Chap. 7. Dielectric Materials and Insulation

Size: px

Start display at page:

Download "Chap. 7. Dielectric Materials and Insulation"

Candace Tucker
6 years ago
Views:

1 Chap. 7. Dielectric Materials and Insulation - The parallel plate capacitor with free space as an insulator: - The electric dipole moment for a pair of opposite changes +Q and -Q separated by a finite distance a. *Although the net charge is zero, this dipole moment gives rise to an electric field in space and interacts with an electric field from other sources. - The dielectric medium has not only the ability to increase capacitance but also the insulating property (low conductivity) so that the charges are conducted from one plate of the capacitor to the other through the dielectric. *The relative permittivity (dielectric constant) depends on the frequency. - Dielectric breakdown: above the dielectric strength, a large discharge current flows through the dielectric due to insulation failure.

2 7.1. Matter Polarization and Relative Permittivity - Definition of relative permittivity: capacitance with vacuum and with a dielectric medium The dielectric constant (relative permittivity) *The increase in the srored charge is due to the polarization of the dielectric induced by an applied field Dipole Moment and Electronic Polarization - The electronic polarization Q a +Q Q net = 0 p = Q a Fig. 7.2: The definition of electric dipole moment.

3 - Atomic polarization: when an atom is placed in an external electric field, it develops an induced dipole moment. Electron cloud C x O E Atomic nucleus (a) A neutral atom in E = 0. Center of negative charge p induced (b) Induced dipole moment in a field Fig. 7.3: The origin of electronic polarization. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) The electronic polarizability:

4 - For an atom with Z number of electrons orbiting the nucleus and all the electrons are contained within a certain spherical region, (Coulomb force = the restoring force under the displacement x) with the spring constant - The equation of motion of the negative charge center: Then, the displacement at any time where ; the oscillation frequency of the center of the electron cloud about the nucleus *In the atomic case, a sinusoidal displacement implies that the electronic charge cloud has an acceleration Classically, EM radiation like a radio antenna Oscillating charge cloud loses energy (oscillation amplitude decreases) - The electronic polarizability:

5 7.1.3 Polarization Vector P - The surface polarization charge : +Q E -Q Bound polarization charges on the surfaces -Q P +Q P (b) V Area = A (a) p total (c) P - Q P +Q P d Fig. 7.4: (a) When a dilectric is placed in an electric field, bound polarization charges appear on the opposite surfaces. (b) The origin of these polarization charges is the polarization of the molecules of the medium. (c) W e can represent the whole dielectric in terms of its surface polarization charges +Q P and -Q P. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

6 - In general, the charge per unit area appearing on the surface of a polarized medium is equal to the component of the polarization vector normal to this surface: - The polarization P induced in a dielectric medium when it is placed in an electric field depends on the field itself: The electric susceptibility Let the electronic polarizability be with N = the no. of molecules per unit vol. so - The field before the insertion of a dielectric medium between two plates: ( free surface charge density) After the insertion of the dielectric, Using, we have From the definition

7 7.1.4 Local Field and Clausius-Mossotti Equation - Under the assumption that the field acting on an individual atom or molecules is uniform within the dielectric,. However, the induced polarization depends on the actual field experienced by the molecule. *There are polarized molecules within the dielectric with their negative and positive charges separated so that the field is not constant on the atomic scale. E loc Electric field at atomic scale E loc E E = V / d x Fig. 7.6: The electric field inside a polarized dielectric at the atom ic scale is not uniform. T he local field is the actual field that acts on a m olecules. It can be calculated by removing that molecules and evaluating the field at that point from the charges on the plates and the dipoles surrounding the point. (E is the electric field.) From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) aterials.u sask.c a

8 - The actual field experienced by a molecules in a dielectric is defined as the local field. *This local field depends not only on the free charges on the plates but also on the arrangement of all the polarized molecules around a given position (point). - Evaluation of : 1) remove the molecule at the given point 2) calculate the field at this point coming from all sources, including neighboring polarized molecules - In the simplest case of a material with a cubic crystal structure, or a liquid (no crystal structure, Lorentz field, t hen From (, the Clausius-Mossotti equation

9 7.3 Polarization Mechanisms - Ionic, Orientational (Dipolar), Interfacial Polarizations Ionic Polarization - NaCl, KCl, LiBr: pairs of oppositely charged neighboring ions (dipole moments) under no electric field. p + p (a) Cl Na + x p' + p' (b) E Fig. 7.8: (a) A NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion is zero. (b) In the presence of an applied field the ions become slightly displaced which leads to a net average dipole moment per ion.

