7.3 Ferroelectric materials

Ferroelectric materials are fascinating substances with unique electrical properties. They exhibit spontaneous electric polarization that can be reversed by applying an external electric field. This polarization arises from the displacement of ions within the crystal structure, creating a non-centrosymmetric arrangement.

These materials transition between ferroelectric and paraelectric phases at the Curie temperature. Below this temperature, they possess spontaneous polarization, while above it, they become centrosymmetric. This behavior leads to interesting applications in memory devices, sensors, and actuators.

Ferroelectric materials overview

• Ferroelectric materials exhibit spontaneous electric polarization that can be reversed by applying an external electric field
• Ferroelectricity arises from the displacement of ions within the crystal structure, leading to a non-centrosymmetric arrangement
• Ferroelectric materials are a subclass of pyroelectric materials, which in turn are a subclass of piezoelectric materials

Ferroelectric vs paraelectric phases

• In the ferroelectric phase, the material possesses a spontaneous electric polarization even in the absence of an external electric field
• The paraelectric phase occurs above the Curie temperature, where the material loses its spontaneous polarization and becomes centrosymmetric
• The transition between ferroelectric and paraelectric phases is accompanied by changes in the crystal structure and dielectric properties

Spontaneous electric polarization

Origin of spontaneous polarization

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• Spontaneous polarization originates from the displacement of ions within the crystal structure, creating a net electric dipole moment
• The displacement of ions is caused by the minimization of the free energy of the system, which favors a non-centrosymmetric arrangement
• The direction of spontaneous polarization is determined by the symmetry of the crystal structure and the relative positions of the ions

Temperature dependence of polarization

• The magnitude of spontaneous polarization decreases with increasing temperature due to thermal vibrations disrupting the ordered arrangement of ions
• At the Curie temperature, the spontaneous polarization vanishes, and the material transitions to the paraelectric phase
• The temperature dependence of polarization can be described by the Landau-Devonshire theory, which considers the free energy expansion in terms of the order parameter (polarization)

Ferroelectric domains

Domain walls and boundaries

• Ferroelectric materials consist of regions called domains, each with a uniform polarization direction
• Domain walls are the boundaries between adjacent domains with different polarization orientations
• The formation of domains minimizes the electrostatic energy and strain energy associated with the spontaneous polarization
• Domain walls can be classified as 180° or non-180° (e.g., 90°) depending on the angle between the polarization directions of the adjacent domains

Domain switching and hysteresis

• Domain switching occurs when an external electric field is applied, causing the polarization of domains to align with the field direction
• The process of domain switching is hysteretic, meaning that the polarization does not immediately follow the applied electric field
• The hysteresis loop (polarization vs. electric field) is a characteristic feature of ferroelectric materials, exhibiting coercive field and remanent polarization

Perovskite crystal structure

Unit cell and lattice parameters

• Many ferroelectric materials adopt the perovskite crystal structure with the general formula ABO3 (e.g., BaTiO3, PbTiO3)
• The perovskite unit cell consists of a corner-sharing network of BO6 octahedra, with the A cation occupying the space between the octahedra
• The lattice parameters of the perovskite structure are influenced by the sizes of the A and B cations and the degree of distortion from the ideal cubic structure

Displacement of central cation

• In the ferroelectric phase, the central cation (B cation) is displaced from the center of the BO6 octahedron, creating a net electric dipole moment
• The displacement of the B cation is typically along one of the crystallographic axes (e.g., [001], [110], or [111])
• The magnitude and direction of the B cation displacement determine the strength and orientation of the spontaneous polarization

Curie temperature and phase transitions

First and second order transitions

• Ferroelectric materials undergo a phase transition at the Curie temperature (Tc), where they transform from the ferroelectric phase to the paraelectric phase
• First-order phase transitions exhibit a discontinuous change in the order parameter (polarization) at Tc, accompanied by a latent heat
• Second-order phase transitions show a continuous change in the order parameter at Tc, with no latent heat involved
• The order of the phase transition depends on the material and can be influenced by factors such as composition, strain, and external fields

Curie-Weiss law above Curie temperature

• Above the Curie temperature, the dielectric permittivity of ferroelectric materials follows the Curie-Weiss law: ε = C / (T - T0)
• C is the Curie constant, T is the temperature, and T0 is the Curie-Weiss temperature (which may differ from the actual Curie temperature)
• The Curie-Weiss law describes the divergence of the dielectric permittivity as the temperature approaches the Curie point from above
• Deviations from the Curie-Weiss law can occur due to factors such as local inhomogeneities, defects, or quantum fluctuations

Ferroelectric hysteresis loop

Polarization vs electric field

• The ferroelectric hysteresis loop represents the relationship between the polarization (P) and the applied electric field (E)
• As the electric field is increased, the polarization initially increases linearly (paraelectric region) and then exhibits a rapid increase (ferroelectric switching)
• The hysteresis loop is characterized by the saturation polarization (Ps), remanent polarization (Pr), and coercive field (Ec)
• The shape and characteristics of the hysteresis loop depend on factors such as the material composition, crystal structure, and temperature

Coercive field and remanent polarization

• The coercive field (Ec) is the minimum electric field required to switch the polarization direction of the ferroelectric domains
• The remanent polarization (Pr) is the remaining polarization when the electric field is reduced to zero after saturation
• A high coercive field indicates a strong resistance to polarization switching, while a high remanent polarization suggests a stable ferroelectric state
• The coercive field and remanent polarization can be tuned by modifying the material composition, microstructure, or applying external stresses

