Electrical Properties

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Electrical Properties
• How are electrical conductance and resistance characterized? • What are the physical phenomena that distinguish conductors, semiconductors, and insulators?

Electrical Conduction
• Ohm's Law: DV = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s) I e - A (cross sect. area) DV L • Resistivity, r and Conductivity, s: -- geometry-independent forms of Ohm's Law conductivity -- Resistivity is a material property & is independent of sample

Conductivity: Comparison
-1 -1 • Room T values (Ohm-m) = ( - m) METALS conductors Polystyrene <10 -14 Polyethylene -15 -10 -17 Soda-lime glass 10 Concrete -9 Aluminum oxide <10 -13 CERAMICS POLYMERS insulators -11 7 Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 Silicon 4 x 10 -4 Germanium 2 x 10 GaAs 10 -6 SEMICONDUCTORS semiconductors Selected values from Tables 18.1, 18.3, and 18.4, Callister 7e.

Energy States: Insulators & Semiconductors
-- Higher energy states not accessible due to gap (> 2 eV). • Semiconductors: -- Higher energy states separated by smaller gap (< 2 eV). Energy filled band valence empty filled states GAP ? Energy filled band valence empty filled states GAP

Intrinsic vs Extrinsic Conduction
# electrons = # holes (n = p) --case for pure Si • Extrinsic: --n ≠ p --occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms) • n-type Extrinsic: (n >> p) no applied electric field 5+ 4 + Phosphorus atom valence electron Si atom conduction hole • p-type Extrinsic: (p >> n) no applied electric field Boron atom 3 + 4 Adapted from Figs (a) & 18.14(a), Callister 7e.

p-n Rectifying Junction
• Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current. • Processing: diffuse P into one side of a B-doped crystal. • Results: + - p-type n-type Adapted from Fig , Callister 7e. --No applied potential: no net current flow. --Forward bias: carrier flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. + - p-type n-type --Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow. + - p-type n-type

Properties of Rectifying Junction
Fig , Callister 7e. Fig , Callister 7e.

Transistor MOSFET MOSFET (metal oxide semiconductor field effect transistor) Fig , Callister 7e. Fig , Callister 7e.

Integrated Circuit Devices
Fig , Callister 6e. Integrated circuits - state of the art ca. 50 nm line width > 100,000,000 components on chip chip formed layer by layer Al is the “wire”

Ferroelectric Ceramics
Ferroelectric Ceramics are dipolar below Curie TC = 120ºC cooled below Tc in strong electric field - make material with strong dipole moment Fig , Callister 7e.

Piezoelectric Materials
Piezoelectricity – application of pressure produces current at rest compression induces voltage applied voltage induces expansion Adapted from Fig , Callister 7e.

Summary • Electrical conductivity and resistivity are:
-- material parameters. -- geometry independent. • Electrical resistance is: -- a geometry and material dependent parameter. • Conductors, semiconductors, and insulators... -- differ in accessibility of energy states for conductance electrons. • For metals, conductivity is increased by -- reducing deformation -- reducing imperfections -- decreasing temperature. • For pure semiconductors, conductivity is increased by -- increasing temperature -- doping (e.g., adding B to Si (p-type) or P to Si (n-type).

Chapter 20: Magnetic Properties
ISSUES TO ADDRESS... • How do we measure magnetic properties? • What are the atomic reasons for magnetism? • How are magnetic materials classified? • Materials design for magnetic storage. • What is the importance of superconducting magnets?

Applied Magnetic Field
• Created by current through a coil: Applied magnetic field H current I N = total number of turns L = length of each turn • Relation for the applied magnetic field, H: applied magnetic field units = (ampere-turns/m) current

Response to a Magnetic Field
• Magnetic induction results in the material current I B = Magnetic Induction (tesla) inside the material • Magnetic susceptibility, c (dimensionless) c measures the material response relative to a vacuum. H B vacuum c = 0 > 0 < 0

Magnetic Susceptibility
• Measures the response of electrons to a magnetic field. • Electrons produce magnetic moments: Adapted from Fig. 20.4, Callister 7e. magnetic moments electron nucleus spin • Net magnetic moment: --sum of moments from all electrons. • Three types of response...

3 Types of Magnetism Magnetic induction B (tesla)
permeability of a vacuum: (1.26 x 10-6 Henries/m) Magnetic induction B (tesla) ferromagnetic e.g. Fe3O4, NiFe2O4 ferrimagnetic e.g. ferrite(), Co, Ni, Gd (3) ( c as large as 10 6 !) (2) paramagnetic e.g., Al, Cr, Mo, Na, Ti, Zr ( c ~ 10 -4 ) vacuum ( c = 0) -5 diamagnetic ( c ~ -10 ) (1) e.g., Al 2 O 3 , Cu, Au, Si, Ag, Zn Strength of applied magnetic field (H) (ampere-turns/m) Plot adapted from Fig. 20.6, Callister 7e. Values and materials from Table 20.2 and discussion in Section 20.4, Callister 7e.

