What is dielectric constant. Dielectric constant of air as a physical quantity

Relative dielectric constant environment ε - dimensionless physical quantity, characterizing the properties of the insulating (dielectric) medium. Associated with the effect of polarization of dielectrics under the influence electric field(and with the value of the dielectric susceptibility of the medium characterizing this effect). The value ε shows how many times the force of interaction between two electric charges in a medium is less than in a vacuum. Relative permittivity air and most other gases in normal conditions close to unity (due to their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are high for substances with molecules that have a large electric dipole. The relative dielectric constant of ferroelectrics is tens and hundreds of thousands.

Practical Application

The dielectric constant of dielectrics is one of the main parameters in the design of electrical capacitors. The use of materials with high dielectric constant can significantly reduce physical dimensions capacitors.

The dielectric constant parameter is taken into account when designing printed circuit boards. The value of the dielectric constant of the substance between the layers, in combination with its thickness, affects the value of the natural static capacitance of the power layers, and also significantly affects the characteristic impedance of the conductors on the board.

Frequency dependence

It should be noted that the dielectric constant largely depends on the frequency of the electric magnetic field. This should always be taken into account, since reference tables usually contain data for a static field or low frequencies down to a few units of kHz without specifying this fact. At the same time, there are also optical methods for obtaining the relative dielectric constant based on the refractive index using ellipsometers and refractometers. The value obtained by the optical method (frequency 10-14 Hz) will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency zero), the relative dielectric constant under normal conditions is approximately 80. This is the case down to infrared frequencies. Starting at approximately 2 GHz ε r starts to fall. In the optical range ε r is approximately 1.8. This is quite consistent with the fact that in the optical range the refractive index of water is 1.33. In a narrow frequency range, called optical, dielectric absorption drops to zero, which actually provides a person with the mechanism of vision in earth's atmosphere saturated with water vapor. With further increase in frequency, the properties of the medium change again.

Dielectric constant values ​​for some substances

Substance	Chemical formula	Measurement conditions	Characteristic value of ε r
Aluminum	Al	1 kHz	-1300 + 1.3Template:Ei
Silver	Ag	1 kHz	-85 + 8Template:Ei
Vacuum	-	-	1
Air	-	Normal conditions, 0.9 MHz	1.00058986 ± 0.00000050
Carbon dioxide	CO2	Normal conditions	1,0009
Teflon	-	-	2,1
Nylon	-	-	3,2
Polyethylene	[-CH 2 -CH 2 -] n	-	2,25
Polystyrene	[-CH 2 -C(C 6 H 5)H-] n	-	2,4-2,7
Rubber	-	-	2,4
Bitumen	-	-	2,5-3,0
Carbon disulfide	CS 2	-	2,6
Paraffin	C 18 N 38 − C 35 N 72	-	2,0-3,0
Paper	-	-	2,0-3,5
Electroactive polymers	−	−	2-12
Ebonite	(C 6 H 9 S) 2	−	2,5-3,0
Plexiglas (plexiglass)	-	-	3,5
Quartz	SiO2	-	3,5-4,5
Silicon dioxide	SiO2	−	3,9
Bakelite	-	-	4,5
Concrete	−	−	4,5
Porcelain	−	−	4,5-4,7
Glass	−	−	4,7 (3,7-10)
Fiberglass FR-4	-	-	4,5-5,2
Getinax	-	-	5-6
Mica	-	-	7,5
Rubber	−	−	7
Polycor	98% Al 2 O 3	-	9,7
Diamond	−	−	5,5-10
Table salt	NaCl	−	3-15
Graphite	C	−	10-15
Ceramics	−	−	10-20
Silicon	Si	−	11.68
Bor	B	−	2.01
Ammonia	NH 3	20°C	17
		0 °C	20
		−40 °C	22
		−80 °C	26
Ethyl alcohol	C 2 H 5 OH or CH 3 -CH 2 -OH	−	27
Methanol	CH3OH	−	30
Ethylene glycol	HO-CH 2 -CH 2 -OH	−	37
Furfural	C5H4O2	−	42

VIRTUAL LABORATORY WORK No. 3 ON

SOLID STATE PHYSICS

Guidelines for implementation laboratory work No. 3 in the section of “Solid State” physics for students of technical specialties of all forms of study

Krasnoyarsk 2012

Reviewer

Candidate of Physical and Mathematical Sciences, Associate Professor O.N. Bandurina

(Siberian State Aerospace University

named after academician M.F. Reshetnev)

Published by decision of the ICT methodological commission

Determination of the dielectric constant of semiconductors. Virtual laboratory work No. 3 on solid state physics: Guidelines for performing laboratory work No. 3 in the section of “Solid State” physics for technical students. specialist. all forms of education / compiled by: A.M. Kharkov; Sib. state aerospace univ. – Krasnoyarsk, 2012. – 21 p.

