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Complied by:
Prof. Vijaya Agarwala BE, MTech, PhD
Professor and Head, Center of Excellence Nanotechnology
&
Professor, Metallurgical and Materials Engineering and
IIT Roorkee
Electrical and Electronic Materials
L-3, T-1, P-0
4 credits: CWS-25%, MTE-25%, ETE-50%
Electrical and Electronic Materials 2
Electrical and Electronic Materials
Electrical Materials- High Current/ voltage
Electronic Materials- Low Current/ voltage
Why??
Any thing to do with the mechanism in atomic or electronic levels??
If yes how?
Accordingly how you classify the materials, study their behaviour in the
given environment…
Course comprises of 6 modules (36 Lectures):
Module-1 Basic concept of Material Science (10 L)
Module-2 Conduction in conductors (4 L)
Module-3 Wave theory (7L)
Module-4 Semiconductors (6 L)
Module-5 Magnetic Materials (4 L )
Module-6 Superconductors & Dielectric Materials (5 L)
Basic Materials Science Concepts
Module-1
Contents
4
S No
(units)
Topics
1 Atomic bonding energy
2 Crystal systems
3 Allotropes of carbon
4 Stacking sequence
5 Miller Index
6 X’ tal defects
7 Phase and phase diagrams
8 Nano X’ tal
9 Single X’ tal bulk growth
10 Epitaxial growth - coatings
11 Tutorial 1
Basic Materials Science concepts- Module 1
Electrical and Electronic Materials
1. From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (© McGraw-
Hill, 2005)
2. Callister’s Materials Science
and Engineering
Adapted Version (©
3.www.chem.qmul.ac.uk/surface
s/scc/scat1_1b.htm
4. Wikipedia, the free encyclopedia
5. Introduction to
Physics of the Solid State
6. Materials Science by
V. Raghavan.
References:
5
Electrical and Electronic Materials
The shell model of the atom in which electrons are confined to live within
certain shells and in subshells within shells
Fig 1.3
Electrical and Electronic Materials
Force is considered the change in potential energy, E, over a change in position.
F = dE/dr
Fig 1.8
The formation of ionic bond between Na and Cl atoms in NaCl. The attraction
Is due to coulombic forces.
Electrical and Electronic Materials
Fig 1.10
Sketch of the potential energy per ion-pair in solid NaCl. Zero energy
corresponds to neutral Na and Cl atoms infinitely separated.
Electrical and Electronic Materials
Electrical and Electronic Materials Fig 1.12
The origin of van der Walls bonding between water molecules.
(a) The H2O molecule is polar and has a net permanent dipole moment
(b) Attractions between the various dipole moments in water gives rise to
van der Walls bonding
Electrical and Electronic Materials 11
Covalent bonding
-sharing of electron
-strong bond, so high MP
-directional, low electrical conductivity
Metallic Bonding
-random movements of electron, electron cloud
-high electrical conductivity
Crystal Systems
• Most solids are crystalline with their atoms arranged in a
regular manner.
• Long-range order : the regularity can extend throughout the
crystal.
• Short-range order : the regularity does not persist over
appreciable distances. eg. amorphous materials such as glass
and wax.
• Liquids have short-range order, but lack long-range order.
• Gases lack both long-range and short-range order
Ref: http://me.kaist.ac.kr/upload/course/MAE800C/chapter2-1.pdf
12
Electrical and Electronic Materials
Crystal Structures (Contd…)
• Five regular arrangements of lattice points that can
occur in two dimensions.
(a) square; (b) primitive rectangular;
(c) centered rectangular; (d) hexagonal;
(e) oblique.
13
Electrical and Electronic Materials
Point lattice
14
Electrical and Electronic Materials
Unit cell
Lattice parameters: a, b, c, α, β and γ
15
Electrical and Electronic Materials
Crystal systems and
Bravais lattice
16
Electrical and Electronic Materials
Number of lattice points per cell
Where,
Ni = number of interior points,
Nf = number of points on faces,
Nc = number of points on corners.
17
Electrical and Electronic Materials
base-centered arrangement
of points is not a new lattice
18
Electrical and Electronic Materials
Any of the fourteen Bravais lattices may be referred to a
combinatin of primitive unit cells.
Face centered cubic lattice
shown may be referred to
the primitive cubic cell and
rhombohedral cell
(indicated by dashed lines,
its axial angle between a is
600, and each of its side is
√2 a, where a is the lattice
parameter of cubic cell.
19
Electrical and Electronic Materials
FCC
20
Electrical and Electronic Materials
000, ½ ½ 0, ½ 0 ½ , 0 ½ ½
¼ ¼ ¼ , ¾ ¾ ¼, ¾ ¼ ¾, ¼ ¾ ¾
21
Electrical and Electronic Materials
22
Electrical and Electronic Materials
23
Electrical and Electronic Materials
BCC
BCC
24
Electrical and Electronic Materials
HCP
25
Electrical and Electronic Materials
DC
26
Electrical and Electronic Materials
Electrical and Electronic Materials 27
A C G H
D F I J
G
H
I
J
x
Z
000, ½ ½ 0, ½ 0 ½ , 0 ½ ½
¼ ¼ ¼ , ¾ ¾ ¼, ¾ ¼ ¾, ¼ ¾ ¾
ZnS
28
Electrical and Electronic Materials
3a 3b 5a 5b
SiO2
29
Electrical and Electronic Materials
Graphite
30
Electrical and Electronic Materials
C60
31
Electrical and Electronic Materials
Fig 1.43
Three allotropes of carbon
Electrical and Electronic Materials
CNT
33
Electrical and Electronic Materials
34
NaCl
Electrical and Electronic Materials
Coordination number
Number of nearest neighbors of an atom in the crystal lattice
35
Electrical and Electronic Materials
5
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)
SIMPLE CUBIC STRUCTURE (SC)
36
Electrical and Electronic Materials
Polonium is a chemical element with the symbol Po
and atomic number 84, discovered in 1898 by Marie
and Pierre Curie. A rare and highly radioactive
element ...
6
• APF for a simple cubic structure = 0.52
Adapted from Fig. 3.19,
Callister 6e.
ATOMIC PACKING FACTOR
37
Electrical and Electronic Materials
• Coordination # = 8
7
Adapted from Fig. 3.2,
Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE (BCC)
38
Electrical and Electronic Materials
a
R
8
• APF for a body-centered cubic structure = 0.68
Unit cell c ontains:
1 + 8 x 1/8
= 2 atoms/unit cell
Adapted from
Fig. 3.2,
Callister 6e.
ATOMIC PACKING FACTOR: BCC
39
Electrical and Electronic Materials
9
• Coordination # = 12
Adapted from Fig. 3.1(a),
Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
FACE CENTERED CUBIC STRUCTURE (FCC)
40
Electrical and Electronic Materials
Unit cell c ontains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
a
10
• APF for a body-centered cubic structure = 0.74
Adapted from
Fig. 3.1(a),
Callister 6e.
ATOMIC PACKING FACTOR: FCC
41
Electrical and Electronic Materials
14
Example: Copper
Data from Table inside front cover of Callister (see next slide):
• crystal structure = FCC: 4 atoms/unit cell
• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)
• atomic radius R = 0.128 nm (1 nm = 10 cm)
-7
Compare to actual: Cu = 8.94 g/cm 3
Result: theoretical Cu = 8.89 g/cm 3
THEORETICAL DENSITY, 
42
Electrical and Electronic Materials
15
Element
Aluminum
Argon
Barium
Beryllium
Boron
Bromine
Cadmium
Calcium
Carbon
Cesium
Chlorine
Chromium
Cobalt
Copper
Flourine
Gallium
Germanium
Gold
Helium
Hydrogen
Symbol
Al
Ar
Ba
Be
B
Br
Cd
Ca
C
Cs
Cl
Cr
Co
Cu
F
Ga
Ge
Au
He
H
At. Weight
(amu)
26.98
39.95
137.33
9.012
10.81
79.90
112.41
40.08
12.011
132.91
35.45
52.00
58.93
63.55
19.00
69.72
72.59
196.97
4.003
1.008
Atomic radius
(nm)
0.143
------
0.217
0.114
------
------
0.149
0.197
0.071
0.265
------
0.125
0.125
0.128
------
0.122
0.122
0.144
------
------
Density
(g/cm 3)
2.71
------
3.5
1.85
2.34
------
8.65
1.55
2.25
1.87
------
7.19
8.9
8.94
------
5.90
5.32
19.32
------
------
Adapted from
Table, "Charac-
teristics of
Selected
Elements",
inside front
cover,
Callister 6e.
