This document discusses key concepts related to electrical conductivity and semiconductor materials. It begins by outlining issues to address, such as how conductivity is characterized for conductors, semiconductors, and insulators. It then discusses intrinsic and extrinsic conductivity in semiconductors and how factors like doping and temperature affect conductivity. The document also covers concepts like band structure, charge carriers, the Hall effect, and p-n rectifying junctions.

1. Chapter 18 - 1
ISSUES TO ADDRESS...
• How are electrical conductance and resistance
characterized?
• What are the physical phenomena that distinguish
conductors, semiconductors, and insulators?
• For metals, how is conductivity affected by
imperfections, temperature, and deformation?
• For semiconductors, how is conductivity affected
by impurities (doping) and temperature?
Electrical Properties of Materials
• Dielectric Materials and their Application?

2. Chapter 18 - 2
• Scanning electron micrographs of an IC:
Fig. (d) from Fig. 12.27(a), Callister & Rethwisch 3e.
(Fig. 12.27 is courtesy Nick Gonzales, National
Semiconductor Corp., West Jordan, UT.)
• A dot map showing location of Si (a semiconductor):
-- Si shows up as light regions. (b)
View of an Integrated Circuit
0.5mm
(a)(d)
45mm
Al
Si
(doped)
(d)
• A dot map showing location of Al (a conductor):
-- Al shows up as light regions. (c)
Figs. (a), (b), (c) from Fig. 18.27, Callister
& Rethwisch 8e.

3. Chapter 18 - 3
Electrical Conduction
• Ohm's Law: V = I R
voltage drop (volts = J/C)
C = Coulomb
resistance (Ohms)
current (amps = C/s)


1

• Conductivity, 
• Resistivity, :
-- a material property that is independent
of sample size and geometry

 
RA
l
surface area
of current flow
current flow
path length
J = σ ξ
where ξ =
𝑉
𝑙

4. Chapter 18 - 4
Electrical Properties
• Which will have the greater resistance?
• Analogous to flow of water in a pipe
• Resistance depends on sample geometry and
size.
D
2D

R1 
2l

D
2






2

8l
D2

l

l
2

R2 
l

2D
2






2

l
D2

R1
8

5. Chapter 18 - 5
Definitions
Further definitions
J =   <= another way to state Ohm’s law
J  current density
  electric field potential = V/
fluxalike
areasurface
current
A
I

Electron flux conductivity voltage gradient
J =  (V/ )

6. Chapter 18 - 6
• Room temperature values (Ohm-m)-1 = ( - m)-1
Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 8e.
Conductivity: Comparison
Silver 6.8 x 107
Copper 6.0 x 107
Iron 1.0 x 107
METALS Conductors
Silicon 4 x 10-4
Germanium 2 x 10 0
GaAs 10-6
SEMICONDUCTORS
Semiconductors
Polystyrene <10
-14
Polyethylene 10-15
-10-17
Soda-lime glass 10
Concrete 10-9
Aluminum oxide <10-13
CERAMICS
POLYMERS
Insulators
-10
-10-11

7. Chapter 18 - 7
What should be the minimum diameter (D) of Cu wire so that V < 1.5 V?
Example: Conductivity Problem
Cu wire I = 2.5 A- +
V
Solve to get D > 1.87 mm
< 1.5 V
2.5 A
6.07 x 107 (Ohm-m)-1
100 m
I
V
A
R 



4
2
D

l  100 m

8. Chapter 18 -
Electrical Resistivity Vs. Temperature
• Conductors,
• Semiconductors,
• Insulators
• Superconductors.
8

9. Chapter 18 - 9
Electrical Conductivity Vs.
Temperature

10. Chapter 18 -10
Electron Energy Band Structures

11. Chapter 18 -
11
Band Structure Representation
Adapted from Fig. 18.3,
Callister & Rethwisch 8e.
a). The conventional representation of
the electron energy band structure for a
solid material at the equilibrium
interatomic separation.
b). Electron energy versus interatomic
separation for an aggregate of atoms,
illustrating how the energy band
structure at the equilibrium separation
in (a) is generated.

