1. Engineering Materialsby
NareN
Assistance Professor
Department of Physics
K L University
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2. Electrical Properties
Electrical Properties of materials 
Their responses to an applied field
Electrical Conduction
Electron Band Structure of a materials
Materials
Metals
Semiconductors
Insulators
Dielectric characteristics
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3. Electrical Conduction in Metals
Ohm’s Law
At constant temperature the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor.
Macroscopic form
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4. Resistance R = r (L/A) Electrical Conduction in Metals
The opposing force offered by the material to the flow of current.
Depends on
Nature of the material (ρ).
Temperature.
Geometry/ dimensions (length L, area of cross section A)
R = r (L/A)
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5. Resistivity Electrical Conduction in Metals It is a material property.
It defines how difficult is it for current to flow.
Geometry independent.
Temperature dependent.
surface area
of current flow
current flow path length
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6. Examples of Resistivity (ρ)
Electrical Conduction in Metals
Examples of Resistivity (ρ)
Ag (Silver): 1.59×10-8 Ω·m
Cu (Copper): 1.68×10-8 Ω·m
Graphite (C): (3 to 60)×10-5 Ω·m
Diamond (C): ~1014 Ω·m
Glass: ~ Ω·m
Pure Germanium: ~ 0.5 Ω·m
Pure Silicon: ~ 2300 Ω·m
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7. Current Density (J) Electrical Conduction in Metals
It is the current flowing through unit area of cross section.
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8. Electrical Conduction in Metals
Ohm's Law -- Microscopic Form
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9. Electrical Conduction in Metals
Experimental verification of ohm’s law
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10. Electrical Conduction in Materials
Electrical conductivity varies between different materials by over 27 orders of magnitude,
the greatest variation of any physical property
Metals:  > (.m)-1
Semiconductors: 10-6 <  < (.m)-1
Insulators:  < (.m)-1
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11. Energy Band Structuresin
Solids
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12. Energy Band Structures in solids
In most of solids conduction is by electrons.
σ depend on no. of electrons available
The no. of electrons available for conduction depends on
Arrangement of electrons states or levels with respect to energy.
The manner in which these states are occupied by electrons.
Current carriers
electrons in most solids
ions can also carry (particularly in liquid solutions)
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13. Energy Band Structures in solids
IONIZATION
If a sufficient amount of energy is absorbed by an electron, it is possible for that electron to be completely removed from the influence of the atom
For ionization to take place, there must be a transfer of energy that results in a change in the internal energy of the atom.
NEGATIVE ION
Isolated Atom
An atom having more than its normal amount of electrons acquires a negative charge
POSITIVE ION
The atom that gives up some of its normal electrons is left with fewer negative charges than positive charges
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14. Energy Band Structures in solids
When atoms are spaced far enough apart
Gas :
Very little influence upon each other, and are very much like lone atoms.
Solid :
The forces that bind these atoms together greatly modify the behavior of the other electrons.
One consequence of this close proximity of atoms is to cause the individual energy levels of an atom to break up and form bands of energy.
Discrete (separate and complete) energy levels still exist within these energy bands, but there are many more energy levels than there were with the isolated atom.
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15. Energy Band Structures in solids
The difference in the energy arrangement between an isolated atom and the atom in a solid.
Notice that the isolated atom (such as in gas) has energy levels, whereas the atom in a solid has energy levels grouped into ENERGY BANDS.
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16. Energy Band Structures in solids
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17. Energy Band Structures in solids
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18. WHY ENERGY BANDS ARE FORMED?
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19. Electronic Band Structures
Electrons of one atom are perturbed by the electrons and nuclei of the adjacent atoms.
Results in splitting of atomic states into a series of closely spaced electron states to from what are called ELECTRON ENERGY BAND.
Extent of splitting depends on interatomic separation.
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20. Electronic Band Structures
Schematic plot of electron energy versus interatomic separation for an aggregate of 12 atoms
Upon close approach, each of the 1s and 2s atomic states splits to form an electron energy
band consisting of 12 states.
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21. Electronic Band Structures
Valence band – filled – highest occupied energy levels
Conduction band – empty – lowest unoccupied energy levels
At Equilibrium spacing :
Band formation may not occur
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22. Electronic Band Structures
With in each band the energy states are discrete.
No. of states with in each band will equal the total of all states contributed by the N atoms.
s band consists of N states
p band consists of 3N states
Electrical properties of a solid depends on its electron band structure.
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23. Electronic Band Structures
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24. Energy Band Structure
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25. Electronic Band Structures
The concept of energy bands is particularly important in classifying materials as conductors, semiconductors, and insulators.
An electron can exist in either of two energy bands, the conduction band or the valence band.
All that is necessary to move an electron from the valence band to the conduction band so it can be used for electric current, is enough energy to carry the electron through the forbidden band.
The width of the forbidden band or the separation between the conduction and valence bands determines whether a substance is an insulator, semiconductor, or conductor.
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26. Electronic Band Structures
Energy level diagrams to show the difference between insulators, semiconductors, and conductors.
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27. Electronic Band Structures
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28. Electronic Band Structures
The energy corresponding to the highest filled state at 0 K is called the Fermi energy
Cu-3d10 4s1- One 4s electron
Mg-12-Two 3s electrons
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29. Conduction in Solids Presence of an electric field :
Accelerated
Electrons with energies greater than the Fermi energy ( Ef )
Conduction process
Free electrons
Holes – SMC & Insulators
Electrical conductivity is a direct function 
no: of free electrons and holes.
Distinction between conductors and nonconductors (insulators and semiconductors) -----
lies in the numbers of these free electron and hole charge carriers.