Characteristics of Selected Elements at 20C
43
Electrical and Electronic Materials
metals •ceramic s •polymer s
16
Metals have...
• close-packing
(metallic bonding)
• large atomic mass
Ceramics have...
• less dense packing
(covalent bonding)
• often lighter elements
Polymers have...
• poor packing
(often amorphous)
• lighter elements (C,H,O)
Composites have...
• intermediate values
Data from Table B1, Callister 6e.
DENSITIES OF MATERIAL CLASSES
44
Electrical and Electronic Materials
Electrical and Electronic Materials 45
Physical Properties
•Acoustical properties
•Atomic properties
•Chemical properties
•Electrical properties
•Environmental properties
•Magnetic properties
•Optical properties
•Density
Mechanical properties
•Compressive strength
•Ductility
•Fatigue limit
•Flexural modulus
•Flexural strength
•Fracture toughness
•Hardness
•Poisson's ratio
•Shear modulus
•Shear strain
•Shear strength
•Softness
•Specific modulus
•Specific weight
•Tensile strength
•Yield strength
•Young's modulus
18
• Most engineering materials are polycrystals.
• Nb-Hf-W plate with an electron beam weld.
• Each "grain" is a single crystal.
• If crystals are randomly oriented,
overall component properties are not directional.
• Crystal sizes typ. range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
Adapted from Fig. K,
color inset pages of
Callister 6e.
(Fig. K is courtesy of
Paul E. Danielson,
Teledyne Wah Chang
Albany)
1 mm
POLYCRYSTALS
46
Electrical and Electronic Materials
19
• Single Crystals
-Properties vary with
direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
200 mm
Data from Table 3.3,
Callister 6e.
(Source of data is R.W.
Hertzberg, Deformation
and Fracture Mechanics
of Engineering
Materials, 3rd ed., John
Wiley and Sons, 1989.)
Adapted from Fig.
4.12(b), Callister 6e.
(Fig. 4.12(b) is courtesy
of L.C. Smith and C.
Brady, the National
Bureau of Standards,
Washington, DC [now
the National Institute of
Standards and
Technology,
Gaithersburg, MD].)
SINGLE VS POLYCRYSTALS
47
Electrical and Electronic Materials
Face-Centered Cubic
Nanoparticles
• Figure (a) shows the 12 neighbors that surround an atom
(darkened circle) located in the center of a cube for a FCC lattice.
• Figure (b) presents another perspective of the 12 nearest neighbors.
These 13 atoms constitute the smallest theoretical nanoparticle for an
FCC lattice.
• Figure (c) shows the 14-sided polyhedron, called a
dekatessarahedron, that is generated by connecting the atoms with
planer faces
48
Electrical and Electronic Materials
If another layer of 42 atoms is layed around the 13-atom
nanoparticle, one obtains a 55-atom nanoparticle with the
same dekatessarahedron shape.
Lager nanoparticles with the same polyhedral shape are
obtained by adding more layers, and the
sequence of numbers in the resulting particles, N
N=1, 13, 55, 147,.., which are called structural magic numbers.
49
Electrical and Electronic Materials
Atoms in nano clusters
• For n layers, the number of
atoms N and the number of
atoms on the surface Nsurf
in this FCC nanoparticle is
given by the formula,
N = 1/3(10 n3 −15 n2 +11 n −3)
Nsurf =10n2 − 20n +12
50
Electrical and Electronic Materials
Atomic packing
• In two dimensions the most efficient way to pack identical circles is
equilateral triangle arrangement shown in figure (a).
• A second hexagonal layer of spheres can be placed on top of the first
to form the most efficient packing of two layers, as shown in figure (b).
• For efficient packing, the third layer can be placed either above the
first layer with an atom at the location indicated by T or in the third
possible arrangement with an atom above the position marked by X on
the figure.
• In the first case a hexagonal lattice with a hexagonal close packed
(HCP) structure is generated, and in the second case a face-centered
cubic lattice results.
51
Electrical and Electronic Materials
Voids
X on figure is called an
octahedral site
The radius(aoct) of octahedral
site is = 0.41421ao
where ao is the radius of
the spheres.
There are also smaller
sites, called tetrahedral
sites, labeled T
This is a smaller site since its
radius aT= 0.2247ao
52
Electrical and Electronic Materials
Void types
53
Electrical and Electronic Materials
Stacking sequences: FCC & HCP
54
Electrical and Electronic Materials
55
Electrical and Electronic Materials
56
Electrical and Electronic Materials
HCP structure
57
Stacking sequence
Electrical and Electronic Materials
58
Electrical and Electronic Materials
Fig 1.40
Electrical and Electronic Materials
Lattice
directions- MI
The direction of any line
in a lattice
may be described by first
drawing a line through
the origin parallel
to the given line and
then giving the
coordinates of any point
on the line
through the origin.
-smallest integer value
- Negative directions are
shown by bars eg.
0,0,0
-
60
Electrical and Electronic Materials
Plane designation by Miller indices
-Miller indices are always cleared of
fractions
- If a plane is parallel to a given
axis, its fractional intercept on that
axis is taken as infinity, Miller index
is zero
- If a plane cuts a negative axis, the
corresponding index is negative
and is written with a bar over it.
-Planes whose indices are the
negatives of one another are
parallel and lie on opposite sides of
the origin, e.g., (210) and (-2ī0).
-- Planes belonging to the same
family is denoted by curly bracket ,
{hkl}
61
Electrical and Electronic Materials
Fig 1.41
Labeling of crystal planes and typical examples in the cubic lattice
Electrical and Electronic Materials
Miller indices of lattice planes
63
Electrical and Electronic Materials
Miller Index
64
Electrical and Electronic Materials
The hexagonal unit cell :
Miller –Bravais indices of planes and directions
66
Electrical and Electronic Materials
Zone= zonal planes + zonal axis
-Zone axis and (hkl) the zonal plane
All shaded planes belong to the same zone
i.e parallel to an axis called zone axsis 67
Electrical and Electronic Materials
u v w
h1 k1 l1
h2 k2 l2
71
Electrical and Electronic Materials
Crystal defects
72
1.Point defect-
Vacancy,
Impurity atoms ( substitutional and interstitial)
Frankel and Schottky defect ( ionic solids & nonstochiometric)
2. Line defect-
Edge dislocation
Screw dislocation,
Mixed dislocation
3. Surface defects-
Grain boundaries
Twin boundary
Surfaces, stacking faults
Interphases
Electrical and Electronic Materials
73
Electrical and Electronic Materials
74
Electrical and Electronic Materials
75
Electrical and Electronic Materials
Frankel and Schottky defect
76
Electrical and Electronic Materials
77
Electrical and Electronic Materials
Non stochiometry
78
Conduction in ionic crystal
ZnO crystal containing extra Zn2+
Crystal is electronically neutral, (i.e. 2+ & 2- )
Zn2+
O2-
Electrical and Electronic Materials
Dislocation line and b are perpendicular to each other
79
Electrical and Electronic Materials
Movement of edge dislocation
80
Electrical and Electronic Materials
81
Electrical and Electronic Materials
Cause of slip
82
Electrical and Electronic Materials
Elastic stress field responsible for electron scattering and
increase in electrical resistivity
lattice strain around dislocation
83
Electrical and Electronic Materials
84
Electrical and Electronic Materials
The closest packed plane and the closest packed direction of FCC
The plane and directions for the dislocation movement
85
Electrical and Electronic Materials
Tensile specimen
- breaks
How does the dislocation
affect the failure?