Siberian State Aerospace

University named after academician M.F. Reshetneva, 2012

Introduction………………………………………………………………………………………...4

Admission to laboratory work……………………………………………………...4

Preparation of laboratory work for defense……………………………………...4

Determination of the dielectric constant of semiconductors…………........5

Theory of the method………………………………………………………………………………......5

Methodology for measuring dielectric constant…………………..……..11

Processing of measurement results………………………..………………………16

Test questions…………..………………………………………………….17

Test……………………………………………………………………………….17

References…………………………………………………………………………………20

Appendix………………………………………………………………………………………21

INTRODUCTION

Data guidelines contain descriptions of laboratory work in which virtual models from the course “Solid State Physics” are used.

Admission to laboratory work:

Conducted by a teacher in groups with a personal survey of each student. For admission:

1) Each student first prepares his personal notes for this laboratory work;

2) The teacher individually checks the formatting of the notes and asks questions about theory, measurement techniques, installation and processing of results;

3) The student answers questions asked;

4) The teacher allows the student to work and puts his signature on the student’s notes.

Preparation of laboratory work for defense:

The work, fully completed and prepared for defense, must meet the following requirements:

Completion of all points: all calculations of the required values, all tables filled in ink, all graphs drawn, etc.

The schedules must satisfy all the requirements of the teacher.

For all values ​​in tables, the corresponding unit of measurement must be written.

The conclusions for each graph were recorded.

The answer was written out in the prescribed form.

Conclusions based on the answer were recorded.

DETERMINATION OF DIELECTRIC CONTINUITY OF SEMICONDUCTORS

Theory of the method

Polarization is the ability of a dielectric to polarize under the influence of an electric field, i.e. change the location of connected charged dielectric particles in space.

The most important property of dielectrics is their ability to undergo electrical polarization, i.e. under the influence of an electric field, a directed displacement of charged particles or molecules occurs over a limited distance. Under the influence of an electric field, charges in both polar and non-polar molecules are displaced.

There are more than a dozen various types polarization. Let's look at some of them:

1. Electronic polarization is a displacement of electron orbits relative to a positively charged nucleus. It occurs in all atoms of any substance, i.e. in all dielectrics. Electronic polarization is established within 10 -15 –10 -14 s.

2. Ionic polarization– displacement relative to each other of oppositely charged ions in substances with ionic bonds. Its establishment time is 10 -13 –10 -12 s. Electronic and ionic polarization are among the instantaneous or deformation types of polarization.

3. Dipole or orientation polarization due to the orientation of the dipoles in the direction of the electric field. Polar dielectrics have dipole polarization. Its establishment time is 10 -10 –10 -6 s. Dipole polarization is one of the slow or relaxation types of polarization.

4. Migration polarization observed in inhomogeneous dielectrics, in which electric charges accumulate at the boundary of the inhomogeneity region. The processes of establishing migration polarization are very slow and can take place over minutes and even hours.

5. Ion-relaxation polarization is caused by excessive transfer of weakly bound ions under the influence of an electric field over distances exceeding the lattice constant. Ion-relaxation polarization manifests itself in some crystalline substances in the presence of impurities in the form of ions or loose packing of the crystal lattice. Its establishment time is 10 -8 –10 -4 s.

6. Electronic relaxation polarization arises due to excess “defect” electrons or “holes” excited by thermal energy. This type of polarization, as a rule, causes a high dielectric constant.

7. Spontaneous polarization– spontaneous polarization that occurs in some substances (for example, Rochelle salt) in a certain temperature range.

8. Elastic-dipole polarization associated with elastic rotation of dipoles through small angles.

9. Residual polarization– polarization that remains in some substances (electrets) for a long time after the electric field is removed.

10. Resonant polarization. If the frequency of the electric field is close to the natural frequency of oscillations of the dipoles, then the vibrations of the molecules can increase, which will lead to the appearance of resonant polarization in the dipole dielectric. Resonant polarization is observed at frequencies lying in the region of infrared light. A real dielectric can simultaneously have several types of polarization. The occurrence of one or another type of polarization is determined physical and chemical properties substances and the range of frequencies used.

Main parameters:

ε – dielectric constant– measure of a material’s ability to polarize; this is a quantity that shows how many times the force of interaction of electric charges in a given material is less than in a vacuum. A field appears inside the dielectric, directed opposite to the external one.

The external field strength weakens compared to the field of the same charges in vacuum by ε times, where ε is the relative dielectric constant.

