Dielectric Constant

12 Key excerpts on "Dielectric Constant"

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  Practical Guide to Materials Characterization

  Techniques and Applications

  • Khalid Sultan(Author)
  • 2022(Publication Date)
  • Wiley-VCH

    (Publisher)

  6 Dielectric Measurements

  6.1 Introduction

  Materials having a high value of electrical resistivity can be dielectrics or insulators. The best dielectric material is always the best insulator but not vice versa. The various parameters associated with dielectric materials can be defined as follows.

  Capacitance: The main property of a capacitor is the storage of the electrical charge Q, which on a capacitor can be expressed as Q = CV, where V represents the voltage applied and C the capacitance. The quantity capacitance C is linked with the geometrical and the material factor. If the capacitor has a large plate with an area and thickness d then in a vacuum the geometrical capacitance is given by

  (6.1)

  Here ε0 represents the permittivity of a vacuum and is also known as the Dielectric Constant. By inserting a ceramic material, having permittivity ε΄, between the plates of the capacitor, then

  (6.2)

  Here K is known as the relative Dielectric Constant or relative permittivity, which is the property of a material interpreting the capacitance of a circuit element.

  Dielectric loss factor: This factor is usually denoted by ε˝ and is defined by Equation (6.3 ), which in a broader sense is the major factor for applying dielectric materials as insulating material:

  (6.3)

  where ε΄ represents the Dielectric Constant and tan δ the dissipation factor. It is desired to have a high Dielectric Constant and, in particular, a very small loss angle for this purpose. High Dielectric Constant materials must be utilized in applications where a high capacitor in the smallest physical space is desired and the dissipation factor, tan δ

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  Electronic Packaging Materials and Their Properties

  • Michael Pecht, Rakish Agarwal, F. Patrick McCluskey, Terrance J. Dishongh, Sirus Javadpour, Rahul Mahajan(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  1 PROPERTIES OF ELECTRONIC PACKAGING MATERIALS

  1.1 Electrical Properties

  Signal processing is critical for the operation of an electronic system, and materials, along with their architectures, play an important role in the propagation of signals, especially for circuits operating at high speeds and at high electrical frequency. The electrical properties of major importance in material selection include the Dielectric Constant, loss tangent, dielectric strength, volumetric resistivity, surface resistance, and arc resistance. These electrical properties are defined and discussed with standard test methods (refer to Table 1 ) wherever applicable. Some of these properties exhibit subtle differences and some are known by more than one term.

  Dielectric Constant, ε . The Dielectric Constant of an insulating material is the ratio of the measured capacitance with the dielectric material between two electrodes to the capacitance with a vacuum or free space between the electrodes. The Dielectric Constant is a dimensionless number also referred to as the relative permittivity. Table 2 lists Dielectric Constants of some electronic. Test method ASTM D150 is used to measure the Dielectric Constant.

  To account for the electrical power loss to an insulating material subject to a sinusoidally time-varying applied potential, a complex number called permittivity is defined as

  ε = ε ' − ε "

  ⁢

  ( 1 )

  where the imaginary part ε,” is the electrical power loss factor, and the real part, ε’, is the Dielectric Constant of the insulatorvmaterial.

  Most materials possess a Dielectric Constant that depends on the frequency of the applied electromagnetic field. The dependence on electrical frequency is due to the orientational (defined by reorientation of inherent dipoles in the material), ionic (defined by displacement of ions of molecules), and electronic polarization (defined by the shift in the electronic cloud of atoms) of the material. Figure 1A

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  Steady Electric Fields and Currents

  Elementary Electromagnetic Theory

  • B. H. Chirgwin, C. Plumpton, C. W. Kilmister(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER 4 DIELECTRICS 4.1 The effects of a dielectric In Chapter 1 we defined insulators as substances on which, or inside which, electric charge is unable to move continuously. Experiments show that when a piece of insulating material is introduced into a region where an electric field is already established the field is modified, the distributions of charge and the forces acting on the conductors alter, and the potentials of the con-ductors change. In addition, the insulator itself experiences (ponderomotive) forces ; this is illustrated experimentally when dust particles and small pieces of paper are attracted to a charged body such as a gramophone record. Faraday investigated another electrostatic property of an insulating material^ viz. its effect on the capacitance of a condenser. He found that when the region of the field inside a condenser (e.g. between the plates of a parallel plate condenser, or between the spheres of a spherical condenser) was filled with an insulating substance the capacitance of the condenser was multiplied by a factor K (>1) which he was able to measure. The factor K does not depend upon the charge or potential of the capacitor, but varies from one material to another. Faraday called this factor the specific inductive capacity of the material; the modern name is Dielectric Constant. More recently it has been found that, under a wider range of conditions than those of Faraday's, investigations, the Dielectric Constant of a given material alters. However, for the steady conditions of an electrostatic field of moderate intensity, K may be taken to be independent of the field quantities. When an insulator is situated in a field which presumably penetrates into the material of the insulator we call the substance of the insulator a dielectric.