86
Electrical and Electronic Materials
Dislocation line and b are parallel to each other 87
Electrical and Electronic Materials
By resolving, the contribution
from both types of
dislocations can be
determined
88
Electrical and Electronic Materials
TEM
-dislocaions
89
Electrical and Electronic Materials
3. Surface defects
90
Electrical and Electronic Materials
Low angle GB
91
Electrical and Electronic Materials
92
Electrical and Electronic Materials
94
Electrical and Electronic Materials
Stacking fault
-occurs when there is a
flaw in the stacking
sequence
96
Electrical and Electronic Materials
Interfaces of phases
Coherent semi-coherent incoherent
Al-Cu system
97
Electrical and Electronic Materials
Definition of Phase:
• A phase is a region of material that is chemically
uniform, physically distinct, and (often)
mechanically separable.
• A phase is a physically separable part of the
system with distinct physical and chemical
properties. System - A system is that part of the
universe which is under consideration.
• In a system consisting of ice and water in a
glass jar, the ice cubes are one phase, the water
is a second phase, and the humid air over the
water is a third phase. The glass of the jar is
another separate phase.
98
Electrical and Electronic Materials
Gibbs' phase rule proposed by Josiah Willard Gibbs
The phase rule is an expression of the number of variables
in equation(s) that can be used to describe a system in equilibrium.
Degrees of freedom, F
F = C − P + 2
Where,
P is the number of phases in thermodynamic equilibrium with each other
C is the number of components
99
Electrical and Electronic Materials
Phase rule at constant pressure
• Condensed systems have no gas phase. When their
properties are insensitive to the (small) changes in
pressure, which results in the phase rule at constant
pressure as,
F = C − P + 1
100
Electrical and Electronic Materials
Types of Phase diagram
101
1. Unary phase diagram
2. Binary phase diagrams
3. Ternary phase diagram
Electrical and Electronic Materials
Unary phase diagram
Critical pressure Liquid
phase
Pressure
Temperature
Solid Phase gaseous phase
102
Electrical and Electronic Materials
Binary phase diagrams
1. Binary isomorphous systems (complete
solid solubility)
2. Binary eutectic systems (limited solid
solubility)
3. Binary systems with intermediate
phases/compounds
103
Electrical and Electronic Materials
Binary phase diagram
- isomorphous system
104
Electrical and Electronic Materials
The Lever Rule
Finding the amounts of phases in a two phase region:
1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Fraction of a phase is determined by taking the
length of the tie line to the phase boundary for the
other phase, and dividing by the total length of tie
line
The lever rule is a mechanical
analogy to the mass balance
calculation. The tie line in the
two-phase region is analogous to
a lever balanced on a fulcrum.
105
Electrical and Electronic Materials
microstrucures
106
Electrical and Electronic Materials
Binary phase diagram
–2. limited solubility
• A phase diagram for a
binary system
displaying an eutectic
point.
107
Electrical and Electronic Materials
Cu-Ag system
108
Electrical and Electronic Materials
Sn-Bi system
109
Electrical and Electronic Materials
Pb-Sn system
110
Electrical and Electronic Materials
Pb-Sn system
111
Electrical and Electronic Materials
Mechanism
of growth
Pb-Sn system
112
Electrical and Electronic Materials
Fig 1.69
Electrical and Electronic Materials
The equilibrium phase diagram of the Pb-Sn alloy.
The microstructure on the left show the observations at various points during the cooling
of a 90% Pb-10% Sn from the melt along the dashed line (the overall alloy composition
remains constant at 10% Sn).
Pb-Sn system
Cu- Zn system
114
Electrical and Electronic Materials
Ternary phase diagrams
MgO-Al2O3-SiO2 system at 1 atm. pressure Fe-Ni-Cr ternary alloy system
115
Electrical and Electronic Materials
Formation of nano crystallites/ grains
Nuclei of the solid phase form and they grow to
consume all the liquid at the solidus line.
13 atoms constitute to a theoretical nano-
particle for a FCC lattice having two layers. 55
and 147 atoms for 3 and 4 layer clusters.
If the size of the crystallites are in the nanometer
range, they are called nanocrystals/grains.
High temperature structure
can be retained at lower
temperature by quenching.
116
Electrical and Electronic Materials
Single crystal
A single crystal solid is a material in
which the crystal lattice of the entire
sample is continuous
no grain boundaries- grain boundaries can
have significant effects on the physical
and electrical properties of a material
single crystals are of interest to electric
device applications
118
Electrical and Electronic Materials
Doping
119
 Minute addition of elements in a controlled way to
the matrix is called doping.
 During Bulk crystal growth dopents can be added
 An epitaxial layer can be doped during deposition
by adding impurities to the source gas, such as
arsine, phosphine or diborane. The concentration
of impurity in the gas phase determines its
concentration in the deposited film.
 Doping can be done by diffusion, allowing the
dopents to diffuse at elevated temperature.
 Ion implantation- bombarding the dopants at high
speed
Electrical and Electronic Materials
120
Crystal Growth Techniques
1. Czochralski (CZ)
2. Bridgman (and variations)
3. Various floating zone methods
Thin films: Epitaxial growth
techniques
Electrical and Electronic Materials
Czochralski process
The process is named after Polish
scientist Jan Czochralski
Crystal growth method is used to obtain
single crystals
e.g. semiconductors : silicon, germanium
and gallium arsenide
metals : palladium, platinum, silver, gold
inorganinic/ceramics: salts, and synthetic
gemstones 121
Electrical and Electronic Materials
122
quartz Seed
introduction
-Kept in Ar atmosphere
-Process variables:
•Pulling speed
•Rotation speed
Electrical and Electronic Materials
Melting of
polycrystalline Si
with doping
Crystal growth
begins
Crystal
pulling
Single xtal
residue of
melted Si
Czochralski
•Resistance or RF
heating
•Melt contained in
quartz or Si3N4
crucible
•Chamber under
Argon
•Si melts 1421°C
123
Electrical and Electronic Materials
125
300 mm diameter wafers
2 metres in length, weighing
few hundred kilograms
Crucibles
used in
Czochralski
method
Crucible after
being used
Electrical and Electronic Materials
126
 The next step up, 450 mm, was introduction in 2012.
 Silicon wafers are typically about 0.2 - 0.75 mm thick
 Polished to a very high flatness for making
integrated circuits, or textured for making solar cells
Electrical and Electronic Materials
127
• During growth, the walls of the crucible dissolve into the
melt and Czochralski silicon therefore contains oxygen
at a typical concentration of 1018 cm−3.
• Oxygen impurities can have beneficial effects some times:
- Carefully chosen annealing conditions can allow the
formation of oxygen precipitates.
- These have the effect of trapping unwanted transition metal
impurities in a process known as gettering
Electrical and Electronic Materials
Bridgman Technique
128
• Uses a crucible
• Requires seed crystal
• Directional solidification
• Precise temperature gradient required
Electrical and Electronic Materials
Floating Zone Techniques
EB Floating Zone (electron beam) Floating Zone RF (radio frequency)
130
• Refractory, alloys including Nb, Ta, Mo and W
• Vacuum melting chamber, annular EB gun
• Crystal rotator and translator
• No crucible
•0.5–50 mm/min growth rates, 110 mm dia Nb
reported
Requires multiple passes to achieve pure
crystal,• Molten zone stability critical: Surface
tension, Cohesion, Levitation
Distribution coefficient=con. of imp. In solid
con. of imp. in liquid
Electrical and Electronic Materials
Thin films: Epitaxial growth
131
Epitaxy,
The term epitaxy comes from the Greek roots,
epi, meaning "above“
taxis, meaning "in ordered manner“
 Epitaxial growth refers to the method of depositing a
monocrystalline film on a monocrystalline substrate.
 The deposited film is denoted as epitaxial film or
epitaxial layer.
Electrical and Electronic Materials
Applications
132
Epitaxy is used in nanotechnology and in semiconductor
fabrication.
Semiconductor materials (technologically important ) are,
silicon-germanium, gallium nitride, gallium arsenide,
indium phosphide and graphene.
Epitaxy is also used to grow layers of pre-doped silicon
on the polished sides of silicon wafers, before they are
processed into semiconductor devices. This is typical of
power devices, such as those used in pacemakers, vending
machine controllers, automobile computers, etc.
Electrical and Electronic Materials
Methods
133
1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition.