12. Chapter 18 -12
Conduction & Electron Transport
• Metals (Conductors):
-- for metals empty energy states are adjacent to filled states at 0 K.
-- two types of band
structures for metals
-- thermal energy
excites electrons
into empty higher
energy states.
- partially filled band
such as Cu.
- empty band that
overlaps filled band
such as Mg.
filled
band
Energy
partly
filled
band
empty
band
GAP
filledstates
Partially filled band
Energy
filled
band
filled
band
empty
band
filledstates
Overlapping bands
EF
EF is the energy of the highest filled state at 0 K.

13. Chapter 18 -13
Energy Band Structures: Insulators
& Semiconductors
• Insulators:
-- wide band gap (> 4 eV)
-- few electrons excited
across band gap
Energy
filled
band
filled
valence
band
filledstates
GAP
empty
band
conduction
• Semiconductors:
-- narrow band gap (< 4 eV)
-- more electrons excited
across band gap
Energy
filled
band
filled
valence
band
filledstates
GAP
?
empty
band
conduction

14. Chapter 18 -14

15. Chapter 18 -
Electrical Conductivity of Metals
• Room Temperature Electrical Conductivities
for Nine Common Metals and Alloys
15

16. Chapter 18 -16
Metals: Influence of Temperature and
Impurities on Resistivity
• Presence of imperfections increases resistivity
-- grain boundaries
-- dislocations
-- impurity atoms
-- vacancies
These act to scatter
electrons so that they
take a less direct path.
• Resistivity
increases with:
 =
T (ºC)-200 -100 0
1
2
3
4
5
6
Resistivity,
(10-8Ohm-m)
0
d
-- %CW
+ deformation
i
-- wt% impurity
+ impurity
t
-- temperature
thermal

17. Chapter 18 -17
Estimating Conductivity
Adapted from Fig. 7.16(b), Callister & Rethwisch 8e.
• Question:
-- Estimate the electrical conductivity  of a Cu-Ni alloy that has a
yield strength of 125 MPa.
mOhm10x30 8
 
16
)mOhm(10x3.3
1 



Yieldstrength(MPa)
wt% Ni, (Concentration C)
0 10 20 30 40 50
60
80
100
120
140
160
180
21 wt% Ni
Adapted from Fig.
18.9, Callister &
Rethwisch 8e.
wt% Ni, (Concentration C)
Resistivity,
(10-8Ohm-m)
10 20 30 40 50
0
10
20
30
40
50
0
125
CNi = 21 wt% Ni
From step 1:
30

18. Chapter 18 -
Charge Carriers in Insulators and
Semiconductors
Two types of electronic charge
carriers:
Free Electron
– negative charge
– in conduction band
Hole
– positive charge
– vacant electron state in
the valence band
Adapted from Fig. 18.6(b),
Callister & Rethwisch 8e.
Move at different speeds - drift velocities, a few mm/s, (Classically),
Move at - Fermi velocities ~ 106 m/s. (Quantum Mechanically),
These Charge Carriers;

19. Chapter 18 -19
Intrinsic Semiconductors
• Pure material semiconductors: e.g., silicon &
germanium
– Group IVA materials
• Compound semiconductors
– III-V compounds
• Example: GaAs & InSb
– II-VI compounds
• Example: CdS & ZnTe
– The wider the electronegativity difference between
the elements the wider the energy gap.

20. Chapter 18 -20
Intrinsic Semiconduction in Terms of
Electron and Hole Migration
Adapted from Fig. 18.11,
Callister & Rethwisch 8e.
electric field electric field electric field
• Electrical Conductivity can be given by:
# electrons/m3 electron mobility
# holes/m3
hole mobilityhe epen mm
• Concept of electrons and holes:
+-
electron hole
pair creation
+-
no applied applied
valence
electron Si atom
applied
electron hole
pair migration
[The electron mobility characterizes how quickly an electron can move
through a metal or semiconductor, when pulled by an electric field].

