A dielectric (or dielectric material) 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. If a
dielectric is composed of weakly bonded molecules, those molecules not
only become polarized, but also reorient so that their symmetry axes
align to the field.
The study of dielectric properties concerns storage and dissipation of
electric and magnetic energy in materials. Dielectrics are
important for explaining various phenomena in electronics, optics,
solid-state physics, and cell biophysics.
2 Electric susceptibility
2.1 Dispersion and causality
3.1 Basic atomic model
3.2 Dipolar polarization
3.3 Ionic polarization
3.3.1 Ionic polarization of cells
5.1 Debye relaxation
5.2 Variants of the Debye equation
9 Some practical dielectrics
10 See also
12 Further reading
13 External links
Although the term insulator implies low electrical conduction,
dielectric typically means materials with a high polarizability. The
latter is expressed by a number called the relative permittivity. The
term insulator is generally used to indicate electrical obstruction
while the term dielectric is used to indicate the energy storing
capacity of the material (by means of polarization). A common example
of a dielectric is the electrically insulating material between the
metallic plates of a capacitor. The polarization of the dielectric by
the applied electric field increases the capacitor's surface charge
for the given electric field strength.
The term "dielectric" was coined by
William Whewell (from
"dia-electric") in response to a request from Michael Faraday. A
perfect dielectric is a material with zero electrical conductivity
(cf. perfect conductor), thus exhibiting only a displacement
current; therefore it stores and returns electrical energy as if it
were an ideal capacitor.
Electric susceptibility and Permittivity
The electric susceptibility χe of a dielectric material is a measure
of how easily it polarizes in response to an electric field. This, in
turn, determines the electric permittivity of the material and thus
influences many other phenomena in that medium, from the capacitance
of capacitors to the speed of light.
It is defined as the constant of proportionality (which may be a
tensor) relating an electric field E to the induced dielectric
polarization density P such that
displaystyle mathbf P =varepsilon _ 0 chi _ e mathbf E ,
where ε0 is the electric permittivity of free space.
The susceptibility of a medium is related to its relative permittivity
displaystyle chi _ e =varepsilon _ r -1.
So in the case of a vacuum,
displaystyle chi _ e =0.
The electric displacement D is related to the polarization density P
displaystyle mathbf D = varepsilon _ 0 mathbf E +mathbf P
= varepsilon _ 0 (1+chi _ e )mathbf E = varepsilon _ r varepsilon _
0 mathbf E .
Dispersion and causality
In general, a material cannot polarize instantaneously in response to
an applied field. The more general formulation as a function of time
displaystyle mathbf P (t)=varepsilon _ 0 int _ -infty ^ t chi
_ e (t-t')mathbf E (t'),dt'.
That is, the polarization is a convolution of the electric field at
previous times with time-dependent susceptibility given by χe(Δt).
The upper limit of this integral can be extended to infinity as well
if one defines χe(Δt) = 0 for Δt < 0. An instantaneous response
Dirac delta function
Dirac delta function susceptibility χe(Δt) =
It is more convenient in a linear system to take the Fourier transform
and write this relationship as a function of frequency. Due to the
convolution theorem, the integral becomes a simple product,
displaystyle mathbf P (omega )=varepsilon _ 0 chi _ e (omega
)mathbf E (omega ).
Note the simple frequency dependence of the susceptibility, or
equivalently the permittivity. The shape of the susceptibility with
respect to frequency characterizes the dispersion properties of the
Moreover, the fact that the polarization can only depend on the
electric field at previous times (i.e., χe(Δt) = 0 for Δt < 0),
a consequence of causality, imposes Kramers–Kronig constraints on
the real and imaginary parts of the susceptibility χe(ω).
Basic atomic model
Electric field interaction with an atom under the classical dielectric
In the classical approach to the dielectric model, a material is made
up of atoms. Each atom consists of a cloud of negative charge
(electrons) bound to and surrounding a positive point charge at its
center. In the presence of an electric field the charge cloud is
distorted, as shown in the top right of the figure.
