Advanced Vitreous State The Physical Properties of Glass Dielectric - PowerPoint PPT Presentation

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, Bethlehem, PA 18015 H.Jain@Lehigh.edu h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 1

Resources  Fundamental of Inorganic Glasses, A.K. Varshneya, Soc. Glass Tech, 2006  Principles of Electronic Materials and Devices by S. Kasap, 3 rd Ed., McGraw Hill, 2006. Source of colored diagrams. Recommended for clear, concise description.  Dielectric and Waves, A.R. von Hippel, John Wiley, 1954  Engineering Dielectrics, Vol. IIA, R. Batnikas and R.M. Eichhorn, eds. ASTM STP 783, 1983 h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 2

What is a dielectric?  Dia+electric i.e. poorly electric and can sustain electric field without appreciable current.  Uses:  Insulation for wires, cables, electrical equipment  Capacitors  Devices for propagation of e.m. waves  (Piezoelectric transducers, time devices)  (Memory elements)  Microelectronics ….. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 3

Dielectrics in microelectronics: (a) Gate dielectrics, (b) Tunneling oxides in memory devices, (SiO x N y ) (c) Capacitors, (d) Interconnect dielectrics, (e) Isolation dielectrics Modern complemen tary metal- oxide- semiconduc tor (CMOS) microproce ssors Electronic and Ionic polarizations are most important. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 4

Principal Dielectric Properties: Why bother?  1. Dielectric constant,  ’  High for charge storage device e.g. capacitor, gate dielectric  Low for faster signal transmission (speed ~ 1/  )  2. Dielectric (energy) loss,  ”  High for microwave heating  Low for signal transmission  3. Dielectric breakdown  High for most insulating applications e.g. tunneling oxides  Low for fuses (?) h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 5

Rigid insulators : glass, ceramics, porcelain, epoxies..  Advantages of glass & ceramics over polymers  Superior dielectric properties  No creep or deformation at RT  Greater stability in hostile environment  Other desirable characteristics  Suitable thermal and mechanical properties  Ability to form seals with metals/ceramics  No porosity h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 6

How can we understand this?  Note that the addition of alkali oxide to silica increases the MHz- GHz frequency dielectric constant monotonically.  The increase is higher for the larger alkali. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 7

Dielectric in static (dc) field Q o  V = C o V Q o = charge on the plates V = voltage C o = capacitance of a parallel plate capacitor in free space. Units: Coulomb/Volt = Farad C o  Area of plates (neglect edge effect)  1/separation between the plates (a) Parallel plate capacitor in vacuum. =  0 A/d (b) As a slab of insulating material is inserted between the plates, there  0 = 8.854x10 -12 F/m is an external current flow indicating that more charge is stored on the plates. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 8

Capacitance of a dielectric  r  Q  C Q C o o  r = relative permittivity, Q = charge on the plates with a dielectric medium > Q o So that C > C o and  r >1.0 Goal: Understand the origin of  r and manipulate its value by material design. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 9

Coulomb’s law and electric field Force between two charges in vacuum : F 0 = q 1 q 2 /4  0 r 2 Coulomb’s law – Proven to better than 2 ppb Electric field in vacuum, E 0 = q 1 /4  0 r 2 Force between two charges in dielectric : F = q 1 q 2 /4  0  r r 2 Electric field in dielectric, E = q 1 /4  0  r r 2 The field in dielectric is reduced by  r . The dielectric is not neutral, but must have non-uniform charge  charges are shifted as the dielectric gets polarized. Displaced charge produces electrical force given by displacement vector D =  0  r E , so that in general  r is a tensor (of course, scalar for glass). Dielectric constant is a macroscopic/engineering property! h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 10

Polarization in general! Macro Former President Bill Clinton warned Saturday that the country is becoming increasingly polarized despite the historic nature of the Democratic primary. Micro h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 11

Microscopic view: The simplest unit of polarization: Dipole, where positive charge is displaced with respect to its countercharge. Define dipole moment: p = charge x separation (-Q to +Q) Define polarization P = dipole moment / volume For small fields: p  E loc or p =  E loc , where  is polarizability and E loc is local electric field acting on the specific dipole. If there are N dipoles/vol, P = N p = N  E loc h.jain@lehigh.edu h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 12 12

Dielectric susceptibility,  Experimentally, P  E , so that P =  E  is dielectric susceptibility; describes the bulk response of the material. Two sources of charge on the plates: (i) Charge from connection to the battery (ii) Charge induced by the bound charge from the polarization of the dielectric. This bound surface charge/area = P D = D 0 + P =  0 E +  E Also D =  0  r E So that  =  0 (  r -1) h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 13

Local (or Lorenz) electric field in a solid, E loc Zero for cubic crystals E loc = E + E spherical cavity + E dipoles and glasses 1  P So that local or Lorenz field, E loc = E ext + P/3  0 = E ext (  r +2)/3 E S  3 o   1   N P =N  E loc =  0 (  r -1) E ext Claussius Mossotti Eq. r Micro  Macro    2 3 r o h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 14

Polarization Mechanisms 1.Electronic polarization 2.Ionic/atomic polarization 3.Dipolar/orientational polarization a) ‘Jellyfish’ polarization 4.Interfacial polarization Nature has two types of processes: relaxation or resonance. 1 and 2 are resonance processes 3 and 4 are relaxation processes h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 15

Electronic polarizability of an atom,  e The force due to applied field pulls the nucleus and electron cloud apart. In equilibrium, it is balanced by the Coulombic attraction between them. The induced electronic dipole moment Z = # of electrons in the atom, x =   2 2 Z e     p Ze x E distance between the nucleus and ( )   e β the center of negative charge,  =   constant, E = electric field http://hypertextbook.com/physics/electricity/dielectrics/stretching.html h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 16

Electronic polarizability of inert gas ~ Z When E is removed, the electron cloud will return, and oscillate with its natural frequency  0 =2  f 0 Ze 2  e  m e  o 2 1 / 2          o Zm   e •  e  Z. Its resonance freq. (in UV) is ~ independent of Z. •  e is ~T independent. Use high Z elements to increase refractive index of a glass. h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 17

Electronic polarizability General remarks - ***tips for material design***: •  e determines n in the visible region, and at lower freq. • In a given column  e increases with atom radius. •  e for anions >> for cations. Note: Above  e values are by Pauling and Tessman et al. Others have given different values, depending on the compositions used for self- consistency (see Kittel, p.391). h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 18 18

Ionic polarizability,  i 1-d NaCl crystal: Without E, net dipole moment is 0. With E, cations and anions move in opposite direction, producing net polarization. P i = N i  i E loc   i depends on the bonding between cation and anion – more difficult to model when bonding is complex as in solids with mixed bonding.   i is also ~ T independent (if structure does not change).   0 is in the IR – why? It depends on reduced ion mass (  ) << m e (also bonding). h.jain@lehigh.edu Advanced Vitreous State - The Properties of Glass: Dielectric Properties - Lecture 1 19