21. Chapter 18 -21
Number of Charge Carriers
Intrinsic Conductivity
  )s/Vm45.085.0)(C10x6.1(
m)(10
219
16



mm

 

he
i
e
n
For GaAs ni = 4.8 x 1024 m-3
For Si ni = 1.3 x 1016 m-3
• Ex: GaAs
he epen mm
• for intrinsic semiconductor n = p = ni
  = ni|e|(me + mh)

22. Chapter 18 -22
Intrinsic Semiconductors:
Conductivity vs T
• Data for Pure Silicon:
--  increases with T
-- opposite to metals
Adapted from Fig. 18.16,
Callister & Rethwisch 8e.
material
Si
Ge
GaP
CdS
band gap (eV)
1.11
0.67
2.25
2.40
Selected values from Table 18.3,
Callister & Rethwisch 8e.

ni  e
Egap / kT

  ni e me mh 

23. Chapter 18 -
23
Temperature variation of conductivity (Band gap
determination)
 = n|e|me + p|e|mh
Strong exponential dependence of
carrier concentration in intrinsic
semiconductors
Temperature dependence of
mobility's is weaker.
n = p  A exp (- Eg /2 kT)
  C exp (- Eg /2 kT)

24. Chapter 18 -
24
Temperature variation of conductivity (II)
  B
g
k
E
T
p
21
ln



ln(n) = ln(p)  ln(A) - Eg /2 kT
n = p  A exp (- Eg /2 kT)   C exp (- Eg /2 kT)
Plotting log of  , p, or n vs. 1/T produces a straight line.
Slope is Eg/2k; gives band gap energy. Plot of ln p vs. 1/T

25. Chapter 18 -
25
Temperature variation of Conductivity (III)
Extrinsic semiconductors
• low T: all carriers due to
extrinsic excitations
• mid T: most dopants ionized
(saturation region)
• high T: intrinsic generation
of carriers dominates

26. Chapter 18 -26

27. Chapter 18 -27
• Intrinsic:
-- case for pure Si
-- # electrons = # holes (n = p)
• Extrinsic:
-- electrical behavior is determined by presence of impurities
that introduce excess electrons or holes
-- n ≠ p
Intrinsic vs Extrinsic Conduction
3+
• p-type Extrinsic: (p >> n)
no applied
electric field
Boron atom
4+ 4+ 4+ 4+
4+
4+4+4+4+
4+ 4+ hep m
hole
• n-type Extrinsic: (n >> p)
no applied
electric field
5+
4+ 4+ 4+ 4+
4+
4+4+4+4+
4+ 4+
Phosphorus atom
valence
electron
Si atom
conduction
electron
een m
Adapted from Figs. 18.12(a)
& 18.14(a), Callister &
Rethwisch 8e.

28. Chapter 18 -28
Extrinsic Semiconductors: Conductivity vs.
Temperature
• Data for Doped Silicon:
--  increases with doping
-- reason: imperfection sites
lower the activation energy to
produce mobile electrons.
• Comparison: intrinsic vs
extrinsic conduction...
-- extrinsic doping level:
1021/m3 of a n-type donor
impurity (such as P).
-- for T < 100 K: "freeze-out“,
thermal energy insufficient to
excite electrons.
-- for 150 K < T < 450 K: "extrinsic"
-- for T >> 450 K: "intrinsic"
Adapted from Fig. 18.17, Callister & Rethwisch
8e. (Fig. 18.17 from S.M. Sze, Semiconductor
Devices, Physics, and Technology, Bell
Telephone Laboratories, Inc., 1985.)
Conductionelectron
concentration(1021/m3)
T (K)6004002000
0
1
2
3
freeze-out
extrinsic
intrinsic
doped
undoped

29. Chapter 18 -
Hall Effect
• Discovered in 1879 A.D. by Edwin Hall.
• The development of an electric field between the two
faces of a current-carrying material whose faces are
perpendicular to a magnetic field.
• Used to measure the type (p toward right and n
toward left) of majority charge carriers in a material,
• Concentration, and
• Mobility of charge carriers
Schematic demonstration of the Hall
effect. Positive and/or negative
charge carriers that are part of the Ix
current are deflected by the magnetic
field Bz and give rise to the Hall
voltage VH
𝑉𝐻 =
𝑅 𝐻 𝐼 𝑥 𝐵 𝑧
𝑑
𝑅 𝐻 =
1
𝑛|𝑒|
• Dependence of Hall coefficient,
specimen thickness, and magnetic
filed
• Hall coefficient for metals,
• For metals, electron mobility in
terms of Hall coefficient and
conductivity