Piezoelectric properties of ferroelectrics

Direct and converse piezoelectric effect

• Ferroelectric materials exhibit piezoelectric properties, which couple mechanical stress/strain with electric polarization
• The direct piezoelectric effect occurs when an applied mechanical stress generates an electric polarization in the material
• The converse piezoelectric effect describes the mechanical strain produced in the material when an electric field is applied
• The piezoelectric coefficients (dij) quantify the relationship between stress, strain, and electric field/polarization

Electromechanical coupling and applications

• The electromechanical coupling in ferroelectric materials allows for the interconversion between electrical and mechanical energy
• Ferroelectric piezoelectric materials find applications in sensors (e.g., pressure, acceleration), actuators (e.g., precision positioning), and transducers (e.g., ultrasonic)
• The high piezoelectric coefficients and electromechanical coupling factors of some ferroelectric materials (e.g., PZT) make them suitable for these applications
• The performance of ferroelectric piezoelectric devices can be optimized by controlling the composition, crystal orientation, and domain structure

Pyroelectric properties of ferroelectrics

Temperature-dependent polarization changes

• Ferroelectric materials also exhibit pyroelectric properties, where a change in temperature induces a change in the spontaneous polarization
• As the temperature increases, the spontaneous polarization decreases due to the increased thermal vibrations and the tendency towards a centrosymmetric structure
• The pyroelectric effect is a result of the temperature-dependent changes in the polarization, which can be harnessed for various applications

Pyroelectric coefficient and applications

• The pyroelectric coefficient (pi) quantifies the change in spontaneous polarization with respect to temperature (dPs/dT)
• Materials with high pyroelectric coefficients are sensitive to small temperature changes and can be used in thermal imaging, infrared detectors, and thermal energy harvesting
• Pyroelectric devices often operate in the temperature range below the Curie point, where the spontaneous polarization is significant
• The pyroelectric response can be enhanced by optimizing the material composition, crystal orientation, and thermal properties (e.g., heat capacity, thermal conductivity)

Common ferroelectric materials

Barium titanate (BaTiO3)

• Barium titanate is a widely studied ferroelectric material with the perovskite structure
• It undergoes a series of phase transitions with decreasing temperature: cubic (paraelectric) → tetragonal → orthorhombic → rhombohedral (ferroelectric)
• BaTiO3 has a relatively high dielectric constant, making it useful for capacitor applications
• The ferroelectric properties of BaTiO3 can be tuned by doping with other elements (e.g., Sr, Ca) or forming solid solutions

Lead zirconate titanate (PZT)

• Lead zirconate titanate is a solid solution of PbZrO3 and PbTiO3, with the general formula Pb(Zr(x)Ti(1-x))O3
• PZT exhibits excellent piezoelectric and ferroelectric properties, with high piezoelectric coefficients and electromechanical coupling factors
• The composition of PZT can be varied to optimize its properties for specific applications (e.g., high-sensitivity sensors, high-strain actuators)
• PZT thin films can be fabricated using various deposition techniques (e.g., sol-gel, sputtering, pulsed laser deposition) for integration into microelectronic devices

Ferroelectric device applications

Ferroelectric random-access memory (FeRAM)

• FeRAM is a non-volatile memory technology that utilizes the polarization states of ferroelectric materials for data storage
• Each memory cell consists of a ferroelectric capacitor and a transistor, where the polarization direction represents the binary data (0 or 1)
• FeRAM offers fast read/write speeds, low power consumption, and high endurance compared to other non-volatile memory technologies
• Challenges in FeRAM development include scaling to smaller cell sizes, improving data retention, and reducing the effects of polarization fatigue

Ferroelectric field-effect transistors (FeFETs)

• FeFETs are a type of transistor that incorporates a ferroelectric material as the gate dielectric
• The polarization state of the ferroelectric gate modulates the channel conductivity, enabling non-volatile memory functionality
• FeFETs offer the potential for high-density, low-power, and fast memory applications, as well as the possibility of logic-in-memory architectures
• Key challenges in FeFET development include achieving stable polarization switching, minimizing leakage current, and ensuring compatibility with CMOS processing

Relaxor ferroelectrics

Diffuse phase transitions

• Relaxor ferroelectrics exhibit a diffuse phase transition, where the transition from the ferroelectric to the paraelectric phase occurs over a broad temperature range
• The diffuse phase transition is characterized by a broad peak in the dielectric permittivity vs. temperature curve, rather than a sharp peak as in normal ferroelectrics
• The origin of the diffuse phase transition is attributed to the presence of nanoscale polar regions (polar nanoregions) with different local Curie temperatures
• Relaxor behavior is often observed in complex perovskite solid solutions with chemical disorder and local structural distortions

Frequency-dependent dielectric response

• Relaxor ferroelectrics exhibit a frequency-dependent dielectric response, where the dielectric permittivity and loss tangent vary with the applied AC frequency
• At low frequencies, the polar nanoregions can respond to the applied electric field, leading to a high dielectric permittivity
• As the frequency increases, the polar nanoregions become unable to follow the rapidly changing field, resulting in a decrease in the dielectric permittivity
• The frequency dispersion of the dielectric properties is a characteristic feature of relaxor ferroelectrics and can be described by various theoretical models (e.g., Vogel-Fulcher law)
• Relaxor ferroelectrics find applications in high-performance capacitors, piezoelectric transducers, and electro-optic devices due to their unique dielectric and electromechanical properties