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30. Conduction in Metals Metals
For an electron to become free, it must be excited or promoted into one of the empty and available energy states above Ef .
Very little energy is required to promote electrons into the low-lying empty states.
Electrons are not locally bound to any particular atom
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31. Conduction in Metals -- Thermal energy puts many electrons into
filled
band
empty
filled states
Overlapping bands
filled
band
Energy
partly
empty
GAP
filled states
Partially filled band
• Metals (Conductors):
-- Thermal energy puts
many electrons into
a higher energy state.
• Energy States:
-- for metals nearby
energy states
are accessible
by thermal
fluctuations.
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32. Conduction in Insulators & SMC
Empty States adjacent to the top of the filled valence band are not available.
To become free, therefore, electrons must be promoted across the energy band
and into empty states at the bottom of the conduction band.
This is possible only by supplying to an electron the difference in energy between these two states, which is approximately equal to the band gap energy Eg
Excitation energy
 Nonelectrical source
Heat or light
Number of electrons excited thermally (by heat energy) depends -->
1.Energy band gap width
2.Temperature
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33. Conduction in Insulators & SMC
1. Eg is small – conduction is high
2. Eg is large – conduction is low
At a given Temperature
SMC – Narrow
Insulators Widely
Width of the band gap
Increasing the temperature
Thermal energy increases
Conductivity increases
No of electrons excitation more
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34. Conduction in Insulators & SMC
Bonding
valence electrons are not as strongly bound to the atoms
Semiconductors
covalent
electrons are more easily removed
by thermal excitation
ionic or
strongly covalent
valence electrons are
tightly bound
Insulating material
electrons are highly localized
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35. Conduction in Insulators & SMC
Width of the band gap
• Insulators:
-- Higher energy states not
accessible due to gap (> 2 eV).
• Semiconductors:
-- Higher energy states separated
by smaller gap (< 2 eV).
Energy
filled
band
valence
empty
filled states
GAP
Energy
filled
band
valence
empty
filled states
GAP ?
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36. Conduction in Insulators & SMC
Width of the band gap
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37. Electron Mobility Absence of Electric field: (E=0)
1. Electrons move randomly through out the crystal in conductors
2. Net current – ZERO ( any direction)
3. No Drift velocity
Presence of Electric field:
1.Electrons are accelerated in a single direction
2.This acceleration is opposed by the internal damping forces or frictional forces.
due to scattering of electrons by imperfections
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38. Electron Mobility 1. Impurity atoms 2. Vacancies 3.Dislocations
imperfection's
1. Impurity atoms
2. Vacancies
3.Dislocations
4.Thermal vibration
5.Interstitial atoms
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39. Electron Mobility Each Scattering or Collision occurs:
A) e- losses kinetic energy
Transfer to the lattice of metal
B) Changes its direction of motion
e- - lattice scattering
1. Existence of resistance
2. Warming up of the metals
Ex: Electrical heaters
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40. vd = eE Electron Mobility
Electrons move randomly but with a net drift in the direction opposite to the electric field.
scattering phenomenon
resistance
used to describe
1. mobility of an electron
2. drift velocity
It is represents the average electron velocity in the direction of the force imposed by the applied field. It is directly proportional to the electric field.
vd = eE
e – electron mobility [m2/V-s].
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41.  = Nee e Electron Mobility
Electrical conductivity proportional to number of free electrons per unit volume, Ne, and electron mobility, e
 = Nee e
Nmetal >> Nsemi
metal > semi
metal >> semi
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42. Electrical resistivity of metals
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43. Electrical resistivity of metals
Metals are extremely good conductors of electricity
large numbers of free electrons
excited into empty states above the Fermi energy
Discuss conduction in metals in terms of the resistivity
crystalline defects serve as scattering centers for conduction electrons
increasing their number
raises the resistivity
concentration of these imperfections
temperature, composition
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44. Electrical resistivity of metals
total = thermal+impurity+deformation
experimentally
Matthiessen’s rule
The electrical resistivity versus temperature for copper and three copper–nickel alloys, one of which has been deformed.
Influence of Temperature :
pure metal and all the copper–nickel alloys
Thermal, impurity, and deformation contributions to the resistivity are indicated at -100⁰ c
* increase with temperature in thermal vibrations and other lattice irregularities
Resistivity rises linearly with temperature *
T Vibrations and lattice defects
 electron scattering increases
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45. Electrical resistivity of metals
Influence of Impurities
Impurity resistivity ρi is related to the impurity concentration Ci in terms of the atom fraction (at%100)
where A is a composition-independent constant (impurity and host metals)
Two-phase alloy consisting of α and β phases
where the V’s and ρ’s represent volume fractions and individual resistivities for the respective phases.
The influence of nickel impurity additions on the room temperature resistivity of copper
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46. Electrical resistivity of metals
Influence of Plastic Deformation
Raises the electrical resistivity
Result of increased numbers of electron-scattering dislocations.
Its influence is much weaker than that of increasing temperature or the presence of impurities.
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47. Electrical characteristics of commercial alloys
Silver
Best material for electrical conduction
Very expensive
Copper
To achieve low resistance
Remove gases included in metal
Soft material
Mechanical strength  CuBe is used
Aluminium
Weight
More resistant to corrosion
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48. Electrical characteristics of commercial alloys
Furnace heating elements
high electrical resistivity
energy loss by electrons
dissipated as heat energy
Ex: Nichrome, a nickel–chromium alloy
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49. Semiconductors
Semiconductors have a resistivity/resistance between that of conductors and insulators
Their electrons are not free to move but a little energy will free them for conduction
Their resistance decreases with increase in temperature
Electrical properties are extremely sensitive to the presence of impurities.
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50. INTRINIC SEMICONDUCTORS
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51. The Silicon, Si, Atom
Silicon has a valency of 4 i.e. 4 electrons in its outer shell
Each silicon atom shares its 4 outer electrons with 4 neighbouring atoms
These shared electrons – bonds – are shown as horizontal and vertical lines between the atoms
This picture shows the shared electrons U

