Inelectromagnetism, adielectric (ordielectric medium) is anelectrical insulator that can bepolarised by an appliedelectric field. When a dielectric material is placed in an electric field,electric charges do not flow through the material as they do in anelectrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causingdielectric polarisation. Because ofdielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weaklybonded molecules, those molecules not only become polarised, but also reorient so that theirsymmetry axes align to the field.[1]
Although the terminsulator implies lowelectrical conduction,dielectric typically means materials with a highpolarisability. The latter is expressed by a number called therelative permittivity.Insulator is generally used to indicate electrical obstruction whiledielectric is used to indicate theenergy storing capacity of the material (by means of polarisation). A common example of a dielectric is the electrically insulating material between the metallic plates of acapacitor. The polarisation of the dielectric by the applied electric field increases the capacitor's surface charge for the given electric field strength.[1]
Aperfect dielectric is a material with zero electrical conductivity (cf.perfect conductor infinite electrical conductivity),[9] thus exhibiting only adisplacement current; therefore it stores and returns electrical energy as if it were an ideal capacitor.
Theelectric susceptibility of a dielectric material is a measure of how easily itpolarises in response to an electric field. This, in turn, determines the electricpermittivity of the material and thus influences many other phenomena in that medium, from the capacitance ofcapacitors to thespeed of light.
It is defined as the constant of proportionality (which may be atensor) relating an electric field to the induced dielectric polarisation density such that
In general, a material cannot polarise instantaneously in response to an applied field. The more general formulation as a function of time is
That is, the polarisation is aconvolution of the electric field at previous times with time-dependent susceptibility given by. The upper limit of this integral can be extended to infinity as well if one defines for. An instantaneous response corresponds toDirac delta function susceptibility .
It is more convenient in a linear system to take theFourier transform and write this relationship as a function of frequency. Due to theconvolution theorem, the integral becomes a simple product,
The susceptibility (or equivalently the permittivity) is frequency dependent. The change of susceptibility with respect to frequency characterises thedispersion properties of the material.
Moreover, the fact that the polarisation can only depend on the electric field at previous times (i.e., for), a consequence ofcausality, imposesKramers–Kronig constraints on the real and imaginary parts of the susceptibility.
Electric field interaction with an atom under the classical dielectric model
In the classical approach to the dielectric, the 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 simpledipole using thesuperposition principle. A dipole is characterised by itsdipole moment, a vector quantity shown in the figure as the blue arrow labeledM. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure. This is not 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 calledrelaxation time; an exponential decay.
This is the essence of the model in physics. The behaviour of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behaviour. Important questions are:
Is the electric field constant, or does it vary with time? At what rate?
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?
The relationship between the electric fieldE and the dipole momentM gives rise to the behaviour of the dielectric, which, for a given material, can be characterised by the functionF defined by the equation:
When both the type of electric field and the type of material have been defined, one then chooses the simplest functionF that correctly predicts the phenomena of interest. Examples of phenomena that can be so modelled include:
Dipolar polarisation is a polarisation that is either inherent topolar molecules (orientation polarisation), or can be induced in any molecule in which the asymmetric distortion of the nuclei is possible (distortion polarisation). Orientation polarisation results from a permanent dipole, e.g., that arises from the 104.45° angle between the asymmetric bonds between oxygen and hydrogen atoms in the water molecule, which retains polarisation in the absence of an external electric field. The assembly of these dipoles forms a macroscopic polarisation.
When an external electric field is applied, the distance between charges within each permanent dipole, which is related tochemical bonding, remains constant in orientation polarisation; however, the direction of polarisation itself rotates. This rotation occurs on a timescale that depends on thetorque and surrounding localviscosity of the molecules. Because the rotation is not instantaneous, dipolar polarisations 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 causesfriction and heat.
When an external electric field is applied atinfrared 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 polarisation disappears above the infrared.
Ionic polarisation is polarisation caused by relative displacements between positive and negativeions inionic crystals (for example,NaCl).
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 do not correspond, polarisation arises in molecules or crystals. This polarisation is calledionic polarisation.
Ionic polarisation causes theferroelectric effect as well as dipolar polarisation. The ferroelectric transition, which is caused by the lining up of the orientations of permanent dipoles along a particular direction, is called anorder-disorder phase transition. The transition caused by ionic polarisations in crystals is called adisplacive phase transition.
Ionic polarisation enables the production of energy-rich compounds in cells (theproton pump inmitochondria) and, at theplasma membrane, the establishment of theresting potential, energetically unfavourable transport of ions, and cell-to-cell communication (theNa+/K+-ATPase).
