Electrical

Properties
of Materials
Lecture 9
by

Dr. Khatijah Aisha Yaacob

1
 Content of the lecture

1. Electrical Conduction
2. Conduction in Terms of Band & Atomic
Bond Models
3. Effect of Temperature & Impurities on
the  of Metal & Semiconductor

2
1.Electrical
Conduction
 Electrical Conduction
In order to understand the electrical properties of a material, we need to
define the most fundamental aspect underlying the concept: definition of
conduction.
Ohm’s Law defines the RESISTANCE in a material

• Ohm's Law:
DV = I R
voltage drop (volts = J/C) resistance (Ohms)
C = Coulomb
current (amps = C/s)
A
(cross section area ) -e I
DV
L

4
 Electrical Conduction
• Resistance: geometry dependent
V
R
I L R changes when either
(a) L or/and
L A
 (b) A changes
A

• Resistivity (Ohm-m) L
 = DV A E A

L I J -V DV +V
e-
Electric field DV Current I Electric field,
intensity, E density, J E
E = DV/L
L A
J Current density,
J = I/A
• geometry-independent forms
of Ohm's Law
• intrinsic material property
 Electrical Conduction
• Resistivity (Ohm-m)
 = DV A E • geometry-independent forms
 of Ohm's Law
L I J • intrinsic material property
Electric field DV Current I
intensity, E density,
L J
A
Rewrite the equations using 
• Conductivity • Resistance, R:
1 L L
 R 
A A


 = nq
E
• Current density, J: 
J
n = number of charge carriers E
 q/e = electron charge (1.602 x 10-19C) J  E

 = mobility of charge carriers
 Current Density

Further definitions

– another way to state Ohm’s law is by defining it using current

density equation  J =  
current I
J  current density   like a flux
surface area A

  electric field potential = V/ or (DV/D  )

J =  (DV/D )

Electron flux conductivity voltage gradient

7
 Current Carriers

1. electrons (or holes)

2. ions can also carry current
– in liquid solutions
– in conductive ceramics
 Anionic conductor e.g. O2- moves in an oxide
material like CeO2+x conducting electricity.
Concept used for solid oxide fuel cell.

8
9
 Comparison of
Conductivity of 4 types of
Materials
-1 -1
• Room T values (Ohm-m) = ( - m)
insulators
METALS conductors CERAMICS
7 -10 -10 -11
Silver 6.8 x 10 Soda-lime glass 10
7
Copper 6.0 x 10 Concrete 10 -9
7
Iron 1.0 x 10 Aluminum oxide <10 -13

SEMICONDUCTORS POLYMERS
Silicon 4 x 10 -4
-14
Polystyrene <10
Germanium 2 x 10 0

10 -6 Polyethylene 10-15 -10 -17

GaAs
 But not all ceramics are bad
conductors. There is a class of
ceramics that can conduct
electricity or have unique
electrical properties
They are called: Electroceramics, examples are
1. Superconductors – YBa2Cu3O7 (no resistance at all!)
2. Semiconductor – TiO2 & In:SnO2 (excellent conduction
almost at par with metals – use as electrodes in solar
cell)
3. Ionic conductors – use in solid oxide fuel cell and
batteries
 Similarly, polymer can be made
conducting as well. For example,
organic led emitting diodes (OLED)
utilises conducting polymer.

Integration of conductive particles as

filler in a matrix of insulating
polymer could induce electrical
conduction in a polymer composite.
 Semiconductor among all
conductive materials is
considered interesting because
the conduction can be
controlled. Semiconductors
have therefore found
applications in various
electronics devices.
View of an Integrated Circuit
(IC)
• Scanning electron microscope images of an IC: (a)

0.5 mm
• A dot map showing location of Si (a semiconductor):
-- Si shows up as light regions.
(b)

• A dot map showing location of Al (a conductor):

-- Al shows up as light regions.
(c)

14
Silicon is one of the most used
semiconductor material known
to human kind.
Why do you think Si is widely
used? Discuss with a person
next to you and make a list in
the box provided.
 From Sand to Computer
SiO2 Si Ore Si wafer
production

