric properties of Zn-doped BZT films were investigated as a function of
The dielectric properties of Zn-doped BZT films reveal that the dielectric constant initially decreases and then increases with higher Zn content, while the dielectric loss consistently decreases at room temperature Additionally, it is observed that the Curie temperature of Zn-doped BZT films is lower compared to that of pure BZT films.
Chen et al showed a low leakage current density of 7.65 10 -7 A/cm 2 at 60
V, and large breakdown strength of 4 MV/cm in Sr-doping BZT thin films In addition, it not only exhibits an almost linear and acceptable change (∆C/C
~13.6%) of capacitance from room temperature to 180 o Cbut also a large capacitance density of 1.7 nF/mm 2 at 100 kHz, which shows great potential for coupling and decoupling applications [42]
Amrit P Sharma et al investigated the ferroelectric phase transition of BZT/BCT thin films, revealing relaxor behavior at temperatures above room temperature These nanostructures exhibit impressive discharge and charge energy densities of 9.74 J/cm³ and 26.55 J/cm³, respectively Additionally, the heterostructures demonstrate high dielectric permittivity, substantial polarization, and elevated energy density characteristics, making them promising candidates for high power and energy density device applications.
Minh D Nguyen et al showed that La-doping enhanced the relaxor behavior in lead-free BZT thin films by introducing a disorder at the A sites
(Ba 2+ ) of BZT unit cell, which can be achieved by donor substitution of La 3+ for
Ba 2+ ions The results achieved the optimum values of 72.2 J/cm 3 recoverable energy-storage density and 78.2% energy-storage efficiency under a high 3.8
A 5 mol % La-doping concentration demonstrates a remarkable MV/cm electric breakdown strength, indicating that optimal La-doping can enhance relaxor behavior This enhancement leads to a significant improvement in both energy-storage performance and breakdown strength.
Numerous studies indicate that doping with barium titanate (BTO) materials has significantly improved energy-storage density and efficiency in pulse-power systems Specifically, La-doping has enhanced the properties of BZT thin films, making them a promising eco-friendly option for next-generation advanced energy-storage capacitor applications This analysis led to the research focus on the "Effect of Zr and La based co-doping on electrical properties of lead-free barium titanate BaTiO3 thin films."
EXPERIMENTS AND METHODS
Fabrication of BZT and BLZT thin films by sol-gel spin coating method…
by sol-gel spin coating method
The properties of the fabricated films were investigated using advanced measurement and analysis techniques The crystallographic characteristics of the thin films were assessed through X-ray diffraction (XRD) with a PANalytical diffractometer utilizing Cu-Kα radiation (wavelength: 1.5405 Å) The microstructure of the BZT thin films was examined via cross-sectional high-resolution scanning electron microscopy (HRSEM) using a Zeiss-1550 system Additionally, the ferroelectric properties of the materials were analyzed through polarization hysteresis loop measurements conducted with the aixACCT TF2000 Analyzer.
2.1 Fabrication of BZT and BLZT thin films by sol-gel spin coating method
Overview of sol-gel spin coating method
The sol-gel process is a wet chemical method used for synthesizing various nanostructures, particularly metal oxide nanoparticles This technique involves dissolving a molecular precursor, typically a metal alkoxide, in water or alcohol, followed by heating and stirring to facilitate hydrolysis or alcoholysis, resulting in a gel Given that the gel produced is wet, it must be dried using suitable methods tailored to the intended properties and applications of the final product.
The sol-gel technique offers a unique approach to preparing porous materials in a single step, ensuring a uniform atomic-scale distribution of components through low-temperature synthesis and precise control over the microstructure of the final product This method involves two phases: a sol, which is a colloidal suspension of solid particles, and a gel, an interconnected network of solid-phase particles within a liquid medium Key advantages of sol-gel methods include high yields, low operational temperatures, and reduced production costs Additionally, sol-gel synthesis allows for the manipulation of the physico-chemical properties of the resulting compounds by carefully adjusting the parameters throughout the synthesis process.
The reaction mechanisms of sol-gel method consist of two main reactions:
(1) hydrolysis of precursors in acidic or basic media and (2) condensation of hydrolysis products
Hydrolysis reaction: in this reaction, a nucleophilic substitution mechanism is hypothesized, which results in the replacement of an alkoxy group with a hydroxyl
The condensation reaction occurs simultaneously with hydrolysis, where partially hydrolyzed alkoxy molecules can either interact with another hydroxyl-bearing species to release water or react with the alkoxy group to form an alcohol molecule.