52. Silicon – the crystal lattice
If we extend this arrangement throughout a piece of silicon…
We have the crystal lattice of silicon
This is how silicon looks when it is 0 K
It has no free electrons – it cannot conduct electricity – therefore it behaves like an insulator U

53. Electron Movement in Silicon
At room temperature
An electron may gain enough energy to break free of its bond…
It is then available for conduction and is free to travel throughout the material U

54. Hole Movement in SiliconU

55. Hole Movement in Silicon
This hole can also move… U

56. Heating Silicon U

57. Intrinsic Conduction Take a piece of silicon…
And apply a potential difference across it…
This sets up an electric field throughout the silicon – seen here as dashed lines U

58. Intrinsic Conduction U

59. Intrinsic Conduction U

60. Intrinsic Semiconductors
Consider nominally pure semiconductor at T = 0 K
There is no electrons in the conduction band
At T > 0 K a small fraction of electrons is thermally excited into the conduction band, “leaving” the same number of holes in the valence band U

61. This hole is positive, and so can attract nearby electrons which then move out of their bond etc.
Thus, as electrons move in one direction, holes effectively move in the other direction
Electron moves to fill hole
As electron moves in one direction hole effectively moves in other U

62. EXTRINIC SEMICONDUCTORSU

63. Prepared by adding (doping) impurities to intrinic semiconductors
Doping is the incorporation of [substitutional] impurities (trivalent or pentavalent) into a semiconductor according to our requirements
In other words, impurities are introduced in a controlled manner
Electrical Properties of Semiconductors can be altered drastically by adding minute amounts of suitable impurities to the pure crystals U

64. Doping Pentavalent Group VA elements Trivalent Group III A elements
Phosphorous
Arsenic
Antimony
Trivalent
Group III A elements
Boron
Gallium
Indium U

65. The Phosphorus Atom Phosphorus is number 15 in the periodic table
It has 15 protons and 15 electrons – 5 of these electrons are in its outer shell U

66. Doping – Making n-type Silicon
We now have an electron that is not bonded – it is thus free for conduction U

67. Doping – Making n-type Silicon
As more electrons are available for conduction we have increased the conductivity of the material
Phosphorus is called the dopant
If we now apply a potential difference across the silicon… U