Silicon wafer

Fabrication

16
Applications
 IC Component

Packed in polymer
packaging

Metal contact

Semiconductor inside

17
 2. Conduction in
Terms of Band &
Atomic Bond Models
Different class of Material
has different atomic
bonding and different
arrangement of the
outermost electrons in an
electron band structures
This in return differentiate the
materials in term of their
electrical properties.
3 Types of Possible Electron
Band Structures of Solids

How do we get these diagrams? Look at the

next slide for an example of Silicon. 20
Silicon Atom Electrons in the third shell
can be freed/release if
these electrons are excited
or stimulated. Most of the
time these electrons involve
in covalent bonding in a
Nucleus solid.
Third E level
(shell)

Second E
level (shell)
Electrons in the first and
First E level second level are closely
(shell) bound to the nucleus
(electrostatic)
 Energy Band Diagram
(e.g. Si)

Conduction band

Energy gap
Shell 3
Valance band
3s2 ,3p2
Energy gap

Second band (shell 2)

Nucleus 2s2 ,2s6
Third E level Energy gap
(shell)
Second band (shell 1)
1s2
Second E level
(shell)
Nucleus

First E level
(shell)
Energy band diagram for the atom
22
 Free Electrons for
Conduction
 Conductivity occurs when electrons accelerate in response to an external force
like electric field or from lights
 Conductivity will depends on the number of electrons available taking part in
the conductivity
 Not all electrons in an atom will conduct electricity
 The number of electrons available for conductivity depends on the
arrangements of electrons states or levels and the manner in which the
electrons occupying these states
 For conductivity to happen, electrons must be free (e.g. not involve in crystal
bonding)
 Free electrons can be found in an empty or available energy states
(normally at the outer most energy level)
 Electrons can be free by exciting them to the available energy state
23
 Band Gap?
Energy
Semiconductors:
empty • Higher energy states separated by smaller gap
band (< 2 eV).
GAP •Excitation possible to evoke conductivity.
•Electrons from valance band can jump across
filled the band gap to occupy the empty conduction
valence band
band
filled states

Band Gap (Eg)

filled •A region where electrons cannot occupy
band •Intrinsic property of materials.
•E.g. Si has band gap of 1.2eV whereas GaAs (a
well known red LED material) has band gap of ~
3.1eV.

24
 Energy Band Diagram in Metals
• To conduct electricity, electrons
must occupy the outer energy Energy band diagram of metals. 2 types as seen here:
level. These electrons are free
electrons which can roam free 1. Partly filled valance band 2. Empty band overlaps
and are responsible for with the valance band
conductivity Energy Energy
• From atomic model, due to empty
metallic bonding in metal, band
valance electrons in metal have GAP empty
freedom in movement (electron band
gas), uniformly distributed partly
throughout the lattice of ion filled filled
cores. valence valence
band band

filled states
• Some excitation (thermal
filled states
fluctuations) is required to give
rise to large number of free
filled filled
electrons which will conduct
band band
electricity
25
 Energy Band Diagram in
Insulators
Insulators:
empty
Energy band
•Higher energy states not accessible due to gap
•Electron in the valance band require far too large of
GAP energy for them to jump to the conduction band.
•From atomic model point of view, for electrically
filled insulating material, interatomic bonding is ionic or
valence strongly covalent. The valance electrons are tightly
band bound or shared with individual atoms. Electrons are
filled states

highly localised.
•In semiconductor, covalent bonding in the material is
filled not as strong as that of insulators (rather weak), the
band valance electrons are not as strongly bound to the
atoms as that of the insulator. Hence, electrons can be
easily excited (by heat or lights) to the conduction
band.
 Excitation in Semiconductor

Conduction band Free

electron
Energy External
gap energy
Valance band
Free electron

For electron to carry charge it needs to Si

be in the conduction band. Electron
ought to jump across the band gap and
reside at the conduction band to be energy
free. The process is called
Si
EXCITATION.
How do we get holes?