If the vacuum between the capacitor plates is replaced by a dielectric, then as a result of polarization the capacitance increases. This is the basis for a simple definition of dielectric constant:

where C 0 is the capacitance of the capacitor, between the plates of which there is a vacuum.

C d is the capacitance of the same capacitor with a dielectric.

The dielectric constant ε of an isotropic medium is determined by the relation:

(2)

where χ is the dielectric susceptibility.

D = tan δ – dielectric loss tangent

Dielectric losses – losses electrical energy, caused by the flow of currents in dielectrics. A distinction is made between through conduction current I sk.pr, caused by the presence of a small number of easily mobile ions in dielectrics, and polarization currents. With electronic and ion polarization, the polarization current is called the displacement current I cm; it is very short-lived and is not recorded by instruments. Currents associated with slow (relaxation) types of polarization are called absorption currents I abs. In the general case, the total current in the dielectric is determined as: I = I abs + I sk.pr. After polarization is established, the total current will be equal to: I=I rms. If in a constant field polarization currents arise at the moment the voltage is turned on and off, and the total current is determined in accordance with the equation: I = I sk.pr, then in an alternating field polarization currents arise at the moment the voltage polarity changes. As a result, losses in the dielectric in an alternating field can be significant, especially if the half-cycle of the applied voltage approaches the time of polarization establishment.

In Fig. 1(a) shows a circuit equivalent to a capacitor with a dielectric located in an alternating voltage circuit. In this circuit, a capacitor with a real dielectric, which has losses, is replaced by an ideal capacitor C with a parallel active resistance R. In Fig. Figure 1(b) shows a vector diagram of currents and voltages for the circuit under consideration, where U is the voltage in the circuit; I ak – active current; I r – reactive current, which is 90° ahead of the active component in phase; I ∑ - total current. In this case: I а =I R =U/R and I р =I C =ωCU, where ω is the circular frequency of the alternating field.

Rice. 1. (a) – diagram; (b) – vector diagram of currents and voltages

The dielectric loss angle is the angle δ, which complements up to 90° the phase shift angle φ between the current I ∑ and the voltage U in the capacitive circuit. Losses in dielectrics in an alternating field are characterized by the dielectric loss tangent: tan δ=I a /I r.

Limit values The dielectric loss tangent for high-frequency dielectrics should not exceed (0.0001 - 0.0004), and for low-frequency dielectrics - (0.01 - 0.02).

Dependences of ε and tan δ on temperature T and frequency ω

The dielectric parameters of materials depend to varying degrees on temperature and frequency. Large quantity dielectric materials does not allow us to cover the features of all dependencies on these factors.

Therefore, in Fig. 2 (a, b) depicts general trends characteristic of some main groups, i.e. Typical dependences of the dielectric constant ε on temperature T (a) and frequency ω (b) are given.

Rice. 2. Frequency dependence of the real (εʹ) and imaginary (εʺ) parts of the dielectric constant in the presence of an orientational relaxation mechanism

Complex dielectric constant. In the presence of relaxation processes, it is convenient to write the dielectric constant in complex form. If the Debye formula is valid for polarizability:

(3)

where τ is the relaxation time, α 0 is the statistical orientational polarizability. Then, assuming the local field is equal to the external one, we obtain (in the SGS):

Graphs of the dependence of εʹ and εʺ on the product ωτ are shown in Fig. 2. Note that the decrease in εʹ (the real part of ε) occurs near the maximum of εʺ (the imaginary part of ε).

This course of change in εʹ and εʺ with frequency serves as a frequent example of a more overall result, according to which εʹ(ω) on frequency also entails the dependence of εʺ(ω) on frequency. In the SI system, 4π should be replaced by 1/ε 0.

Under the influence of an applied field, molecules in a non-polar dielectric are polarized, becoming dipoles with an induced dipole moment μ And, proportional to the field strength:

(5)

In a polar dielectric, the dipole moment of a polar molecule μ is generally equal to the vector sum of its own μ 0 and induced μ And moments:

(6)

The field strengths produced by these dipoles are proportional to the dipole moment and inversely proportional to the cube of the distance.

For non-polar materials, usually ε = 2 – 2.5 and does not depend on frequency up to ω ≈10 12 Hz. The dependence of ε on temperature is due to the fact that when it changes, the linear dimensions of solids and the volumes of liquid and gaseous dielectrics change, which changes the number of molecules n per unit volume

and the distances between them. Using the relations known from the theory of dielectrics F=n\μ And And F=ε 0 (ε - 1)E, Where F– polarization of the material, for non-polar dielectrics we have:

(7)

When E=const also μ And= const and the temperature change ε ​​is due only to the change in n, which is a linear function of temperature Θ, the dependence ε = ε(Θ) is also linear. For polar dielectrics there are no analytical dependences, and empirical ones are usually used.