30. Chapter 18 -
Computation of Hall Voltage
30
The problem may be solved in two steps, calculation of Hall
coefficient RH and then Hall voltage VH
Now using the Equation for Hall voltage,

31. Chapter 18 -31
• 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.
-- No applied potential:
no net current flow.
-- Forward bias: carriers
flow through p-type and
n-type regions; holes and
electrons recombine at
p-n junction; current flows.
-- Reverse bias: carriers
flow away from p-n junction;
junction region depleted of
carriers; little current flow.
p-n Rectifying Junction
+
+
+
+
+
-
--
-
-
p-type n-type
+ -
+
+
+
+
+
-
-
-
-
-
p-type n-type
Adapted from
Fig. 18.21
Callister &
Rethwisch
8e.
+
++
+
+
--
-
-
-
p-type n-type
- +

32. Chapter 18 -32
Properties of Rectifying Junction
Fig. 18.22, Callister & Rethwisch 8e. Fig. 18.23, Callister & Rethwisch 8e.

33. Chapter 18 -33
Junction Transistor
Fig. 18.24, Callister & Rethwisch 8e.

34. Chapter 18 -
34
Junction Transistor
Emitter-base junction is forward biased, base-collector
junction is reverse biased.
Thus, the base of the PNP transistor must be negative with
respect to the emitter, and the collector must be more
negative than the base.

35. Chapter 18 -
35
PNP Forward-biased junction
Forward biased emitter-base junction, positive terminal
of battery repels emitter holes toward base, while
negative terminal drives base electrons toward emitter

36. Chapter 18 -
36
PNP junction interaction
In reverse-biased junction: negative voltage on collector and
positive voltage on base blocks majority current carriers from
crossing junction.
Increasing forward-bias voltage
of transistor reduces emitter-
base junction barrier.
This allows more carriers to
reach the collector, causing an
increase in current flow from
emitter to collector and through
external circuit.

37. Chapter 18 -
37
MOSFET transistor: two small islands of p-type semiconductor
created within n-type silicon substrate.
Islands connected by narrow p-type channel.
Metal contacts are made to islands (source and drain), one more
contact (gate) is separated from channel by a thin (< 10 nm)
insulating oxide layer.
Gate serves the function of the base in a junction transistor (electric
field induced by gate controls current through the transistor)
MOSFET
(Metal-Oxide-Semiconductor Field Effect Transistor)

38. Chapter 18 -
38
MOSFET
(Metal-Oxide-Semiconductor Field Effect Transistor)
Voltage applied from source encourages carriers (holes in the case shown
below) to flow from the source to the drain through the narrow channel.
Width (and hence resistance) of channel is controlled by intermediate
gate voltage. For example, if positive voltage is applied to the gate, most
of the holes are repelled from the channel and conductivity is decreasing.
Current flowing from the source to the drain is therefore modulated by
the gate voltage (amplification and switching)

39. Chapter 18 -39
MOSFET Transistor
Integrated Circuit Device
• Integrated circuits - state of the art ca. 50 nm line width
– ~ 1,000,000,000 components on chip
– chips formed one layer at a time
Fig. 18.26, Callister &
Rethwisch 8e.
• MOSFET (metal oxide semiconductor field effect transistor)

40. Chapter 18 -
40
Transistors and microelectronic devices
 MOSFET dominates microelectronic industry (memories,
microcomputers, amplifiers, etc.)
 Large Si single crystals are grown and purified. Thin circular
wafers (“chips”) are cut from crystals
 Circuit elements are constructed by selective introduction of
specific impurities (diffusion or ion implantation)
 A single 8” diameter wafer of silicon can contain as many as
1010 - 1011 transistors in total
 Cost to consumer ~ 0.00001c each.

