Electric field dependence of P max and P r values for BZT thin films at various annealing temperatures, measured until their corresponding electric breakdown strength E BD.. Dependence o
LITERATURE REVIEWS
Overview of ferroelectric and relaxor ferroelectric properties
Perovskites and tungsten bronze exhibit the most exceptional piezoelectric and ferroelectric properties among various structures The perovskite-structured relaxor materials are under extensive investigation due to their ability to accommodate a wide range of cation substitutions at both A and B sites without significantly altering the overall structure, allowing for complete solid solutions across various compositions Notably, perovskites demonstrate a high degree of anisotropy in their piezoelectric properties compared to other structures These materials can easily undergo phase transitions, with the mineral perovskite (CaTiO₃) exhibiting an orthorhombic structure The ideal perovskite follows the general formula ABO₃, where the A-site cations have valences ranging from +1 to +3, while the B-site is occupied by cations with valences of +3, +4, or +5 The structure can be visualized as BO₆ octahedra sharing corners in three dimensions, creating a symmetric arrangement, with A cations occupying the spaces formed by eight BO₆ octahedra, resulting in 12-fold oxygen coordination for A cations and 6-fold coordination for B cations.
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 radius of the A-site cation in 12 coordination and the B-site cation in 6 coordination, along with the radius of the oxygen ion, are crucial parameters The tolerance factor, denoted as \( t \), should ideally range from 0.95 to 1.04 for cubic symmetry, while a larger value is expected 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 seen a surge in interest for new material fabrication Ferroelectrics are compounds with a permanent dipole moment, characterized by spontaneous polarization that can be reversed by an external electric field, particularly below the Curie temperature (T_c) The arrangement of cations and anions within these materials creates dipole moments in each unit cell, allowing for the measurement of polarization through surface current A key feature 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 T_c, a transformation occurs from ferroelectric to paraelectric phase, with paraelectric materials exhibiting normal dielectric behavior without hysteresis Further details on hysteresis will be discussed in the next 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 is randomly oriented at high temperatures As the temperature decreases, these dipoles become orderly aligned within a domain, all pointing in the same direction, a phenomenon observed in hydrogen-bonded ferroelectric materials Conversely, displacive transitions are characterized by a polarization catastrophe, where the displacement of an ion from its equilibrium position results in local electric fields that overpower the elastic-restoring forces, leading to a permanent dipole moment Barium titanate (BTO) is a prime example of a displacive ferroelectric.
Ferroelectric materials experience either first or second order phase transitions In a second order phase transition, the spontaneous polarization (\$P_s\$) gradually decreases as the temperature rises, ultimately reaching zero.
The transition in triglycine sulfate is classified as a second-order type, while barium titanate experiences a first-order transition, characterized by a sudden drop in polarization to zero at the critical temperature (\$T_c\$) These first and second-order transitions are illustrated schematically 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 internal ordering of dipoles within a dielectric material, independent of external influences This phenomenon is driven by various atomic mechanisms, and the overall polarization, denoted as \$P_{\text{total}}\$ can be expressed mathematically.
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 (\(P_e\)) occurs when an electric field distorts the symmetrical distribution of electron clouds in atoms or molecules, leading to a displacement of the outer electron clouds relative to the positively charged atomic cores.
Atomic or ionic polarization (\$P_i\$) occurs in an ionic lattice when positive ions are displaced toward the direction of an applied electric field, while negative ions move in the opposite direction This displacement results in an apparent dipole moment for the entire structure.
Orientational polarization (P₀) occurs when molecules with permanent dipole moments align due to an asymmetric charge distribution, a phenomenon also referred to as dipole polarization.
Space charge polarization (P_sc) occurs at elevated electric fields when carrier injection plays a significant role In materials with a high density of charge carriers, the migration of these carriers leads to the formation of space charges at interfaces or grain boundaries, which is crucial for understanding this phenomenon.
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 a unique polarization behavior characterized by a closed curve known as the hysteresis loop, which sets them apart from conventional dielectric materials The hysteresis loop is a key indicator for identifying ferroelectrics, and its rectangular shape is crucial for the functionality of memory cells Additionally, the relationship between the electric field and polarization is linear, further defining the properties of these materials.