Conduction Free
band electron
Energy
External
gap energy
Valance
band

Holes for pure semiconductor formed

when electrons are being excited to
the conduction band

28
Movement of Charge Carriers

valence electron hole electron hole

Si atom
electron pair creation pair migration

- + - +

no applied electric field applied electric field applied electric field

 Mobility in Semiconductor
 When electric field is applied, force is brought onto the free electrons
 These electrons will experience acceleration in an opposite direction
as the direction of the applied field
 In a perfect crystals, these electrons will accelerates as long as there is
the field
 But this is not the case
 There is a ‘frictional force’ which counter the acceleration and slows
down these electrons and scatters them
 Scattering centres  vacancies, interstitial, impurities
 Parameters used to describe the extent of scattering  drift velocity
(vd) and mobility (e) of an electron
 Conductivity can be rewritten to include the mobility

vd  e   n e e
30
Conductivity of Intrinsic
Semiconductor

  nqe  pqh
 Charge Carriers in
Semiconductor
Two charge carrying mechanisms
in semiconductor
Electron :negative charge
Hole : equal & opposite positive
charge
Move at different speeds  drift
velocity

Higher temp. promotes more electrons into the conduction band.

For each one electron created, one hole is also created. The
number of electron = number of holes.

  as T
32
 3. Effect of
Temperature &
Impurities on the  of
Metal & Semiconductor
 In metals,  as T
6
Impurity increases the
resistivity in Copper


5
Resistivity, 
-8 Ohm-m)

4 Deformed Cu + 1.12%
Ni has higher resistivity
3 than un-deformed one.
Resistivity,

2 Pure Cu has the lowest

(10

resistivity
1

0
-200 -100 0 T (°C)

Total Resistivity in Metal is a sum f contributions from thermal vibration, t,

impurities, i and plastic deformation, d
tot = t + I + d (Mattiessen’s rule).
 Why is Resistivity increases
with T?
 At higher temperature  more thermal vibration (lattice vibration = phonon)
 More difficult for electrons to pass through if the thermal vibration is higher
(resistivity increases)

T = High temperature
T = low temperature

35
In metals,  as Impurities 

• Imperfections increase resistivity

-- grain boundaries These act to scatter
-- dislocations electrons so that they
-- impurity atoms take a less direct path.
-- vacancies

• Resistivity,  Total resistivity,  =

increases with: thermal
•Temperature + impurity
+ deformation
•wt% impurity
•%cold work
36
 What would the
effect of
temperature and
impurities to a
semiconductor?
 Semiconductor

Doped Pure
Extrinsic Intrinsic
n-type p-type
Pure silicon, pure germanium,
pure GaAs
 Pure (Intrinsic)
Semiconductors
 Pure material semiconductors: e.g., silicon &
germanium
– Group IVA materials
 Compound semiconductors
– III-V compounds
 Eg: GaAs & InSb
– II-VI compounds
 Eg: CdS & ZnTe
– The wider the electronegativity difference
between the elements the wider the energy
gap.
39
40
Pure Semiconductors: Conductivity vs T
 E gap / kT
 undoped  e
In pure Si, conductivity increases
with temperature due to more Energy
excitation that could happen.
empty
? band
GAP
electrical conductivity,  electrons
(Ohm-m) -1 filled can cross
10 4 valence gap at

filled states
band higher T
10 3
10 2 filled
band
10 1
10 0 pure material band gap (eV)
(undoped) Si 1.11
10 -1 Ge 0.67
10 -2 GaP 2.25
50 10 0 1 000 CdS 2.40
T(K)
41
 Conductivity of Intrinsic
Semiconductor
 Intrinsic: (n = p)
For pure semiconductor, the number of electron is equal to the
number of holes

n = number of
electrons

p = number of
holes

 For every electron being excited out to the conduction band,

one hole will be created. Note that free electron comes from the
valance electron (i.e. excited from valance electron) 42
 Conductivity of Extrinsic
Semiconductor
 Extrinsic ≠ p
In extrinsic semiconductors, conduction comes from the electrons or holes
supplied y the impurity (dopant) atoms added to a semiconductor. The number
of electrons, n or holes, p will depends on the concentration of the impurity
atoms added

n-type Extrinsic: (n >> p). p-type Extrinsic: (p >> n).

