Permittivity

The permittivity ε (from Latin: permittere = permit, let, let through ), also known as dielectric permittivity or dielectric function indicates the permeability of a material for electric fields. Also, the vacuum is assigned a permittivity, as well as in vacuum can adjust electric fields or electromagnetic fields propagate.

The relative permittivity, also called permittivity or dielectric constant of a medium is the ratio of its permittivity to that of the vacuum ( constant electric field ).

It features the field-weakening effects of the dielectric polarization of the medium and is closely related to the electric susceptibility. In English-language literature and in relation to the semiconductor technology, the relative permittivity is also called (kappa ) or with k as in the low-k dielectrics.

The terms " dielectric constant " for permittivity and " relative permittivity " for relative permittivity have been deprecated and should not be used, especially because this is - unlike the name suggests - to no constants are, but a strong frequency dependence exists.

Explanation of the example permittivity insulating materials

As permittivity refers to a material property of electrically insulating, polar or non-polar substances, which are also known as dielectrics. This property has an effect if the substance interacts with an electric field, such as when it is in a capacitor. In a material filled capacitor, the charge carriers of the insulation material based on the electric field vector and form a polarization field that opposes the external field and this weakens. This phenomenon of field weakening can be characterized describe that the insulating material is assigned a factor to the electric field constant ( permittivity of vacuum ) when adopting a given excitation electric field. From the external electrical stimulation, also known as the electric flux density, the electric field by the permittivity given by:

At a constant electrical excitation and increasing values ​​of the electric field strength decreases. In this way, the field-weakening effect in the same electric excitation is detected, i.e., for a given electric flux density or a predetermined electric charge. Under the influence of a voltage applied to the capacitor plates fixed voltage U and the electric field ( plate separation d), the electrical excitation results with the permittivity to:

The electric susceptibility is the relative permittivity on:

Linked. The susceptibility is a measure of the density of the insulation material -bound carrier, based on the density of free charge carriers. Read more in the article is electric susceptibility.

In electrodynamics and also in electrostatics is the permittivity is used to describe the above phenomena as the proportionality factor in the relationship between electric flux density and electric field strength:

In matter, this equation only the lowest order of a generally non-linear relationship is: In the case of large field strengths we group either the permittivity as a field strength dependent and writes, or one introduces in addition to other Taylor coefficients, etc., which describes the field dependence of:

In the vacuum as a reference material of an insulating material, the relative permittivity is considered

The permittivity is a proportionality between the charge density and the second partial derivative of the potential field. You can be calculated from the Poisson equation of electrostatics.

Permittivity of free space

The permittivity of vacuum is also called electric field constant, as in the current draft of the German International size system. Other names are dielectric constant, dielectric constant of the vacuum and influence constant.

In a vacuum exists between the magnetic field constant μ0, the permittivity of vacuum and the vacuum speed of light c0 following predicted by Maxwell and in 1857 by Wilhelm Eduard Weber and Rudolf Kohlrausch experimentally confirmed relation:

In the International System of Units ( SI ) system takes the return of the electromagnetic to the mechanical variables in the definition of the current ( amps), the amounts that can be the permittivity of the vacuum with any degree of accuracy from the precisely defined physical constants and calculate:

The unity of the permittivity can be expressed here as:

Since air can only polarize slightly, can often be approximated by the permittivity of air in sufficient accuracy.

Numerical value and unit

In addition to the Coulomb's law, the Ampère law and Faraday 's law of induction, the relation between μ0 and c0 another link electromagnetic and mechanical units, which fall to be considered in the choice of an electromagnetic system of units.

Depending on the unit system used here is changing the representation of the permittivity analogously to the preparation of.

The conditions in the SI unit system are given above. In unit systems that explicitly attribute the electromagnetic sizes of mechanical basic variables, namely the different variants of the CGS system of units is chosen as a dimensionless number:

Relative permittivity

For the following designations are used:

• Relative permittivity (designation according to standard)
• Relative dielectric constant (deprecated)
• Permittivity (deprecated)
• Permittivity

The designation as a constant is not appropriate, since, in general, a function of several parameters, in particular the frequency and the temperature.

Only for isotropic media is a scalar quantity. In this simplest case, it indicates the factor by which the voltage drops to a capacitor when the same geometry replacing an assumed between the capacitor electrode through a dielectric vacuum, non-conductive material. In the experiment, you can understand this, when a volume of air is replaced by the capacitor electrodes, eg by a dielectric liquid. For a plate capacitor, it is sufficient to push a dielectric object between the electrodes.

Relative permittivity in crystalline structures

Generally, however, a second order tensor, which reflects the crystalline (or other ordered ) the structure of matter and therefore the directionality of the factors. The Tensoreigenschaft the permittivity is the basis for the crystal optics.