Magnetic Moments for 3 Types
No Applied Applied Magnetic Field (H = 0) Magnetic Field (H) (1) diamagnetic none opposing Adapted from Fig. 20.5(a), Callister 7e. Adapted from Fig. 20.5(b), Callister 7e. (2) paramagnetic random aligned Adapted from Fig. 20.7, Callister 7e. (3) ferromagnetic ferrimagnetic aligned

Ferro- & Ferri-Magnetic Materials
• As the applied field (H) increases... --the magnetic moment aligns with H. B sat H Adapted from Fig , Callister 7e. (Fig adapted from O.H. Wyatt and D. Dew-Hughes, Metals, Ceramics, and Polymers, Cambridge University Press, 1974.) H H • “Domains” with aligned magnetic induction (B) H Magnetic moment grow at expense of poorly H aligned ones! H = 0 Applied Magnetic Field (H)

Permanent Magnets • Process: • Hard vs Soft Magnets B B
2. apply H, cause alignment 3. remove H, alignment stays! => permanent magnet! Adapted from Fig , Callister 7e. 4 Negative H needed to demagnitize! . Coercivity, HC Applied Magnetic Field (H) 1. initial (unmagnetized state) large coercivity --good for perm magnets --add particles/voids to make domain walls hard to move (e.g., tungsten steel: Hc = 5900 amp-turn/m) • Hard vs Soft Magnets small coercivity--good for elec. motors (e.g., commercial iron Fe) Adapted from Fig , Callister 7e. (Fig from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, John Wiley and Sons, Inc., 1976.) Applied Magnetic Field (H) B Hard Soft

Magnetic Storage • Information is stored by magnetizing material.
• Head can... -- apply magnetic field H & align domains (i.e., magnetize the medium). -- detect a change in the magnetization of the medium. recording head recording medium Adapted from Fig , Callister 7e. (Fig from J.U. Lemke, MRS Bulletin, Vol. XV, No. 3, p. 31, 1990.) Image of hard drive courtesy Martin Chen. Reprinted with permission from International Business Machines Corporation. • Two media types: -- Particulate: needle-shaped g-Fe2O3. +/- mag. moment along axis. (tape, floppy) Adapted from Fig , Callister 7e. (Fig courtesy P. Rayner and N.L. Head, IBM Corporation.) ~2.5 mm Adapted from Fig (a), Callister 7e. (Fig (a) from M.R. Kim, S. Guruswamy, and K.E. Johnson, J. Appl. Phys., Vol. 74 (7), p. 4646, ) ~120 nm --Thin film: CoPtCr or CoCrTa alloy. Domains are ~ nm! (hard drive)

Superconductivity Hg Copper (normal) 4.2 K Adapted from Fig , Callister 7e. Tc = temperature below which material is superconductive = critical temperature

Limits of Superconductivity
26 metals + 100’s of alloys & compounds Unfortunately, not this simple: Jc = critical current density if J > Jc not superconducting Hc = critical magnetic field if H > Hc not superconducting Hc= Ho (1- (T/Tc)2) Adapted from Fig , Callister 7e.

This research area was stagnant for many years. Everyone assumed Tc,max was about 23 K Many theories said you couldn’t go higher 1987- new results published for Tc > 30 K ceramics of form Ba1-x Kx BiO3-y Started enormous race. Y Ba2Cu3O7-x Tc = 90 K Tl2Ba2Ca2Cu3Ox Tc = 122 K tricky to make since oxidation state is quite important Values now stabilized at ca. 120 K Suddenly everyone was doing superconductivity. Everyone was doing similar work, making discoveries, & rushing to publish so they could claim to have done it first. Practically, daily new high temp. records were set.

Meissner Effect Superconductors expel magnetic fields
This is why a superconductor will float above a magnet normal superconductor Adapted from Fig , Callister 7e.

Current Flow in Superconductors
Type I current only in outer skin - so amount of current limited Type II current flows within wire M H Type I Type II complete diamagnetism mixed state HC1 HC2 HC normal

Summary • A magnetic field can be produced by: • Magnetic induction:
-- putting a current through a coil. • Magnetic induction: -- occurs when a material is subjected to a magnetic field. -- is a change in magnetic moment from electrons. • Types of material response to a field are: -- ferri- or ferro-magnetic (large magnetic induction) -- paramagnetic (poor magnetic induction) -- diamagnetic (opposing magnetic moment) • Hard magnets: large coercivity. • Soft magnets: small coercivity. • Magnetic storage media: -- particulate g-Fe2O3 in polymeric film (tape or floppy) -- thin film CoPtCr or CoCrTa on glass disk (hard drive)