2. Liquid-phase epitaxy (LPE)
3. Solid-phase epitaxy is used primarily for crystal-damage healing
4. Molecular-beam epitaxy (MBE)
Electrical and Electronic Materials
134
1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition
Silicon is most commonly deposited from
silicon tetrachloride in hydrogen at 1200 °C:
SiCl4(g) + 2H2(g) ↔ Si(s) + 4HCl(g)
Growth rates above 2µ per minute produce
polycrystalline silicon.
Electrical and Electronic Materials
Hydrogenated amorphous silicon
135
 High-quality hydrogenated amorphous silicon
films (a-Si:H) have been produced by decomposition
of low-pressure silane gas on a very hot surface with
deposition on a nearby, typically 210 °C substrate.
 A high-temperature tungsten filament provides the
surface for heterogeneous thermal decomposition of
the low-pressure silane and subsequent evaporation
of atomic silicon and hydrogen.
The silane reaction occurs at 650 °C :
SiH4 → Si + 2H2
 The substrates: flat, oxide-free, single-crystal silicon
Electrical and Electronic Materials
2. Liquid-phase
136
From the melt containing dissolved semiconductor
on solid substrates.
The thermal expansion coefficient of substrate and grown
layer should be similar
Deposition rates for films range from 0.1 to 1 μm/minute.
Doping can be achieved by the addition of dopants.
Example :
ternary and quarternary III-V compounds
on gallium arsenide (GaAs) and
indium phosphide (InP) substrates
.
Electrical and Electronic Materials
3. Solid-phase
137
Solid Phase Epitaxy (SPE) is a transition between the
amorphous and crystalline phases of a material.
It is usually done by first depositing a film of
amorphous material on a crystalline substrate.
The substrate is then heated to crystallize the film.
The single crystal substrate serves as a template for
crystal growth.
The annealing step used to recrystallize or heal silicon
layers amorphized during ion implantation is also
considered one type of Solid Phase Epitaxy.
Electrical and Electronic Materials
4. Molecular-beam
138
In MBE, a source material is heated to produce an
evaporated beam of particles.
These particles travel through a very high vacuum
(10-8 Pa; practically free space) to the substrate,
where they condense.
MBE has lower throughput than other forms of
epitaxy.
This technique is widely used for growing III-V
semiconductor crystals.
Electrical and Electronic Materials
139
Lattice matching- essential condition for the epitaxial growth
 Matching of lattice structures between two different
semiconductor materials, allows a region of band gap change to
be formed in a material without introducing a change in crystal
structure.
 It allows construction of advanced light-emitting diodes and
diode lasers.
For example, gallium arsenide, aluminium gallium arsenide, and
aluminium arsenide have almost equal lattice constants, making it
possible to grow almost arbitrarily thick layers of one on the other
one.
Electrical and Electronic Materials
140
The beginning of the grading layer will have a
ratio to match the underlying lattice and the alloy
at the end of the layer growth will match the
desired final lattice.
For example, Indium gallium phosphide layers
with a band-gap above 1.9 eV can be grown on
Gallium Arsenide wafers with index grading
Lattice grading
Electrical and Electronic Materials
Design of semiconducting compound materials
141
Ternary and quaternary compounds
Basic criteria
Eg requirements
Application oriented
1. Design GaxAl(1-x)As for different
device applications.
2. How can GaxIn(1-x)AsyP(1-y) compound
is designed for device applications?
3. What is gradedsemiconducting
compound?
Electrical and Electronic Materials
Electrical and Electronic Materials 142
1. i. Consider a multicomponent alloy containing N elements. If w1, w2, w3,…..,wN are
the weight fractions of the components 1, 2, 3, …..,N in the alloy and M1, M2,
M3,……..,MN are the respective atomic masses of the elements, show that the
atomic fraction of the ith component is given by,
ni = wi ∕ Mi
------------------------------
w1 ∕M1+w2 ∕M2+------------+wN ∕MN
ii. Consider the semiconducting II-VI compound cadmium selenide, CdSe. Given the
atomic masses of Cd and Se, find the weight fraction of Cd and Se in the
compound and grams of Cd and Se needed to make 100 grams of CdSe.
2. Explain the general bonding principle of atoms to form a crystalline solid with the
help of energy verses inter-atomic distance plot.
3. i. State various physical and mechanical properties of materials.
ii. Explain how the bonding type affect the above properties. Give examples.
Indian Institute of Technology Roorkee
Department of Metallurgical and Materials Engineering
MT-202 Electrical and Electronic Materials
Tutorial 1
Electrical and Electronic Materials 143
4.
i.
ii.
iii.
iv.
v.
vi.
Define and explain the following with the help of suitable diagrams
Space lattice
Unit cell and lattice parameters
Crystal systems
Bravais lattice and their classification
Origin for the creation of FCC Bravais lattice from a primitive cubic lattice
Crystal voids and their coordinates
5. Calculate the following:
i.
ii.
iii.
iv.
v.
vi.
vii.
viii
.
Effective number of atoms in SC, BCC, FCC, HCP unit cells
Relationship between the size of the unit cell and atomic diameter in SC, BCC,
FCC, HCP unit cells
Packing factors of BCC, FCC, HCP unit cells
Packing factor of a diamond cubic crystal structure
Coordination numbers of BCC, FCC, HCP crystal lattice
c/a ratio for an ideal HCP unit cell
Size of largest sphere that can fit into the tetrahedral & octahedral interstitial sites
of a close packed structures without distorting the unit cell.
Volume of unit cell of germanium in cubic meters, the atomic radius of Ge having
Diamond Cubic structure being 1.223 Ao
Electrical and Electronic Materials 144
6.
i.
ii.
iii
.
iv.
v.
vi.
Show with the help of neat sketches in the unit cell the
following:
Planes whose Miller indices are (111), (210), (010), (0
Ī Ī), (002), (130), (212) and(3 Ī 2).
Directions whose Miller indices are [111], [110], [1Ī0],
[122], [301], [201] and [2 Ī 3].
[1210], [01 Ī0], [Ī011] directions and (1210), (Ī Ī 22),
(1230) planes (Miller Bravais Index) in HCP unit cell
In a cubic unit cell the (hkl) & [hkl] are perpendicular
to each other
Miller index of the direction that is common to both
planes (110) and (111) inside the unit cell of a cubic
crystal.
3 parallel planes of belonging to {111} inside a cubic
unit cell (may be touching the UC).
6 direction <110> on any one {111}
Electrical and Electronic Materials 145
7. i. Given the Si lattice parameter a=0.543 nm. Calculate the number of Si atoms per unit volume, in
nm-3.
ii. Calculate the number of atoms per m2 and per nm2 on the (100), (110), and (111) planes in the Si
crystal as shown in above figure. Which plane has the maximum number of atoms per unit area?
iii. The density of SiO2 is 2.27 g cm-3 . Given that its structure is amorphous, calculate the number of
molecules per unit volume, in nm-3 . Compare your result with (i) and comment on what happens
when the surface of a Si crystal oxidizes. The atomic masses of Si and O are 28.09 and 16,
respectively.
8. In device fabrication, Si is frequently doped by the diffusion of impurities (dopants) at high
temperatures , typically 950-12000C. The energy of vacancy formation in the Si crystal is about
3.6eV. What is the equilibrium concentration of vacancies in a Si crystal at 10000C ? Neglect the
change in the density with temperature which is less than 1 percent in this case.
Electrical and Electronic Materials 146
9 i. Describe with neat sketches, the 3 types of line defects and relate b, Burgers vector with
dislocation line.
ii. Describe planar defects ; grain boundaries and surface defects
iii. How do the defects affect the electrical conductivity of the materials?
10. i. What are the allotropically different forms of carbon?
ii. Give neat sketches of their crystal structures.
iii. How do you classify these materials in terms of electrical conductivity?
11. i. Why single crystals are used for electronic applications? Explain methods of bulk single crystal
growth.
ii. What is epitaxial growth? Explain with one example each of growth for; binary, ternary and
quaternary semiconductor compounds, with the help of Eg vs lattice parameter of the crystal
plot.
iii. What is the significance of ‘ distribution coefficient’ in zone refining?