The hydrolysis and condensation reactions in the sol-gel process are influenced by several key parameters, including the activity of metal alkoxides, the water-to-alkoxide ratio, pH levels, temperature, solvent type, and any additives used Additionally, catalysts are often incorporated to regulate the rate and extent of these reactions By adjusting these processing parameters, it is possible to achieve materials with varied microstructures and surface chemistry.
The basic steps of a typical sol-gel synthesis process are shown in Figure 2.1
Figure 2.1 An overview of the various stages of the sol-gel process
2.1.1.2 Techniques for fabricating films from sol-gel solutions
The sol-gel process can be effectively combined with various deposition techniques, including dip-coating, spin-coating, and spray-coating After preparing a sol with an appropriate composition for the desired coating application, the next step involves depositing it onto the substrate using one of these techniques.
Figure 2.2 Schematic representation of: (a) dip coating; (b) spin coating; and (c) spray coating [45]
Dip coating is an effective and straightforward method for applying a uniform liquid film onto a substrate by immersing it in a solution of hydrolysable metal compounds and withdrawing it at a consistent speed in a humid environment This process results in a homogeneous liquid film on the substrate's surface, making dip coating ideal for creating transparent oxide layers on transparent substrates while ensuring high surface quality and planarity.
Spin coating is a method for applying uniform thin films to flat substrates by depositing a small amount of fluid resin at the center and spinning the substrate at high speeds This process utilizes centrifugal force to spread the resin evenly across the surface, resulting in a thin film that may extend off the edges The final thickness and characteristics of the film are influenced by the resin's properties, including viscosity, drying rate, and surface tension, as well as the spin parameters such as rotational speed, acceleration, and fume exhaust.
The spray-coating method involves atomizing a sol to create a fine mist of droplets using compressed air or pressure A nozzle system then deposits these droplets evenly across the substrate For effective nebulization, the sol must have a lower viscosity compared to dip and spin coating techniques Additionally, coalescence of the fine droplets may occur if the substrate surface is wet.
This study utilizes the sol-gel spin coating method for the fabrication of BZT and BLZT films, highlighting its advantages such as cost-effectiveness, simplicity of equipment, and the ability to easily adjust thickness and composition The sol-gel spin coating process consists of two key stages: the generation of sol and the application of spin coatings, as illustrated in Figure 2.3.
Figure 2.3 Example of processing routes to obtain sol-gel spin coatings [46]
Fabrication of BZT and BLZT Sols
This study focuses on the fabrication of BZT and BLZT materials with a Zr:Ti ratio of 25:75 To investigate the influence of lanthanum doping on the ferroelectric properties of BLZT thin films, doping concentrations of 0%, 3%, 5%, and 8% are utilized The chemical component parameters for the preparation of BZT and BLZT sols are detailed in Table 2.1.
Table 2.1 Parameters of chemical components used to synthesize BZT and BLZT materials
Ba(CH 3 COO) 2 (Barium acetate) 255.42 - -
La(NO 3 ) 3 6H 2 O (lanthanum (III) nitrate hexahydrate) 433.02 - -
Zr(n-C 3 H 7 O) 4 (Zirconium n-propoxide) 70% 327.57 208 1.044 Ti(i-C 3 H 7 O) 4 (Titanium iso propoxide) 98% 284.22 170 1.04
CH 3 OCH 2 CH 2 OH (2-methoxyethanol) 76.10 125 0.965
CH 2 OHCH 2 OH (Ethylene glycol) 76.1 125 0.965
Barium acetate, lanthanum (III) nitrate hexahydrate, zirconium n-propoxide, and titanium isopropoxide serve as the primary starting materials for the synthesis process To effectively dissolve these salts, 2-methoxyethanol (MOE) is utilized as the solvent, while acetic acid acts as a catalyst to ensure the salts are quickly and completely dissolved A flow diagram illustrating the production of BZT and BLZT sols is presented in Figure 2.4.
Figure 2.4 Flow diagram for producing BZT and BLZT sols
To synthesize the desired compound, barium acetate and lanthanum (III) nitrate hexahydrate were combined in varying ratios (0-8% mol La) and dissolved in acetic acid, followed by heating the solution to 120°C and refluxing for 5 hours Concurrently, zirconium n-propoxide and titanium isopropoxide were blended in a specific ratio to achieve the molecular composition of BZT and dissolved in MOE, then heated to 120°C and refluxed for 3 hours Once cooled to room temperature, the Zr-Ti solution was gradually mixed with the Ba-La solution, which was then reheated.