1) As the temperature increases, the volume of the dielectric increases and the dielectric constant decreases slightly. The decrease in ε is especially noticeable during the period of softening and melting of non-polar dielectrics, when their volume increases significantly. In view of high frequency rotation of electrons in orbits (about 10 15 –10 16 Hz), the time for establishing an equilibrium state of electronic polarization is very short and the permeability ε of non-polar dielectrics does not depend on the field frequency in the commonly used frequency range (up to 10 12 Hz).

2) As the temperature increases, the bonds between individual ions weaken, which facilitates their interaction under the influence of an external field and this leads to an increase in ion polarization and dielectric constant ε. Due to the short time it takes to establish the state of ion polarization (about 10 13 Hz, which corresponds to the natural frequency of ion vibrations in crystal lattice) a change in the frequency of the external field in conventional operating ranges has virtually no effect on the value of ε in ionic materials.

3) The dielectric constant of polar dielectrics strongly depends on the temperature and frequency of the external field. With increasing temperature, the mobility of particles increases and the energy of interaction between them decreases, i.e. their orientation is facilitated under the influence of an external field - the dipole polarization and dielectric constant increase. However, this process continues only up to a certain temperature. With a further increase in temperature, permeability ε decreases. Since the orientation of dipoles in the direction of the field is carried out in the process of thermal motion and through thermal motion, the establishment of polarization requires considerable time. This time is so long that in alternating fields of high frequency the dipoles do not have time to orient themselves along the field, and the permeability ε decreases.

Methodology for measuring dielectric constant

Capacitor capacity. Capacitor is a system of two conductors (plates) separated by a dielectric, the thickness of which is small compared to the linear dimensions of the conductors. For example, two flat metal plates, arranged in parallel and separated by a layer of dielectric, form a capacitor (Fig. 3).

If the plates of a flat capacitor are given charges equal in magnitude opposite sign, then the electric field strength between the plates will be twice as large as the field strength at one plate:

(8)

where ε is the dielectric constant of the dielectric filling the space between the plates.

Physical quantity determined by charge ratio q one of the capacitor plates to the potential difference Δφ between the capacitor plates is called capacitance of the capacitor:

(9)

SI unit of electrical capacity – Farad(F). A capacitor with a capacity of 1 F has a potential difference between the plates of which is equal to 1 V when dissimilar charges of 1 C are imparted to the plates: 1 F = 1 C/1 V.

Capacitance of a parallel plate capacitor. The formula for calculating the electrical capacity of a flat capacitor can be obtained using expression (8). In fact, the field strength is: E= φ/εε 0 = q/εε 0 S, Where S– plate area. Since the field is uniform, the potential difference between the plates of the capacitor is equal to: φ 1 – φ 2 = Ed = qd/εε 0 S, Where d– distance between the plates. Substituting into formula (9), we obtain an expression for the electrical capacity of a flat capacitor:

(10)

Where ε 0 – dielectric constant of air; S– area of ​​the capacitor plate, S=hl, Where h– plate width, l– its length; d– distance between the capacitor plates.

Expression (10) shows that the electrical capacity of the capacitor can be increased by increasing the area S its covers, reducing the distance d between them and the use of dielectrics with large values dielectric constant ε.

Rice. 3. Capacitor with a dielectric placed in it

If a dielectric plate is placed between the plates of a capacitor, the capacitance of the capacitor will change. The option of placing a dielectric plate between the capacitor plates should be considered.

Let's denote: d c – thickness of the air gap, d m – thickness of the dielectric plate, l B is the length of the air part of the capacitor, l m is the length of the part of the capacitor filled with a dielectric, ε m is the dielectric constant of the material. Considering that l = l in + l m, a d = d in + d m, then these options can be considered for the following cases:

In case l in = 0, d at = 0 we have a capacitor with a solid dielectric:

(11)

From the equations of classical macroscopic electrodynamics, based on Maxwell’s equations, it follows that when a dielectric is placed in a weak alternating field, varying according to a harmonic law with frequency ω, the complex permittivity tensor takes the form:

(12)

where σ is the optical conductivity of the substance, εʹ is the dielectric constant of the substance, associated with the polarization of the dielectric. Expression (12) can be reduced to next view:

where the imaginary term is responsible for dielectric losses.

In practice, C is measured - the capacitance of a sample shaped like a flat capacitor. This capacitor is characterized by the dielectric loss tangent:

tgδ=ωCR c (14)

or quality factor:

Q c =1/ tanδ (15)

where R c is the resistance, depending mainly on dielectric losses. There are a number of methods for measuring these characteristics: various bridge methods, measurements with conversion of the measured parameter into a time interval, etc. .