12. i. How amorphous semiconductors are prepared? Give an example.
ii. Explain how the nonstoichiometeric, ZnO crystal with excess Zn at the interstitial sites contribute
free electron for conduction.
Electrical and Electronic Materials 147
13
. i.
Consider 50% Pb- 50% Sn solder alloy:
Sketch the microstructure of the alloy at various stages as it is cooled from the melt. What is the
importance of this alloy in electrical applications?
ii. At what temperature does the solid melt? What is the significance of this temperature?
iii. What is the temperature range over which the alloy is a mixture of melt and solid? what is the
micro structure of the solid ?
iv. Consider the solder at room temperature following cooling from 1830C. Assume that the rate of
cooling from 1830C to room temperature is faster than the atomic diffusion rates needed to
change the compositions of the α and β phases in the solid. Assuming the alloy is 1 kg. Calculate
the masses of the following components in the solid.
a) The primary α ( proeutectic), b) α in the whole alloy, c) α in the eutectic solid and
d) β in the alloy ( where is the β phase?)
e) For Pb-40Sn, find the degree of freedom at,
i) liquid region, ii) liquidus, iii) two phase mushy region, iv) solidus and v )at room temperature.
f13_07_pg196

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Basic Concepts of Material Science for Electrical and Electronic Materials Module 1.ppt

  • 1. Complied by: Prof. Vijaya Agarwala BE, MTech, PhD Professor and Head, Center of Excellence Nanotechnology & Professor, Metallurgical and Materials Engineering and IIT Roorkee Electrical and Electronic Materials L-3, T-1, P-0 4 credits: CWS-25%, MTE-25%, ETE-50%
  • 2. Electrical and Electronic Materials 2 Electrical and Electronic Materials Electrical Materials- High Current/ voltage Electronic Materials- Low Current/ voltage Why?? Any thing to do with the mechanism in atomic or electronic levels?? If yes how? Accordingly how you classify the materials, study their behaviour in the given environment… Course comprises of 6 modules (36 Lectures): Module-1 Basic concept of Material Science (10 L) Module-2 Conduction in conductors (4 L) Module-3 Wave theory (7L) Module-4 Semiconductors (6 L) Module-5 Magnetic Materials (4 L ) Module-6 Superconductors & Dielectric Materials (5 L)
  • 3. Basic Materials Science Concepts Module-1
  • 4. Contents 4 S No (units) Topics 1 Atomic bonding energy 2 Crystal systems 3 Allotropes of carbon 4 Stacking sequence 5 Miller Index 6 X’ tal defects 7 Phase and phase diagrams 8 Nano X’ tal 9 Single X’ tal bulk growth 10 Epitaxial growth - coatings 11 Tutorial 1 Basic Materials Science concepts- Module 1 Electrical and Electronic Materials
  • 5. 1. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw- Hill, 2005) 2. Callister’s Materials Science and Engineering Adapted Version (© 3.www.chem.qmul.ac.uk/surface s/scc/scat1_1b.htm 4. Wikipedia, the free encyclopedia 5. Introduction to Physics of the Solid State 6. Materials Science by V. Raghavan. References: 5 Electrical and Electronic Materials
  • 6. The shell model of the atom in which electrons are confined to live within certain shells and in subshells within shells
  • 7. Fig 1.3 Electrical and Electronic Materials Force is considered the change in potential energy, E, over a change in position. F = dE/dr
  • 8. Fig 1.8 The formation of ionic bond between Na and Cl atoms in NaCl. The attraction Is due to coulombic forces. Electrical and Electronic Materials
  • 9. Fig 1.10 Sketch of the potential energy per ion-pair in solid NaCl. Zero energy corresponds to neutral Na and Cl atoms infinitely separated. Electrical and Electronic Materials
  • 10. Electrical and Electronic Materials Fig 1.12 The origin of van der Walls bonding between water molecules. (a) The H2O molecule is polar and has a net permanent dipole moment (b) Attractions between the various dipole moments in water gives rise to van der Walls bonding
  • 11. Electrical and Electronic Materials 11 Covalent bonding -sharing of electron -strong bond, so high MP -directional, low electrical conductivity Metallic Bonding -random movements of electron, electron cloud -high electrical conductivity
  • 12. Crystal Systems • Most solids are crystalline with their atoms arranged in a regular manner. • Long-range order : the regularity can extend throughout the crystal. • Short-range order : the regularity does not persist over appreciable distances. eg. amorphous materials such as glass and wax. • Liquids have short-range order, but lack long-range order. • Gases lack both long-range and short-range order Ref: http://me.kaist.ac.kr/upload/course/MAE800C/chapter2-1.pdf 12 Electrical and Electronic Materials
  • 13. Crystal Structures (Contd…) • Five regular arrangements of lattice points that can occur in two dimensions. (a) square; (b) primitive rectangular; (c) centered rectangular; (d) hexagonal; (e) oblique. 13 Electrical and Electronic Materials
  • 14. Point lattice 14 Electrical and Electronic Materials
  • 15. Unit cell Lattice parameters: a, b, c, α, β and γ 15 Electrical and Electronic Materials
  • 16. Crystal systems and Bravais lattice 16 Electrical and Electronic Materials
  • 17. Number of lattice points per cell Where, Ni = number of interior points, Nf = number of points on faces, Nc = number of points on corners. 17 Electrical and Electronic Materials
  • 18. base-centered arrangement of points is not a new lattice 18 Electrical and Electronic Materials
  • 19. Any of the fourteen Bravais lattices may be referred to a combinatin of primitive unit cells. Face centered cubic lattice shown may be referred to the primitive cubic cell and rhombohedral cell (indicated by dashed lines, its axial angle between a is 600, and each of its side is √2 a, where a is the lattice parameter of cubic cell. 19 Electrical and Electronic Materials
  • 20. FCC 20 Electrical and Electronic Materials 000, ½ ½ 0, ½ 0 ½ , 0 ½ ½ ¼ ¼ ¼ , ¾ ¾ ¼, ¾ ¼ ¾, ¼ ¾ ¾
  • 27. Electrical and Electronic Materials 27 A C G H D F I J G H I J x Z 000, ½ ½ 0, ½ 0 ½ , 0 ½ ½ ¼ ¼ ¼ , ¾ ¾ ¼, ¾ ¼ ¾, ¼ ¾ ¾
  • 28. ZnS 28 Electrical and Electronic Materials 3a 3b 5a 5b
  • 32. Fig 1.43 Three allotropes of carbon Electrical and Electronic Materials
  • 35. Coordination number Number of nearest neighbors of an atom in the crystal lattice 35 Electrical and Electronic Materials
  • 36. 5 • Rare due to poor packing (only Po has this structure) • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) SIMPLE CUBIC STRUCTURE (SC) 36 Electrical and Electronic Materials Polonium is a chemical element with the symbol Po and atomic number 84, discovered in 1898 by Marie and Pierre Curie. A rare and highly radioactive element ...