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 direction of the field, resulting in a single domain within appropriately oriented crystals The saturation polarization, denoted as \( P_s \), can be determined by extrapolating the linear segment on the polarization axis.
As the strength of the electric field decreases, the polarization diminishes but does not return to zero, resulting in remnant polarization (P_r) when the field is completely removed The coercive field (E_c) is the strength needed to eliminate this remnant polarization or to bring the polarization back to zero Additionally, increasing the field in the negative direction aligns the dipoles accordingly, allowing the cycle to be completed by reversing the field direction.
Ferroelectric materials consist of small regions called domains, each exhibiting uniform polarization These domains often have differing orientations, leading to a complex arrangement within the material In a single domain, dipoles align in the same direction, which can be reversed by applying an external electric field The overall polarization in a specific direction is influenced by the balance of oppositely aligned domains; if they occupy equal volumes, the net polarization becomes zero Domain walls separate these regions, and changes in temperature or external electric fields can alter the dipole moment, resulting in domain wall movement, 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 is primarily composed of two conductive plates separated by dielectric materials, often arranged in a parallel-plate configuration Its main function in electronic devices is to store electric energy, quantified by a property known as capacitance This capacitance is determined solely by the physical dimensions of the conductors and the permittivity of the dielectric materials, remaining unaffected by the voltage between the plates or the total charge they hold 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, a process known as charging the capacitor This charging process concludes when the electrical potential from the accumulated charge \( Q \) equals the external voltage \( V \), establishing the relationship \( Q/V = C \), where \( C \) represents the capacitance of the capacitor Additionally, variations in the relative permittivity of the dielectrics due to external bias can cause changes in capacitance, which is defined in terms of incremental change.
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, requiring work to be done and resulting in the storage of electric energy in the dielectrics The stored energy \( W \) can be calculated using a specific formula.
Measuring methods of energy-storage density for dielectric
In research, the energy-storage density, denoted as U, represents the energy stored per unit volume of a dielectric, facilitating convenient comparisons Typically, U values can be determined through two primary methods: the static method and the dynamic method.
Figure 1.11 illustrates a circuit designed for static measurement of energy-storage density Initially, the sample capacitor is charged using an external bias, allowing electric energy to be stored in the dielectric Subsequently, the capacitor is connected to a load resistor (R) through MOSFET switching, enabling the discharge of a portion of the stored energy, which generates a transient current in the closed circuit The discharged energy can be calculated using the I(t) - t curve and the appropriate formula.
The energy density \( U \) can be calculated by taking the ratio of the work \( W \) to the volume of the capacitor, where \( R \) represents the load resistance and \( t \) is the discharge time It is important to highlight that the calculated \( U \) value reflects the recoverable energy-storage density, as some 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 dynamic method allows for the derivation of energy-storage density from formula (1.9) 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 Consequently, by integrating this understanding with formula (1.9), the energy-storage density U can be articulated effectively.
The integral in equation 1.11 represents the relationship between the external applied electrical field \( E \), defined as \( V/d \), and other previously defined variables In dielectrics with high permittivity, the electrical displacement \( D \) closely approximates the electrical polarization \( P \) Consequently, equation (1.11) can be reformulated to reflect this relationship.
The U value of dielectrics can be easily determined through numerical integration of the area between the polarization and the electric field-polarization (P - E) loops, as indicated by formula (1.9) As depicted in Figure 1.12 (a), the polarization rises to its maximum value, P max, when the electric field increases from zero to the maximum E max, resulting in stored electrical energy, U store, represented by the green and red areas During the discharge process from E max to zero, the recoverable electrical energy density is also highlighted.
The release of U reco is illustrated by the green area in the figure, indicating that a portion 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 Additionally, 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 effectively design a dielectric material that achieves high recoverable energy-storage density and efficiency with 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 typical polarization-electric field (P-E) loops and energy-storage characteristics of four types of dielectrics: (a) linear dielectrics with constant permittivity, such as Al₂O₃ and glass; (b) ferroelectrics exhibiting spontaneous polarization, like BaTiO₃ and PbTiO₃; (c) relaxor ferroelectrics featuring nanosized domains, including (Pb,La)(Zr,Ti)O₃ and (Ba,La)(Zr,Ti)O₃; and (d) anti-ferroelectrics with zero net remnant polarization, exemplified by PbZrO₃.