41. Chapter 18 -
Conduction in Polymers and Ionic Materials
Ionic Materials
 The band gap is large and only
very few electrons can be
promoted to the conduction
band by thermal fluctuations
 Cation and anion diffusion can
be directed by the electric field
and can contribute to total
conductivity:
total = electronic + ionic
 High temperatures produce
Frenkel and Schottky defects
(vacancy) which result in
higher ionic conductivity.
41
Polymers
 Polymers are typically good
insulators but can be made to
conduct by doping.
 A few polymers have very high
electrical conductivity - about
one quarter that of copper, or
about twice that of copper per
unit weight.
where nI is the valence and DI, the
diffusion coefficient of a particular ion
A mobility μI may be associated with
each of the ionic species as follows:

42. Chapter 18 -
Typical Room Temperature Electrical Conductivities for
13 Nonmetallic Materials
42

43. Chapter 18 -
Dielectrics
Capacitors and Optics

44. Chapter 18 -
Dielectrics are the materials having permanent electric dipole moment.
Dipole: A dipole is an entity in which equal positive and negative
charges are separated by a small distance..
Dipole Moment (µele ):The product of magnitude of either of the
charges and the separation distance b/w them is called Dipole
Moment. It is directed from negative to positive charge.
µele = q . d  Coul – m
All dielectrics are electrical insulators and they are mainly used to
store electrical energy.
Examples: Mica, glass, plastic, water & polar molecules…
d
q -q
Introduction

45. Chapter 18 -45
Dielectric Materials
Dielectric constant of vacuum is 1 and is close to 1 for air and many
other gases.
When piece of dielectric material is placed between two plates
capacitance can increase significantly.
C = r o A / L
+
_
Dielectric is an insulator in which electric dipoles are induced by
electric field
with r = 81 for water, 20 for acetone, 12 for silicon,
3 for ice, etc.
+ _
+ _
+_
Magnitude of electric dipole moment is p = q d
d

46. Chapter 18 -
46
Capacitance
Voltage V applied to parallel conducting plates
 plates charged by +Q, –Q
electric field E develops between plates
C depends on geometry of plates and material between plates
C = r o A / L =  A / L
+ + + + +
- - - - - -
A is area of plates, L is distance between plates,  is permittivity of
dielectric medium, o is permittivity of vacuum (8.85x10-12 F/m2),
and r is relative permittivity (dielectric constant) of material,
r =  / o = C / Cvac
Ability to store charge  capacitance
C = Q / V [Farads]
Charge can remain even after voltage
removed.

47. Chapter 18 -47

48. Chapter 18 -
48
Dielectric Materials
Dipole orientation along electric field in the capacitor causes charge
redistribution.
Surface nearest to the positive capacitor plate is negatively charged
and vice versa.
Dipole formation/alignment in electric field is called polarization  P = Q’/A
Dipole alignment  extra charge Q’ on plates:
Qt = |Q+Q’| now C = Qt / V
Increased capacitance r = C / Cvac > 1
+ + + + + + + +
- - - - - - - - -
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
Q0 + Q’
-Q0 - Q’
region of no
net charge
net negative charge
at the surface, Q’
net positive charge at
the surface, Q’ = PA
P

49. Chapter 18 -
49
Dielectric Materials
Surface charge density (also called dielectric displacement) is
D = Q/A = oℰ + P and
Polarization is responsible for the increase in charge density above that
for vacuum
Mechanisms: dipole formation/orientation
 electronic (induced) polarization: Electric field displaces negative
electron “clouds” with respect to positive nucleus.
 Ionic materials (induced) polarization: Applied electric field
displaces cations and anions in opposite directions
 molecular (orientation) polarization: Some materials possess
permanent electric dipoles (e.g. H2O). In absence of electric field,
dipoles are randomly oriented. Applying electric field aligns these
dipoles, causing net (large) dipole moment
 Ptotal = Pe + Pi + Po

50. Chapter 18 -
50
Types of Polarization, or Mechanisms of Polarization
electronic polarization
ionic polarization
Molecular (orientation) polarization

51. Chapter 18 -
Dielectric Strength
51
Breakdown: The maximum field
to damage the dielectric medium,
like high electric fields (>108
V/m) excite electrons to
conduction band + accelerate
them to high energies  they
collide with and ionize other
electrons
Avalanche process (or electrical
discharge).
Field necessary is called
dielectric strength or breakdown
strength.