The solution was heated to 120°C and refluxed for three hours, after which 2-methoxyethanol and ethylene glycol were incorporated to modify the viscosity, prevent film cracking, and achieve the target concentration of approximately 0.4 M Following a 24-hour aging period of the hydrolyzed solution, thin film deposition was performed on Pt/Ti/SiO2/Si substrates using the spin coating method.
Fabrication of BZT and BLZT thin films
Fabrication of BZT thin films
In order to determine the crystallization of the barium zirconium titanate (BZT) gel, the thermogravimetric analysis (TGA) - differential scanning calorimetry (DSC) plots are shown in Figure 2.5
Figure 2.5 TGA-DSC plots of BZT material
The study reveals a total mass loss of approximately 31% within the temperature range of 100°C to 600°C Initially, a weight loss of 1.98% occurs due to solvent evaporation, as indicated by the TGA curve and the endothermic peak at 75.48°C in the DSC analysis Subsequently, the most significant mass reduction, around 29.22%, is attributed to the breakdown of the xerogel structure and the combustion of organic compounds, which contributes to the initial formation of the BZT material structure This process is accompanied by three exothermic peaks at 353.25°C, 442.24°C, and beyond.
Methods to investigate the structure and properties of BZT and BLZT films…
X-ray diffraction by crystals was discovered in 1912, and since then it has been the most extensively studied and used technique for materials characterization [47] This method is the most effective methods for determining the crystal structure of materials It provides information on structures, phases, preferred crystal orientations (texture), and other structural parameters, such as average grain size, crystallinity, strain, and crystal defects XRD peaks are produced by constructive interference of a monochromatic beam of X-rays scattered at specific angles from each set of lattice planes in a sample The peak intensities are determined by the atomic positions within the lattice planes Consequently, the XRD pattern is the fingerprint of periodic atomic arrangements in a given material An online search of a standard database for X- ray powder diffraction patterns enables quick phase identification for a large variety of crystalline samples
Scattered X-rays from the sample can interfere either constructively or destructively, allowing detectors to register a signal only at angles of constructive interference, as illustrated in Figure 2.8.
Figure 2.8 Schematic representation of the Bragg’s law for diffraction [48]
The graph's dots represent the building blocks of crystalline materials, where atoms are periodically arranged When an X-ray beam strikes the material, it scatters at various planes, resulting in diffracted X-rays that travel different optical path lengths This path length is determined solely by the distance between crystal planes and the angle of the incident X-ray beam, encapsulated in the renowned Bragg Equation.
E.q 2.4 where is the wavelength of the x-ray beam, is the angle of incidence, is the interplanar spacing of the (hkl) planes, and n is an integer
Figure 2.9 The working principle diagram of X-ray diffractometer and PANalytical X- ray diffractometer (Malvern PANalytical) system [48]
This thesis presents X-ray diffraction (XRD) results obtained using a PANalytical X-ray diffractometer, employing Cu-Kα radiation with a wavelength of 1.5405 Å The instrument operated at a standard power of 1.8 kW, with settings of 45 kV and 40 mA A working principle diagram of the X-ray diffractometer is illustrated in Figure 2.9.
Scanning electron microscopy (SEM) is a versatile tool to reveal the microstructures inside objects
Scanning Electron Microscopy (SEM) generates images by scanning a sample's surface with a focused beam of energetic electrons, with image resolution influenced by both the electron probe's properties and its interaction with the specimen The interaction is determined by the acceleration of incident electrons, which possess significant kinetic energy, leading to the emission of secondary electrons (with energy > C_s), the potentials on the oscilloscope's x and y plates can be approximated by specific equations.
When the applied voltage V max is sufficient to saturate the sample and switch the domains, a distinct hysteresis loop appears on the oscilloscope in x-y mode This allows for the determination of the saturated polarization P s and the coercive field E c, as outlined in equations 2.4 and 2.5.
E.q 2.8 where A is the area of the ferroelectric capacitor and d is the thickness of the ferroelectric thin film
The dielectric constant can also be determined through the polarization according to the following formula:
The study utilized the dynamic hysteresis measurement option of the aixACCT TF-2000 Analyzer to measure the polarization-electric field (P-E) hysteresis loops, as illustrated in Figure 2.11.