The diagram in Figure 1.13 illustrates hysteresis and energy storage density across various materials: (a) linear dielectrics, (b) ferroelectrics, (c) relaxor ferroelectrics, and (d) anti-ferroelectrics The green region in the first quadrant represents the recoverable energy density, denoted as \$U_{\text{reco}}\$ while the red area indicates the energy loss, represented as \$U_{\text{loss}}\$ [32].
Linear dielectrics, while offering higher breakdown fields and lower energy loss, are less suitable for high energy-storage applications due to their smaller polarization values In contrast, ferroelectrics exhibit larger saturated polarization and moderate electric-field endurance, but 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, as they feature larger saturated polarization, smaller remnant polarization, and moderate breakdown fields Additionally, advancements in manufacturing processes, such as glass-crystallization techniques and composite technology, 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, enhancing their potential for energy storage applications.
Overview of barium titanate-based materials
Recent studies have focused on lead-free BaTiO₃-based ceramics due to their environmentally friendly properties and potential value These ceramics exhibit composition-dependent relaxor behavior, which is influenced by the type and rate of ion substitution Notably, when the composition deviates significantly from the base BaTiO₃ and involves heterovalent ion substitution at the 6-coordination number crystallographic site, the relaxor behavior becomes more pronounced.
Barium titanate (BaTiO₃ or BTO) is a widely studied ceramic material known for its exceptional dielectric, ferroelectric, and piezoelectric properties Its high dielectric constant is attributed to its unique perovskite crystal structure.
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 a face-centered cubic lattice, each barium ion is surrounded by 12 oxygen ions, while titanium atoms occupy larger octahedral interstitial positions surrounded by six oxygen ions Due to the significant size difference, the barium ions create a large octahedral site that is unstable for the smaller titanium ions Instead, the titanium ions find minimum-energy positions off-center towards each of the surrounding oxygen ions With a +4 charge, the titanium ions exhibit a high degree of polarization When an electric field is applied, these ions can transition from random to aligned positions, leading to increased bulk polarization and a high dielectric constant.
Barium titanate exhibits 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, where the Ti⁴⁺ ion is centrally located within an octahedron of oxygen ions However, as the temperature drops below 120°C, a displacive transformation occurs, changing the structure to tetragonal, leading to an off-center movement of the Ti⁴⁺ ion towards one of the oxygen ions, which generates spontaneous polarization When an electric field is applied, the Ti⁴⁺ ion shifts to an equivalent off-center position, resulting in reversed polarization, hysteresis in the electric field versus polarization curve, and the manifestation of ferroelectric behavior.
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 domain wall movement restricted by grain boundaries, resulting in a lower dielectric constant at the Curie point At room temperature, coarse-grained BaTiO₃ ceramics have a dielectric constant ranging from 1500 to 2000, while fine-grained BaTiO₃ shows a significantly higher dielectric constant of approximately 3500.
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) ceramic material is recognized for its high dielectric properties, making it suitable for piezoelectric applications like ceramic sonar transducers However, its ferroelectric characteristics, particularly a sharp dielectric response near the Curie temperature of approximately 120 °C, limit its effectiveness for energy storage due to high remanent polarization (Pₗ) and poor thermal stability Doping is a well-established method to enhance the electrical properties of electroceramics, as substituting A and/or B cation sites in ABO₃ perovskites with appropriate acceptor, donor, or isovalent impurity ions can significantly modify their electrical behavior.
Doping barium titanate with isovalent Zr 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\(_c\)) Additionally, the substitution concentration of Ti\(^{4+}\) ions, which have an atomic weight of 47.9 and an ionic radius of 0.0605 nm, plays a crucial role in this process.