This can be reduced to a simple dipole using the superposition
principle. A dipole is characterized by its dipole moment, a vector
quantity shown in the figure as the blue arrow labeled M. It is the
relationship between the electric field and the dipole moment that
gives rise to the behavior of the dielectric. (Note that the dipole
moment points in the same direction as the electric field in the
figure. This isn't always the case, and is a major simplification, but
is true for many materials.)
When the electric field is removed the atom returns to its original
state. The time required to do so is the so-called relaxation time; an
This is the essence of the model in physics. The behavior of the
dielectric now depends on the situation. The more complicated the
situation, the richer the model must be to accurately describe the
behavior. Important questions are:
Is the electric field constant or does it vary with time? At what
Does the response depend on the direction of the applied field
(isotropy of the material)?
Is the response the same everywhere (homogeneity of the material)?
Do any boundaries or interfaces have to be taken into account?
Is the response linear with respect to the field, or are there
The relationship between the electric field E and the dipole moment M
gives rise to the behavior of the dielectric, which, for a given
material, can be characterized by the function F defined by the
displaystyle mathbf M =mathbf F (mathbf E )
When both the type of electric field and the type of material have
been defined, one then chooses the simplest function F that correctly
predicts the phenomena of interest. Examples of phenomena that can be
so modeled include:
Group velocity dispersion
Dipolar polarization is a polarization that is either inherent to
polar molecules (orientation polarization), or can be induced in any
molecule in which the asymmetric distortion of the nuclei is possible
(distortion polarization). Orientation polarization results from a
permanent dipole, e.g., that arising from the 104.45° angle between
the asymmetric bonds between oxygen and hydrogen atoms in the water
molecule, which retains polarization in the absence of an external
electric field. The assembly of these dipoles forms a macroscopic
When an external electric field is applied, the distance between
charges within each permanent dipole, which is related to chemical
bonding, remains constant in orientation polarization; however, the
direction of polarization itself rotates. This rotation occurs on a
timescale that depends on the torque and surrounding local viscosity
of the molecules. Because the rotation is not instantaneous, dipolar
polarizations lose the response to electric fields at the highest
frequencies. A molecule rotates about 1 radian per picosecond in a
fluid, thus this loss occurs at about 1011 Hz (in the microwave
region). The delay of the response to the change of the electric field
causes friction and heat.
When an external electric field is applied at infrared frequencies or
less, the molecules are bent and stretched by the field and the
molecular dipole moment changes. The molecular vibration frequency is
roughly the inverse of the time it takes for the molecules to bend,
and this distortion polarization disappears above the infrared.
Ionic polarization is polarization caused by relative displacements
between positive and negative ions in ionic crystals (for example,
If a crystal or molecule consists of atoms of more than one kind, the
distribution of charges around an atom in the crystal or molecule
leans to positive or negative. As a result, when lattice vibrations or
molecular vibrations induce relative displacements of the atoms, the
centers of positive and negative charges are also displaced. The
locations of these centers are affected by the symmetry of the
displacements. When the centers don't correspond, polarization arises
in molecules or crystals. This polarization is called ionic
Ionic polarization causes the ferroelectric effect as well as dipolar
polarization. The ferroelectric transition, which is caused by the
lining up of the orientations of permanent dipoles along a particular
direction, is called an order-disorder phase transition. The
transition caused by ionic polarizations in crystals is called a
displacive phase transition.
Ionic polarization of cells
Ionic polarization enables the production of energy-rich compounds in
cells (the proton pump in mitochondria) and, at the plasma membrane,
the establishment of the resting potential, energetically unfavourable
transport of ions, and cell-to-cell communication (the Na+/K+-ATPase).
All cells in animal body tissues are electrically polarized – in
other words, they maintain a voltage difference across the cell's
plasma membrane, known as the membrane potential. This electrical
polarization results from a complex interplay between protein
structures embedded in the membrane called
Ion transporterion ion
pumps and ion channels.
