What Are The Definition of Dielectric Constant & Dielectric Material?

Introduction to Dielectric Constants and Materials

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. The ability of a dielectric to polarize and reduce an applied electric field is characterized by its dielectric constant.

The dielectric constant, also known as relative permittivity (εᵣ) or specific inductive capacity, is a dimensionless number that indicates the relative permittivity (ability to store electric field energy) of a dielectric material. It is defined as the ratio of the electric permittivity of the material (ε) to the permittivity of free space (ε₀):

εᵣ = ε / ε₀

Where:
– εᵣ = Dielectric constant (relative permittivity)
– ε = Permittivity of the dielectric material
– ε₀ = Permittivity of free space = 8.854 x 10⁻¹² F/m

The dielectric constant (εᵣ) is always greater than or equal to 1. A perfect vacuum has a dielectric constant of exactly 1. Typical dielectric materials have dielectric constants ranging from slightly above 1 to around 100. Materials with high dielectric constants are capable of greater energy storage and charge separation when placed in an electric field.

Some common dielectric materials and their typical dielectric constants are shown in the table below:

As seen in the table, the dielectric constants of materials can vary widely. Vacuum and dry air have dielectric constants very close to 1. Most polymers have relatively low dielectric constants from 2-10. Ceramics and inorganic materials tend to have higher dielectric constants. Specially formulated ferroelectric ceramics like barium titanate can have extremely high dielectric constants over 1000.

The dielectric constant is a function of various factors such as temperature, frequency, orientation, mixture, pressure, and molecular structure of the material. It is not a constant value and can vary significantly based on these parameters.

Importance of Dielectric Constant

The dielectric constant of a material is an essential parameter in many electrical, electronic, and optical applications. It is a measure of the material’s ability to store electrical energy and its interaction with electric fields. The dielectric constant determines important properties and behaviors such as:

Capacitance

The dielectric constant directly affects the capacitance of capacitors. Capacitors are two-terminal electrical components used to store electric charge and energy in an electric field. They consist of two conducting plates separated by a dielectric material.

The capacitance (C) of a parallel plate capacitor is given by:

C = εᵣ · ε₀ · A / d

Where:
– C = Capacitance in farads (F)
– εᵣ = Dielectric constant of the material between the plates
– ε₀ = Permittivity of free space = 8.854 x 10⁻¹² F/m
– A = Area of the plates in square meters (m²)
– d = Distance between the plates in meters (m)

As seen from the equation, the capacitance is directly proportional to the dielectric constant (εᵣ) of the material between the plates. Using a material with a higher dielectric constant allows for greater charge storage and increased capacitance in a capacitor of a given size. This is why high-dielectric ceramics like barium titanate are used to make high-value ceramic capacitors.

Transmission Line Impedance

The dielectric constant of the insulating material affects the characteristic impedance of transmission lines and coaxial cables. Transmission lines are used to carry high-frequency electrical signals. The characteristic impedance (Z₀) of a transmission line is given by:

Z₀ = √(L/C)

Where:
– Z₀ = Characteristic impedance in ohms (Ω)
– L = Inductance per unit length in henries per meter (H/m)
– C = Capacitance per unit length in farads per meter (F/m)

The capacitance (C) is directly proportional to the dielectric constant (εᵣ) of the insulating material, while the inductance (L) is unaffected. Therefore, using a dielectric with a higher εᵣ decreases the characteristic impedance.

Transmission lines and coaxial cables are usually designed to have a specific characteristic impedance, such as 50 Ω, 75 Ω, or 300 Ω, to minimize reflections and power loss. The impedance can be controlled by adjusting the dimensions and the dielectric material of the cable.

Velocity of Propagation

The dielectric constant determines the velocity at which an electromagnetic wave or electrical signal travels through a material. The velocity of propagation (v) is given by:

v = c / √εᵣ

Where:
– v = Velocity of propagation in meters per second (m/s)
– c = Speed of light in vacuum = 299,792,458 m/s
– εᵣ = Dielectric constant of the material

A higher dielectric constant results in slower velocity of propagation. The velocity of electromagnetic waves in vacuum is the speed of light (c), but it is slower in materials by a factor of the square root of the dielectric constant. For example, an optical fiber with a dielectric constant of 2.25 will have a propagation velocity about 2/3 the speed of light.