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+ ions with Zr 4+ ions transforms ferroelectric micro-domains into dynamic polar nano-regions (PRNs), leading to a transition from normal ferroelectric behavior to relaxor behavior as Zr concentration increases BZT ceramics maintain normal ferroelectric behavior with Zr concentrations below 10 mol.% and exhibit relaxor behavior above 20 mol.% The larger ionic radius of Zr 4+ expands the lattice parameters of BZT and decreases the ferroelectric-paraelectric phase transition Additionally, Zr 4+ ions are more chemically stable than Ti 4+ ions, reducing conduction caused by electron hopping and improving BZT properties Research by Sun et al demonstrated a remarkable energy storage density of 30.4 J/cm³ and an energy efficiency of 81.7% at room temperature for lead-free BaZr 0.2 Ti 0.8 O 3 thin films These films also showed excellent thermal stability and fatigue endurance across a wide temperature range Liang et al reported an ultrahigh recoverable energy density of 78.7 J/cm³ and efficiency of 80.5% in BaZr 0.35 Ti 0.65 O 3 film capacitors, with impressive energy storage capabilities even at elevated temperatures.
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 even lead-based systems Their high dielectric constant, low dielectric loss, and significant tunability make BZT capacitors highly promising for modern electronic applications However, it is important to note that their dielectric properties are influenced by temperature and frequency.
Doping is a widely used technique to enhance the electrical and other properties of barium titanate (BTO) and barium zirconate titanate (BZT) materials Various dopants, including Zn²⁺, Ca²⁺, Sr²⁺, Sm³⁺, and La³⁺, can substitute for the A sites in the ABO₃ perovskite structure, functioning as electron acceptors to improve dielectric properties.
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 constant of Zn-doped BZT films initially decreases and then increases with higher Zn content, while the dielectric loss consistently decreases at room temperature Additionally, 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 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, significant polarization, and elevated energy density characteristics, making them promising 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
The electric breakdown strength of 5 mol % La-doping is measured in MV/cm, indicating that an optimal concentration of 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 significantly enhances energy-storage density and efficiency in pulse-power systems Notably, La-doping has improved the properties of BZT thin films, making them a promising environmentally friendly option for next-generation advanced energy-storage capacitors This analysis led to the selection of the research topic: “Effect of Zr and La based co-doping on electrical properties of lead-free barium titanate BaTiO 3 thin films.”
EXPERIMENTS AND METHODS
Fabrication of BZT and BLZT thin films by sol-gel spin coating method…
by sol-gel spin coating method
Modern measurement and analysis techniques were employed to investigate the properties of the fabricated films The crystallographic properties of the thin films were analyzed using X-ray diffraction (XRD) with a PANalytical diffractometer and Cu-Kα radiation (wavelength: 1.5405 Å) Additionally, the microstructure of the BZT thin films was examined through cross-sectional high-resolution scanning electron microscopy (HRSEM) using a Zeiss-1550 system The ferroelectric properties of the materials were assessed by polarization hysteresis loop measurements conducted with an 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 induce gel formation through hydrolysis or alcoholysis After the gel is produced, it is essential to dry it using suitable methods tailored to the desired properties and applications of the gel.
The sol-gel technique offers a unique approach to preparing porous materials in a single step, ensuring a homogeneous atomic-scale distribution of components This low-temperature synthesis method allows for precise control over the microstructure of the final product Sol-gel chemistry consists of two phases: a sol, which is a colloidal suspension of solid particles, and a gel, an interconnected network of these particles within a liquid phase Key advantages of sol-gel methods include high yield, low operational temperatures, and reduced production costs Additionally, sol-gel synthesis enables 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 alongside the hydrolysis reaction, where partially hydrolyzed alkoxy molecules can either react with another hydroxyl-bearing species to eliminate water or interact with the alkoxy group to produce 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/alkoxide ratio, solution pH, 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 diverse microstructures and surface chemistries.
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 integrated with various deposition techniques, including dip-coating, spin-coating, and spray-coating To produce a coating, the sol must first be prepared with a composition tailored for the specific application, followed by its deposition onto the substrate using the chosen technique.
Figure 2.2 Schematic representation of: (a) dip coating; (b) spin coating; and (c) spray coating [45]
Dip coating is an effective and consistent method for applying a wet liquid film by immersing a substrate in a solution of hydrolysable metal compounds or particles, followed by a controlled withdrawal into a humid environment This technique results in a uniform liquid film on the substrate's surface, making it ideal for creating transparent oxide layers on transparent substrates with excellent planarity and surface quality.