52. Chapter 18 -52

53. Chapter 18 -
Frequency Dependence of the
Dielectric Constant
53

54. Chapter 18 -
Frequency Relaxation;
54
Dipole orientation for one and
reversed polarity of an alternating
field
𝑓𝑟𝑒𝑙𝑎𝑥=
1
𝑡 𝑟𝑒𝑙𝑎𝑥
A minimum time to reorientate the charge
particles in the direction of the field.
Variation of dielectric constant with
frequency of an alternating electric field.
Electronic, ionic and orientation
polarization contributions to the
dielectric constant are indicated.

55. Chapter 18 -
Effect of temperature and Frequency on εr

56. Chapter 18 -56
Ferroelectric Ceramics
• Experience spontaneous polarization i.e. polarization in the
absence of an electric field.
• Occurrence of permanent electric dipole moment (similar to
ferromagnetic materials)
Fig. 18.35, Callister &
Rethwisch 8e.
BaTiO3 -- ferroelectric below
its Curie temperature (120ºC)

57. Chapter 18 -57
Piezoelectric Materials
stress-free with applied
stress
Adapted from Fig. 18.36, Callister & Rethwisch 8e. (Fig. 18.36)
Piezoelectricity (Pressure electricity)
– application of stress induces voltage (polarization)
– application of voltage induces dimensional change
Piezoelectric materials convert
mechanical strain into
electricity (microphones, strain
gauges, sonar detectors).
Piezoelectric materials include
barium titanate BaTiO3, lead
titanate (PbTiO3), lead zirconate
PbZrO3, potassium niobate
(KNbO3), quartz etc.
https://upload.wikimedia.org/wikipedia/commons/c/c4/SchemaPiezo.gif

58. Chapter 18 -
Piezo-electricity (Pressure Electricity)

59. Chapter 18 -
59

60. Chapter 18 -
Piezoelectric Coefficient
• The rate of change of polarization with stress at constant field
OR
• The rate of change of strain with electric field at constant
stress.
– Unit: C/N or m/V
• Two types of stress: linear & shear (along each of 3 axis, so 6
possibilities occurs,
• Thus in general:
𝑷𝒊 = 𝒊 𝒅𝒊𝒋 𝑻𝒋 (with i = 1,2,3; j = 1 .. 6)
and 𝑺𝒋 = 𝒊 𝒅𝒊𝒋 𝑬𝒊
where 𝒅𝒊𝒋 is the piezoelectric coefficient, S is strain, T is stress,
and ‘E’ denotes the electric field strength.
60

61. Chapter 18 -
Peizo-electric coefficients and Relative permittivity of
some materials
61

62. Chapter 18 -62
• Electrical conductivity and resistivity are:
-- material parameters
-- geometry independent
• Conductors, semiconductors, and insulators...
-- differ in range of conductivity values
-- differ in availability of electron excitation states
• For metals, resistivity is increased by
-- increasing temperature
-- addition of imperfections
-- plastic deformation
• For pure semiconductors, conductivity is increased by
-- increasing temperature
-- doping [e.g., adding B to Si (p-type) or P to Si (n-type)]
• Other electrical characteristics
-- ferroelectricity
-- piezoelectricity
Summary

63. Chapter 18 -
63
Summary: Make sure you understand language and concepts:
 Acceptor state
 Capacitance
 Conduction band
 Conductivity, electrical
 Dielectric constant
 Dielectric displacement
 Dielectric strength
 Diode
 Dipole, electric
 Donor state
 Doping
 Electrical resistance
 Electron energy band
 Energy band gap
 Extrinsic semiconductor
 Fermi energy
 Forward bias
 Free electron
 Insulator
 Intrinsic semiconductor
 Ionic conduction
 Junction transistor
 Matthiessen’s rule
 Metal
 Mobility
 MOSFET
 Ohm’s law
 Permittivity
 Piezoelectric
 Polarization
 Polarization, electronic
 Polarization, ionic
 Polarization, orientation
 Rectifying junction
 Resistivity, electrical
 Reverse bias