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  Advanced Electrical and Electronics Materials

  Processes and Applications

  • K. M. Gupta, Nishu Gupta, Ashutosh Tiwari(Authors)
  • 2015(Publication Date)
  • Wiley-Scrivener

    (Publisher)

  o, and is given by

  (9.1)

   

  Here ε

  r

  is dimensionless. The value of ε

  r

  = 1 for air or vacuum, and ε

  r

  > 1 for solids. Its value for diamond is 5.68, for silicon is 12, and for germanium is 16.

  9.4.1 Factors Affecting Dielectric Constant

  Dielectric Constant is influenced by the following main factors.

  1. Frequency f of applied field, and
  2. Temperature T.

  It may decrease or increase with an increase in frequency and temperature. Variation of ε

  r

  as a function of temperature T for HCl is shown in

  Fig. 9.1a

  . In solid state, its value suddenly goes-up beyond 100 K, and then lowers-down gradually.

  Figure 9.1b

  shows variation in ε

  r

  for glass and alumina.

  Figure 9.1

  Dielectric Constant as a function of (a) temperature for hydrogen chloride, and (b) temperature and frequency for glass and alumina

  Here the Dielectric Constant increases with increase in temperature and frequency. Dielectric Constant of some materials and the effect of frequency on them is illustrated in Table 9.1 . With increase in frequency it remains constant for some materials and lowers-down for others.

  Table 9.1

  Dielectric properties of Some Materials

  Dielectric material	Dielectric Constant ε r at frequency	Dielectric strength (MV/m)	Dielectric loss (tan δ)
  	60 Hz	106 Hz
  Polyethylene	2.3	2.3	4	0.0004
  Elastomer	4.0	2.7	25	0.003
  Fused silica	4.0	3.8	10	0.0001
  Nylon 6,6	4.0	3.5	15	0.02
  Waxed paper	4.2	—	—	—
  Bakelite	4.4	4.4	15	0.028
  Transformer oil	5.0	2.5	10	0.0001
  Porcelain	6.0	6.0	5	0.02
  Steatite(MgO.SiO2 )	6.0	6.0	12	0.001
  Soda-lime glass	7.0	7.0	10	0.005
  P.V.C.	7.0	3.4	2	0.05
  Mica (Al2 (OH)2 . AlSi3 O10 .K2 )	8.0	5.0	100	0.0005

  9.5 Dielectric Strength

  The voltage per unit thickness that can be sustained by an insulating material before its breakdown is called as dielectric strength. A good insulating material possesses high dielectric strength. Dielectric strength of some materials is shown in Table 9.1

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  Infrared and Millimeter Waves V8

  Electromagnetic Waves in Matter, Part I

  • Kenneth J. Button(Author)
  • 1983(Publication Date)
  • Academic Press

    (Publisher)

  INFRARED AND MILLIMETER WAVES, VOL. 8 CHAPTER 1 Properties of Dielectric Materials G. W. Chantry National Physical Laboratory Teddington, Middlesex United Kingdom I. II. III. IV. V. INTRODUCTION THE MACROSCOPIC THEORY A. The Response Function B. The Correlation Function and the Cole-Cole Plot C. Corrections for the Internal Field D. Causality and the Kramers-Kronig Relations THE MICROSCOPIC THEORY EXPERIMENTAL METHODS SOME ILLUSTRATIVE EXAMPLES OF SUBMILLIMETER DIELECTRIC MEASUREMENTS A. Polar Liquids B. Nonpolar Liquids C. Solutions of Polar Molecules in Nonpolar Solvents D. Polymers E. Plastic Crystals F. Glasses REFERENCES 1 5 5 9 15 16 21 26 30 30 31 35 38 45 46 47 I. Introduction The study of liquids and polymers by means of far-infrared and submilli-meter spectroscopy forms part of the much larger topic of dielectric physics. A dielectric medium is one in which there are no free charges so the dc conductivity is zero, but the medium can sustain displacement currents and these may have lossy components. Thus dielectrics are all materials that are not metallic, semiconducting, or ionized. If an external field E is applied to a dielectric, the field inside the dielectric is given by D = (e/e 0 )E, (1) where ε is the permittivity of the dielectric and ε 0 the absolute permittivity of free space (8.85418 X 10 12 F/m). In nearly all dielectric work, however, it is customary to write ε = ε/ε 0 to avoid the constant apperance of the ε 0 factor; then ε so defined is the relative permittivity of the medium, i.e., the permit-1 Copyright © 1983 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-147708-8 2 G. W. CHANTRY tivity relative to that of the vacuum. The relative permittivity is complex because it will have a lossy component, and one therefore usually writes g = β ' -/ β , (2) where the caret is used to signify an explicitly complex quantity.