Spin coating is a technique for applying uniform thin films to flat substrates by depositing a small puddle of fluid resin at the center and spinning the substrate at high speeds The centrifugal force spreads the resin to the edges, creating a thin film on the surface The final film thickness and properties are influenced by the resin's characteristics, including viscosity, drying rate, and surface tension, as well as the spin process 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 pressurization A nozzle system then deposits these droplets evenly across the substrate For effective nebulization, the sol's viscosity must be lower than that used in dip and spin coating techniques Additionally, coalescence of the droplets can occur if the substrate surface is wet.
This study utilizes the sol-gel spin coating method to fabricate BZT and BLZT films, highlighting its advantages of simplicity, cost-effectiveness, and flexibility in adjusting thickness and composition The sol-gel spin coating process consists of two primary 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 examined 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 The salts are dissolved in 2-methoxyethanol (MOE), with acetic acid acting as a catalyst to ensure rapid and complete dissolution A flow diagram illustrating the production of BZT and BLZT sols is provided in Figure 2.4.
Figure 2.4 Flow diagram for producing BZT and BLZT sols
Barium acetate and lanthanum (III) nitrate hexahydrate were combined in varying ratios (0-8% mol La) and dissolved in acetic acid, then heated to 120 °C and refluxed for 5 hours Subsequently, zirconium n-propoxide and titanium isopropoxide were mixed to achieve the desired molecular composition of BZT and dissolved in MOE, also heated to 120 °C This Zr-Ti solution was refluxed for 3 hours, and after cooling to room temperature, it was gradually combined with the Ba-La solution.
The solution was heated to 120 °C and refluxed for 3 hours To adjust the viscosity, prevent film cracking, and achieve the desired concentration, 2-methoxyethanol and ethylene glycol were added, resulting in a final concentration of approximately 0.4 M After aging the hydrolyzed solution for 24 hours, 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% is attributed 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 of around 29.22% is linked to the breakdown of the xerogel structure and the combustion of organic compounds, which facilitates the initial formation of the BZT material structure This process is associated with three exothermic peaks observed 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 capture signals 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 dots in the graph represent the building blocks of crystalline material, where atoms are arranged periodically due to its crystalline nature When an incident X-ray beam interacts with the material, it is scattered at various planes, resulting in diffracted X-rays that travel different optical path lengths This path length is determined solely by the distance between the crystal planes and the angle of incidence of the X-ray beam, encapsulated in the well-known 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 XRD results obtained using a PANalytical X-ray diffractometer, utilizing Cu-Kα radiation with a wavelength of 1.5405 The instrument operated at a normal power of 1.8 kW, with settings of 45 kV and 40 mA A diagram illustrating the working principle of the X-ray diffractometer is provided 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 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 energies below 50 eV This emission efficiency is affected by the surface geometry, chemical characteristics, and bulk composition of the sample SEM's high resolution is particularly advantageous for analyzing nanomaterials, where nanoscale structural features are crucial for understanding properties and functionalities The electron beam interacts with the sample's atoms, producing various signals that provide insights into texture, chemical composition, crystalline arrangement, and constituent orientation Additionally, SEM is capable of identifying surface fractures, inspecting contaminations, revealing spatial variations in chemical compositions, and analyzing crystalline structures.
This thesis utilized scanning electron microscopy (SEM) to analyze the cross-section and measure the thickness of BLZT thin films The microstructure of these films was examined using High Resolution Scanning Electron Microscopy (HRSEM: Zeiss-1550) at the Technology and MESA+ Institute for Nanotechnology, University of Twente, Netherlands.
In ferroelectric thin films, key parameters to assess include remanent polarization (\$P_r\$), saturated polarization (\$P_s\$), coercive field (\$E_c\$), breakdown field (\$E_{BD}\$), relative dielectric permittivity, and loss factor The phenomenon of ferroelectric hysteresis is associated with the growth and reorientation of electrical polarization within domains in response to the applied electric field.
Figure 2.10 illustrates the schematic of a Sawyer-Tower circuit designed for hysteresis measurement of ferroelectric thin films This circuit employs a large series capacitor to assess the variation in polarization of the sample ferroelectric capacitors in relation to voltage changes.