Group V atoms doped in Silicon Group III doped in Slicon

4+ 4+ 4+ 4+ 4+ 4+ 4+ 4+

4+ 5+ 4+ 4+ 4+ 3+ 4+ 4+
  n e e
4+ 4+ 4+ 4+ 4+ 4+ 4+ 4+   p e h
no applied electric field
no applied electric field
Phosphorus atom valence electron hole
Si atom conduction electron
Boron atom
43
 Donor Atom and Acceptor Atom

Boron (Group III) has 3 valance electrons. Antimony (Group VI) is a donor atom in
All 3 electrons perform bonding with the Silicon. 4 valance electrons in Sb
Si atoms, lack one electron  hole forms perform bonding with Si. 1 extra electron
B is an acceptor atom in Silicon. Main remains. Electrons must be ionised to
charge carrier in p-type Si is hole. The ‘free’ the extra electron. Main charge
number of holes, p depends on the carrier in n-type Si is electron with
amount of B added. number of electrons, n depends on the
amount of Sb added. 44
 Donor and Acceptor
States
Energy Energy

Conduction
Conduction
band Donor
band
Acceptor State
State
filled filled
valence valence

filled states
filled states

band band

filled filled
band band

N-type where n >> p

P-type where p >> n
Excitation of large number of electrons from
Electrons excitation to acceptor states donor level to the conduction band inducing
leaving behind holes. Holes are used for significant amount of free electrons for
conduction. conduction. 45
 Effect of Temperature on 
Doped Silicon:
--  increases when Si is doped
-- reason: imperfection sites
lower the activation energy to
produce mobile electrons.

At high temperature
4 -- At high temperatures,
10
conductivity is dominated by
3 excitation of electrons form the
10
intrinsic Si
electrical conductivity,

2
Pure Silicon:
(Ohm-m) -1

10
-- Conductivity depends on the
10
1 temperature. As temperature
increases more valance electrons
0 get extra energy to excite to
10
conduction band.
-1 -- Conductivity in pure Si is less at
10
lower temperatures compared to
-2
doped Si
10
50 10 0 1 000
46
T(K)
  T in
Semiconductor; Extrinsic Region
•Electrons from dopant atoms are now
Why? ionised and could occupy the
conduction band and to be free for
conductivity
Freeze out region doped

undoped
•Depends on the concentration of
•All electrons are dopant
bound to atoms 3
•Thermal energy is too
Intrinsic Region
small for excitation or
ionisation 2 •Electrons from the
extrinsic lattice will get excited to
freeze-out

intrinsic
the conduction band
concentration (1021/m3)
conduction electron

0 200 400 600 T (K)

47
 Example of an Integrated Circuit
Device
 Integrated circuits - state of the art ca. 50 nm line width
– 1 Mbyte cache on board
– > 100,000,000 components on chip
– chip formed layer by layer
 Al is the “wire”

48
 Extending Moore’s Law
An exponential can’t last
forever, but you can delay
forever for a while…
–Gordon Moore

130nm process
70nm gate

90nm process
50nm gate

65nm process
30nm gate
45nm process
20nm prototype

32nm process
15nm prototype

22nm process
Copyright © 2005 Intel Malaysia 10nm prototype
8
Moore’s Law

Performance

“… the number of
transistors on a chip
doubles every 24
months ...”
Gordon Moore
Circa 1975

1970 1980 1990 2000 2010 2020

 Breaking Barriers to Moore’s
Law 1 Billion
K
1,000,000

100,000 Pentium®4 Processor

Pentium® II Processor
10,000 Pentium® III Processor
Pentium® Processor Pentium® Pro Processor
1,000
i486™ Processor
i386™ Processor
100 80286 The
TheNumber
NumberofofTransistors
TransistorsPer
Per
8086 Chip
10 Chipwill
willDouble
DoubleEvery
Every1818
Months
Months
1
’75 ’80 ’85 ’90 ’95 ’00 ’05 ’10 ’15
Source: Intel

Integrated Packaging + Silicon Technology

development essential
7