Figure 2.11 Equipment for measuring ferroelectric properties of materials BLZT
This chapter provides an overview of the synthesis and fabrication methods for BLZT thin films, highlighting the use of thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) to determine an effective heat treatment process The phase composition of the BLZT films was analyzed through X-ray diffraction (XRD) using a PANalytical diffractometer, while the microstructure was examined via high-resolution scanning electron microscopy (HRSEM) Additionally, the ferroelectric properties of the BZT and BLZT thin films were assessed through polarization hysteresis loop measurements with the aixACCT TF2000 Analyzer.
RESULTS AND DISCUSSION
Effect of annealing temperature (T a ) on properties of BZT thin films
Cross-sectional SEM images of BZT thin films grown on the Pt/Ti/SiO 2 /Si substrates at various annealing temperatures (450 o C – 700 o C) are shown in Figure 3.1
Figure 3.1 Cross-sectional SEM images of BZT thin films, grown on Pt/Ti/SiO 2 /Si, at various annealing temperatures (a) 450 o C, (b) 500 o C, (c) 600 o C, (d) 650 o C, (e) 675 o C, (f) 700 o C
The fabricated films exhibited a dense structure, uniform appearance, and strong bonding with the substrate, except for those annealed at 700 °C, which displayed holes and non-uniformity This irregularity is attributed to the crystallization of the perovskite phase, as elaborated in the following section.
The thickness of BZT thin films depends on their annealing temperature (T a ) At lower temperatures (450 °C), the measured thickness is quite large, about
As the annealing temperature increases, the thickness of the films decreases from 500 nm to 376 nm due to the greater combustion of organic solvents and the crystallization process Higher temperatures influence the thermal fluctuations affecting the amorphous phase, leading to the formation of the perovskite phase, which increases the density of the films This increase in density is the primary reason for the reduction in thin film thickness at elevated annealing temperatures.
The crystalline structure of BZT thin films as a function of annealing temperature, characterized using XRD measurement, is shown in Figure 3.2 (a)
The X-ray diffraction (XRD) patterns of barium zirconate titanate (BZT) thin films, deposited on a Pt/Ti/SiO2/Si substrate, reveal significant changes at different annealing temperatures (Ta) A schematic representation illustrates the relationship between the phase transition of BZT thin films and varying annealing temperatures.
The XRD results indicated that a pure polycrystalline perovskite phase of BZT films starts at the annealing temperature of 675 o C and is clearly observed at
At annealing temperatures of 700 °C, BZT thin films exhibit a predominant (110) orientation along with a minor (100) orientation In contrast, films annealed at lower temperatures show almost no distinct peaks characteristic of the polycrystalline perovskite phase, indicating low crystallinity and a prevalence of amorphous and pyrochlore phases Figure 3.2 (b) illustrates the presence of an amorphous phase at temperatures below 600 °C, while higher temperatures lead to the emergence of the pyrochlore phase This highlights the significant impact of annealing temperature (T a) on the phase transition of BZT thin films.
Therefore, the heat treatment process for fabricating BZT films can be optimized based on the above analysis results
Ferroelectric properties and breakdown strength ( E BD )
This section discusses how the annealing temperature (T a ) influences the ferroelectric properties and breakdown strength (E BD ) of BZT thin films The polarization-electric field (P-E) hysteresis of BZT thin films at different annealing temperatures ranging from 450 °C to 700 °C is illustrated in Figure 3.3 (a), with measurements conducted at 1000 kV/cm and a frequency of 1 kHz.
At low temperatures of 450 °C, 500 °C, and 600 °C, the P-E loops are notably slim, indicating limited polarization In contrast, as the temperature rises, the P-E loops become increasingly coarse, leading to a significant increase in both maximum polarization (P max) and remnant polarization (P r).
Figure 3.3 Polarization-electric field (P-E) hysteresis loops and (b) values of P max , P r and P max - P r for BZT thin films at various annealing temperatures The measurements were performed at 1000 kV/cm and 1 kHz
The analysis of P-E hysteresis loops revealed that the values of P max, P r, and P max - P r increase with higher annealing temperatures (T a), indicating a correlation with changes in the crystalline structure of BZT films At lower annealing temperatures, an amorphous phase was present, resulting in a linear-like (or paraelectric) behavior and consequently lower polarization values In contrast, higher annealing temperatures promoted the formation of a polycrystalline perovskite phase, which exhibited enhanced polarization due to its ferroelectric properties.