In neurons, the types of ion channels in the membrane usually vary
across different parts of the cell, giving the dendrites, axon, and
cell body different electrical properties. As a result, some parts of
the membrane of a neuron may be excitable (capable of generating
action potentials), whereas others are not.
In physics, dielectric dispersion is the dependence of the
permittivity of a dielectric material on the frequency of an applied
electric field. Because there is a lag between changes in polarization
and changes in the electric field, the permittivity of the dielectric
is a complicated function of frequency of the electric field.
Dielectric dispersion is very important for the applications of
dielectric materials and for the analysis of polarization systems.
This is one instance of a general phenomenon known as material
dispersion: a frequency-dependent response of a medium for wave
When the frequency becomes higher:
dipolar polarization can no longer follow the oscillations of the
electric field in the microwave region around 1010 Hz;
ionic polarization and molecular distortion polarization can no longer
track the electric field past the infrared or far-infrared region
around 1013 Hz, ;
electronic polarization loses its response in the ultraviolet region
around 1015 Hz.
In the frequency region above ultraviolet, permittivity approaches the
constant ε0 in every substance, where ε0 is the permittivity of the
free space. Because permittivity indicates the strength of the
relation between an electric field and polarization, if a polarization
process loses its response, permittivity decreases.
Dielectric relaxation is the momentary delay (or lag) in the
dielectric constant of a material. This is usually caused by the delay
in molecular polarization with respect to a changing electric field in
a dielectric medium (e.g., inside capacitors or between two large
Dielectric relaxation in changing electric
fields could be considered analogous to hysteresis in changing
magnetic fields (for inductors or transformers). Relaxation in general
is a delay or lag in the response of a linear system, and therefore
dielectric relaxation is measured relative to the expected linear
steady state (equilibrium) dielectric values. The time lag between
electrical field and polarization implies an irreversible degradation
of Gibbs free energy.
In physics, dielectric relaxation refers to the relaxation response of
a dielectric medium to an external, oscillating electric field. This
relaxation is often described in terms of permittivity as a function
of frequency, which can, for ideal systems, be described by the Debye
equation. On the other hand, the distortion related to ionic and
electronic polarization shows behavior of the resonance or oscillator
type. The character of the distortion process depends on the
structure, composition, and surroundings of the sample.
Debye relaxation is the dielectric relaxation response of an ideal,
noninteracting population of dipoles to an alternating external
electric field. It is usually expressed in the complex permittivity ε
of a medium as a function of the field's frequency ω:
displaystyle hat varepsilon (omega )=varepsilon _ infty +
frac Delta varepsilon 1+iomega tau ,
where ε∞ is the permittivity at the high frequency limit, Δε =
εs − ε∞ where εs is the static, low frequency permittivity, and
τ is the characteristic relaxation time of the medium. Separating the
real and imaginary parts of the complex dielectric permittivity
displaystyle varepsilon '=varepsilon _ infty + frac (varepsilon
_ s -varepsilon _ infty ) (1+omega ^ 2 tau ^ 2 )
displaystyle varepsilon ''= frac (varepsilon _ s -varepsilon _
infty )omega tau 1+omega ^ 2 tau ^ 2
The dielectric loss is also represented by:
displaystyle tan delta = frac varepsilon '' varepsilon ' =
frac (varepsilon _ s -varepsilon _ infty )omega tau varepsilon _ s
+varepsilon _ infty omega ^ 2 tau ^ 2
This relaxation model was introduced by and named after the physicist
Peter Debye (1913). It is characteristic for dynamic polarization
with only one relaxation time.
Variants of the Debye equation
This equation is used when the dielectric loss peak shows symmetric
This equation is used when the dielectric loss peak shows asymmetric
This equation considers both symmetric and asymmetric broadening
Kohlrausch–Williams–Watts function (Fourier transform of stretched
Curie-von Schweidler law
This shows the response of dielectrics to an applied DC field to
behave according to a power law, which can be expressed as an integral
over weighted exponential functions.
