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CHAPTER
13Electrical and Magnetic Properties
8-1
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Electric Conduction Classical Model
Metallic bonds make free movement of valence electrons
possible.
Outer valence electrons are completely free to move
between positive ion cores.
Positive ion cores vibrate with greater amplitude with
increasing temperature.
The motion of electrons are random and restricted in
absence of electric field.
In presence of electric field, electrons attain directed drift
velocity.
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Ohms Law
Ohms law states that electric current flow I is directly
proportional to the applied voltage V and inverselyproportional to resistance of the wire.
i = V/R where i = electric current (A)V = potential difference (V)
R = resistance of wire ()
Electric resistivity = RA/l where l = length of theconductor and A = Cross-sectional area of the conductor.
Electric Conductivity = 1/
Microscopic Ohm's law
J = E/ J= Current density A/m2
E = electric field V/m
Silicon
Germanium
Polyethylene
Polystyrene
Silver
Copper
Gold
Semi-
conductors
InsulatorsConduc
- tors
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Drift Velocity of Electrons
Electrons accelerate when electric field E is applied and
collide with ion cores .
After collision, they accelerate again.
Electron velocity varies in a saw tooth manner.
Drift velocityVd
= E where = electron mobility m2/(V.s)
Direction of current flow is apposite to that of electron flow.
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Electrical Resistivity
Electrical resistivity total = T + r
T = Thermal component : Elastic waves (phonons)generated due to vibration of electron core scatterelectrons.
Resistivity increases with temperature.
Alloying increases resistivity.
Resistivity increases with temperature.
r = Residual component : Due to
structural imperfections like
dislocations.
T = 0C(1+TT)
0C = Resistivity at 00C
T = Coefficient of resistivity.
T = Temperature of the metal
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Energy Bond Model of Electric Conduction
Valence electrons are delocalized, interact and
interpenetrate each other.
Their sharp energy levels are broadened into energy
bands.
Example:- Sodium has 1 valence electron (3S1). If there
are N sodium atoms, there are N distinct 3S1 energy levelsin 3S band.
Sodium is a good conductor
since it has half filled outer
orbital
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Energy Band Structures and Conductivity
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Conduction In Terms of Band and Atomic Bonding
Conduction in Metal
Only the electrons with energies greater than Fermi energy
can be accelerated in the presence of an electric field and
participating in the conduction process, which are called
free electrons.
In metals there are empty states just above the Fermi
levels, where electrons can be promoted.
The promotion energy is extremely small. The energy
provided by electric field is sufficient to excite largenumbers of electrons into the empty/ conduction band.
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(a) Before and (b) after electron excitation
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Conduction In Terms of Band and Atomic Bonding
Semiconductor and Insulator
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(a) Before and (b) after electron excitation
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Energy Band Structures and Bonding
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Semiconductivity
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For every electron excited into the conduction band they
left behind a vacancy of electron in the valence band(Fig.above).
The position of the vacancy may be thought as moving by
the motion of other valence electrons that fill in the
vacancy. The vacancy is called hole and havepositivecharge (+1.6 10-19 C).
Thus in the present of electric filed the electrons and holes
move in opposite directions and both can be scatter by
lattice imperfections
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Conduction in Intrinsic Semiconductors
Semiconductors: Conductors between good conductors
and insulators.
Intrinsic Semiconductors: Pure semiconductors and
conductivity depends on inherent properties.
Example: Silicon and Germanium each atom contributes
4 valence electrons for covalent bond.
Valence electrons are excited
away from their bonding
position when they are
excited.
Moved electron leaves
a hole behind.
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Intrinsic Semiconductor
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Extrinsic Semiconductor
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n-Type Extrinsic Semiconductor
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p-Type Extrinsic Semiconductor
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Effect of Doping on Carrier Concentration
The mass action law: np = ni2 where ni (constant) is
intrinsic concentration of carriers in a semiconductor.
Since the semiconductor
must be electrically neutral
Na
+ n = Nd
+ p
where Na and Nd are
concentrations of negative
donor and positive acceptors.
In a n-type semiconductor, Na = 0 and n>>p
hence nn = Nd andpn = ni2/nn=ni
2/Nd
np = ni2/pp = ni
2/Na
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Carrier Concentration
For Si at 300K, intrinsic carrier concentration ni=1.5 x
1016 carier/m2
For extrinsic silicon doped with arsenic
nn = 1021 electrons/m3
pn = 2.25 x 1011 holes/m3
As the concentration of
impurities increase ,
mobility of carriers
decrease.
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Effect of Temperature on Electrical Conductivity
Electrical conductivity increases with temperature as more
and more impurity atoms are ionized. Exhaustion range: temperature
at which donor atom becomes
completely ionized .
Saturation range: Acceptoratoms become completely
ionized.