10 - In the presence of the field, : ( = ionic polarizability) ( = the no. of ion pairs) The Clausius-Mossotti equation for ionic polarization Orientational (Dipolar) Polarization - Molecules with permanent dipole moments: HCl - For all molecules that align perfectly with the electric field, - Due to thermal fluctuations, dipole alignment along the electric field will be perturbed (thermal energy ; 5 degrees of freedom) For, strong dipole alignment with the field For, no dipole alignment with the field - The torque experienced by the dipole [See Fig. 7.9c] where The max. potential energy ( )

11 τ +Q Cl - H + p o = aq θ F = Q E E p o (a) F -Q (c) p av = 0 p av 0 E (b) Fig. 7.9: (a) A HCl molecule possesses a permanent dipole moment, p o (b) In the absence of a field, thermal agitation of the molecules results in zero net average dipole moment per molecule. (c) A dipole such as HCl placed in a field experiences a torque which tries to rotate it to align p o with the field E. (d) In the presence of an applied field the dipoles try to rotate to align with the field against thermal agitation. There is now a net average dipole moment per molecule along the field. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) sask.ca (d) - Simply,, but using Boltzmann statistics, Thus, the dipolar orientational poarizability

12 7.3.3 Interfacial Polarization - Accumulation of charges at an interface between two materials or between two regions within a material Electrode Electrode Dielectric E Fixed charge Mobile charge (a) E Accumulated charge (b) Grain boundary or interface (c) Fig. 7.10: (a) A crystal with equal number of mobile positive ions and fixed negative ions. In the basence of a field there is no net separation betw een all the positive charges and all the negative charges. (b) In the presence of an applied field the m obile positive ions m igrate tow ards the negative electrode and accum ulate there. T here is now an overall separation betw een the negative charges and positive charges in the dielectric. T he dielectric therefore exhibits interfacial polarization. (c) G rain boundaries and interfaces betw een different m aterials frequently give rise to interfacial polarization. (E is the electric field.) From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) a terials.u sask.c a

13 7.4 Frequency Dependence: Dielectric Constant and Dielectric Loss - The polarization of the medium under ac conditions leads to an ac dielectric constant that is generally different than the static dielectric constant. At any instant, where 1) Thermal agitation (fluctuations): randomization of the dipole orientations 2) the molecular rotation in a viscous medium (interactions with neighbors): dipoles can not respond instantaneously to the changes in the applied field. *If the field changes too rapidly, then the dipoles can not follow the field and thus remain randomly oriented. At high frequencies, since the field can not induce a dipole moment. - The polarizability changes from its maximum value to zero as the frequency of the field is increased: - The field at time : the induce dipole moment, relax *The relaxation time = *The relaxation process in the induced dipole moment is achieved by random collisions. The excess dipole moment

14 p α d (0)E o p-α d (0)E α d (0)E E t E o E t 0 Fig. 7.11: The dc field is suddenly changed from Eo to E at time t = 0. The induced dipole moment p has to decrease from α d (0)Eo to a final value of α d (0)E. The decrease is achieved by random collisions of molecules in the gas. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) - The rate at which the induced dipole moment is changing is :

15 - For an ac field, where ; the orientational polarizability - At low frequencies, and p is in phase with E. *The rate of relaxation is much faster than the frequency of the field or the rate at which the polarization is being changed; p then closely follows E. - At high frequencies, the rate of relaxation is much slower than the frequency of the field and the polarization p can no longer follow the variations in the field. - Complex dielectric constant: The real part decreases from its maximum value, corresponding to, to 1 at high frequencies when as. The imaginary part is zero at low and high frequencies but peaks at when or when : represents the energy lost in the dielectric medium as the dipoles are oriented against random collisions by the field.

16 P = P o sin(ωt+φ) E = E o sinωt ε r ' and ε r '' ε r ' ε r (0) ε r '' 1 ω v = V o sinωt 0.01 / τ 0.1 / τ 1 / τ 10 / τ 100 / τ (a) Fig. 7.12: (a) An ac field is applied to a dipolar medium. The polarization P (P = Np) is out of phase with the ac field. The relative permittivity is a complex number with real (εr') and imaginary (ε r'') parts that exhibit frequency dependence. (E is the electric field.) From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) sask.ca (b) Loss tangent (loss factor): peaks just beyond

17 - Polarization mechanisms : orientatuonal, ionic, electronic, interfacial (polymer PET; orientational, crystal KCl; ionic) Interfacial and space charge ε r ' Orientational, Dipolar ε r '' Ionic Electronic ε r ' = 1 ƒ Radio Infrared Ultraviolet light Fig. 7.14: The frequency dependence of the real and imaginary parts of the dielectric constant in the presence of interfacial, orientational, ionic and electronic polarization mechanisms. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

18 - Typical examples of "orientational" polarization due to dipolar side group and "ionic" polarization due to the displacement of K + and Cl PET at 115 C ε 2.6 r ' ε r ' ε r '' ε 2.45 r '' Frequency (Hz) (a) KCl ε r ' ε r '' Frequency ( Hz) (b) Fig. 7.15: Real and imaginary parts of the dielectric constant, εr' and εr'', vs frequency for (a) a polymer, PET, at 115 C and (b), an ionic crystal, KCl, at room temperature. Both exhibit relaxation peaks but for different reasons. (Data for (a) from Dielectric Analysis, DEA, by Kasap and Nomura (1995) and data for (b) from C. Smart, G.R. Wilkinson, A.M. Karo, J.R. Hardy, International Conference on Lattice Dynamics, Copenhagen, 1963, as quoted by D.H. Martin, The study of the vibration of Crystal Lattices by far Infra-Red Spectroscopy, Advances in Physics, 14, (No ), pp , 1965) From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