Figure 2.10 The schematic drawing of a Sawyer-Tower circuit used for hysteresis measurement of ferroelectric thin film [49]
An alternating voltage is applied to electrodes on a ferroelectric sample placed on an oscilloscope's horizontal plate, with the horizontal axis representing the electric field across the sample A linear capacitor connected in series with the sample allows the voltage across it to reflect the sample's polarization, which is shown on the oscilloscope's vertical axis By ensuring that the capacitance of the linear capacitor is significantly larger than that of the ferroelectric sample, 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 clear hysteresis loop appears on the oscilloscope in x-y mode The saturated polarization \$P_s\$ and the coercive field \$E_c\$ can be calculated using 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:
This study presents the measurement of polarization-electric field (P-E) hysteresis loops using the dynamic hysteresis measurement option of the ferroelectric module in an aixACCT TF-2000 Analyzer, 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 It discusses the heat treatment process for BZT and BLZT films, guided by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) techniques The phase composition of the BLZT film was analyzed using X-ray diffraction (XRD) with a PANalytical diffractometer and Cu-Kα radiation Additionally, the microstructure of the BZT thin films was examined through cross-sectional measurements using High Resolution Scanning Electron Microscopy (HRSEM) The ferroelectric properties of the BZT and BLZT thin films were assessed via 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 and uniform appearance with strong bonding to the substrate, except for those annealed at 700 °C, which displayed holes and a lack of uniformity This irregularity is attributed to the crystallization of the perovskite phase, as will be discussed 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 Additionally, the crystallization process influenced by thermal fluctuations affects the amorphous phase, leading to the formation of the perovskite phase and an increase in film density This combination of factors results in the reduction of 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 XRD patterns of BZT thin films, deposited on Pt/Ti/SiO₂/Si, reveal variations based on different annealing temperatures (T_a) Additionally, a schematic illustrates the relationship between phase transitions and annealing temperature for these BZT thin films.
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 700 °C, the films exhibit a predominant (110) orientation along with a minor (100) orientation However, when annealed at lower temperatures, distinct peaks characteristic of the polycrystalline perovskite phase are nearly absent, indicating low crystallinity and the presence of mainly amorphous and pyrochlore phases Figure 3.2 (b) illustrates the existence of an amorphous phase at annealing temperatures below 600 °C, while higher temperatures reveal the emergence of a 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 the impact of annealing temperature (T_a) on the ferroelectric properties and breakdown strength (E_BD) of BZT thin films The polarization-electric field (P-E) hysteresis of these films at different annealing temperatures ranging from 450 °C to 700 °C is illustrated in Figure 3.3 (a), with measurements taken at 1000 kV/cm and a frequency of 1 kHz.
At low temperatures (450 °C, 500 °C, 600 °C), the P-E loops are notably slim, as illustrated in Figure 3.3 (a) In contrast, at elevated temperatures, the P-E loops become increasingly coarse, accompanied by a rapid rise 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 the 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 At lower annealing temperatures, BZT films exhibited an amorphous phase, as confirmed by XRD analysis, resulting in a linear-like (or paraelectric) behavior and consequently lower polarization values In contrast, higher annealing temperatures led to the formation of a polycrystalline perovskite phase in BZT films, which is associated with 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 a low electric field up to the electric breakdown strength (E BD), which is the maximum electric field a dielectric capacitor can endure before failure, at a frequency of 1 kHz and room temperature The analysis of the P-E loops revealed that P max increases with the electric field for all BZT films, while P r remains low and shows minimal variation, 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 the maximum polarization (P max) and remnant polarization (P r) values for BZT thin films is analyzed at different annealing temperatures, measured up to their electric breakdown strength (E BD) The data presented were 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 E BD values recorded are 5050 kV/cm at 450 °C, 7000 kV/cm at 500 °C, 4820 kV/cm at 600 °C, 3100 kV/cm, 1610 kV/cm, and 1315 kV/cm for the respective temperatures.
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 discusses 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 The results from these P-E hysteresis loops will be used to determine 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 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 Figure 3.5 illustrates the relationship between these energy-storage metrics and the applied electric field Notably, both volumetric energy-storage density (U store) and recoverable energy-storage density (U reco) increase with the application of the electric field.
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 a function of 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 is significantly high at low annealing temperatures, as illustrated in Figure 3.6 (b), but it decreases with higher annealing temperatures Notably, the film annealed at 500 °C reached an impressive 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% The amorphous structure of the film at this temperature, as confirmed by XRD results, significantly enhances its energy storage properties.