When measuring capacitance C and dielectric loss tangent D = tanδ, this work used a technique developed by the GOOD WILL INSTRUMENT Co Ltd company. The measurements were carried out on a precision immittance meter - LCR-819-RLC. The device allows you to measure capacitance in the range of 20 pF–2.083 mF, loss tangent in the range of 0.0001–9999 and apply a bias field. Internal bias up to 2 V, external bias up to 30 V. Measurement accuracy is 0.05%. Test signal frequency 12 Hz -100 kHz.

In this work, measurements were carried out at a frequency of 1 kHz in the temperature range of 77 K< T < 270 К в нулевом магнитном поле и в поле 5 kOe. Образцы для измерений имели форму параллелепипеда с размерами 2*3*4 мм (х=0.1), где d = 2 мм – толщина образца, площадь грани S = 3*4 мм 2 .

In order to obtain temperature dependences, the cell with the sample is placed in a flow of coolant (nitrogen) passed through a heat exchanger, the temperature of which is set by the heater. The heater temperature is controlled by a thermostat. Feedback from a temperature meter to a thermostat allows you to set the speed of temperature measurement or stabilize it. A thermocouple is used to control the temperature. In this work, the temperature changed at a rate of 1 degree/min. This method allows you to measure temperature with an error of 0.1 degrees.

The measuring cell with the sample attached to it is placed in a flow cryostat. The cell is connected to the LCR meter by shielded wires through a connector in the cryostat cap. The cryostat is placed between the poles of the FL-1 electromagnet. The magnet power supply allows you to obtain magnetic fields up to 15 kOe. To measure the magnetic field strength H, a thermally stabilized Hall sensor with an electronics unit is used. To stabilize the magnetic field, there is feedback between the power supply and the magnetic field meter.

The measured values ​​of capacitance C and loss tangent D = tan δ are related to the values ​​of the desired physical quantities εʹ and εʺ by the following relations:

(16)

(17)

№	C(pF)	Re(ε’)	T (°K)	tan δ	Qc	Im(ε”)	ω (Hz)	σ (ω)
	3,805	71,66		0,075	13,33	5,375	10 3
	3,838			0,093
	3,86			0,088
	3,849			0,094
	3,893			0,106
	3,917			0,092
	3,951			0,103
	3,824			0,088
	3,873			0,105
	3,907			0,108
	3,977			0,102
	4,031			0,105
	4,062			0,132
	4,144			0,109
	4,24			0,136
	4,435			0,175
	4,553			0,197
	4,698			0,233
	4,868			0,292
	4,973			0,361
	5,056			0,417
	5,164			0,491
	5,246			0,552
	5,362			0,624
	5,453			0,703
	5,556			0,783
	5,637			0,867
	5,738			0,955
	5,826			1,04
	5,902			1,136

Table No. 1. Gd x Mn 1-x S, (x=0.1).

Dielectrić chemical penetratioń capacity medium - a physical quantity that characterizes the properties of an insulating (dielectric) medium and shows the dependence of electrical induction on the electric field strength.

It is determined by the effect of polarization of dielectrics under the influence of an electric field (and with the value of the dielectric susceptibility of the medium characterizing this effect).

There are relative and absolute dielectric constants.

The relative dielectric constant ε is dimensionless and shows how many times the force of interaction between two electric charges in a medium is less than in a vacuum. This value for air and most other gases under normal conditions is close to unity (due to their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are large for substances with molecules that have a large electric dipole moment. The relative dielectric constant of ferroelectrics is tens and hundreds of thousands.

The absolute dielectric constant in foreign literature is denoted by the letter ε; in domestic literature, the combination is predominantly used, where is the electric constant. Absolute dielectric constant is used only in the International System of Units (SI), in which induction and electric field strength are measured in different units. In the SGS system there is no need to introduce absolute dielectric constant. The absolute dielectric constant (like the electrical constant) has the dimension L −3 M −1 T 4 I². In International System of Units (SI) units: =F/m.

It should be noted that the dielectric constant largely depends on the frequency of the electromagnetic field. This should always be taken into account, since reference tables usually contain data for a static field or low frequencies down to a few kHz without indicating this fact. At the same time, there are also optical methods for obtaining the relative dielectric constant based on the refractive index using ellipsometers and refractometers. The value obtained by the optical method (frequency 10-14 Hz) will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency zero), the relative dielectric constant under normal conditions is approximately 80. This is the case down to infrared frequencies. Starting at approximately 2 GHz ε r starts to fall. In the optical range ε r is approximately 1.8. This is quite consistent with the fact that in the optical range the refractive index of water is 1.33. In a narrow frequency range, called optical, dielectric absorption drops to zero, which actually provides a person with the mechanism of vision [ source not specified 1252 days] in the earth's atmosphere saturated with water vapor. With further increase in frequency, the properties of the medium change again. You can read about the behavior of the relative dielectric constant of water in the frequency range from 0 to 10 12 (infrared region) at (English)

The dielectric constant of dielectrics is one of the main parameters in the development of electrical capacitors. The use of materials with high dielectric constant can significantly reduce the physical dimensions of capacitors.