All cells in animal body tissues are electrically polarised – in other words, they maintain a voltage difference across the cell'splasma membrane, known as themembrane potential. This electrical polarisation results from a complex interplay betweenion transporters andion channels.
In neurons, the types of ion channels in the membrane usually vary across different parts of the cell, giving thedendrites,axon, andcell 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 polarisation and changes in the electric field, the permittivity of the dielectric is a complex function of the frequency of the electric field. Dielectric dispersion is very important for the applications of dielectric materials and the analysis of polarisation systems.
This is one instance of a general phenomenon known asmaterial dispersion: a frequency-dependent response of a medium for wave propagation.
When the frequency becomes higher:
The dipolar polarisation can no longer follow the oscillations of the electric field in themicrowave region around 1010Hz,
The ionic polarisation and molecular distortion polarisation can no longer track the electric field past theinfrared or far-infrared region around 1013 Hz,
The electronic polarisation loses its response in the ultraviolet region around 1015 Hz.
In the frequency region above ultraviolet, permittivity approaches the constantε0 in every substance, whereε0 is the permittivity of the free space. Because permittivity indicates the strength of the relation between an electric field and polarisation, if a polarisation process loses its response, permittivity decreases.
Dielectric relaxation is the momentary delay (or lag) in thedielectric constant of a material. This is usually caused by the delay in molecular polarisation with respect to a changing electric field in a dielectric medium (e.g., inside capacitors or between two largeconducting surfaces). Dielectric relaxation in changing electric fields could be considered analogous tohysteresis in changingmagnetic fields (e.g., ininductor ortransformercores). Relaxation in general is a delay or lag in the response of alinear system, and therefore dielectric relaxation is measured relative to the expected linear steady state (equilibrium) dielectric values. The time lag between electrical field and polarisation implies an irreversible degradation ofGibbs free energy.
Inphysics,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 offrequency, which can, for ideal systems, be described by the Debye equation. On the other hand, the distortion related to ionic and electronic polarisation shows behaviour of theresonance oroscillator 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 permittivityε of a medium as a function of the field'sangular frequencyω:
whereε∞ is the permittivity at the high frequency limit,Δε =εs −ε∞ whereεs is the static, low frequency permittivity, andτ is the characteristicrelaxation time of the medium. Separating into the real part and the imaginary part of the complex dielectric permittivity yields:[10]
Note that the above equation for is sometimes written with in the denominator due to an ongoing sign convention ambiguity whereby many sources represent the time dependence of the complex electric field with whereas others use. In the former convention, the functions and representing real and imaginary parts are given by whereas in the latter convention. The above equation uses the latter convention.[11]
The dielectric loss is also represented by the loss tangent:
This relaxation model was introduced by and named after the physicistPeter Debye (1913).[12] It is characteristic for dynamic polarisation with only one relaxation time.
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.
Paraelectricity is the nominal behaviour of dielectrics when the dielectric permittivity tensor is proportional to the unit matrix, i.e., an appliedelectric field causes polarisation and/or alignment of dipoles only parallel to the applied electric field. Contrary to the analogy with a paramagnetic material, no permanentelectric dipole needs to exist in a paraelectric material. Removal of the fields results in the dipolar polarisation returning to zero.[13] The mechanisms that causesparaelectric behaviour are distortion of individualions (displacement of the electron cloud from the nucleus) and polarisation of molecules or combinations of ions or defects.
Paraelectricity can occur incrystal phases where electric dipoles are unaligned and thus have the potential to align in an externalelectric field and weaken it.
Most dielectric materials are paraelectrics. A specific example of a paraelectric material of high dielectric constant isstrontium titanate.
TheLiNbO3 crystal isferroelectric below 1430K, and above this temperature it transforms into a disordered paraelectric phase. Similarly, otherperovskites also exhibit paraelectricity at high temperatures.
Paraelectricity has been explored as a possible refrigeration mechanism; polarising a paraelectric by applying an electric field underadiabatic process conditions raises the temperature, while removing the field lowers the temperature.[14] Aheat pump that operates by polarising 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 depolarising it, would result in refrigeration.
Tunable dielectrics are insulators whose ability to store electrical charge changes when a voltage is applied.[15]
Generally,strontium titanate (SrTiO 3) is used for devices operating at low temperatures, whilebarium strontium titanate (Ba 1−xSr xTiO 3) substitutes for room temperature devices. Other potential materials include microwave dielectrics and carbon nanotube (CNT) composites.[15][16][17]
In 2013, multi-sheet layers of strontium titanate interleaved with single layers ofstrontium oxide produced a dielectric capable of operating at up to 125 GHz. The material was created viamolecular beam epitaxy. The two have mismatched crystal spacing that produces strain within the strontium titanate layer that makes it less stable and tunable.[15]
Systems such asBa 1−xSr xTiO 3 have a paraelectric–ferroelectric transition just below ambient temperature, providing high tunability. Films suffer significant losses arising from defects.
Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.
Commercially manufactured capacitors typically use asolid dielectric material with highpermittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as thecapacitor dielectric.[18]
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 permittivityε and thicknessd between two conducting plates with uniform charge densityσε. In this case the charge density is given by
From this, it can easily be seen that a largerε leads to greater charge stored and thus greater capacitance.
Dielectric materials used for capacitors are also chosen such that they are resistant toionisation. This allows the capacitor to operate at higher voltages before the insulating dielectric ionises and begins to allow undesirable current.
Adielectric resonator oscillator (DRO) is an electronic component that exhibitsresonance of the polarisation 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 lowdissipation factor. Such resonators are often used to provide a frequency reference in an oscillator circuit. An unshielded dielectric resonator can be used as adielectric resonator antenna (DRA).
From 2002 to 2004, the United StatesArmy Research Laboratory (ARL) conducted research on thin film technology. Barium strontium titanate (BST), a ferroelectric thin film, was studied for the fabrication of radio frequency and microwave components, such as voltage-controlled oscillators, tunable filters and phase shifters.[19]
The research was part of an effort to provide the Army with highly-tunable, microwave-compatible materials for broadband electric-field tunable devices, which operate consistently in extreme temperatures.[20] This work improved tunability of bulk barium strontium titanate, which is a thin film enabler for electronics components.[21]
In a 2004 research paper, U.S. ARL researchers explored how small concentrations of acceptor dopants can dramatically modify the properties of ferroelectric materials such as BST.[22]
Researchers "doped" BST thin films with magnesium, analyzing the "structure, microstructure, surface morphology and film/substrate compositional quality" of the result. The Mg doped BST films showed "improved dielectric properties, low leakage current, and good tunability", meriting potential for use in microwave tunable devices.[19]
Dielectric materials can be solids, liquids, or gases. (A highvacuum can also be a useful,[23] nearly lossless dielectric even though its relativedielectric 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 includeporcelain,glass, and mostplastics. Air,nitrogen andsulfur hexafluoride are the three most commonly usedgaseous dielectrics.
Mineral oil is used extensively inside electricaltransformers as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical gradecastor oil, are often used inhigh voltage capacitors to help preventcorona discharge and increase capacitance.
Because dielectrics resist the flow of electricity, the surface of a dielectric may retainstranded excess electrical charges. This may occur accidentally when the dielectric is rubbed (thetriboelectric effect). This can be useful, as in aVan de Graaff generator orelectrophorus, or it can be potentially destructive as in the case ofelectrostatic discharge.
Specially processed dielectrics, calledelectrets (which should not be confused withferroelectrics), may retain excess internal charge or "frozen in" polarisation. Electrets have a semi-permanent electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry, for instance in theElectret microphone found in telephones, headsets, videorecorders etc.
Some dielectrics can generate a potential difference when subjected to mechanicalstress, or (equivalently) change physical shape if an external voltage is applied across the material. This property is calledpiezoelectricity. Piezoelectric materials are another class of very useful dielectrics.
Some ioniccrystals andpolymer dielectrics exhibit a spontaneous dipole moment, which can be reversed by an externally applied electric field. This behaviour is called theferroelectric effect. These materials are analogous to the wayferromagnetic materials behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.
^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 ofnonmetals 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." (p. 1) (Technology Press of MIT and John Wiley, NY, 1954).
^abcLee, 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). "Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics".Nature.502 (7472):532–536.Bibcode:2013Natur.502..532L.doi:10.1038/nature12582.hdl:2117/21213.PMID24132232.S2CID4457286.
^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.hdl:10356/93905.
^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.ISBN978-1-4244-2744-4.S2CID15835472.
^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
^abCole, M. W.; Geyer, R. G. (2004). "Novel tunable acceptor doped BST thin films for high quality tunable microwave devices".Revista Mexicana de Fisica.50 (3): 232.Bibcode:2004RMxF...50..232C.
^Cole, M. W.; Hubbard, C.; Ngo, E.; Ervin, M.; Wood, M.; Geyer, R. G. (July 2002). "Structure–property relationships in pure and acceptor-doped Ba1−xSrxTiO3 thin films for tunable microwave device applications".Journal of Applied Physics.92 (1):475–483.Bibcode:2002JAP....92..475C.doi:10.1063/1.1484231.ISSN0021-8979.