Figure 3.4 illustrates the relationship between electric field strength and the maximum polarization (P max) and remnant polarization (P r) values for BZT thin films subjected to various annealing temperatures Measurements were taken from low electric fields up to the electric breakdown strength (E BD) at a frequency of 1 kHz and room temperature The analysis of the P-E loops revealed that maximum polarization increases with higher electric fields across all BZT films, while remnant polarization values remain low and largely unchanged, particularly at lower annealing temperatures Notably, the film annealed at 500 °C exhibited the highest P max value of 10.9 C/cm².
The electric field dependence of maximum polarization (P max) and remanent polarization (P r) values for BZT thin films varies with different annealing temperatures, as illustrated in Figure 3.4 These measurements were conducted until reaching the electric breakdown strength (E BD), with data derived from the corresponding polarization-electric field (P-E) loops.
The breakdown strength (E BD) values of BZT thin films at different annealing temperatures are presented in Table 3.1 The results indicate that E BD values are 5050 kV/cm at 450 °C, 7000 kV/cm at 500 °C, 4820 kV/cm at 600 °C, 3100 kV/cm at 700 °C, 1610 kV/cm at 800 °C, and 1315 kV/cm at 900 °C.
65o o C, 675 o C and 700 o C, respectively Clearly, the film annealed at 500 o C obtained the highest breakdown strength (E BD ), up to 7000 kV/cm, thus showing better energy storage performances
Table 3.1 Breakdown strength E BD values of BZT thin films at various annealing temperatures
This section explores the impact of annealing temperature (T a ) on the energy-storage properties of BZT thin films, with temperatures investigated at 450 °C, 500 °C, 600 °C, 650 °C, 675 °C, and 700 °C Polarization-electric field (P-E) hysteresis loops were measured at 1 kHz and room temperature to evaluate the performance of the films The findings from these P-E hysteresis loops will facilitate the determination of key energy-storage parameters for BZT capacitors, including storage energy density, recoverable energy density, and energy-storage efficiency, as outlined in equations 1.9 and 1.10 in the chapter.
The study analyzed the volumetric energy-storage density (U store), charge loss energy-storage density (U loss), recoverable energy-storage density (U reco), and energy-storage efficiency (η) of BZT thin films at different annealing temperatures The findings, illustrated in Figure 3.5, demonstrate that both U store and U reco increase with the application of an electric field across the BZT thin films.
BZT films increase at all annealing temperatures On the contrary, energy- storage efficiency (η) value of BZT films decreased slightly with increasing electric field
Figure 3.6 (a) illustrates the relationship between energy-storage densities and recoverable energy-storage in BZT thin films as influenced by annealing temperatures Notably, the film annealed at 500 °C achieved the highest energy storage (U store) of 45.6 J/cm³ and recoverable energy storage (U reco) of 30.92 J/cm³.
The energy-storage efficiency (η) of BZT films exhibits high values at lower annealing temperatures, as illustrated in Figure 3.6 (b), but decreases as the annealing temperature rises Notably, the film annealed at 500 °C achieved a significant energy-storage efficiency of 67.8%.
The analysis indicates that the film annealed at 500 °C exhibits the highest recoverable energy-storage density of 30.9 J/cm³, along with an impressive energy-storage efficiency of 67.8% This enhancement in energy storage properties is attributed to the film's amorphous structure, as confirmed by XRD results.
Effects of La-doping on properties of BZT thin films
Cross-sectional SEM images of BZT thin films grown on the Pt/Ti/SiO 2 /Si substrates with various La-doping contents are shown in Figure 3.8
Figure 3.8 SEM images of BL5ZT thin films
It can be seen that the films show a very compact film structure and a good bonding state with the substrate
XRD patterns of BLZT thin films grown on Pt/Ti/SiO2/Si reveal that undoped BZT films exhibit a pyrochlore phase with minimal characteristic peaks of the polycrystalline perovskite phase, indicating low crystallinity and the presence of amorphous structures In contrast, La-doped BZT thin films crystallize exclusively in a pure perovskite phase, predominantly oriented in (110) with a minor (100) orientation, showing no signs of secondary phase formation Notably, the (110) and (200) peak positions shift to higher 2-theta values as La3+ ion doping increases, leading to a gradual decrease in out-of-plane lattice parameters, which are approximately 4.050, 4.038, and 4.032 Å for 3, 5, and 8 mol.% La-doped BZT films, respectively This trend indicates successful doping of La3+ ions into the A sites of the Ba(Zr0.25Ti0.75)O3 unit cell and highlights the enhanced crystallization ability of BZT thin films with La doping.