19 7.8. Piezoelectricity, Ferroelectricity, and Pyroelectricity Piezoelectricity - Quartz (crystalline SiO 2 ) and BaTiO 3 become polarized under a mechanical stress: Charges appear on the surface of the crystal voltage difference Force P = 0 P V (a) (b) V V (c) Fig. 7.35: The piezoelectric effect. (a) A piezoelectric crystal with no applied stress or field. (b) The crystal is strained by an applied force which induces polarization in the crystal and generates surface charges. (c) An applied field causes the crystal to become strained. In this case the field compresses the crystal. (d) The strain changes direction when the field is reversed, and now the crystal is extended. The dashed rectangle is the original sample size in (a). From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) (d)

20 - Noncentrosymmetric in the presence of an applied force from venter of symmetry A y A' O P = 0 x P B B' (a) A'' (b) P = 0 P B'' (c) Fig. 7.37: A hexagonal unit cell has no center of symmetry. (a) In the absence of an applied force the centers of mass for positive and negative ions coincide. (b) Under an applied force along y the centers of mass for positive and negative ions are shifted which results in a net dipole moment P along y. (c) When the force is along a different direction, along x, there may not be a resulting net dipole moment in that direction though there may be a net P along a different direction (y). From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

21 7.8.3 Ferroelectric and Pyroelectric Crystals - Permanently polarized even in the absence of an applied field; Below the Curie temp T c, the crystal becomes spontaneously polarized by the distortion of the crystal structure. Ba 2+ O 2- Ti 4+ (a) BaTiO 3 cubic crystal structure above 130 C a a c (b) BaTiO 3 cubic structure above 130 C (c) BaTiO 3 tetragonal structure below 130 C Fig. 7.41: BaTiO3 has different crystal structures above and below 130 C which leads to different dielectric properties. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McG raw-h ill, 2002)

22 - Existing charges on the plates in ferroelectric crystals: instead of defining - Pyroelectric coefficient: Temperature change = δt Heat δp δv Fig. 7.43: The heat absorbed by the crystal increases the temperature by δt which induces a change δp in the polarization. This is the pyroelectric effect. The change δp gives rise to a change δv in the voltage which can be measured.

23 7.9 Additional Topics: Electric Displacement & Depolarization Field - Electric Displacement (D) and Free Charges +Q free Qfree +Q Q free P +Q P Q free E o E V o Vacuum V Dielectric C o C Electrometer (a) Electrometer (b) Fig. 7.45: (a) Parallel plate capacitor with free space between plates which has been charged to a voltage Vo. There is no battery to maintain the voltage constant across the capacitor. The electrometer measures the voltage difference across the plates and, in principle, does no affect the measurement. (b) After the insertion of the dielectric, the voltage difference is V, less than Vo and the field in the dielectric is less than o.

24 - In the free space (vacuum), with d = the separation of the plates Inserting a dielectric to fit between the plates, the net charges are. +Q free -Q P Gauss surface da E Dielectric Fig. 7.46: Consider a Gauss surface just around the right plate and within the dielectric encompassing both +Q free and -Q P. (E is the electric field.) The Gauss's law gives, then the polarization charge density and (polarization vector) Thus,

25 - Electric Displacement : or - Depolarizing Field : two electric fields - one from the free charges the other from the polarization charges in the opposite direction -Q +Q P + Q P free -Q free E dep E E o Fig. 7.47: The field E inside the dielectric can be considered to be the sum of the field E 0 due to the free charges (Qfree) and a field due E dep to the polarization of the dielectric, called the depolarization field. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

26 - For the dielectric plate,. Since, - In general, where the depolarization factor. E o Applied field E dep E o Applied field P (a) Polarized spherical dielectric E dep = 0 (b) Thin rod dielectric Fig. 7.48: (a) Polarization and the depolarizing field in a spherical shaped dielectric placed in an applied field E 0. (b) Depolarization field in a thin rod placed in an applied field is nearly zero. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002)

27 [Reading Assignment] 7.5. Gauss's Law and Boundary Conditions 7.6. Dielectric Breakdown and Insulation Strength 7.7. Capacitor Dielectric Materials [Homework] 1) Prob. #7.1 2) Prob. #7.4

Advanced Vitreous State The Physical Properties of Glass

Advanced Vitreous State The Physical Properties of Glass Dielectric Properties of Glass Lecture 1: Dielectric in Static Field Himanshu Jain Department of Materials Science & Engineering Lehigh University,