The capacitance of the capacitors is determined:

Where ε r- dielectric constant of the substance between the plates, ε O- electrical constant, S- area of ​​the capacitor plates, d- distance between the plates.

The dielectric constant parameter is taken into account when developing printed circuit boards. The value of the dielectric constant of the substance between the layers, in combination with its thickness, affects the value of the natural static capacitance of the power layers, and also significantly affects the characteristic impedance of the conductors on the board.

RESISTANCE electrical, physical quantity equal to electrical resistance ( cm. ELECTRICAL RESISTANCE) R of a cylindrical conductor of unit length (l = 1 m) and unit cross-sectional area (S = 1 m 2).. r = R S/l. In Si, the unit of resistivity is Ohm. m. Resistivity can also be expressed in Ohms. cm. Resistivity is a characteristic of the material through which current flows and depends on the material from which it is made. Resistivity equal to r = 1 Ohm. m means that a cylindrical conductor made of of this material, length l = 1 m and with a cross-sectional area S = 1 m 2 has a resistance R = 1 Ohm. m. The value of resistivity of metals ( cm. METALS), which are good conductors ( cm. CONDUCTORS), can have values ​​of the order of 10 - 8 – 10 - 6 Ohms. m (for example, copper, silver, iron, etc.). The resistivity of some solid dielectrics ( cm. DIELECTRICS) can reach a value of 10 16 -10 18 Ohm.m (for example, quartz glass, polyethylene, electroporcelain, etc.). The resistivity value of many materials (especially semiconductor materials ( cm. SEMICONDUCTOR MATERIALS)) significantly depends on the degree of their purification, the presence of alloying additives, thermal and mechanical treatments, etc. The value s, the reciprocal of the resistivity, is called conductivity: s = 1/r Specific conductivity is measured in siemens ( cm. SIEMENS (conductivity unit)) per meter S/m. Electrical resistivity (conductivity) is a scalar quantity for an isotropic substance; and tensor - for an anisotropic substance. In anisotropic single crystals, the anisotropy of electrical conductivity is a consequence of the anisotropy of the inverse effective mass ( cm. EFFECTIVE MASS) electrons and holes.

1-6. ELECTRICAL CONDUCTIVITY OF INSULATION

When turning on the insulation of a cable or wire on constant voltage U a current i passes through it, varying with time (Fig. 1-3). This current has constant components - conduction current (i ∞) and absorption current, where γ is the conductivity corresponding to the absorption current; T is the time during which the current i abs drops to 1/e of its original value. For infinitely long time i abs →0 and i = i ∞. The electrical conductivity of dielectrics is explained by the presence in them of a certain amount of free charged particles: ions and electrons.

The most characteristic feature of most electrical insulating materials is ionic electrical conductivity, which is possible due to contaminants inevitably present in the insulation (impurities of moisture, salts, alkalis, etc.). In a dielectric with an ionic conductivity, Faraday's law is strictly observed - the proportionality between the amount of electricity passing through the insulation and the amount of substance released during electrolysis.

As the temperature increases, the resistivity of electrical insulating materials decreases and is characterized by the formula

where_ρ o, A and B are constants for a given material; T - temperature, °K.

A greater dependence of insulation resistance on moisture occurs with hygroscopic insulating materials, mainly fibrous (paper, cotton yarn, etc.). Therefore, fibrous materials are dried and impregnated, as well as protected by moisture-resistant shells.

Insulation resistance can decrease with increasing voltage due to the formation of space charges in the insulating materials. The additional electronic conductivity created in this case leads to an increase in electrical conductivity. There is a dependence of conductivity on voltage in very strong fields (Ya. I. Frenkel’s law):

where γ o - conductivity in weak fields; a is constant. All electrical insulating materials are characterized by certain values ​​of insulation conductivity G. Ideally, the conductivity of insulating materials is zero. For real insulating materials, the conductivity per unit cable length is determined by the formula

In cables with an insulation resistance of more than 3-10 11 ohm-m and communication cables, where dielectric polarization losses are significantly greater than thermal losses, conductivity is determined by the formula

Insulation conductivity in communications technology is an electrical parameter of a line that characterizes energy loss in the insulation of cable cores. The dependence of the conductivity value on frequency is shown in Fig. 1-1. The reciprocal of conductivity, the insulation resistance, is the ratio of the DC voltage applied to the insulation (in volts) to the leakage voltage (in amperes), i.e.

where R V is the volumetric insulation resistance, which numerically determines the obstacle created by the passage of current through the thickness of the insulation; R S - surface resistance, which determines the obstacle to the passage of current along the insulation surface.