Figure 3.9 XRD patterns of BLZT thin films grown on Pt/Ti/SiO 2 /Si with various La- doping contents
Ferroelectric properties and breakdown strength ( E BD )
In this section, the effect of La-doping on ferroelectric properties and breakdown strength (E BD ) of BZT thin films will be presented
The room-temperature polarization-electric field (P-E) hysteresis of BZT thin films with varying La doping contents was analyzed at 1000 kV/cm and 1 kHz frequency The undoped BZT film exhibited very slim P-E loops, while La-doped BZT films showed progressively coarser loops, resulting in significant increases in both maximum polarization (P max) and remnant polarization (P r) Notably, P max and P r rose sharply from the undoped BZT to the 3 mol.% La-doped BLZT thin films, with values of ~1.56 and 0.10 μC/cm² for the undoped film, and 9.27 and 3.89 μC/cm² for the 3 mol.% La-doped film, respectively Additionally, the difference (P max - P r) increased dramatically with La content up to 5%, but began to decline with further doping.
The polarization-electric field (P-E) hysteresis loops for BZT thin films with varying La doping contents (0-8 mol.%) are depicted in Figure 3.10 The measurements, conducted at 1000 kV/cm and 1 kHz, highlight key parameters including maximum polarization (P max), remnant polarization (P r), and the difference between these values (P max - P r).
The electric field dependence of maximum polarization (P max) and remanent polarization (P r) values for BZT thin films with varying La doping contents is illustrated in Figure 3.11 The findings reveal that both maximum and remanent polarization values rise with increasing electric field across all BLZT films Notably, the highest P max value recorded is 12.9 μC/cm² for the 5 mol.% La-doped BLZT thin films.
The electric breakdown strength (E BD) values of BZT thin films at different annealing temperatures are presented in Table 3.3, revealing values of 3100 kV/cm, 1000 kV/cm, 1650 kV/cm, and 1070 kV/cm for La contents of 0%, 3%, 5%, and 8%, respectively The undoped BZT thin film exhibits the highest breakdown strength of 3100 kV/cm due to its amorphous microstructure Notably, the 5% La-doped BZT thin film also demonstrates a significant breakdown strength of 1650 kV/cm.
The electric field dependence of maximum polarization (P max) and remnant polarization (P r) values for La-doped BZT thin films was analyzed across different La doping levels, measured up to their respective electric breakdown strength (E BD) These findings were derived from the corresponding polarization-electric field (P-E) loops.
Table 3.3 Electric breakdown strength (E BD ) of BZT thin films with various La doping contents
This section examines the impact of La doping on the energy-storage properties of BZT thin films, focusing on doping levels of 0%, 3%, 5%, and 8% Polarization-electric field (P-E) hysteresis loops were measured at 1 kHz and room temperature to evaluate these effects The findings from the P-E hysteresis loops will be used to calculate key parameters for the energy-storage properties of BZT capacitors, including storage energy density, recoverable energy density, and energy-storage efficiency, as outlined in equations 1.9 and 1.10 in Chapter 1.
The relationship between volumetric energy-storage density, recoverable energy-storage density, and energy-storage efficiency in BZT thin films with varying La doping levels is illustrated in Figure 3.12 The data reveals that both volumetric energy-storage density (U store) and recoverable energy-storage density (U reco) increase as the applied electric field intensifies across all films However, the energy-storage efficiency (η) of the BZT films exhibits a slight decrease with the rising electric field.
The relationship between volumetric energy-storage density (U store), recoverable energy-storage density (U reco), and energy-storage efficiency (η) is influenced by the applied electric field in BZT thin films with different levels of La doping, specifically at 0%, 3%, 5%, and 8%.
The data were calculated from the corresponding P-E loops
The energy-storage densities and recoverable energy-storage of BZT thin films with varying La doping contents are illustrated in Figure 3.13 (a) The maximum energy-storage density (U store) reaches 13.5 J/cm³ for 0% La doping, 5.2 J/cm³ for 3%, 11.5 J/cm³ for 5%, and 5.0 J/cm³ for 8% La doping In terms of recoverable energy-storage density (U reco), the values are 5.0 J/cm³ for 0%, 2.7 J/cm³ for 3%, 7.0 J/cm³ for 5%, and 2.5 J/cm³ for 8% La doping.