68. Extrinsic Conduction – n-type SiliconU

69. U

70. U

71. U

72. This crystal has been doped with a pentavalent impurity.
The free electrons in n type silicon support the flow of current. U

73. The Boron Atom Boron is number 5 in the periodic table
It has 5 protons and 5 electrons – 3 of these electrons are in its outer shell U

74. Doping – Making p-type Silicon
Notice we have a hole in a bond – this hole is thus free for conduction U

75. Doping – Making p-type Silicon
Boron is the dopant in this case
If we now apply a potential difference across the silicon… U

76. Extrinsic Conduction – p-type siliconU

77. U

78. U

79. U

80. This crystal has been doped with a trivalent impurity.
The holes in p type silicon contribute to the current.
Note that the hole current direction is opposite to electron current
so the electrical current is in the same direction U

81. U

82. U

83. Extrinsic conductivity—p type
Every acceptor generates excess mobile holes (p=Na).
Now holes totally outnumber electrons, so conductivity equation switches to p domination. U

84. Ef=Edonor= Ec-0.05eV
Ef=Eacceptor= Ev+0.05eV U

85. • N-type Extrinsic: (n >> p) • P-type Extrinsic: (p >> n)
• Intrinsic:
# electrons = # holes (n = p)
--case for pure Si
• Extrinsic:
--n ≠ p
--occurs when DOPANTS are added with a different
# valence electrons than the host (e.g., Si atoms)
• N-type Extrinsic: (n >> p)
• P-type Extrinsic: (p >> n) U

86. Variation of carrier concentration with temperature in intrinsic semiconductorsU

87. Variation of carrier concentration with temperature in extrinsic semiconductorsU

88. U

89. U

90. U

91. The converse transition can also happen.
An electron in CB recombines with a hole in VB and generate a photon.
The energy of the photon will be in the order of Eg.
If this happens in a direct band-gap s/c, it forms the basis of LED’s and LASERS.
Conduction Band e-
photon +
Valance Band U

92. Wide band gaps between VB and CB
Insulators :
The magnitude of the band gap determines the differences between insulators, s/c‘s and metals.
The excitation mechanism of thermal is not a useful way to promote an electron to CB even the melting temperature is reached in an insulator.
Even very high electric fields is also unable to promote electrons across the band gap in an insulator.
CB (completely empty)
Eg~several electron volts
VB (completely full)
Wide band gaps between VB and CB U

93. Metals : CB CB VB VB No gap between valance band and conduction band
These two bands looks like as if partly filled bands and it is known that partly filled bands conducts well.
This is the reason why metals have high conductivity. CB CB VB VB
Touching VB and CB
Overlapping VB and CB
No gap between valance band and conduction band U

94. The Concept of Effective Mass :
Comparing
Free e- in vacuum
If the same magnitude of electric field is applied to both electrons in vacuum and inside the crystal, the electrons will accelerate at a different rate from each other due to the existence of different potentials inside the crystal.
The electron inside the crystal has to try to make its own way.
So the electrons inside the crystal will have a different mass than that of the electron in vacuum.
This altered mass is called as an effective-mass.
In an electric field
mo =9.1 x 10-31
Free electron mass
An e- in a crystal
In an electric field
In a crystal
m = ?
m* effective mass U

95. Direct an indirect-band gap materials :
Direct-band gap s/c’s (e.g. GaAs, InP, AlGaAs)
For a direct-band gap material, the minimum of the conduction band and maximum of the valance band lies at the same momentum, k, values.
When an electron sitting at the bottom of the CB recombines with a hole sitting at the top of the VB, there will be no change in momentum values.
Energy is conserved by means of emitting a photon, such transitions are called as radiative transitions. E CB e- k + VB U

96. For an indirect-band gap material; the minimum of the CB and maximum of the VB lie at different k-values.
When an e- and hole recombine in an indirect-band gap s/c, phonons must be involved to conserve momentum.
Indirect-band gap s/c’s (e.g. Si and Ge) E CB
Phonon e-
Atoms vibrate about their mean position at a finite temperature.These vibrations produce vibrational waves inside the crystal.
Phonons are the quanta of these vibrational waves. Phonons travel with a velocity of sound .
Their wavelength is determined by the crystal lattice constant. Phonons can only exist inside the crystal. Eg k + VB U

97. The transition that involves phonons without producing photons are called nonradiative (radiationless) transitions.
These transitions are observed in an indirect band gap s/c and result in inefficient photon producing.
So in order to have efficient LED’s and LASER’s, one should choose materials having direct band gaps such as compound s/c’s of GaAs, AlGaAs, etc… U

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