Beyond these ranges, temperature does not changeconductivity substantially.
Further increase in temperature results in intrinsicconduction becoming dominant and is called intrinsicrange.
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Semiconductor Devices pn Junction
pn junction if formed by doping a single crystal of silicon
first by n-type and then by p type material. Also produced by diffusion and impurities.
Majority carriers cross over the junction and recombine
but the process stops later as electrons repelled by negative
ions giving rise to depleted zones. Under equilibrium conditions, there exists abarrierto
majority carrier flow.
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Reverse and Forward Biased pn Junction
Reverse biased: n-type is connected to the positive
terminal and p-type to negative. Majority carrier electrons and holes move away from
junction and current does not flow.
Leakage current flows due to minority carriers.
Forward biased: n-type is connected to negative terminaland p-type to positive.
Majority carriers are repelled to the junction and
recombine and the current flows.
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Application of pn Junction Diode
Rectifier Diodes: Converts alternating voltage into direct
voltage (rectification). When AC signal is applied to diode, current flows only
whenp-region is positive and hence half way rectification
is achieved.
Signal can be further
smoothened by using
electronics.
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Breakdown Diodes (Zener Diodes)
Zener diodes have small breakdown currents.
With application ofbreakdown voltage, in reverse bias,reverse current increases rapidly.
Electrons gain sufficient energy to knock more electrons
from covalent bonds.
These are available for conduction in reverse bias.
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Bipolar Junction Transistor
BJT consists of two pn junctions occurring sequentially
on a single crystal.
Can serve as current amplifier.
Emitter: n-type emits
electrons.
Base: p-type, o.1mm thick,
controls flow of charge.
Collector: n-type, collects
charge carrier.
Emitter base junction is forward
biased and collector base junction
is reverse biased.
Small base current can be used to control large collector
current.
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Magnetic Properties
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Magnetic Fields and Quantities
Magnetic Dipole
In magnetic materials there are south and north poles.These two poles is called dipoles.
Magnetic force is shown as imaginary lines from North toSouth. Magnetic force also can think as magnetic field.
Within a magnetic field the force exerts a torque andproduce magnetic moment. For example a magneticcompass needle lines up with the earths magnetic field.
The magnetic moment as
designated by an arrow
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Magnetic Fields
Ferromagnetic materials: Iron, cobalt and nickel -providestrong magnetic field when magnetized.
Magnetism is dipolarup to atomic level.
Magnetic fields are also produced by current carrying
conductors. Magnetic field of a solenoid is
H = 0.4 n i / l A/m
n = number of turnsl = length
i = current
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Magnetic Induction
If demagnetized iron bar is placed inside a solenoid, themagnetic field outside solenoid increases.
The magnetic field due to the bar adds to that of solenoid -Magnetic induction (B) .
Intensity of Magnetization (M) : Induced magneticmoment per unit volume
B = 0H + 0 M = 0(H+M)
0 = permeability of free space
= 4 x 10-7 (Tm/A) In most cases 0 >0 H
Therefore B =~ M
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Magnetic Permeability
Magnetic permeability = = B/H Magnetic susceptibility = Xm = M/H
For vacuum = 0 = = 4 x 10-7 (Tm/A)
Relative permeability = r = / 0
B = 0 rH
Relative permeability is
measure of induced magnetic field.
Magnetic materials thatare easily magnetized
have high magnetic
permeability.
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Types of Magnetism
Diamagnetism:Diamagnetism:
A very weak and non permanent magnetism.
Persist only when external field is being applied.
The magnitude of magnetic moment is very small and in opposite
direction to the applied field.
r
< 1 , m= -10-5 (-ve)
Paramagnetism:Paramagnetism:
Each atom possesses a permanent dipole moment. But the orientation
is random.
The orientation of magnetic moments are align in the direction ofexternal field when external magnetic field is applied.
r
>1 , m= 10-5 ~ 10-2 (+ve)
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Anti-Ferromagnetism:Anti-Ferromagnetism:
The alignment of the spin moments of
neighboring atoms or ions are exactly inopposite directions and canceling each
other.
Ferrimagnetism:Ferrimagnetism:
Similar to ferromagnetism but the source
of the net moment is different.
A permanent magnetization but the
saturation magnetizations are not as highas for ferromagnets.
Example Fe3O4
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Magnetic Moments
Adapted from Fig.
20.5(a), Callister 7e.
No Applied
Magnetic Field (H= 0)
Applied
Magnetic Field (H)
(1) diamagnetic
none
opposing
Adapted from Fig.
20.5(b), Callister 7e.
(2) paramagnetic
random
aligned
Adapted from Fig. 20.7,
Callister 7e.
(3) ferromagnetic
ferrimagnetic
aligned
aligned
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Ferromagnetism
The permanent magnetic moment is exist even in the absence of an
external magnetic field.