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 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, all La-doped BZT thin films crystallize in a pure perovskite phase without secondary phases, predominantly showing (110) orientation alongside a minor (100) orientation Notably, the (110) and (200) peak positions shift to higher 2-theta values as La³⁺ doping increases, leading to a gradual decrease in out-of-plane lattice parameters This trend suggests successful incorporation of La³⁺ ions, which have a smaller ionic radius (1.32 Å), into the A sites of the Ba(Zr₀.₂₅Ti₀.₇₅)O₃ unit cell, with out-of-plane lattice parameters measuring approximately 4.050, 4.038, and 4.032 Å for 3, 5, and 8 mol.% La-doped BZT thin films, respectively Thus, La doping significantly enhances the crystallization capability of BZT thin films.
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, revealing that the P-E loops of undoped BZT films are slim, while La-doped films exhibit coarser loops This change results in a significant increase in both maximum polarization (P max) and remnant polarization (P r), with values rising from ~1.56 and 0.10 μC/cm² for undoped BZT to 9.27 and 3.89 μC/cm² for 3 mol.% La-doped BLZT thin films Notably, the difference (P max - P r) increases dramatically with La content up to 5%, but begins to decline with further doping.
The P-E hysteresis loops of BZT thin films with varying La doping contents (0-8 mol.%) are illustrated in Figure 3.10, showcasing the values of maximum polarization (P max), remnant polarization (P r), and the difference between them (P max - P r) These measurements were conducted at an electric field of 1000 kV/cm and a frequency of 1 kHz.
Figure 3.11 illustrates the relationship between the electric field and the maximum polarization (P max) and remanent polarization (P r) values for BZT thin films with different La doping levels The findings reveal that both P max and P r values rise with increasing electric field across all BLZT films Notably, the highest P max value of 12.9 μC/cm² is achieved in 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 The results indicate that E BD values are 3100 kV/cm for undoped BZT, 1000 kV/cm for 3% La-doped, 1650 kV/cm for 5% La-doped, and 1070 kV/cm for 8% La-doped films The undoped BZT thin film exhibits the highest breakdown strength of 3100 kV/cm due to its microstructure in the amorphous phase, while the 5% La-doped BZT thin film also shows 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 at different La doping levels, measured up to their respective electric breakdown strength (E BD) The data 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 discusses the impact of La doping on the energy-storage properties of BZT thin films, with doping levels of 0%, 3%, 5%, and 8% being examined Polarization-electric field (P-E) hysteresis loops were measured at 1 kHz and room temperature The results from these P-E hysteresis loops will be used to calculate 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 chapter 1.
Figure 3.12 illustrates the relationship between volumetric energy-storage density, recoverable energy-storage density, and energy-storage efficiency in BZT thin films with varying La doping levels as a function of the applied electric field It is evident that both volumetric energy-storage density (U store) and recoverable energy-storage density (U reco) increase with a higher electric field across all films However, the energy-storage efficiency (η) of the BZT films shows a slight decrease as the electric field intensifies.
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 La doping levels, specifically at 0%, 3%, 5%, and 8%.
The data were calculated from the corresponding P-E loops
Figure 3.13 (a) illustrates the relationship between energy-storage densities and recoverable energy-storage in BZT thin films with varying La doping levels The maximum energy-storage density (\$U_{store}\$) reaches values of 13.5 J/cm³, 5.2 J/cm³, 11.5 J/cm³, and 5.0 J/cm³ for La doping contents of 0%, 3%, 5%, and 8%, respectively In contrast, the recoverable energy-storage density (\$U_{reco}\$) is measured at 5.0 J/cm³, 2.7 J/cm³, 7.0 J/cm³, and 2.5 J/cm³ for the corresponding doping levels.
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 its larger difference between maximum and remnant polarization However, this performance declines with increased La-doping levels.
The energy-storage efficiency (\( \eta \)), defined as the ratio of \( U_{\text{reco}} \) to \( U_{\text{store}} \), demonstrated values of 37.0%, 51.9%, 60.7%, and 50.0% for La doping contents of 0%, 3%, 5%, and 8%, respectively This trend indicates that the efficiency (\( \eta \)) increases with higher La-doping content, peaking at a maximum of 60.7%.