See also: Ferroelectricity
Paraelectricity is the ability of many materials (specifically
ceramics) to become polarized under an applied electric field. Unlike
ferroelectricity, this can happen even if there is no permanent
electric dipole that exists in the material, and removal of the fields
results in the polarization in the material returning to zero. The
mechanisms that cause paraelectric behaviour are the distortion of
individual ions (displacement of the electron cloud from the nucleus)
and polarization of molecules or combinations of ions or defects.
Paraelectricity can occur in crystal phases where electric dipoles are
unaligned and thus have the potential to align in an external electric
field and weaken it.
An example of a paraelectric material of high dielectric constant is
The LiNbO3 crystal is ferroelectric below 1430 K, and above this
temperature it transforms into a disordered paraelectric phase.
Similarly, other perovskites also exhibit paraelectricity at high
Paraelectricity has been explored as a possible refrigeration
mechanism; polarizing a paraelectric by applying an electric field
under adiabatic process conditions raises the temperature, while
removing the field lowers the temperature. A heat pump that
operates by polarizing the paraelectric, allowing it to return to
ambient temperature (by dissipating the extra heat), bringing it into
contact with the object to be cooled, and finally depolarizing it,
would result in refrigeration.
Tunable dielectrics are insulators whose ability to store electrical
charge changes when a voltage is applied.
Generally, strontium titanate (SrTiO
3) is used for devices operating at low temperatures, while barium
strontium titanate (Ba
3) substitutes for room temperature devices. Other potential materials
include microwave dielectrics and carbon nanotube (CNT)
In 2013 multi-sheet layers of strontium titanate interleaved with
single layers of strontium oxide produced a dielectric capable of
operating at up to 125 GHz. The material was created via
molecular beam epitaxy. The two have mismatched crystal spacing that
produces strain within the strontium titanate layer that makes it less
stable and tunable.
Systems such as Ba
3 have a paraelectric–ferroelectric transition just below ambient
temperature, providing high tunability. Such films suffer significant
losses arising from defects.
Main article: Capacitor
Charge separation in a parallel-plate capacitor causes an internal
electric field. A dielectric (orange) reduces the field and increases
Commercially manufactured capacitors typically use a solid dielectric
material with high permittivity as the intervening medium between the
stored positive and negative charges. This material is often referred
to in technical contexts as the capacitor dielectric.
The most obvious advantage to using such a dielectric material is that
it prevents the conducting plates, on which the charges are stored,
from coming into direct electrical contact. More significantly,
however, a high permittivity allows a greater stored charge at a given
voltage. This can be seen by treating the case of a linear dielectric
with permittivity ε and thickness d between two conducting plates
with uniform charge density σε. In this case the charge density is
displaystyle sigma _ varepsilon =varepsilon frac V d
and the capacitance per unit area by
displaystyle c= frac sigma _ varepsilon V = frac varepsilon
From this, it can easily be seen that a larger ε leads to greater
charge stored and thus greater capacitance.
Dielectric materials used for capacitors are also chosen such that
they are resistant to ionization. This allows the capacitor to operate
at higher voltages before the insulating dielectric ionizes and begins
to allow undesirable current.
A dielectric resonator oscillator (DRO) is an electronic component
that exhibits resonance of the polarization response for a narrow
range of frequencies, generally in the microwave band. It consists of
a "puck" of ceramic that has a large dielectric constant and a low
dissipation factor. Such resonators are often used to provide a
frequency reference in an oscillator circuit. An unshielded dielectric
resonator can be used as a dielectric resonator antenna (DRA).
Some practical dielectrics
Dielectric materials can be solids, liquids, or gases. In addition, a
high vacuum can also be a useful, nearly lossless dielectric even
though its relative dielectric constant is only unity.