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  Prediction of Polymer Properties

  • Jozef Bicerano(Author)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  CHAPTER 9 ELECTRICAL PROPERTIES 9.A. Background Information The electrical properties of polymers are important in many applications [1]. The most widespread electrical application of polymers is the insulation of cables. In recent years, high-performance polymers have become important in the electronics industry; as encapsulants for electronic components, as interlayer dielectrics, and as printed wiring board materials. The Dielectric Constant (or permittivity) , and the dissipation factor (or power factor or electrical loss tangent) tan &, which are dimensionless quantities, are the key electrical properties. The Dielectric Constant , is a measure of the polarization of the medium between two charges when this medium is subjected to an electric field. A larger value of , implies greater polarization of the medium between the two charges. Vacuum contains nothing that could be polarized, and therefore has ,=1. All materials have ,>1. The Dielectric Constant of a nonconducting material is generally defined as the ratio of the capacities of a parallel plate condenser with and without the material placed between the plates. The Dielectric Constant of a polymer is a function of the following variables: 1. Temperature of measurement. The most common temperature where electrical properties are reported in standard reference books is room temperature (298K±5K, with some variation). 2. Rate (frequency) of measurement. The most common two frequencies at which the electrical properties are reported in standard reference tables are one kilohertz (1 kHz=1000 Hertz) and one megahertz (1 MHz=1000000 Hertz). 3. Structure and composition of polymer, and especially the presence of any polar groups. 4. Morphology of specimens, and especially any crystallinity and/or orientation. 5. Impurities, fillers, plasticizers, other additives, and moisture (water molecules) in polymer.

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  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  This parameter can be measured using an impedance analyzer similar to measuring the Dielectric Constant. We can compare how lossy different dielectric materials are relative to each other. The real part of the complex Dielectric Constant is a measure of a material’s charge-storing ability. The magnitude of tan δ indicates the inefficiency of the material in terms of the charge-storing ability. In an ideal dielectric, which does not exist, polarization processes are assumed to occur without any electrical energy waste, with no energy wasted during charge storage, that is, tan δ = 0. In many real dielectrics, the tan δ values range from ~10 −5 to 10 −2. Some special applications, such as ceramic materials used as dielectric resonators for microwave communications, require very low tan δ values. In this case, the values of a parameter defined as the quality factor (Q) are reported. The quality factor of a dielectric (Q d) is defined as Q d ≈ 1 tan δ (7.97) We can also show that tan δ is the ratio of the imaginary and real parts of the complex Dielectric Constant (k *). The Dielectric Constant is defined as ɛ r * = C / C 0, and because Q = CV, Q = ɛ r * C 0 V. The current I total = dQ/dt = C (dV/dt), or I total = ɛ r * C 0 (d V d t) (7.98) If V = V 0 exp(jωt), then dV/dt =. jωV 0 exp(jωt) = jωV ; therefore, I total is I total = ɛ r * C 0 (d V d t) = (ɛ ′ r − j ɛ” r) C 0 j ω V (7.99) To derive Equation 7.99, we substituted for the complex Dielectric Constant in terms of its real and imaginary parts (see Equation 7.68). I total = j ω ɛ ′ r C 0 V + ω ɛ” r C 0 V (7.100) Note that to derive this equation, we used the. value j 2 = −1. Now compare Equations 7.95 and 7.100. The first term of Equation 7.100 represents the charge-storage in the dielectric, that is, the charging current. The second term is the magnitude of the loss current (I loss)