  • 37. 6 • APF for a simple cubic structure = 0.52 Adapted from Fig. 3.19, Callister 6e. ATOMIC PACKING FACTOR 37 Electrical and Electronic Materials
  • 38. • Coordination # = 8 7 Adapted from Fig. 3.2, Callister 6e. (Courtesy P.M. Anderson) • Close packed directions are cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. BODY CENTERED CUBIC STRUCTURE (BCC) 38 Electrical and Electronic Materials
  • 39. a R 8 • APF for a body-centered cubic structure = 0.68 Unit cell c ontains: 1 + 8 x 1/8 = 2 atoms/unit cell Adapted from Fig. 3.2, Callister 6e. ATOMIC PACKING FACTOR: BCC 39 Electrical and Electronic Materials
  • 40. 9 • Coordination # = 12 Adapted from Fig. 3.1(a), Callister 6e. (Courtesy P.M. Anderson) • Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. FACE CENTERED CUBIC STRUCTURE (FCC) 40 Electrical and Electronic Materials
  • 41. Unit cell c ontains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a 10 • APF for a body-centered cubic structure = 0.74 Adapted from Fig. 3.1(a), Callister 6e. ATOMIC PACKING FACTOR: FCC 41 Electrical and Electronic Materials
  • 42. 14 Example: Copper Data from Table inside front cover of Callister (see next slide): • crystal structure = FCC: 4 atoms/unit cell • atomic weight = 63.55 g/mol (1 amu = 1 g/mol) • atomic radius R = 0.128 nm (1 nm = 10 cm) -7 Compare to actual: Cu = 8.94 g/cm 3 Result: theoretical Cu = 8.89 g/cm 3 THEORETICAL DENSITY,  42 Electrical and Electronic Materials
  • 43. 15 Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H At. Weight (amu) 26.98 39.95 137.33 9.012 10.81 79.90 112.41 40.08 12.011 132.91 35.45 52.00 58.93 63.55 19.00 69.72 72.59 196.97 4.003 1.008 Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------ Density (g/cm 3) 2.71 ------ 3.5 1.85 2.34 ------ 8.65 1.55 2.25 1.87 ------ 7.19 8.9 8.94 ------ 5.90 5.32 19.32 ------ ------ Adapted from Table, "Charac- teristics of Selected Elements", inside front cover, Callister 6e. Characteristics of Selected Elements at 20C 43 Electrical and Electronic Materials
  • 44. metals •ceramic s •polymer s 16 Metals have... • close-packing (metallic bonding) • large atomic mass Ceramics have... • less dense packing (covalent bonding) • often lighter elements Polymers have... • poor packing (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values Data from Table B1, Callister 6e. DENSITIES OF MATERIAL CLASSES 44 Electrical and Electronic Materials
  • 45. Electrical and Electronic Materials 45 Physical Properties •Acoustical properties •Atomic properties •Chemical properties •Electrical properties •Environmental properties •Magnetic properties •Optical properties •Density Mechanical properties •Compressive strength •Ductility •Fatigue limit •Flexural modulus •Flexural strength •Fracture toughness •Hardness •Poisson's ratio •Shear modulus •Shear strain •Shear strength •Softness •Specific modulus •Specific weight •Tensile strength •Yield strength •Young's modulus
  • 46. 18 • Most engineering materials are polycrystals. • Nb-Hf-W plate with an electron beam weld. • Each "grain" is a single crystal. • If crystals are randomly oriented, overall component properties are not directional. • Crystal sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). Adapted from Fig. K, color inset pages of Callister 6e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm POLYCRYSTALS 46 Electrical and Electronic Materials
  • 47. 19 • Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: • Polycrystals -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (Epoly iron = 210 GPa) -If grains are textured, anisotropic. 200 mm Data from Table 3.3, Callister 6e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) Adapted from Fig. 4.12(b), Callister 6e. (Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) SINGLE VS POLYCRYSTALS 47 Electrical and Electronic Materials
  • 48. Face-Centered Cubic Nanoparticles • Figure (a) shows the 12 neighbors that surround an atom (darkened circle) located in the center of a cube for a FCC lattice. • Figure (b) presents another perspective of the 12 nearest neighbors. These 13 atoms constitute the smallest theoretical nanoparticle for an FCC lattice. • Figure (c) shows the 14-sided polyhedron, called a dekatessarahedron, that is generated by connecting the atoms with planer faces 48 Electrical and Electronic Materials
  • 49. If another layer of 42 atoms is layed around the 13-atom nanoparticle, one obtains a 55-atom nanoparticle with the same dekatessarahedron shape. Lager nanoparticles with the same polyhedral shape are obtained by adding more layers, and the sequence of numbers in the resulting particles, N N=1, 13, 55, 147,.., which are called structural magic numbers. 49 Electrical and Electronic Materials
  • 50. Atoms in nano clusters • For n layers, the number of atoms N and the number of atoms on the surface Nsurf in this FCC nanoparticle is given by the formula, N = 1/3(10 n3 −15 n2 +11 n −3) Nsurf =10n2 − 20n +12 50 Electrical and Electronic Materials
  • 51. Atomic packing • In two dimensions the most efficient way to pack identical circles is equilateral triangle arrangement shown in figure (a). • A second hexagonal layer of spheres can be placed on top of the first to form the most efficient packing of two layers, as shown in figure (b). • For efficient packing, the third layer can be placed either above the first layer with an atom at the location indicated by T or in the third possible arrangement with an atom above the position marked by X on the figure. • In the first case a hexagonal lattice with a hexagonal close packed (HCP) structure is generated, and in the second case a face-centered cubic lattice results. 51 Electrical and Electronic Materials
  • 52. Voids X on figure is called an octahedral site The radius(aoct) of octahedral site is = 0.41421ao where ao is the radius of the spheres. There are also smaller sites, called tetrahedral sites, labeled T This is a smaller site since its radius aT= 0.2247ao 52 Electrical and Electronic Materials
  • 53. Void types 53 Electrical and Electronic Materials
  • 54. Stacking sequences: FCC & HCP 54 Electrical and Electronic Materials
  • 59. Fig 1.40 Electrical and Electronic Materials
  • 60. Lattice directions- MI The direction of any line in a lattice may be described by first drawing a line through the origin parallel to the given line and then giving the coordinates of any point on the line through the origin. -smallest integer value - Negative directions are shown by bars eg. 0,0,0 - 60 Electrical and Electronic Materials
  • 61. Plane designation by Miller indices -Miller indices are always cleared of fractions - If a plane is parallel to a given axis, its fractional intercept on that axis is taken as infinity, Miller index is zero - If a plane cuts a negative axis, the corresponding index is negative and is written with a bar over it. -Planes whose indices are the negatives of one another are parallel and lie on opposite sides of the origin, e.g., (210) and (-2ī0). -- Planes belonging to the same family is denoted by curly bracket , {hkl} 61 Electrical and Electronic Materials
  • 62. Fig 1.41 Labeling of crystal planes and typical examples in the cubic lattice Electrical and Electronic Materials
  • 63. Miller indices of lattice planes 63 Electrical and Electronic Materials
  • 64. Miller Index 64 Electrical and Electronic Materials
  • 65. The hexagonal unit cell : Miller –Bravais indices of planes and directions 66 Electrical and Electronic Materials
  • 66. Zone= zonal planes + zonal axis -Zone axis and (hkl) the zonal plane All shaded planes belong to the same zone i.e parallel to an axis called zone axsis 67 Electrical and Electronic Materials u v w h1 k1 l1 h2 k2 l2
  • 68. Crystal defects 72 1.Point defect- Vacancy, Impurity atoms ( substitutional and interstitial) Frankel and Schottky defect ( ionic solids & nonstochiometric) 2. Line defect- Edge dislocation Screw dislocation, Mixed dislocation 3. Surface defects- Grain boundaries Twin boundary Surfaces, stacking faults Interphases Electrical and Electronic Materials
  • 72. Frankel and Schottky defect 76 Electrical and Electronic Materials
  • 74. Non stochiometry 78 Conduction in ionic crystal ZnO crystal containing extra Zn2+ Crystal is electronically neutral, (i.e. 2+ & 2- ) Zn2+ O2- Electrical and Electronic Materials
  • 75. Dislocation line and b are perpendicular to each other 79 Electrical and Electronic Materials
  • 76. Movement of edge dislocation 80 Electrical and Electronic Materials
  • 78. Cause of slip 82 Electrical and Electronic Materials
  • 79. Elastic stress field responsible for electron scattering and increase in electrical resistivity lattice strain around dislocation 83 Electrical and Electronic Materials
  • 81. The closest packed plane and the closest packed direction of FCC The plane and directions for the dislocation movement 85 Electrical and Electronic Materials
  • 82. Tensile specimen - breaks How does the dislocation affect the failure? 86 Electrical and Electronic Materials
  • 83. Dislocation line and b are parallel to each other 87 Electrical and Electronic Materials