Controlled changes in dielectric constant can be used to manipulate the velocity of propagation, which is the basis for dielectric delay lines and phase shifters used in radio and microwave circuits.

Reflectance and Transmittance

The dielectric constant, along with the magnetic permeability, determines the reflectance and transmittance of electromagnetic waves at the interface between two materials. When an electromagnetic wave encounters a boundary between different dielectrics, some of the energy is reflected, while the rest is transmitted or refracted.

The reflection coefficient (Γ) for normal incidence is given by:

Γ = (√εᵣ₁ – √εᵣ₂) / (√εᵣ₁ + √εᵣ₂)

Where:
– Γ = Reflection coefficient (ratio of reflected to incident electric field strength)
– εᵣ₁ = Dielectric constant of the first medium
– εᵣ₂ = Dielectric constant of the second medium

A larger difference between the dielectric constants results in higher reflectance. Conversely, materials with closely matched dielectric constants allow more energy to be transmitted. Controlling the dielectric constants is important for antireflection coatings, impedance matching, and energy transmission in optical and radio frequency applications.

Dielectric Polarization Mechanisms

Dielectric materials can be polarized by several mechanisms depending on the frequency of the applied field and the molecular structure of the material. The main polarization mechanisms are:

Electronic Polarization

Electronic polarization occurs in all dielectrics at high frequencies (above 10¹⁴ Hz). It is due to the displacement of the negatively charged electron cloud relative to the positive atomic nucleus in the presence of an electric field. The electron cloud becomes asymmetrically distributed, creating a small electric dipole moment. Electronic polarization has a small contribution to the overall polarization and dielectric constant.

Ionic Polarization

Ionic polarization happens in ionic crystals and ceramics at frequencies below 10¹³ Hz. It is caused by the displacement of positive and negative ions in opposite directions under an applied electric field. The ions are not free to move throughout the material, but they can slightly shift from their equilibrium positions, inducing a net dipole moment. Ionic polarization can result in much larger dielectric constants than electronic polarization.

Orientational (Dipolar) Polarization

Orientational or dipolar polarization occurs in materials that have permanent molecular dipoles, such as polar liquids and polymers. In the absence of an electric field, the dipoles are randomly oriented, resulting in zero net polarization. When an electric field is applied, the dipoles tend to align with the field direction, producing a net polarization. Orientational polarization is highly dependent on temperature and frequency and is often the dominant mechanism at radio and microwave frequencies. It is responsible for the very high dielectric constant of water.

Interfacial (Space Charge) Polarization

Interfacial or space charge polarization happens in heterogeneous dielectrics, such as composites, multiphase materials, and materials with defects or impurities. It is due to the accumulation of charge carriers at the interfaces or boundaries between different regions in the material. The charges can be impurity ions, injected electrons, or protons. Interfacial polarization occurs at very low frequencies and can result in extremely high dielectric constants, as seen in some ferroelectric ceramics.

The total polarization of a dielectric material is the sum of contributions from all the polarization mechanisms present. Each polarization mechanism has a characteristic frequency response known as dielectric relaxation or dispersion.

Frequency Dependence of Dielectric Constant

The dielectric constant of a material is not constant over all frequencies but varies with the frequency of the applied electric field. This phenomenon is called dielectric dispersion or relaxation. As the frequency increases, the slower polarization mechanisms drop out in succession, leading to a decrease in the dielectric constant.

At optical frequencies (10¹⁴ Hz and above), only electronic polarization contributes to the dielectric constant. The ions are too heavy to follow the rapid oscillations of the field, so ionic polarization ceases. Orientational polarization of permanent dipoles is also ineffective at high frequencies because the dipoles cannot keep up with the fast reversals of the electric field.

In the infrared to microwave range (10⁹ to 10¹² Hz), ionic polarization starts to contribute, and the dielectric constant increases. At radio and lower microwave frequencies (10⁶ to 10⁹ Hz), orientational polarization of dipolar molecules becomes significant, leading to a further rise in dielectric constant.