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  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  The imaginary part of the complex dielec-tric constant ( ) ′′ ε r is a measure of the dielectric losses that occur during the charge-storage process. 7.13.2 R EAL D IELECTRICS AND I DEAL D IELECTRICS An ideal dielectric is a hypothetical material with zero dielectric losses (i.e., ′ ε = 0 r ). This means that all the applied electrical energy is used to cause the polarization that leads to charge storage only. A real dielectric is a material that does have some dielectric losses. All dielectric materials have some level of dielectric loss because the displacements of ions, electron clouds, and so on, can-not occur without resistance from neighboring atoms or ions. The dielectric losses increase if the applied field switches in such a way that the polarization mechanisms can follow these changes in the applied electric field. It usually is desirable to minimize or lower the dielectric losses for micro-electronic devices. However, dielectric losses can be useful for applications in which heat must be generated. A common example is that of a microwave oven. The water molecules in food, which are permanent dipoles, tumble around during the polarization caused by the microwave’s electric field. The resultant dielectric losses cause the generation of heat (Vollmer 2004). While developing materials for capacitors to store charge (Section 7.2.2), we prefer to use a low-loss dielectric; in other words, we want a small ′′ ε r . The need for increasing the Dielectric Constant ( k , or what we now refer to as ′ ε r ) while maintaining the dielectric losses at small levels poses a problem because polarization processes are required to achieve higher Dielectric Constants. When these polarization processes occur, they cause dielectric losses. Polarization and dielectric losses originate from the same basic processes (some type of displacement of ions and electron clouds, in addition to the reorientation or rotation of dipoles, etc.; see Figure 7.8).

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  An Introduction to the Physics of Interstellar Dust

  • Endrik Krugel(Author)
  • 2007(Publication Date)
  • CRC Press

    (Publisher)

  1 The dielectric permeability We begin by acquainting ourselves with the polarization of matter. The fun-damental quantity describing how an interstellar grain responds to an electro-magnetic wave is the dielectric permeability which relates the polarization of matter to the applied field. We recall the basic equations of electrodynamics and outline how plane waves travel in an infinite non-conducting (dielectric) medium and in a plasma. We summarize the properties of harmonic oscilla-tors, including the absorption, scattering and emission of light by individual dipoles. Approximating a solid body by an ensemble of such dipoles (identical harmonic oscillators), we learn how its dielectric permeability changes with frequency. This study is carried out for • a dielectric medium where the electron clouds oscillate about the atomic nuclei • and a metal where the electrons are free. 1.1 How the electromagnetic field acts on dust At the root of all phenomena of classical electrodynamics, such as the inter-action of light with interstellar dust, are Maxwell’s formulae. They can be written in different ways and the symbols, their names and meaning are not universal, far from it. Before we exploit Maxwell’s equations, we therefore first define the quantities which describe the electromagnetic field. 1.1.1 Electric field and magnetic induction A charge q traveling with velocity v in a fixed electric field E and a fixed magnetic field of flux density B experiences a force F = q E + 1 c v × B , (1.1) called the Lorentz force; the cross × denotes the vector product. B is also called magnetic induction. Equation (1.1) shows what happens mechanically to a charge in an electromagnetic field and we use it to define E and B . 1 2 The dielectric permeability The force F has an electric part, q E , which pulls a positive charge in the direction of E , and a magnetic component, ( q/c ) v × B , working perpendicular to v and B .

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  Fundamentals of Physics

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The electric field within the dielectric material filling the space between the plates is 1.4 × 10 6 V/m. (a) Calculate the Dielectric Constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface. 55 M The space between two concentric conducting spherical shells of radii b = 1.70 cm and a = 1.20 cm is filled with a substance of Dielectric Constant κ = 23.5. A potential difference V = 73.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q′ induced along the surface of the inner shell. Additional Problems 56 In Fig. 25.33, the battery potential difference V is 10.0 V and each of the seven capacitors has capacitance 10.0 μF. What is the charge on (a) capacitor 1 and (b) capacitor 2? 57 SSM In Fig. 25.34, V = 9.0 V, C 1 = C 2 = 30 μF, and C 3 = C 4 = 15 μF. What is the charge on capacitor 4? C 1 C 2 V – + Figure 25.33 Problem 56. 41 E SSM A coaxial cable used in a transmission line has an inner radius of 0.10 mm and an outer radius of 0.60 mm. Cal- culate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene. 42 E A parallel-plate air-filled capacitor has a capacitance of 50 pF. (a) If each of its plates has an area of 0.35 m 2 , what is the separation? (b) If the region between the plates is now filled with material having κ = 5.6, what is the capacitance? 43 E Given a 7.4 pF air-filled capacitor, you are asked to convert it to a capacitor that can store up to 7.4 μJ with a maximum potential difference of 652 V. Which dielectric in Table 25.5.1 should you use to fill the gap in the capacitor if you do not allow for a margin of error? 44 M You are asked to construct a capacitor having a capaci- tance near 1 nF and a breakdown potential in excess of 10 000 V.