  • 84. By resolving, the contribution from both types of dislocations can be determined 88 Electrical and Electronic Materials
  • 86. 3. Surface defects 90 Electrical and Electronic Materials
  • 87. Low angle GB 91 Electrical and Electronic Materials
  • 90. Stacking fault -occurs when there is a flaw in the stacking sequence 96 Electrical and Electronic Materials
  • 91. Interfaces of phases Coherent semi-coherent incoherent Al-Cu system 97 Electrical and Electronic Materials
  • 92. Definition of Phase: • A phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. • A phase is a physically separable part of the system with distinct physical and chemical properties. System - A system is that part of the universe which is under consideration. • In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air over the water is a third phase. The glass of the jar is another separate phase. 98 Electrical and Electronic Materials
  • 93. Gibbs' phase rule proposed by Josiah Willard Gibbs The phase rule is an expression of the number of variables in equation(s) that can be used to describe a system in equilibrium. Degrees of freedom, F F = C − P + 2 Where, P is the number of phases in thermodynamic equilibrium with each other C is the number of components 99 Electrical and Electronic Materials
  • 94. Phase rule at constant pressure • Condensed systems have no gas phase. When their properties are insensitive to the (small) changes in pressure, which results in the phase rule at constant pressure as, F = C − P + 1 100 Electrical and Electronic Materials
  • 95. Types of Phase diagram 101 1. Unary phase diagram 2. Binary phase diagrams 3. Ternary phase diagram Electrical and Electronic Materials
  • 96. Unary phase diagram Critical pressure Liquid phase Pressure Temperature Solid Phase gaseous phase 102 Electrical and Electronic Materials
  • 97. Binary phase diagrams 1. Binary isomorphous systems (complete solid solubility) 2. Binary eutectic systems (limited solid solubility) 3. Binary systems with intermediate phases/compounds 103 Electrical and Electronic Materials
  • 98. Binary phase diagram - isomorphous system 104 Electrical and Electronic Materials
  • 99. The Lever Rule Finding the amounts of phases in a two phase region: 1. Locate composition and temperature in diagram 2. In two phase region draw the tie line or isotherm 3. Fraction of a phase is determined by taking the length of the tie line to the phase boundary for the other phase, and dividing by the total length of tie line The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum. 105 Electrical and Electronic Materials
  • 101. Binary phase diagram –2. limited solubility • A phase diagram for a binary system displaying an eutectic point. 107 Electrical and Electronic Materials
  • 102. Cu-Ag system 108 Electrical and Electronic Materials
  • 103. Sn-Bi system 109 Electrical and Electronic Materials
  • 104. Pb-Sn system 110 Electrical and Electronic Materials
  • 105. Pb-Sn system 111 Electrical and Electronic Materials
  • 107. Fig 1.69 Electrical and Electronic Materials The equilibrium phase diagram of the Pb-Sn alloy. The microstructure on the left show the observations at various points during the cooling of a 90% Pb-10% Sn from the melt along the dashed line (the overall alloy composition remains constant at 10% Sn). Pb-Sn system
  • 108. Cu- Zn system 114 Electrical and Electronic Materials
  • 109. Ternary phase diagrams MgO-Al2O3-SiO2 system at 1 atm. pressure Fe-Ni-Cr ternary alloy system 115 Electrical and Electronic Materials
  • 110. Formation of nano crystallites/ grains Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line. 13 atoms constitute to a theoretical nano- particle for a FCC lattice having two layers. 55 and 147 atoms for 3 and 4 layer clusters. If the size of the crystallites are in the nanometer range, they are called nanocrystals/grains. High temperature structure can be retained at lower temperature by quenching. 116 Electrical and Electronic Materials
  • 111. Single crystal A single crystal solid is a material in which the crystal lattice of the entire sample is continuous no grain boundaries- grain boundaries can have significant effects on the physical and electrical properties of a material single crystals are of interest to electric device applications 118 Electrical and Electronic Materials
  • 112. Doping 119  Minute addition of elements in a controlled way to the matrix is called doping.  During Bulk crystal growth dopents can be added  An epitaxial layer can be doped during deposition by adding impurities to the source gas, such as arsine, phosphine or diborane. The concentration of impurity in the gas phase determines its concentration in the deposited film.  Doping can be done by diffusion, allowing the dopents to diffuse at elevated temperature.  Ion implantation- bombarding the dopants at high speed Electrical and Electronic Materials
  • 113. 120 Crystal Growth Techniques 1. Czochralski (CZ) 2. Bridgman (and variations) 3. Various floating zone methods Thin films: Epitaxial growth techniques Electrical and Electronic Materials
  • 114. Czochralski process The process is named after Polish scientist Jan Czochralski Crystal growth method is used to obtain single crystals e.g. semiconductors : silicon, germanium and gallium arsenide metals : palladium, platinum, silver, gold inorganinic/ceramics: salts, and synthetic gemstones 121 Electrical and Electronic Materials
  • 115. 122 quartz Seed introduction -Kept in Ar atmosphere -Process variables: •Pulling speed •Rotation speed Electrical and Electronic Materials Melting of polycrystalline Si with doping Crystal growth begins Crystal pulling Single xtal residue of melted Si
  • 116. Czochralski •Resistance or RF heating •Melt contained in quartz or Si3N4 crucible •Chamber under Argon •Si melts 1421°C 123 Electrical and Electronic Materials
  • 117. 125 300 mm diameter wafers 2 metres in length, weighing few hundred kilograms Crucibles used in Czochralski method Crucible after being used Electrical and Electronic Materials
  • 118. 126  The next step up, 450 mm, was introduction in 2012.  Silicon wafers are typically about 0.2 - 0.75 mm thick  Polished to a very high flatness for making integrated circuits, or textured for making solar cells Electrical and Electronic Materials
  • 119. 127 • During growth, the walls of the crucible dissolve into the melt and Czochralski silicon therefore contains oxygen at a typical concentration of 1018 cm−3. • Oxygen impurities can have beneficial effects some times: - Carefully chosen annealing conditions can allow the formation of oxygen precipitates. - These have the effect of trapping unwanted transition metal impurities in a process known as gettering Electrical and Electronic Materials
  • 120. Bridgman Technique 128 • Uses a crucible • Requires seed crystal • Directional solidification • Precise temperature gradient required Electrical and Electronic Materials
  • 121. Floating Zone Techniques EB Floating Zone (electron beam) Floating Zone RF (radio frequency) 130 • Refractory, alloys including Nb, Ta, Mo and W • Vacuum melting chamber, annular EB gun • Crystal rotator and translator • No crucible •0.5–50 mm/min growth rates, 110 mm dia Nb reported Requires multiple passes to achieve pure crystal,• Molten zone stability critical: Surface tension, Cohesion, Levitation Distribution coefficient=con. of imp. In solid con. of imp. in liquid Electrical and Electronic Materials
  • 122. Thin films: Epitaxial growth 131 Epitaxy, The term epitaxy comes from the Greek roots, epi, meaning "above“ taxis, meaning "in ordered manner“  Epitaxial growth refers to the method of depositing a monocrystalline film on a monocrystalline substrate.  The deposited film is denoted as epitaxial film or epitaxial layer. Electrical and Electronic Materials
  • 123. Applications 132 Epitaxy is used in nanotechnology and in semiconductor fabrication. Semiconductor materials (technologically important ) are, silicon-germanium, gallium nitride, gallium arsenide, indium phosphide and graphene. Epitaxy is also used to grow layers of pre-doped silicon on the polished sides of silicon wafers, before they are processed into semiconductor devices. This is typical of power devices, such as those used in pacemakers, vending machine controllers, automobile computers, etc. Electrical and Electronic Materials
  • 124. Methods 133 1. vapor-phase epitaxy (VPE), a modification of chemical vapour deposition. 2. Liquid-phase epitaxy (LPE) 3. Solid-phase epitaxy is used primarily for crystal-damage healing 4. Molecular-beam epitaxy (MBE) Electrical and Electronic Materials
  • 125. 134 1. vapor-phase epitaxy (VPE), a modification of chemical vapour deposition Silicon is most commonly deposited from silicon tetrachloride in hydrogen at 1200 °C: SiCl4(g) + 2H2(g) ↔ Si(s) + 4HCl(g) Growth rates above 2µ per minute produce polycrystalline silicon. Electrical and Electronic Materials
