8/14/2019 Kuliah_13_KXEX 1110

1/56

CHAPTER

13Electrical and Magnetic Properties

8-1

8/14/2019 Kuliah_13_KXEX 1110

2/56

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.

8/14/2019 Kuliah_13_KXEX 1110

3/56

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

8/14/2019 Kuliah_13_KXEX 1110

4/56

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.

8/14/2019 Kuliah_13_KXEX 1110

5/56

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

8/14/2019 Kuliah_13_KXEX 1110

6/56

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

8/14/2019 Kuliah_13_KXEX 1110

7/56

Energy Band Structures and Conductivity

8/14/2019 Kuliah_13_KXEX 1110

8/56

8/14/2019 Kuliah_13_KXEX 1110

9/56

8/14/2019 Kuliah_13_KXEX 1110

10/56

8/14/2019 Kuliah_13_KXEX 1110

11/56

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.

8/14/2019 Kuliah_13_KXEX 1110

12/56

(a) Before and (b) after electron excitation

8/14/2019 Kuliah_13_KXEX 1110

13/56

Conduction In Terms of Band and Atomic Bonding

Semiconductor and Insulator

8/14/2019 Kuliah_13_KXEX 1110

14/56

(a) Before and (b) after electron excitation

8/14/2019 Kuliah_13_KXEX 1110

15/56

Energy Band Structures and Bonding

8/14/2019 Kuliah_13_KXEX 1110

16/56

8/14/2019 Kuliah_13_KXEX 1110

17/56

8/14/2019 Kuliah_13_KXEX 1110

18/56

Semiconductivity

8/14/2019 Kuliah_13_KXEX 1110

19/56

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

8/14/2019 Kuliah_13_KXEX 1110

20/56

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.

8/14/2019 Kuliah_13_KXEX 1110

21/56

Intrinsic Semiconductor

8/14/2019 Kuliah_13_KXEX 1110

22/56

Extrinsic Semiconductor

8/14/2019 Kuliah_13_KXEX 1110

23/56

n-Type Extrinsic Semiconductor

8/14/2019 Kuliah_13_KXEX 1110

24/56

8/14/2019 Kuliah_13_KXEX 1110

25/56

8/14/2019 Kuliah_13_KXEX 1110

26/56

p-Type Extrinsic Semiconductor

8/14/2019 Kuliah_13_KXEX 1110

27/56

8/14/2019 Kuliah_13_KXEX 1110

28/56

8/14/2019 Kuliah_13_KXEX 1110

29/56

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

8/14/2019 Kuliah_13_KXEX 1110

30/56

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.

8/14/2019 Kuliah_13_KXEX 1110

31/56

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.

8/14/2019 Kuliah_13_KXEX 1110

32/56

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.

8/14/2019 Kuliah_13_KXEX 1110

33/56

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.

8/14/2019 Kuliah_13_KXEX 1110

34/56

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.

8/14/2019 Kuliah_13_KXEX 1110

35/56

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.

8/14/2019 Kuliah_13_KXEX 1110

36/56

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.

8/14/2019 Kuliah_13_KXEX 1110

37/56

Magnetic Properties

8/14/2019 Kuliah_13_KXEX 1110

38/56

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

8/14/2019 Kuliah_13_KXEX 1110

39/56

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

8/14/2019 Kuliah_13_KXEX 1110

40/56

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

8/14/2019 Kuliah_13_KXEX 1110

41/56

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.

8/14/2019 Kuliah_13_KXEX 1110

42/56

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)

8/14/2019 Kuliah_13_KXEX 1110

43/56

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

8/14/2019 Kuliah_13_KXEX 1110

44/56

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

8/14/2019 Kuliah_13_KXEX 1110

45/56

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

8/14/2019 Kuliah_13_KXEX 1110

46/56

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.

8/14/2019 Kuliah_13_KXEX 1110

47/56

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

8/14/2019 Kuliah_13_KXEX 1110

48/56

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.

8/14/2019 Kuliah_13_KXEX 1110

49/56

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.

8/14/2019 Kuliah_13_KXEX 1110

50/56

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.

8/14/2019 Kuliah_13_KXEX 1110

51/56

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.

8/14/2019 Kuliah_13_KXEX 1110

52/56

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.

8/14/2019 Kuliah_13_KXEX 1110

53/56

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

8/14/2019 Kuliah_13_KXEX 1110

54/56

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

8/14/2019 Kuliah_13_KXEX 1110

55/56

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

8/14/2019 Kuliah_13_KXEX 1110

56/56

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)