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  Theory of Electric Polarization

  Dielectrics in Static Fields

  • Bozzano G Luisa(Author)
  • 2012(Publication Date)
  • Elsevier Science

    (Publisher)

  C H A P T E R VI STATISTICAL-MECHANICAL THEORIES O F T H E Dielectric Constant §35. Introduction In contradistinction to the theories discussed in Chapter V, which use the continuum approach for the environment of the molecule, in this chapter the molecular structure of matter wiM be taken into account explicitly. To this end we shall use the methods of statistical mechanics which provide a way of obtaining macroscopic quantities when the properties of the molecules and the molecular interactions are known. In the statistical-mechanical theories of the Dielectric Constant simplified models are often used for the molecules and the intermolecular forces to make the calculations tractable. For example, a molecule is represented by an ideal dipole and a scalar polarizability or by an ideal dipole in the centre of a dielectric sphere, and the molecular interaction is taken to follow a hard-sphere or a Lennard-Jones potential. Even for these simplified models the calculations are often too difficult to perform, since the system com-prises a very large number of molecules (of the order of 10 2 3 ) exerting long-range (dipole-dipole) forces on each other. Therefore, in many cases one has to be content with approximate expressions or series expansions with respect to the density. All statistical-mechanical theories of the Dielectric Constant start from the consideration that the polarization ^ , given in eqn. (2.43): 4 π ^ = D is equal to the dipole density P, when the influence of higher multipole densities may be neglected (compare sections 6 and 7). By definition, we may write for the dipole density Ρ of a homogeneous system: P K = < M > , (6.1) where V is the volume of the dielectric under consideration and is its average total (dipole) moment (the brackets < > denote a statistical mech- 206 C. J. F. BOTTCHER anical average). If we assume the system to be isotropic, we also have, according to eqn.

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  Fundamentals of Physics, Extended

  • David Halliday, Robert Resnick, Jearl Walker(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  In a region that is completely filled by a dielectric, all electrostatic equations con- taining ε 0 must be modified by replacing ε 0 with κε 0 . The effects of adding a dielectric can be understood physi- cally in terms of the action of an electric field on the permanent or induced electric dipoles in the dielectric slab. The result is the formation of induced charges on the surfaces of the dielectric, which results in a weakening of the field within the dielectric for a given amount of free charge on the plates. Gauss’ Law with a Dielectric When a dielectric is pres- ent, Gauss’ law may be generalized to ε 0 ∮ κE → ⋅ d A → = q. (25.6.7) Here q is the free charge; any induced surface charge is accounted for by including the Dielectric Constant κ inside the integral. 1 Figure 25.1 shows plots of charge versus potential differ- ence for three parallel-plate capacitors that have the plate areas and separations given in the table. Which plot goes with which capacitor? Capacitor Area Separation 1 A d 2 2A d 3 A 2d Questions a b c V q Figure 25.1 Question 1. Checkpoint 25.6.1 We have two dielectric materials that will completely fill the gap between the plates of a charged, isolated capacitor. Dielectric 1 has a small Dielectric Constant; dielectric 2 has a larger Dielectric Constant. We insert dielectric 1 and then remove it. Then we insert dielec- tric 2. (a) How do the free charges compare in the two situations: q 1 = q 2 , q 1 > q 2 , or q 1 < q 2 ? (b) How do the induced charges compare: q 1 ʹ = q 2 ʹ , q 1 ʹ > q 2 ʹ , or q 1 ʹ < q 2 ʹ ? (c) How do the potential differences between the plates compare: V 1 = V 2 , V 1 > V 2 , or V 1 < V 2 ? 782 CHAPTER 25 CAPACITANCE 2 What is C eq of three capacitors, each of capacitance C, if they are connected to a battery (a) in series with one another and (b) in parallel? (c) In which arrangement is there more charge on the equivalent capacitance? 3 (a) In Fig.

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