% due to the slimmer P-E loop, and then decreases with a further increase in dopant content
The analysis reveals that the 5 mol.% La-doped BZT film exhibits a high recoverable energy-storage density of approximately 7.0 J/cm³ and an energy-storage efficiency of 60.7% at an electric field strength of 1650 kV/cm This indicates that La-doped BZT thin films are promising lead-free materials for environmentally friendly energy-storage devices.
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 examines the dependence of La-doping on the dielectric constant by presenting the ε–E curves of BZT films with La doping levels ranging from 0% to 8% These measurements were conducted at an electric field of 120 kV/cm and a frequency of 1000 Hz, as illustrated in Figure 3.14(a).
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 a value of 164 for a doping concentration of 3% mol, as detailed 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 require energy storage devices to exhibit excellent performance at room temperature and maintain thermal stability The growing demand for high-temperature energy storage solutions, particularly in sectors like automotive (e.g., hybrid electric vehicles operating at approximately 140°C) and underground oil and gas exploration (with working temperatures around 200°C), highlights the importance of dielectric capacitors in these new applications.
The temperature-dependent polarization of BZT thin films was evaluated at an annealing temperature of 500 °C across a range of operating temperatures from 30 to 200 °C The P-E loops, measured at 4000 kV/cm and a frequency of 1000 Hz, exhibited a gradual broadening as the operating temperature increased, as shown in Figure 3.15 (a).
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.
The analysis of P-E loops revealed that the values of U store and U reco were calculated, as illustrated in Figure 3.16 (a) With increasing operating temperatures, U store values showed a slight rise, while U reco values remained nearly unchanged, leading to a minor decrease in energy storage efficiency (η), as depicted in Figure 3.16 (b) The fluctuation in U reco was less than 2.4%, and the change in η was under 5.9%, indicating strong temperature stability across a broad range of operating temperatures.
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 section discusses the frequency-dependent polarization of BZT thin films annealed at 500 °C, measured across a wide frequency range of 100 to 10,000 Hz The P-E hysteresis loops, recorded 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–
In the low-frequency region (up to 1000 Hz), the nucleation rate is influenced by defects at the film/electrode interfaces and within the film itself When an electric field is applied, most nuclei involved in the transformation emerge from these defects, leading to a slower nucleation rate in this frequency range.
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 dependence of operating frequencies on key parameters for BZT thin film annealed at 500 °C is illustrated in Figure 3.18 It shows the variations in maximum power (P max), received power (P r), and the difference between them (P max - P r), alongside the energy conversion values (E c) Additionally, the figure highlights the energy storage density (U) and energy-storage efficiency (η) under these conditions.
4000 kV/cm and room temperature
In the high-frequency range of 1000-10000 Hz, both the remanent polarization (P r) and the electric field (E c) increase significantly with frequency, attributed to a rise in nucleation sites for opposite domains during transformation The P-E loops become broader at lower frequencies within this range, indicating greater 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 the energy-storage density and efficiency remain relatively stable as the frequency increases from 100 to 1000 Hz, primarily due to the constancy of the maximum polarization (P max).
The efficiency value (\(\eta\)) remains relatively stable with increasing frequency, reaching 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 frequencies (100-1000 Hz), a high P max – P r and small E c are observed, resulting in a significant U reco and a large η value under an electric field of 4000 kV/cm These findings suggest that it is possible to achieve both high energy storage density and efficiency by adjusting the operating frequencies.
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 these devices over extended cycling periods Consequently, the fatigue in polarization and piezoelectric properties has emerged as a key area of academic research in recent decades This section will focus on 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 Subfigure (a) presents the P-E loops after 0.1, 10^4, 10^6, and 10^9 cycles, while subfigure (b) shows the values of P max, P r, and P max – P r as a function of the number of charge-discharge cycles, conducted at 4000 kV/cm, 1 kHz, and room temperature The fatigue testing involved applying a bipolar electric field with a specific 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 and 0.4 µC/cm², respectively, with a P max – P r value of 5.3 µC/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 across various charge-discharge cycles It also presents the maximum polarization (P max) and remnant polarization (P r) values as a function of the number of charge-discharge cycles, measured 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).