At very low frequencies and DC, interfacial polarization and the motion of charge carriers can cause very high dielectric constants in some materials. However, this is often accompanied by high dielectric loss and leakage current.

The frequency dependence of dielectric constant can be modeled by various relaxation theories, such as the Debye, Cole-Cole, and Havriliak-Negami equations. These models describe the complex dielectric constant (ε*) as a function of frequency:

ε*(ω) = ε'(ω) – jε”(ω)

Where:
– ε*(ω) = Complex dielectric constant at angular frequency ω
– ε'(ω) = Real part of the dielectric constant (relative permittivity)
– ε”(ω) = Imaginary part of the dielectric constant (dielectric loss)
– j = Imaginary unit (√-1)

The real part (ε’) represents the energy storage capacity, while the imaginary part (ε”) represents the energy dissipation or loss in the material.

Dielectric Loss and Dissipation Factor

An ideal dielectric material would be a perfect insulator with no conduction or energy dissipation. However, real dielectrics always have some level of conductive and dielectric losses, especially at high frequencies.

Dielectric loss is the dissipation of energy through the movement of charges in an alternating electromagnetic field. It is caused by several factors, such as conduction losses, dipole relaxation, and resonance effects. Dielectric loss is quantified by the loss tangent (tan δ) or dissipation factor, which is the ratio of the imaginary to the real part of the complex dielectric constant:

tan δ = ε” / ε’

A low loss tangent is desirable in most applications to minimize power loss and heating of the material. Dielectric losses are important in high-frequency and high-power applications, such as radio frequency and microwave circuits, where they can lead to signal attenuation, noise, and thermal management issues.

Breakdown Strength and Dielectric Strength

Dielectric strength, also known as breakdown strength, is the maximum electric field that a dielectric material can withstand before it experiences failure and becomes electrically conductive. When the applied electric field exceeds the dielectric strength, the material undergoes dielectric breakdown, which is a sudden and often destructive increase in current flow.

Dielectric breakdown can occur through various mechanisms, such as:

• Intrinsic breakdown: caused by the direct ionization of atoms and electrons in the material by the high electric field.
• Thermal breakdown: caused by the thermal runaway and melting of the material due to Joule heating from conduction currents.
• Electromechanical breakdown: caused by the mechanical deformation and rupture of the material due to the electrostatic forces.
• Defect and impurity-related breakdown: caused by the electric field enhancement and conduction at defects, voids, or impurities in the material.

The dielectric strength is usually expressed in units of volts per meter (V/m) or kilovolts per millimeter (kV/mm). It depends on factors such as the chemical composition, microstructure, thickness, electrode geometry, and environmental conditions of the material.

Some typical dielectric strength values for common materials are:

High dielectric strength is crucial for insulation materials in high-voltage applications, such as power transmission, transformers, and capacitors. A higher dielectric strength allows for thinner insulation layers and more compact designs. However, dielectric materials with high dielectric constants often have lower dielectric strengths due to their higher polarizability and conductivity.

Applications of Dielectric Materials

Dielectric materials are used in a wide range of electrical, electronic, and optical applications. Some of the main applications are:

Capacitors

Dielectric materials are used as the insulating layer between the conducting plates in capacitors. The dielectric constant and breakdown strength of the material determine the capacitance and voltage rating of the capacitor. Different types of dielectrics are used depending on the requirements of energy density, frequency response, temperature stability, and cost:

• Ceramic capacitors: use high-dielectric ceramics such as barium titanate, strontium titanate, and lead zirconate titanate for high capacitance values in small sizes.
• Film capacitors: use polymer films such as polypropylene, polyester, and polyphenylene sulfide for high stability and low losses.
• Electrolytic capacitors: use a thin oxide layer on aluminum or tantalum as the dielectric for high capacitance and voltage ratings.
• Mica and glass capacitors: use natural or synthetic mica and glass sheets for high precision and temperature stability.
• Vacuum and gas-filled capacitors: use a vacuum or inert gas as the dielectric for high voltage and high power applications.

Insulators and Dielectrics

Dielectric materials with high resistivity and dielectric strength are used as electrical insulators to separate and isolate conductors at different potentials. Some common insulating materials are:

• Polymers: such as polyethylene, PVC, Teflon