A practical assessment of the quality of the insulating materials used is the specific volumetric resistance ρ V expressed in ohm-centimeters (ohm*cm). Numerically, ρ V is equal to the resistance (in ohms) of a cube with a 1 cm edge made of a given material, if the current passes through two opposite faces of the cube. Specific surface resistance ρ S is numerically equal to the surface resistance of the square (in ohms) if current is supplied to the electrodes delimiting two opposite sides of this square.

The insulation resistance of a single-core cable or wire is determined by the formula

Humidity properties of dielectrics

Moisture resistance – this is the reliability of the insulation when it is in an atmosphere of water vapor close to saturation. Moisture resistance is assessed by changes in electrical, mechanical and other physical properties after the material is in an atmosphere with high and high humidity; on moisture and water permeability; by moisture and water absorption.

Moisture permeability – the ability of a material to transmit moisture vapor in the presence of a difference in relative air humidity on both sides of the material.

Moisture absorption – the ability of a material to sorb water when exposed for a long time in a humid atmosphere close to a state of saturation.

Water absorption – the ability of a material to absorb water when immersed in water for a long time.

Tropical resistance and tropicalization equipment – protection of electrical equipment from moisture, mold, rodents.

Thermal properties of dielectrics

To characterize the thermal properties of dielectrics, the following quantities are used.

Heat resistance– the ability of electrical insulating materials and products to withstand high temperatures and sudden temperature changes without harm to them. Determined by the temperature at which a significant change in mechanical and electrical properties is observed, for example, tensile or bending deformation under load begins in organic dielectrics.

Thermal conductivity– the process of heat transfer in a material. It is characterized by an experimentally determined thermal conductivity coefficient λ t. λ t is the amount of heat transferred in one second through a layer of material 1 m thick and a surface area of ​​1 m 2 with a temperature difference between the surfaces of the layer of 1 °K. The thermal conductivity coefficient of dielectrics varies over a wide range. The lowest values ​​of λ t have gases, porous dielectrics and liquids (for air λ t = 0.025 W/(m K), for water λ t = 0.58 W/(m K)), high values have crystalline dielectrics (for crystalline quartz λ t = 12.5 W/(m K)). The thermal conductivity coefficient of dielectrics depends on their structure (for fused quartz λ t = 1.25 W/(m K)) and temperature.

Thermal expansion dielectrics are assessed by the temperature coefficient of linear expansion: . Materials with low thermal expansion, as a rule, have higher heat resistance and vice versa. The thermal expansion of organic dielectrics significantly (tens and hundreds of times) exceeds the expansion of inorganic dielectrics. Therefore, the dimensional stability of parts made of inorganic dielectrics during temperature fluctuations is significantly higher compared to organic ones.

1. Absorption currents

Absorption currents are displacement currents of various types of slow polarization. Absorption currents at a constant voltage flow in the dielectric until an equilibrium state is established, changing their direction when the voltage is turned on and off. With an alternating voltage, absorption currents flow during the entire time the dielectric is in the electric field.

In general electric current j in a dielectric is the sum of the through current j sk and absorption current j ab

j = j sk + j ab.

The absorption current can be determined through the bias current j cm - rate of change of the electrical induction vector D

The through current is determined by the transfer (movement) of various charge carriers in the electric field.

2. Electronic electrical conductivity is characterized by the movement of electrons under the influence of a field. In addition to metals, it is present in carbon, metal oxides, sulfides and other substances, as well as in many semiconductors.

3. Ionic – caused by the movement of ions. It is observed in solutions and melts of electrolytes - salts, acids, alkalis, as well as in many dielectrics. It is divided into intrinsic and impurity conductivity. Intrinsic conductivity is due to the movement of ions obtained during dissociation molecules. The movement of ions in an electric field is accompanied by electrolysis – transfer of a substance between electrodes and its release on the electrodes. Polar liquids are more dissociated and have higher electrical conductivity than non-polar liquids.

In nonpolar and weakly polar liquid dielectrics (mineral oils, silicone liquids), electrical conductivity is determined by impurities.

4. Molion electrical conductivity – caused by the movement of charged particles called molions. It is observed in colloidal systems, emulsions , suspensions . The movement of molions under the influence of an electric field is called electrophoresis. During electrophoresis, unlike electrolysis, no new substances are formed; the relative concentration of the dispersed phase in different layers of the liquid changes. Electrophoretic conductivity is observed, for example, in oils containing emulsified water.