  • 126. Hydrogenated amorphous silicon 135  High-quality hydrogenated amorphous silicon films (a-Si:H) have been produced by decomposition of low-pressure silane gas on a very hot surface with deposition on a nearby, typically 210 °C substrate.  A high-temperature tungsten filament provides the surface for heterogeneous thermal decomposition of the low-pressure silane and subsequent evaporation of atomic silicon and hydrogen. The silane reaction occurs at 650 °C : SiH4 → Si + 2H2  The substrates: flat, oxide-free, single-crystal silicon Electrical and Electronic Materials
  • 127. 2. Liquid-phase 136 From the melt containing dissolved semiconductor on solid substrates. The thermal expansion coefficient of substrate and grown layer should be similar Deposition rates for films range from 0.1 to 1 μm/minute. Doping can be achieved by the addition of dopants. Example : ternary and quarternary III-V compounds on gallium arsenide (GaAs) and indium phosphide (InP) substrates . Electrical and Electronic Materials
  • 128. 3. Solid-phase 137 Solid Phase Epitaxy (SPE) is a transition between the amorphous and crystalline phases of a material. It is usually done by first depositing a film of amorphous material on a crystalline substrate. The substrate is then heated to crystallize the film. The single crystal substrate serves as a template for crystal growth. The annealing step used to recrystallize or heal silicon layers amorphized during ion implantation is also considered one type of Solid Phase Epitaxy. Electrical and Electronic Materials
  • 129. 4. Molecular-beam 138 In MBE, a source material is heated to produce an evaporated beam of particles. These particles travel through a very high vacuum (10-8 Pa; practically free space) to the substrate, where they condense. MBE has lower throughput than other forms of epitaxy. This technique is widely used for growing III-V semiconductor crystals. Electrical and Electronic Materials
  • 130. 139 Lattice matching- essential condition for the epitaxial growth  Matching of lattice structures between two different semiconductor materials, allows a region of band gap change to be formed in a material without introducing a change in crystal structure.  It allows construction of advanced light-emitting diodes and diode lasers. For example, gallium arsenide, aluminium gallium arsenide, and aluminium arsenide have almost equal lattice constants, making it possible to grow almost arbitrarily thick layers of one on the other one. Electrical and Electronic Materials
  • 131. 140 The beginning of the grading layer will have a ratio to match the underlying lattice and the alloy at the end of the layer growth will match the desired final lattice. For example, Indium gallium phosphide layers with a band-gap above 1.9 eV can be grown on Gallium Arsenide wafers with index grading Lattice grading Electrical and Electronic Materials
  • 132. Design of semiconducting compound materials 141 Ternary and quaternary compounds Basic criteria Eg requirements Application oriented 1. Design GaxAl(1-x)As for different device applications. 2. How can GaxIn(1-x)AsyP(1-y) compound is designed for device applications? 3. What is gradedsemiconducting compound? Electrical and Electronic Materials
  • 133. Electrical and Electronic Materials 142 1. i. Consider a multicomponent alloy containing N elements. If w1, w2, w3,…..,wN are the weight fractions of the components 1, 2, 3, …..,N in the alloy and M1, M2, M3,……..,MN are the respective atomic masses of the elements, show that the atomic fraction of the ith component is given by, ni = wi ∕ Mi ------------------------------ w1 ∕M1+w2 ∕M2+------------+wN ∕MN ii. Consider the semiconducting II-VI compound cadmium selenide, CdSe. Given the atomic masses of Cd and Se, find the weight fraction of Cd and Se in the compound and grams of Cd and Se needed to make 100 grams of CdSe. 2. Explain the general bonding principle of atoms to form a crystalline solid with the help of energy verses inter-atomic distance plot. 3. i. State various physical and mechanical properties of materials. ii. Explain how the bonding type affect the above properties. Give examples. Indian Institute of Technology Roorkee Department of Metallurgical and Materials Engineering MT-202 Electrical and Electronic Materials Tutorial 1
  • 134. Electrical and Electronic Materials 143 4. i. ii. iii. iv. v. vi. Define and explain the following with the help of suitable diagrams Space lattice Unit cell and lattice parameters Crystal systems Bravais lattice and their classification Origin for the creation of FCC Bravais lattice from a primitive cubic lattice Crystal voids and their coordinates 5. Calculate the following: i. ii. iii. iv. v. vi. vii. viii . Effective number of atoms in SC, BCC, FCC, HCP unit cells Relationship between the size of the unit cell and atomic diameter in SC, BCC, FCC, HCP unit cells Packing factors of BCC, FCC, HCP unit cells Packing factor of a diamond cubic crystal structure Coordination numbers of BCC, FCC, HCP crystal lattice c/a ratio for an ideal HCP unit cell Size of largest sphere that can fit into the tetrahedral & octahedral interstitial sites of a close packed structures without distorting the unit cell. Volume of unit cell of germanium in cubic meters, the atomic radius of Ge having Diamond Cubic structure being 1.223 Ao
  • 135. Electrical and Electronic Materials 144 6. i. ii. iii . iv. v. vi. Show with the help of neat sketches in the unit cell the following: Planes whose Miller indices are (111), (210), (010), (0 Ī Ī), (002), (130), (212) and(3 Ī 2). Directions whose Miller indices are [111], [110], [1Ī0], [122], [301], [201] and [2 Ī 3]. [1210], [01 Ī0], [Ī011] directions and (1210), (Ī Ī 22), (1230) planes (Miller Bravais Index) in HCP unit cell In a cubic unit cell the (hkl) & [hkl] are perpendicular to each other Miller index of the direction that is common to both planes (110) and (111) inside the unit cell of a cubic crystal. 3 parallel planes of belonging to {111} inside a cubic unit cell (may be touching the UC). 6 direction <110> on any one {111}
  • 136. Electrical and Electronic Materials 145 7. i. Given the Si lattice parameter a=0.543 nm. Calculate the number of Si atoms per unit volume, in nm-3. ii. Calculate the number of atoms per m2 and per nm2 on the (100), (110), and (111) planes in the Si crystal as shown in above figure. Which plane has the maximum number of atoms per unit area? iii. The density of SiO2 is 2.27 g cm-3 . Given that its structure is amorphous, calculate the number of molecules per unit volume, in nm-3 . Compare your result with (i) and comment on what happens when the surface of a Si crystal oxidizes. The atomic masses of Si and O are 28.09 and 16, respectively. 8. In device fabrication, Si is frequently doped by the diffusion of impurities (dopants) at high temperatures , typically 950-12000C. The energy of vacancy formation in the Si crystal is about 3.6eV. What is the equilibrium concentration of vacancies in a Si crystal at 10000C ? Neglect the change in the density with temperature which is less than 1 percent in this case.
  • 137. Electrical and Electronic Materials 146 9 i. Describe with neat sketches, the 3 types of line defects and relate b, Burgers vector with dislocation line. ii. Describe planar defects ; grain boundaries and surface defects iii. How do the defects affect the electrical conductivity of the materials? 10. i. What are the allotropically different forms of carbon? ii. Give neat sketches of their crystal structures. iii. How do you classify these materials in terms of electrical conductivity? 11. i. Why single crystals are used for electronic applications? Explain methods of bulk single crystal growth. ii. What is epitaxial growth? Explain with one example each of growth for; binary, ternary and quaternary semiconductor compounds, with the help of Eg vs lattice parameter of the crystal plot. iii. What is the significance of ‘ distribution coefficient’ in zone refining? 12. i. How amorphous semiconductors are prepared? Give an example. ii. Explain how the nonstoichiometeric, ZnO crystal with excess Zn at the interstitial sites contribute free electron for conduction.
  • 138. Electrical and Electronic Materials 147 13 . i. Consider 50% Pb- 50% Sn solder alloy: Sketch the microstructure of the alloy at various stages as it is cooled from the melt. What is the importance of this alloy in electrical applications? ii. At what temperature does the solid melt? What is the significance of this temperature? iii. What is the temperature range over which the alloy is a mixture of melt and solid? what is the micro structure of the solid ? iv. Consider the solder at room temperature following cooling from 1830C. Assume that the rate of cooling from 1830C to room temperature is faster than the atomic diffusion rates needed to change the compositions of the α and β phases in the solid. Assuming the alloy is 1 kg. Calculate the masses of the following components in the solid. a) The primary α ( proeutectic), b) α in the whole alloy, c) α in the eutectic solid and d) β in the alloy ( where is the β phase?) e) For Pb-40Sn, find the degree of freedom at, i) liquid region, ii) liquidus, iii) two phase mushy region, iv) solidus and v )at room temperature. f13_07_pg196