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Dielectric Properties of Materials

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Dielectric Properties of Materials v.2020.JAN B. Dielectric Properties of Materials mostly organic (PET, PTFE, PP, PS …) • Materials strong covalent interchain, weak bonds intrachains – ceramics / polymers electronic ceramics crystalline inorganic (Al2O3, BaTiO3, glasses …) structural ceramics strong ionic bond (bricks…) – solids in which outer electrons are unable to move through structure • Functions • Properties – energy storage – large C (freq dependent) – insulation – high r, br – new apps: capacitive sensing, … • Objectives – understand underlying energy storage mechanisms – understand insulation breakdown mechanisms – select proper dielectrics (from chips to high-power cables) Reference: S.O. Kasap (4th Ed.) Chap. 7; RJD Tilley (Understanding solids, 2nd Ed) Chap. 11. Dielectric Properties 2102308 1 Dielectric Materials • introduction e r – relative permittivity (er), polarizability (a) • polarization mechanisms – types: electronic, ionic, dipolar, interfacial er () – frequency dependency • br (electric field strength, breakdown field) – gas, liquid, solid • capacitors – ceramic, polymer, electrolytic • nonlinear dielectrics – piezo-, ferro-, pyro-electricity • special cases for EE – see brochure for EE ceramics (self-study) Dielectric Properties 2102308 2 also called “dielectric constant” 7.1 Relative permittivity e r - dielectric is the working material (active component) in capacitors. The simplest structure is the parallel plate capacitor (Fig. 7.1). Without the dielectric (a), the stored charge is Qo. With the dielectric (c), the stored charge increase to Q, or by a factor of er , the relative permittivity. - under electric field E, the constituents of the dielectric (ions, atoms, molecules) become polarized (Fig. 11.3). Internal electric dipole moment (p) induced by E, resulting in observable polarization (P). Qo e o A e re o A Q C Co = = C = ; e r = = V d d Qo Co * i(t) is a displacement current, not conduction current. 1 V Potential Energy:U = CV 2 = Q 2 2 Dielectric Properties 2102308 3 - electric dipole moment (p) or dipole moment (or just dipole) is charge balanced, see A - a mechanism that gives rise to such dipole is electronic polarization, see B - the resulting dipole is proportional to the electric field strength E, the proportionality constant is termed (electronic) polarizability, see C - the relative permittivity (er) is related to the polarizability (a) of materials, see D A. dipole moment: separation of –ve and +ve charges (equal magnitude, charge balance) p can interacts with external Ex. H+-Cl−, p ~ 3.6×10−30 C.m (unit: C·m) B. electronic polarization (all atoms) E C x O Electron cloud Q = 0 Qnet = 0 net p = 0 p 0 Atomic a 0 a = 0 nucleus pinduced = ae Center of negative ( unit: C·m = [F·m2][V/m] ) charge (a: polarizability) (ae: electronic polarizability) pinduced (a) A neutral atom in E = 0. (b) Induced dipole moment in a field Dielectric Properties 2102308 4 The origin of electronic polarization. 30 C. polarizability ae fo 10 f with electric field o x1015 Hz Rn Hook’s Xe Ze = x (restoring force) Ar Kr a ~ Z0.99 Z 2e2 1 e pe = Qa = (Ze)x = ae ae Ne x10-40 F m2 without He Z → large electron cloud → further from nucleus → 2 can be shifted easily → a d x 0.1 x = meZ 2 dt 1 10 100 2 2 Atomic number Z meZ d x 1 d x x = 2 = 2 2 dt 0 dt Electronic polarizability and its resonance frequency vs. the number of electrons in the atom (Z). The dashed line is the best simple harmonic equation: fit line. 1/ 2 ~constant o Zme Ze2 , ae = 2 meo Key message: The heavier the element ( Z ), the higher the electronic polarizability (ae) Dielectric Properties 2102308 5 Before insertion: Qo D. e r &ae V Q Q = = o = o → d Cod e o A Bound polarization Qo = e o A charges on the surfaces bound -Q +Q P P charges After insertion: Qp +Q -Q free E charges (b) ptotal = Qpd → p * p N (Ad ) Q = total = induced p d d Area = A ptotal Qp = (Nae )A (c) * ptot = (p / molecule) × (molecule / volume) × (volume) (a) -Q P +Q V P P Q = Qo + Qp d Q Qp Nae (a) When a dilectric is placed in an electric field, bound polarization e r =1+ =1+ charges appear on the opposite surfaces. (b) The origin of these Qo Qo e o polarization charges is the polarization of the molecules of the medium. (c) We can represent the whole dielectric in terms of its More detail analysis (solid polarized by a local surface polarization charges +QP and -QP. electric field) yields Clausius-Mossotti relation: e −1 Na r = e r + 2 3e o - solid must be homogeneous isotropic (no note: a is atomic-level , e ismaterial-level parameters e r permanent dipoles, dipolar molecules) microscopic macroscopic − a includes other polarization mechanisms Dielectric Properties 2102308 6 Polarization P (C/cm2) definition total dipole moment Bound polarization charges on the surfacPolarizaties on -Q +Q P P volume e r +Q -Q Q d Q E ptotal p