The level of polarizability of a substance is characterized by a special value called dielectric constant. Let's consider what this value is.

Let us assume that the intensity of a uniform field between two charged plates in a vacuum is equal to E₀. Now let's fill the gap between them with any dielectric. which appear at the boundary between the dielectric and the conductor due to its polarization, partially neutralize the effect of charges on the plates. Tension E of this field the tension E₀ will become less.

Experience reveals that when the gap between the plates is sequentially filled with equal dielectrics, the field strengths will be different. Therefore, knowing the value of the ratio of the electric field strength between the plates in the absence of dielectric E₀ and in the presence of dielectric E, one can determine its polarizability, i.e. its dielectric constant. This quantity is usually denoted Greek letterԑ (epsilon). Therefore, we can write:

The dielectric constant shows how many times less of these charges in a dielectric (homogeneous) will be than in a vacuum.

The decrease in the force of interaction between charges is caused by processes of polarization of the medium. In an electric field, electrons in atoms and molecules are reduced in relation to ions, and i.e. appears. those molecules that have their own dipole moment (in particular water molecules) are oriented in the electric field. These moments create their own electric field, counteracting the field that caused their appearance. As a result, the total electric field decreases. In small fields this phenomenon is described using the concept of dielectric constant.

Below is the dielectric constant in vacuum various substances:

Air……………………………....1.0006

Paraffin…………………………....2

Plexiglass (plexiglass)……3-4

Ebonite……………………………..…4

Porcelain……………………………....7

Glass…………………………..…….4-7

Mica……………………………..….4-5

Natural silk............4-5

Slate........................6-7

Amber………………12.8

Water…………………………………...….81

These values ​​of the dielectric constant of substances refer to ambient temperatures in the range of 18–20 °C. So, dielectric constant solids changes slightly with temperature, with the exception of ferroelectrics.

On the contrary, for gases it decreases due to an increase in temperature and increases due to an increase in pressure. In practice it is taken as one.

Impurities in small quantities have little effect on the level of dielectric constant of liquids.

If two arbitrary point charges are placed in a dielectric, then the field strength created by each of these charges at the location of the other charge decreases by ԑ times. It follows from this that the force with which these charges interact with one another is also ԑ times less. Therefore, for charges placed in a dielectric, it is expressed by the formula:

F = (q₁q₂)/(4πԑₐr²),

where F is the interaction force, q₁ and q₂ are the magnitude of the charges, ԑ is the absolute dielectric constant of the medium, r is the distance between point charges.

The value of ԑ can be shown numerically in relative units (relative to the value of the absolute dielectric permittivity of vacuum ԑ₀). The value ԑ = ԑₐ/ԑ₀ is called the relative dielectric constant. It reveals how many times the interaction between charges in an infinite homogeneous medium is weaker than in a vacuum; ԑ = ԑₐ/ԑ₀ is often called complex dielectric constant. The numerical value of the quantity ԑ₀, as well as its dimension, depend on which system of units is chosen; and the value of ԑ - does not depend. So, in the SGSE system ԑ₀ = 1 (this fourth basic unit); in the SI system, the dielectric constant of vacuum is expressed:

ԑ₀ = 1/(4π˖9˖10⁹) farad/meter = 8.85˖10⁻¹² f/m (in this system ԑ₀ is a derived quantity).

Permittivity- this is one of the main parameters characterizing the electrical properties of dielectrics. In other words, it determines how good an insulator a particular material is.

The dielectric constant value shows the dependence of the electrical induction in the dielectric on the electric field strength acting on it. Moreover, its value is influenced not only physical properties the material or medium itself, but also the frequency of the field. As a rule, reference books indicate the value measured for a static or low-frequency field.

There are two types of dielectric constant: absolute and relative.

Relative dielectric constant shows the ratio of the insulating (dielectric) properties of the material under study to similar properties of vacuum. It characterizes the insulating properties of a substance in gaseous, liquid or solid states. That is, it is applicable to almost all dielectrics. The value of the relative dielectric constant for substances in the gaseous state, as a rule, is in the range of 1. For liquids and solids, it can be in a very wide range - from 2 and almost to infinity.

For example, relative dielectric constant fresh water is equal to 80, and for ferroelectrics – tens or even hundreds of units, depending on the properties of the material.

Absolute dielectric constant is a constant value. It characterizes the insulating properties of a particular substance or material, regardless of its location and external factors affecting it.

Usage

Dielectric constant, or rather its values, are used in the development and design of new electronic components, in particular capacitors. Future sizes and electrical characteristics component. This value is also taken into account when developing whole electrical diagrams(especially in high-frequency electronics) and even