The undoped BZT thin film exhibits the highest energy storage capability due to its superior breakdown strength In contrast, the 5 mol.% La-doped BLZT thin film demonstrates optimal energy recovery behavior, attributed to a larger difference between maximum and remnant polarization However, this performance declines with increased La-doping levels.
The energy-storage efficiency (η) of the material was measured at various La doping levels, yielding values of 37.0%, 51.9%, 60.7%, and 50.0% for doping contents of 0%, 3%, 5%, and 8%, respectively, as illustrated in Figure 3.13 (b) This data indicates that η increases with higher La doping content, peaking at a maximum efficiency of 60.7% at 5% La doping.
% due to the slimmer P-E loop, and then decreases with a further increase in dopant content
The analysis indicates that the 5 mol.% La-doped BZT film exhibits a high recoverable energy-storage density of approximately 7.0 J/cm³ and an impressive energy-storage efficiency of 60.7% at an electric field strength of 1650 kV/cm This suggests that La-doped BZT thin films are promising lead-free materials for environmentally friendly energy-storage applications.
Figure 3.13 (a) Energy-storage densities, recoverable energy-storage and (b) energy- storage efficiency measured at the corresponding E BD values, for BZT thin films with various La doping contents
This section explores the relationship between La doping levels and the dielectric constant in BZT films Figure 3.14(a) presents the ε–E curves for BZT films with La doping contents ranging from 0% to 8%, measured at an electric field of 120 kV/cm and a frequency of 1000 Hz.
Figure 3.14 (a) Dielectric constant – electric field (-E) curves and (b) dielectric loss curves of BZT thin films with various doping content, measurement at room temperature frequency 1000 Hz
Dielectric loss measurements in relation to bias voltage exhibit a curvature akin to the tuning curves depicted in Figure 3.14(b) Notably, both the dielectric constant and dielectric loss of La-doped BZT thin films at zero bias show an increase, with the dielectric constant peaking at 164 for a doping concentration of 3% mol, as indicated in Table 3.4.
La-doped BZT thin film This is due to the improvement of the crystallinity of BZT films can be achieved by La-doping (as shown in the XRD analysis)
Table 3.4 The measured dielectric constant, dielectric loss for BZT thin films with various La doping contents (0 - 8%)
Thermal stability, frequency stability and fatigue endurance
Industrial applications necessitate energy storage solutions that not only perform efficiently at room temperature but also exhibit excellent thermal stability The growing demand for high-temperature energy storage devices, particularly dielectric capacitors, is driven by emerging applications in sectors like the automotive industry—specifically hybrid electric vehicles operating at around 140°C—and underground oil and gas exploration, which requires functionality at approximately 200°C.
This section discusses the temperature-dependent polarization of BZT thin films annealed at 500 °C, evaluated across a range of operating temperatures from 30 °C to 200 °C As shown in Figure 3.15 (a), the P-E loops measured at 4000 kV/cm and a frequency of 1000 Hz exhibit a gradual broadening with increasing operating temperature.
Figure 3.15 The operating-temperature dependence of (a) P-E loops, (b) P max , P r and
P max – P r values for BZT thin film at annealing temperature of 500 o C The measurements were performed at 4000 kV/cm and 1000 Hz
As illustrated in Figure 3.15 (b), both the maximum polarization (P max) and remanent polarization (P r) exhibit a slight increase with rising operating temperatures, while the difference between P max and P r remains nearly constant.
Analysis of P-E loop data reveals that as operating temperature rises, U store values show a slight increase while U reco values remain relatively stable, leading to a minor decrease in energy storage efficiency (η) Specifically, U reco fluctuates by less than 2.4%, and η changes by less than 5.9%, indicating strong temperature stability across a broad range of operating conditions.
The operating temperature significantly influences the energy storage density (U) and energy-storage efficiency (η) of BZT thin films, as illustrated in Figure 3.16 These measurements were conducted at an annealing temperature of 500 °C, under an electric field of 4000 kV/cm and a frequency of 1000 Hz.