Permanent magnetic moments are result from un-cancelled electron
spin magnetic moments.The contribution of orbital magnetic moments
are small ( can be neglected).
m= ~106
Because M>>H, B = oH+ oM can be written as B = oM. When an external magnetic field is applied, the materials is said in
Saturation Magnetization (Ms) condition if all of the magnetic dipoles
are mutually aligned with the external field.
Ms= KN
Where K; net magnetic moment per atom
(depend on the type of materials)
N; number of atoms present N = NA / A
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Ferromagnetic elements (Fe, Co, Ni and Gd) produce
large magnetic fields. It is due to spin of the 3d electrons of adjacent atoms
aligning inparallel directions in microscopic domains byspontaneous magnetization.
Random orientation of domains results in no netmagnetization.
The ratio of atomic
spacing to diameter
of 3d orbit must be
1.4 to 2.7.
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Effect of Temperature on Ferromagnetism
Above 0 K, thermal energy causes magnetic dipoles to
deviate from parallel arrangement. At higher temperature, (curie temperature)
ferromagnetism is completely lost and material becomes
paramagnetic.
On cooling, ferromagneticdomains reform.
Examples: Fe 7700C
Co 11230C
Ni 3580C
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Ferromagnetic Domains
Magnetic dipole moments align themselves in parallel
direction called magnetic domains. When demagnetized, domains are rearranged in random
order.
When external magnetic
field is applied the domains
that have moments parallel
to applied filed grow.
When domain growth
finishes, domain rotation
occurs.
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Types of Energies that Determine the Structure
Most stable structure is attained when overallpotential
energy is minimum. Potential energy with a domain is minimized when all
atomic dipoles are aligned in single direction.
Magnetostatic energy: Potential energy produced by its
external field. Formation of multiple
domain reduces
magnetostatic energy.
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Magnetocrystalline Anisotropy Energy
Magnetization with applied field for a single crystal varies
with crystal orientation. Saturation magnetization occurs most easily for the
direction of BCC iron.
Saturation magnetization occurs with highest applied fieldfor direction.
Some grains of polycrystalline
materials need some energy
to rotate their resultant
moment.
This energy is magnetocrystalline anisotropy energy.
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Domain Wall Energy
Domain wall is the region through which the orientation
of the magnetic moment changes gradually. 300 atoms wide due to balance between exchange
force and magnetocrystalline anisotropy.
Equilibrium wall width is width at which sum of two
energies are minimum.
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Magnetostrictive Energy
Magnetostriction: Magnetically induced reversible elastic
strain.
Energy due to mechanical stress created by
magnetostriction is called magnetostriction energy.
It is due to change inbond length caused by rotation of
dipole moments.
Equilibrium domain configuration is reached when sum of
magnetostrictive and domain wall energies are minimum.
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Magnetization and Demagnetization
Magnetization and demagnetization do not follow sameloop.
Once magnetized, remnant induction Br remains evenafter demagnetization.
Negative field Hc (coercive
force) must be applied to
completely demagnetize.
Magnetization loop is
called hysteresis loop.
Area inside the loop
is a measure ofwork done
in magnetizing and
demagnetizing.
f i i l
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Soft Magnetic Materials
Easily magnetized and demagnetized.
Have high initial permeability and low coercitivity. Reach saturation at low applied field.
Must be free from structural defects and highly resistance to electrical
currents.
Low coercive force and high saturation induction are desirable
properties.
The soft magnetic materials have small hysterisis loop ( energy loss is
small).
Hysteresis energy losses: Due to dissipated energy required to push
the domain back and forth.
Imperfections increases hysteresis.
Eddy current energy losses: Induced electric current causes some
stray electric currents resulting from transient voltage.
Source of energy loss by electrical resistance healing.
H d M i M i l
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Hard Magnetic Materials
Difficult to demagnetization.
Have high remanance Br, coercitivity Hc and saturationflux densityMs.
Have low initial permeability.
High hysterisis energy losses.
Energy product rectangle (BH)max, shows the energy required to
demagnetize a magnet material.
The restriction to the domain wall movement can increase the external
field required to demagnetization.
Some energy of the field is converted topotential energy.
Maximum energy product is a measure of magnetic potential energy =
Max (B x H).
Max (B x H) = area oflargest rectangle that can be inscribed in the
second quadrant of the hysteresis loop.
H d S f M
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Hard vs. Soft Magnets
large coercivity--good for perm magnets
--add particles/voids tomake domain wallshard to move (e.g.,tungsten steel:
Hc = 5900 amp-turn/m)
Applied MagneticField (H)
B
Ha
rd
Soft
Hard
small coercivity--good for elec. motors(e.g., commercial iron 99.95 Fe)