Solid dielectrics are perhaps the most commonly used dielectrics in
electrical engineering, and many solids are very good insulators. Some
examples include porcelain, glass, and most plastics. Air, nitrogen
and sulfur hexafluoride are the three most commonly used gaseous
Industrial coatings such as parylene provide a dielectric barrier
between the substrate and its environment.
Mineral oil is used extensively inside electrical transformers as a
fluid dielectric and to assist in cooling.
Dielectric fluids with
higher dielectric constants, such as electrical grade castor oil, are
often used in high voltage capacitors to help prevent corona discharge
and increase capacitance.
Because dielectrics resist the flow of electricity, the surface of a
dielectric may retain stranded excess electrical charges. This may
occur accidentally when the dielectric is rubbed (the triboelectric
effect). This can be useful, as in a
Van de Graaff generator
Van de Graaff generator or
electrophorus, or it can be potentially destructive as in the case of
Specially processed dielectrics, called electrets (which should not be
confused with ferroelectrics), may retain excess internal charge or
"frozen in" polarization. Electrets have a semipermanent electric
field, and are the electrostatic equivalent to magnets. Electrets have
numerous practical applications in the home and industry.
Some dielectrics can generate a potential difference when subjected to
mechanical stress, or (equivalently) change physical shape if an
external voltage is applied across the material. This property is
called piezoelectricity. Piezoelectric materials are another class of
very useful dielectrics.
Some ionic crystals and polymer dielectrics exhibit a spontaneous
dipole moment, which can be reversed by an externally applied electric
field. This behavior is called the ferroelectric effect. These
materials are analogous to the way ferromagnetic materials behave
within an externally applied magnetic field.
often have very high dielectric constants, making them quite useful
Classification of materials based on permittivity
EIA Class 1 dielectric
EIA Class 2 dielectric
Linear response function
Rotational Brownian motion
Paschen's law – variation of
Dielectric strength of gas related to
^ a b c Dielectric. Encyclopædia Britannica: "Dielectric, insulating
material or a very poor conductor of electric current. When
dielectrics are placed in an electric field, practically no current
flows in them because, unlike metals, they have no loosely bound, or
free, electrons that may drift through the material."
^ Arthur R. von Hippel, in his seminal work,
Dielectric Materials and
Applications, stated: "Dielectrics... are not a narrow class of
so-called insulators, but the broad expanse of nonmetals considered
from the standpoint of their interaction with electric, magnetic, or
electromagnetic fields. Thus we are concerned with gases as well as
with liquids and solids, and with the storage of electric and magnetic
energy as well as its dissipation." (Technology Press of MIT and John
Wiley, NY, 1954).
^ Thoms, E.; Sippel, P.; et., al. (2017). "
Dielectric study on
mixtures of ionic liquids". Sci. Rep.
^ Belkin, A.; Bezryadin, A.; Hendren, L.; Hubler, A. (2017). "Recovery
of Alumina Nanocapacitors after High Voltage Breakdown". Sci. Rep.
^ Daintith, J. (1994). Biographical Encyclopedia of Scientists. CRC
Press. p. 943. ISBN 0-7503-0287-9.
^ James, Frank A.J.L., editor. The Correspondence of Michael Faraday,
Volume 3, 1841–1848, "Letter 1798,
William Whewell to Faraday, p.
442". The Institution of Electrical Engineers, London, United
Kingdom, 1996. ISBN 0-86341-250-5
Microwave Engineering – R. S. Rao (Prof.). Retrieved
^ Kao, Kwan Chi (2004).
Dielectric Phenomena in Solids. London:
Elsevier Academic Press. pp. 92–93.
^ Debye, P. (1913), Ver. Deut. Phys. Gesell. 15, 777; reprinted 1954
in collected papers of Peter J.W. Debye. Interscience, New York
^ Chiang, Y. et al. (1997) Physical Ceramics, John Wiley & Sons,
^ Kuhn, U.; Lüty, F. (1965). "Paraelectric heating and cooling with
OH—dipoles in alkali halides".