This study investigates the frequency-dependent polarization of BZT thin films annealed at 500 °C across a broad frequency range of 100–10,000 Hz The P-E hysteresis loops, measured at 4000 kV/cm and room temperature, reveal that while the frequency dependence is minimal, even slight alterations in the P-E loop shapes can significantly affect maximum polarization (P max), remanent polarization (P r), and coercive field (E c) These changes in polarization with frequency are primarily attributed to the accumulation of mobile defects, such as oxygen vacancies, near the film/electrode interfaces, where their high mobility leads to the formation of interfacial layers under an external electric field.
As shown in Figures 3.18 (a) and (b), it is observed that P max, P r , P max - P r , and E c values are almost no significant change in the low-frequency region (100–
The nucleation rate is influenced by low-frequency electric fields (around 1000 Hz), where most nuclei form from defects at the film/electrode interfaces or within the film itself As a result, nucleation occurs gradually in this low-frequency range, as these nuclei begin to emerge immediately upon application of the electric field.
Figure 3.17 The frequencies-temperature dependence of P-E loops for BZT thin film at annealing temperature of 500 o C The measurements were performed at 4000 kV/cm and room temperature
The operating frequencies significantly influence the maximum power (P max), received power (P r), and the difference between them (P max - P r) in BZT thin films annealed at 500 °C Additionally, the electric field (E c) values, energy storage density (U), and energy-storage efficiency (η) are also affected by these frequency variations.
4000 kV/cm and room temperature
In the high-frequency range of 1000-10000 Hz, both the polarization (P r) and electric field (E c) increase significantly as frequency rises, attributed to the greater number of nucleation sites for opposite domains during transformation The P-E loops widen at lower frequencies within this range, indicating increased energy loss and reduced energy efficiency Analysis of the P-E loops from BZT thin films at 4000 kV/cm across various frequencies reveals that energy-storage density and efficiency remain relatively stable as the operating frequency increases from 100 to 1000 Hz, primarily due to the consistency of the maximum polarization (P max).
The efficiency (η) remains relatively stable with frequency increases, achieving 87.2% at 1000 Hz However, when the operating frequency surpasses 1000 Hz, the energy recovery values (U reco) decline from 10.2 to 8.4 J/cm³, accompanied by a slight decrease in energy storage values (U store) This leads to a reduction in efficiency, dropping from 87.8% to 74.7%.
At low frequency ranges of 100-1000 Hz, a high P max –P r and low E c are observed, resulting in a significant U reco and a large efficiency value (η) under an applied electric field of 4000 kV/cm These findings suggest that by adjusting the operating frequencies, it is possible to achieve both high energy storage density and enhanced efficiency simultaneously.
Long-term stability during charge-discharge cycling is crucial for the effective use of energy-storage capacitors in pulse-power electronic systems Enhanced charge-discharge endurance ensures the reliable operation of energy storage devices over extended cycles Consequently, the fatigue in polarization and piezoelectric properties has emerged as a key focus of academic research in recent decades This section will discuss the fatigue in polarization and electrical properties of BZT thin films annealed at 500 °C.
Figure 3.19 illustrates the fatigue behavior of BZT thin films at an annealing temperature of 500 °C across charge-discharge cycles up to 10^9 Part (a) presents the P-E loops after 0.1, 10^4, 10^6, and 10^9 cycles, while part (b) shows the values of P max, P r, and the difference P max – P r as a function of the number of charge-discharge cycles These tests were conducted at 4000 kV/cm, 1 kHz, and room temperature, utilizing a bipolar electric field with a specified pulse height.
At a field strength of 200 kV/cm and a pulse width of 100 kHz (or 5 μs), the P-E loops showed no significant differences, indicating fatigue-free behavior in the sample The values for P max and P r remained stable at 5.7 àC/cm² and 0.4 àC/cm², respectively, with a P max – P r value of 5.3 àC/cm² This stability resulted in consistent U store and U reco values, along with an efficiency (η) that exhibited only a minor fluctuation of approximately 1%, as illustrated in Figures 3.20 (a) and (b).
Figure 3.19 illustrates the comparison of P-E hysteresis loops measured across various charge-discharge cycles It also presents the relationship between maximum polarization (P max) and remanent polarization (P r) values as the number of charge-discharge cycles increases, under an applied electric field of 4000 kV/cm and a frequency of 1 kHz for the BZT thin film, which was annealed at 500°C The fatigue testing involved applying a bipolar electric field with a pulse height of 200 kV/cm and a pulse width of 100 kHz (or 5 μs).