p (b) = = = volume Ad A Area = A ptotal as a function of external electric(c) field (a) -Q P +Q V surfaceP P charge (storage)d (a) When a dilectric is placed in an electric field, bound polarization charges appear on the opposite surfaces. (b) Thedensityorigin of these material responds polarization charges is the polarization of the molecules of the medium. (c) We can represent the whole dielectric in terms of its surface polarization charges +QP and -QQP. P = p = (Na ) = e (e −1) A e o r polarizability excite (atomic/molecular) Dielectric Properties 2102308 7 Ex. 7.2 -40 2 The electronic polarizability of the Ar atom is ae = 1.710 F m . What is the static dielectric 3 constant er of solid Ar (below 84K) if its density is 1.8 g/cm and atomic mass is 39.95. Origin of charge/energy storage: material develops polarization (P) pinduced (=a) binds or draws more charges (Qp) to the electrodes. These charges can be released to do work. (Think of stretched strings) Dielectric Properties 2102308 8 7.2 (electronic) polarization in covalent solids (semiconductors) • to shift electrons in ionic cores need ~ 10 eV (difficult) er EG(eV) • to shift electrons in covalent bonds need ~ 1-2 eV (easy) Ge 16 0.67 • stronger bonds (EG ↑) smaller shifts (x, ae, er) Si 11.9 1.12 C 5.7 5.5 GaAs ? 1.43 SiO2 3.9 9.00 = 13.1, but why? Nae e r =1+ e o ae :ae−core +ae−valence ✓ ✓ (a) Valence electrons in covalent bonds in the absence of an applied field. (b) When an electric field is applied to a covalent solid, the valence electrons in the covalent bonds are shifted very easily with respect to the positive ionic cores. The whole solid becomes polarized due to the collective shift in the negative charge distribution of the valence electrons. Q) why concern with er of “semiconductors”? A1) (device) In depletion layer of p-n junctions, dielectric property (er) is more important than electrical property (s ). A2) (circuit & system) er C CR BW Dielectric Properties 2102308 9 7.3 Polarization Mechanisms 7.3.0 Electronic polarization: (for all neutral atoms) displacement of electrons 7.3.1 Ionic polarization: (for charged ions) displacement of ions. Example: NaCl (below) p = a = Qa p+ p- large (a) x Ð Clausius-Mossotti relation: Cl Na+ 3e e −1 o r ai = N e r + 2 p' p' + - usually ai 10ae (b) E (a) NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion = 0. (b) In the presence of an applied field the ions become slightly displaced which leads to a net average dipole moment per ion. Dielectric Properties 2102308 10 7.3.2 Orientational polarization (or dipolar polarization): re-orienting of molecules with permanent dipole moments. - certain molecule has “permanent” dipole moment due to bonding (see Examples in Box) - similar to ionic but |p+| |p-| for each molecule - under electric fields, molecules are re-oriented such that p align along E as much as possible (atoms/molecules in liquid/solid phase are not free to move) Examples (materials): note strong Polar liquids – water (), temperature acetone, alcohol, electrolyte dependency Polar gases – steam, gaseous HCl () po = Qa Polar solids – glasses p 2 a = o Examples (values): d 3kT p ~ 3.6×10−30 C.m p ~ 6.2×10−30 C.m Dielectric Properties 2102308 11 7.3.3 Interfacial polarization (or space charge polarization): build-up of mobile charges - certain dielectric has mobile charges (electrons, holes, ions) - though they move under electric fields, they cannot leave dielectrics, but pile-up at grain boundaries (polycrystals), at equilibrium, internal field block further charge movement − aif not significant in most cases, except at low frequencies Dielectric Properties 2102308 12 7.3.4 Total polarization 7.3.0 7.3.1 7.3.2 a ae +ai +ad (average) (aif is location specific) 7.3.3 1 dipolar 2 Dipolar solid general trend: 1. semiconductor: concerned with parasitic capacitance ae ai a d 2. insulator: more concerned with breakdown field (br) except those related to valence electrons Dielectric Properties 2102308 13 7.4 Frequency dependency of polarisability and relative permittivity - capacitors are used in applications throughout the frequency spectrum: from low, power line frequencies (50/60 Hz), to high, communications frequencies (MHz/GHz) - dielectric materials may or maynot have time to respond to the excitation (ac frequency), this depends on the dominant polarization mechanism(s) and the ac frequency - generally, the mechanisms which involves heavy masses are slowest, light are fastest (Fig. 11.5) 6 − aif (charge switch positions at grain boundaries), upto 10 Hz 9 − ad (dipoles of molecules rotate in medium), upto 10 Hz 12 − ai (ions stretch/compress), upto 10 Hz 16 17 − ae (electron cloud shifts around nucleus), upto 10 -10 Hz (see slide #5) - frequency dependency of polarisability: atotal = aif + ad + ai + ae a a() = dc 1+ j Dielectric Properties 2102308 14 - when dipoles respond to electric field, there’s a delay (in the case of step function, Fig.
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