What is Dielectric Constant?

To understand the dielectric constant, it is instructive to understand what a dielectric is. A dielectric is a material that polarises when an electric field is applied across it. In simple terms, because of this polarisation, positive charges move in the same direction of the electric field and negative charges move in the opposite direction, creating an electrostatic field that can persist for a long time. Dielectric materials have high resistance to the passage of electric current and so layers of these materials are commonly used in capacitors to improve their performance. The term “dielectric” specifically refers to this application, with the prefix di meaning ‘through’ or ‘across’ [1].

The dielectric constant (ε) of a material can be expressed as the ratio of the capacitance when the material is used as a dielectric in a capacitor against the capacitance when there is no dielectric material used, i.e. in a vacuum. This property is directly proportional to the capacity of the material to store a charge. Dielectric constant should not be mistaken for dielectric strength, which instead is the maximum electric field a pure material is able to sustain before it ionises and starts to conduct electricity.

• What dielectric constant is
• The measurement of dielectric constant
• The different applications that utilise dielectric constant
• Future materials and applications

What is dielectric constant?

A material is considered dielectric if it can store energy when an external electric field is applied across it. A dielectric material improves the storage capacity of a capacitor by cancelling out charges at the electrodes which would have normally added to the external field. The dielectric constant can be expressed by the ratio of the capacitance of a capacitor with the dielectric material to that without the dielectric material.

The dielectric constant of a material can be expressed as

k=\frac{C}{C_{0}}

Where k is the real dielectric constant and C and C0 are capacitance with and without the dielectric, respectively.

Another important property of a dielectric material is its permittivity. The permittivity (ε) of a material is a measure of the ability of the material to be polarised by an electric field or its polarisability.

The capacitance of a capacitor depends on the permittivity ε of the dielectric layer as per the formula below

C=\varepsilon\left(\frac{A}{d}\right)

Where A is the area of the capacitor, and d is the distance between the two conductive plates in the capacitor.

When vacuum is used as a dielectric, the capacitance is given by

C_{0}=\varepsilon_{0}\left(\frac{A}{d}\right)

Where \varepsilon_{0} is the permittivity of vacuum.

The dielectric constant of a material can, therefore, be expressed also as the ratio of its permittivity to the permittivity of vacuum as per the equation below

k=\frac{\varepsilon}{\varepsilon_{0}}

Thus, the dielectric constant is also known as the relative permittivity of the material, and it is dimensionless. The dielectric constant of vacuum is 1. All materials will polarise more than vacuum in an electric field, so the k of any material is always greater than 1.

Measurement of dielectric constant

There are a few measurement systems that can be used to measure dielectric constant. Three of them are discussed below.

Network analysers

This system correlates permittivity (the dielectric constant) by measuring the reflection of transmitted signals against the material. The frequency of the signals is increased at intervals and the entire process is repeated so as to plot the received signals over a certain range, the slope of which correlates to the dielectric constant of the material.

Impedance analysers

These meters are used to measure material properties at lower frequencies. In this method, the voltage of a material is measured and monitored when current is passed through it. Given the physical dimensions of the material and measuring its capacitance and dissipation factor, values of the dielectric constant can be derived.

Software

Raw data measured via instruments that interact with the material in any number of ways (such as applying an electric field across the material or sending and receiving signals to and from the material), can be fed into complex programs, which can compute and present the information required in a more useful manner, namely the exact dielectric constant.

The above systems are adapted to several different tools to create techniques of varying applicability and accuracy. Some of these techniques are via coaxial probe, transmission line, free space, resonant cavity, parallel plate and inductance measurement [2].

Table 1. Comparison between dielectric constant measurement methods [2]

 Measurement Technique Key points Coaxial probe Broadband, convenient, non-destructive. Best for lossy MUTs; liquids and semi-solids Transmission line Broadband. Best for lossy to low loss MUTs; machinable solids Free space Broadband; Non-contacting. Best for flats sheets, powders, high temperatures Resonant cavity Single-frequency; Accurate. Best for low loss MUTs; small samples Parallel plate Accurate. Best for low frequencies; thin, flat sheets Inductance measurement Accurate, simple measurement, a toroidal core structure is required

Applications and materials

Electronics

A low-k dielectric has a low permittivity, or low ability to polarise and hold a charge. Because of this, they can be used to insulate signal-carrying conductors from each other, which is why they are invaluable for very dense multi-layered integrated circuits to guard against performance degradation.

A high-k dielectric has a high permittivity and can easily polarise. This is why they are preferred for capacitors to hold electric charge and for memory cells to store digital data.

Weather

The relative permittivity of air can be monitored for changes that give insight into the humidity and temperature.

Analytical chemistry

Dielectric constant information is important in chromatography as different solvents can have wildly varying polarisabilities.

Information Technology

The dielectric constant of optical fibres is carefully controlled through the introduction of impurities to manipulate their refractive index and therefore the mode of light (data) transmission.

Table 2. Dielectric constant values of common materials [3]

 Material Relative dielectric constant Material Relative dielectric constant Vacuum 1 Mica 4 Air 1 Styrofoam 1.03 Barium titanate 100 Teflon 2.1 Glass 5-10 Porcelain 4-8 Kevlar 3-4.5 Quartz 5 Lead titanate 200 Rubber 2 Celluloid 4 Rubber, Silicone 3.2 Cement 2 Polypropylene 2.25 – 2.5 Diamond 5.87 Silicon 11.8 Paper 3 – 3.5 Potassium niobate 700 Plexiglass 2.6 – 3.5 Potassium tantalate niobate, at 20°C 6000

Future materials and application

By far the greatest use of dielectric constant information is in selecting and creating the best dielectric materials for use in microelectromechanical systems (MEMS). The world of electronics is continuously striving to make faster circuits in smaller packages. The study of dielectric constant is furthering applications in medicine (with micro heart valve development), automation (with faster reaction times for airbag deployment), defence systems (based on bulk ferroelectric technology), space exploration (with extremely sensitive actuators for telescopes) and many more applications in hi-tech gadgetry.