Bài giảng Vật liệu học - Chương 6: Electrical properties

Chapter 6 Electrical properties
 Ohm’s law

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• Ohm's Law:

V=IR

voltage drop (volts = J/C)
resistance (Ohms)
current (amps = C/s)
C = Coulomb

• Resistivity, :
-- a material property that is independent of sample size and

geometry

RA

l

• Conductivity, 




surface area
of current flow
current flow
path length

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

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Which will have the greater resistance?
2

R1 

D



2D



2
D 2
  
2 

8
D 2



R1
R2 

2
2
8
2D  D
  
 2 

Analogous to flow of water in a pipe
 Resistance depends on sample
 geometry and
size.

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Further definitions
J=E

<= another way to state Ohm’s law

J  current density 

current
I

surface area A

like a flux

E  electric field potential = V/
J =  (V/ )
Electron flux

conductivity

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CONDUCTIVITY: COMPARISON
• Room temperature values (Ohm-m)-1 = ( m)-1= S m-1
METALS
CERAMICS
conductors
-10
Silver
6.8 x 10 7
Soda-lime glass 10 -10-11
Copper
6.0 x 10 7
Concrete
10 -9
Iron
1.0 x 10 7
Aluminum oxide <10-13

SEMICONDUCTORS
POLYMERS
Polystyrene
Silicon
4 x 10 -4
Polyethylene
Germanium 2 x 10 0
GaAs
10 -6
semiconductors
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<10
10 -15-10-17
insulators 8

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EXAMPLE:
What is the minimum diameter (D) of the wire so that V < 1.5 V?
(=6.07 x 107 (Ohm-m)-1)
 100 m
I = 2.5 A

Cu wire -

V



100 m

D 2
4
Solve to get
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+

R

< 1.5 V

V

A I

2.5 A
6.07 x 107 (Ohm-m)-1

D > 1.87 mm

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Energy levels of an isolated atom

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ELECTRON ENERGY BAND STRUCTURES

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BAND STRUCTURE REPRESENTATION

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Metals

Insulators

Semiconductors
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CONDUCTION & ELECTRON TRANSPORT
• Metals (Conductors):

partly
filled
band

filled
band

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filled states

- partially filled band
- empty band that
overlaps filled band

filled states

-- for metals empty energy states are adjacent to filled states.
-- thermal energy
Partially filled band
Overlapping bands
excites electrons
Energy
Energy
into empty higher
empty
energy states.
band
empty
-- two types of band
GAP
band
structures for metals

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filled
band

filled
band
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• Insulators:

• Semiconductors:

-- wide band gap (> 4 eV)
-- narrow band gap (< 4 eV)
-- few electrons excited
-- more electrons excited
across band gap
across band gap
empty
Energy
Energy
empty
conduction
conduction
band
band

filled
valence
band
filled
band

?

GAP
filled states

filled states

GAP

filled
valence
band
filled
band
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The Fermi energy is the maximum energy occupied by
an electron at 0K.
Fermi function

where, E is the electron energy, EF is the Fermi energy, and T
is the absolute temperature. Its physical meaning is that: f(E)
is the probability of occupancy for an electron energy
state at energy E by an electron. That is, the probability
that this state is occupied by an electron is f(E), and the
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probability that it is vacant is 1 - f(E).
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CHARGE CARRIERS IN INSULATORS AND SEMICONDUCTORS
Two types of electronic charge
carriers:

Free Electron
– negative charge
– in conduction band
Hole
– positive charge
– in valence band

Move at different speeds - drift velocities
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INTRINSIC SEMICONDUCTORS
Pure material semiconductors: e.g., silicon &
germanium
 Group IVA materials
 Compound semiconductors
– III-V compounds
• Ex: GaAs & InSb
– II-VI compounds
• Ex: CdS & ZnTe
– The wider the electronegativity difference between
the elements the wider the energy gap.

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INTRINSIC SEMICONDUCTION IN TERMS OF
ELECTRON AND HOLE MIGRATION
 Concept of electrons and holes:
valence
electron

electron
hole
pair creation

Si atom

+ -

no applied
electric field

electron
hole
pair migration

applied
electric field

+
applied
electric field

• Electrical Conductivity given by:

# holes/m3

  n e e  p e  h
# electrons/m3
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hole mobility

electron mobility
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