The relative permittivity is a second order tensor (and thus as a function of the light propagation direction with respect to excellent crystal axes ), which is both on the frequency (that is, when viewed from the light of the wavelength ) and by the external electric field and magnetic field is dependent, and also called dielectric function. Especially in English and the size symbol κ is used (refer to the low-k dielectric, and high-k dielectric).

Frequency dependence of the relative permittivity

The permittivity in matter is frequency dependent and can for example be modeled quite well on the simple model of the Lorentz oscillator. This frequency dependence is called dispersion. She is very strong, for example in water.

The frequency-dependent refractive index of a material is available in the following relation for the electrical permittivity and magnetic permeability (both also frequency dependent ):

Approximately applies for transparent materials, as is. The optical dispersion is a term that is also at the frequencies of visible light is not a constant number. In Table works, the numerical value at low frequencies ( order of 50 Hz to 100 kHz) specified, in which molecular dipoles can follow the external field almost instantaneously in the rule. The lag of the molecules relative to the high-frequency electric field is described macroscopically by a complex relative permittivity.

Complex-valued relative permittivity

The relative permittivity is generally complex-valued. Just as with DC fields also form in alternating fields in dielectrics polarization fields, but possibly the applied external field size lag by a certain phase angle. The orientation of the charge carriers in the dielectric in the phase remains (in time) after the repolarization of the applied alternating field back. With increasing frequency, this effect is stronger. It can easily imagine that alternating fields of high frequency by rapid, recurrent Umpolarisieren generate heat losses in insulating materials. At still higher frequencies at which the charge carriers in the band diagram of a crystal can be excited, energy is also absorbed. This phenomena is taken into account that the relative permittivity with complex-valued

Alternatively, with

Will be described, wherein the dielectric loss beyond the imaginary '' permittivity are detected. A widely used application that could exploit the phenomenon of dielectric losses, the heating in the microwave oven. The power loss density of dielectric heating is based on the volume of material:

The dielectric heating is connected to the power loss corresponds to integration over the heating period of an exact volume of material with the electromagnetic waves supplied to the inner energy of a material, as described in thermodynamics. The imaginary part of the complex, relative permittivity is a measure of the ability of a substance to convert electromagnetic field energy in high frequency heat energy.

Temperature dependence

Depending on the temperature, for example, the complex-valued, relative permittivity of water, whose real part has a value of about 80 at room temperature, and is at 95 ° C about 55. The decrease in permittivity depends on the temperature increases with the increasing degree of disorder of the carrier together with an increase in internal energy. Molecular viewed from the polarizability increases due to the increased self-motion of the charge carriers at a higher internal energy; macroscopically viewed, the relative permittivity decreases with increasing temperature.

Relative permittivity of selected materials

Tabulated, comprehensive overviews frequency-and temperature-dependent complex relative permittivities of many materials can be found in and above all in.

Generalizations to the dispersion direction and magnetic field dependence

From Maxwell's equations it follows that a correlation between the refractive index of the electrical permittivity and the magnetic permeability,

Here are μ and of the related optical frequency ( of the order of 1015 Hz in the range ) meant. For gaseous, liquid and solid matter is one greater. However, there are in other states of matter, e.g., in the plasma ( so-called " fourth state " ), and values ​​that may be less than one.

In dispersive materials one has to do with the response of the material to electromagnetic fields with the frequency of light, ie very high frequencies over a wide frequency range. Here, the relationship between the refractive index and the measured at low frequencies taken much more general, and the frequency dependence must be taken into account (see Lorentz Oscillator). In this way the absorption and reflection spectra of the materials can be well represented.

The dielectric constant is used here as a complex quantity, having a real part and an imaginary part (see Section Complex-valued relative permittivity).

The contributions of different mechanisms in the material may be (eg band transitions ) and are added in their frequency dependence in these two components directly - a more detailed description can be found under electric susceptibility. K can be represented via the Kramers -Kronig relation then the ( dispersive ) Relationship between the complex dielectric constant and the optical parameters refractive index n and absorption coefficient. This leads to the theoretical spectra of absorption and reflection, which can be compared with measured spectra and adjusted.

For the calculation of such spectra ( by reflection or absorption ), the quantities n and k of the complex refractive index can be determined directly from the real and imaginary parts of the permittivity in the case of (non- magnetic material):

Reverse is also true:

Also, inter alia, the reflectance R can be calculated. It applies a beam out of the vacuum (or air) coming perpendicularly reflected at an interface with a medium of refractive index:

Due to their crystal structure, the properties of some materials are dependent on the direction, such as the birefringent materials. These materials find applications among others in retardation plates. Mathematically, this can be captured by representation in tensor form, with components for the individual directions to this property. These in turn are to be recognized as a function of frequency and even depending on the direction in varying degrees. In addition to the "natural" direction dependence, the properties can cause a similar directional dependence due to external influences such as a magnetic field ( see magneto-optics ) or pressure.