Solid State Communications. 3 (2):
^ a b c Lee, Che-Hui; Orloff, Nathan D.; Birol, Turan; Zhu, Ye; Goian,
Veronica; Rocas, Eduard; Haislmaier, Ryan; Vlahos, Eftihia; Mundy,
Julia A.; Kourkoutis, Lena F.; Nie, Yuefeng; Biegalski, Michael D.;
Zhang, Jingshu; Bernhagen, Margitta; Benedek, Nicole A.; Kim, Yongsam;
Brock, Joel D.; Uecker, Reinhard; Xi, X. X.; Gopalan, Venkatraman;
Nuzhnyy, Dmitry; Kamba, Stanislav; Muller, David A.; Takeuchi, Ichiro;
Booth, James C.; Fennie, Craig J.; Schlom, Darrell G. (2013).
"Self-correcting crystal may lead to the next generation of advanced
communications". Nature. 502 (7472): 532. Bibcode:2013Natur.502..532L.
doi:10.1038/nature12582. PMID 24132232.
^ Lee, C. H.; Orloff, N. D.; Birol, T.; Zhu, Y.; Goian, V.; Rocas, E.;
Haislmaier, R.; Vlahos, E.; Mundy, J. A.; Kourkoutis, L. F.; Nie, Y.;
Biegalski, M. D.; Zhang, J.; Bernhagen, M.; Benedek, N. A.; Kim, Y.;
Brock, J. D.; Uecker, R.; Xi, X. X.; Gopalan, V.; Nuzhnyy, D.; Kamba,
S.; Muller, D. A.; Takeuchi, I.; Booth, J. C.; Fennie, C. J.; Schlom,
D. G. (2013). "Exploiting dimensionality and defect mitigation to
create tunable microwave dielectrics". Nature. 502 (7472): 532–536.
^ Kong, L.B.; Li, S.; Zhang, T.S.; Zhai, J.W.; Boey, F.Y.C.; Ma, J.
(2010-11-30). "Electrically tunable dielectric materials and
strategies to improve their performances". Progress in Materials
Science. 55 (8): 840–893. doi:10.1016/j.pmatsci.2010.04.004.
^ Giere, A.; Zheng, Y.; Maune, H.; Sazegar, M.; Paul, F.; Zhou, X.;
Binder, J. R.; Muller, S.; Jakoby, R. (2008). "Tunable dielectrics for
microwave applications". 2008 17th IEEE International Symposium on the
Applications of Ferroelectrics. p. 1.
doi:10.1109/ISAF.2008.4693753. ISBN 978-1-4244-2744-4.
^ Müssig, Hans-Joachim. Semiconductor capacitor with praseodymium
oxide as dielectric, U.S. Patent 7,113,388 published 2003-11-06,
issued 2004-10-18, assigned to IHP GmbH- Innovations for High
Performance Microelectronics/Institute Fur Innovative Mikroelektronik
^ Lyon, David (2013). "Gap size dependence of the dielectric strength
in nano vacuum gaps". IEEE Transactions on Dielectrics and Electrical
Insulation. 20 (4). doi:10.1109/TDEI.2013.6571470.
Jackson, John David (August 10, 1998). Classical Electrodynamics (3 rd
ed.). John Wiley & Sons. ISBN 978-0-471-30932-1. 808 or
Scaife, Brendan (September 3, 1998). Principles of Dielectrics
(Monographs on the
Physics & Chemistry of Materials) (2 nd ed.).
Oxford University Press. ISBN 978-0198565574.
Electromagnetism – A chapter from an online textbook
Dielectric Sphere in an Electric Field
DoITPoMS Teaching and Learning Package "
Texts on Wikisource:
"Dielectric". Encyclopedia Americana. 1920.
Encyclopædia Britannica (11th ed.). 1911.